diff --git a/-9E1T4oBgHgl3EQf8gV6/content/tmp_files/2301.03546v1.pdf.txt b/-9E1T4oBgHgl3EQf8gV6/content/tmp_files/2301.03546v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..01ae58c47e8f787cc2e827fb09f7d0c6f0d86acb --- /dev/null +++ b/-9E1T4oBgHgl3EQf8gV6/content/tmp_files/2301.03546v1.pdf.txt @@ -0,0 +1,2086 @@ +DESY 23-001 +UWThPh-2023-1 +Investigation of the scale dependence in the MSR and MS top +quark mass schemes for the tt invariant mass differential cross +section using LHC data +Toni M¨akel¨a∗a,b, Andr´e H. Hoang†c,d, Katerina Lipka‡a,e, and Sven-Olaf Moch§f +aDeutsches Elektronen-Synchrotron, Notkestr. 85, 22607 Hamburg, Germany +bNational Centre for Nuclear Research, Pasteura 7, PL-02-093 Warsaw, Poland +cFaculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria +dErwin Schr¨odinger Institute for Mathematics and Physics, University of Vienna, Boltzmanngasse 9, +A-1090 Vienna, Austria +eFakult¨at f¨ur Mathematik und Naturwissenschaften, Bergische Universit¨at Wuppertal, Gaußstrassse 20, +D-42119 Wuppertal, Germany +fII. Institut f¨ur Theoretische Physik, Universit¨at Hamburg, Luruper Chaussee 149, D-22761 Hamburg, +Germany +January 10, 2023 +Abstract +The computation of the single-differential top quark-antiquark pair (tt) production cross +section at NLO in the fixed-order expansion is examined consistently using the MSR and MS +short-distance top quark mass schemes. A thorough investigation of the dependence of the tt +invariant mass spectrum on the renormalization scales R and µm of the MSR mass mMSR +t +(R) and +MS mass mt(µm), respectively, is carried out. We demonstrate that a scale choice of R ∼ 80 GeV +is important for the stability of the cross-section predictions for the low tt invariant mass range, +which is important for a reliable extraction of the top quark mass. Furthermore, a choice of semi- +dynamical renormalization and factorization scales is preferred. These findings are expected to +remain valid once non-relativistic quasi-bound state effects are included in the low invariant +mass region. +∗toni.makela@cern.ch +†andre.hoang@univie.ac.at +‡katerina.lipka@desy.de +§sven-olaf.moch@desy.de +1 +arXiv:2301.03546v1 [hep-ph] 9 Jan 2023 + +1 +Introduction +The top quark mass mt is a fundamental parameter of the Standard Model and has an important +role in many predictions, both directly and via higher-order corrections. For instance, together with +the values of the strong coupling constant αs and the mass of the Higgs boson, it determines the +stability of the electroweak vacuum [1–4]. Yet, the formal definition of quark masses makes them +renormalization scheme dependent quantities. The frequently used pole mass mpole +t +, which is based +on the picture that real and virtual radiation can be resolved at arbitrarily small energy scales, +suffers from the renormalon ambiguity, a spurious linear infrared (IR) sensitivity of the order of the +QCD scale ΛQCD [5–7].1 In contrast, short-distance mass schemes such as the modified minimal +subtraction (MS) scheme [10, 11] mass mt(µm), or the MSR scheme [12, 13] mass mMSR +t +(R), do not +have this issue, and their renormalization scales µm and R, respectively, act as a finite resolution +scale. This means that real and virtual radiation are treated inclusively for scales below µm and +R, which provides a more suitable description for realistic physical observables. The absence of the +O(ΛQCD) renormalon problem and the additional freedom to adopt suitable scale choices can be +very useful to achieve higher precision. Moreover, the MSR scheme can be related to quark mass +definitions used in parton shower Monte Carlo programs, as worked out conceptually in Refs. [14– +16], see also Refs. [13, 17] for details. For small, but still perturbative R values at around 2 GeV +the MSR mass serves as a viable and renormalon-free proxy for the pole mass concept. +The sensitivity of an observable to mt is always associated to a dynamical physics scale, such as +the inverse Bohr radius ⟨1/rB⟩ ∼ mtαs for the impact of the top quark-antiquark (tt) quasi-bound +state on the tt cross section at the threshold, or the top quark width Γt for the single top resonance +mass distribution. Thus, the scale dependence of mt(µm) and mMSR +t +(R) allows to properly adapt +to these dynamical scales for an observable under consideration. The respective renormalization +group equations (RGEs) and matching relations provide the tool to unambiguously relate the top +quark mass extracted at different dynamical scales. This concept is well known for the running +strong coupling αs and applies to the quark masses as well, particularly for increasing precision. +In this work, the dependence of the invariant mass of the tt pair, mtt, on the MSR mass scale +R and the MS mass scale µm is investigated concurrently for the first time accounting for QCD +corrections. Using experimental measurements of tt production at the LHC at √s = 13 TeV [18], +the next-to-leading order (NLO) prediction of the mtt differential cross section from Refs. [19, 20] +and the scheme implementation procedure of Refs. [21, 22], we demonstrate that the proper scheme +choice is of key importance and affects the size of higher-order corrections as well as the resulting +value of the extracted top quark mass. In Sec. 2, we review the MS and MSR top quark mass +schemes and the formulae to implement them, and in Sec. 3 we carry out a detailed investigation +concerning the best choice of the MSR renormalization scale R. In Sec. 4 we quote the results for +1We note that linear IR sensitivities arise in cross sections whenever cuts on soft radiation are imposed, see e.g. +Ref. [8]. These are associated to nonperturbative corrections in contrast to the pole mass, where the IR sensitivity +arises purely from the choice of scheme [9]. +2 + +mMSR +t +(R = 1 GeV) and higher R values from the fits to the LHC measurements, demonstrating the +impact of the renormalization scale choice. We close in Sec. 5 with a summary and an outlook on +future improvements. +2 +Running mt and the tt pair production cross section at NLO +In terms of a general mass renormalization scale µm, the pole and MS masses are related in +perturbative QCD as +mpole +t += mt(µm) +� +1 + +� +n=1 +dMS +n (µm) +� +a(6) +s (µm) +�n +� +, +(2.1) +where as ≡ αs/π. Here and everywhere else in this study, we explicitly indicate by the superscript +whether we use the strong coupling α(5) +s +in the 5-flavor or α(6) +s +in the 6-flavor scheme. For the +parton distribution functions (PDFs) only the 5-flavor scheme is employed. All quarks except for +the top quark are treated as massless. The coefficients dMS +n (µm) in Eq. (2.1) are known up to four +loops [23] and the first few orders read [24–26] +dMS +1 (µm) = 4/3 + L , +dMS +2 (µm) = 7.1952 + 4.6806L + 1.4167L2 , +dMS +3 (µm) = 54.161 + 21.776L + 9.2026L2 + 1.7940L3 , +(2.2) +where the expansion uses α(6) +s +in the 6-flavor scheme and L = log((µm/m(µm))2). The running of +the MS mass is described by the RGE +µ2 +m +dmt(µm) +dµ2m += − mt(µm) +� +i=0 +γm +i +� +a(6) +s (µ) +�i+1 +, +(2.3) +where the anomalous dimensions γm +i +are known to five loops [27, 28]. The first few orders [29–34] +are given by +γm +0 = 1 , +γm +1 = 3.3750 , +γm +2 = 4.8387 , +γm +3 = −4.5082 . +(2.4) +Electroweak corrections (see, e.g. [35, 36]) are not considered. +The RGE in Eq. (2.3) has the +solution +mt(µ1) = mt(µ0) exp +� +−2 +� +i=0 +� µ1 +µ0 +dµ +µ γm +i +� +a(6) +s (µ) +�i+1 +� +, +(2.5) +yielding the MS mass at a scale µ1 via evolution from the known mass at a reference scale µ0. +Here and below we quote relations at O(α3 +s) and evolution equations at O(α4 +s). +We have also +3 + +used these relations in our analysis for determining numerical values for the quark masses (and the +strong coupling), even though our cross section analysis is based on a fixed-order theory description +at NLO. Since the mass (and strong coupling) matching relations and RGE equations are well +convergent series and no subtle cancellations between the different ingredients need to be taken +care of (which would be the case for the PDFs) this approach is fully consistent and has the +advantage that the theoretical uncertainties in the numerical values of the masses (and the strong +coupling) are eliminated entirely from our analysis. We recommend this approach also for future +phenomenological analyses. For implementing different mass schemes in the analytic expression for +the differential mtt cross sections at NLO, see Eq. (2.14) below, only the O(αs) coefficients from +Eqs. (2.1) and (2.6) are used. +The MS mass is by construction a 6-flavor quantity and should only be used in observables +where the dynamical scale of the top-quark mass sensitivity is of order mt or larger, i.e. µm ≳ mt. +The MSR mass is, like the MS mass mass, determined from top-quark self-energy corrections [13, +17], but designed such that all virtual and off-shell top-quark quantum fluctuations are integrated +out in the on-shell limit.2 The MSR mass mMSR +t +(R) is therefore a 5-flavor quantity and its R- +dependence properly captures all radiation off the top quark that is soft in the top quark rest +frame, which is not the case for the MS mass. The MSR mass is the proper choice if the dynamical +scale of the top quark mass sensitivity is below mt, i.e. R ≲ mt. +The pole and MSR masses are related as +mpole +t += mMSR +t +(R) + R +∞ +� +n=1 +dMSR +n +� +a(5) +s (R) +�n +, +(2.6) +where the coefficients dMSR +n +read [13] +dMSR +1 += 4/3 , +dMSR +2 += 8.1330 +dMSR +3 += 71.602 . +(2.7) +In the limit R → mt(mt), mMSR +t +(R) approaches the MS mass mt(mt) and matches on it in analogy +to the 5-flavor and 6-flavor strong coupling, see below. In contrast to the logarithmic µm evolution +of mt(µm), the R-evolution of mMSR +t +(R) is linear and captures the correct physical logarithms +for observables with mt dependence, generated at dynamical scales R < mt, such as resonances, +thresholds, and low-energy endpoints [37]. The mass renormalization constant of the MSR mass +only contains the on-shell self-energy corrections for scales larger than R in contrast to the pole +mass which contains self-energy corrections at all scales. So while the MSR mass is numerically +close to the pole mass for small R at low orders, it is free of the pole mass renormalon problem. +Formally the MSR mass approaches the pole mass for R → 0, but the Landau pole prevents taking +2We are using the natural MSR mass definition (MSRn), where virtual top-quark loops are integrated out consis- +tently, see [13]. +4 + +this limit in practice. For small R values in the range of 1 to 2 GeV the MSR mass captures the +kinematic particle mass interpretation commonly associated of the pole mass. Within perturbative +uncertainties at NLO, where we can still ignore the pole mass renormalon problem, the scheme +choice mMSR +t +(R = 1 GeV) is therefore a proxy for the pole mass scheme. The matching of the +5-flavor MSR mass to the 6-flavor MS mass at the scale R = mt(mt) reads [13] +mMSR +t +(mt) += +mt(mt) +� +1 + 0.10357 +� +a(5) +s (mt) +�2 ++ 1.8308 +� +a(5) +s (mt) +�3 +� +, +(2.8) +and the inverse at the scale R = mMSR +t +(mMSR +t +) reads [13] +mt(mt) += +mMSR +t +� +mMSR +t +� � +1 − 0.10357 +� +a(5) +s (mMSR +t +) +�2 +− 1.6927 +� +a(5) +s (mMSR +t +) +�3 � +. +(2.9) +The matching starts at O(α2 +s), where virtual top quark loops first appear.3 These relations are in +close analogy to the corresponding strong coupling matching relation which reads +a(6) +s (mt) = a(5) +s (mt) +� +1 − 0.15278 +� +a(5) +s (mt) +�2 +− 0.54881 +� +a(5) +s (mt) +�3 � +. +(2.10) +The MSR mass at an arbitrary scale R is then obtained from a given MS mass, applying Eq. (2.8), +and evolving the scale R from mt(mt) to the desired value by solving the RGE +R d +dRmMSR +t +(R) = −R +� +n +γR +n +� +a(5) +s (R) +�n+1 +, +(2.11) +where the anomalous dimensions γR +n are given by [17] +γR +0 = 4/3 +γR +1 = 3.0219 , +γR +2 = 2.8047 , +γR +3 = −73.257 . +(2.12) +The solution of Eq. (2.11) yields +mMSR +t +(mt) − mMSR +t +(R) = − +� +n=0 +γR +n +� mt +R +dR′ � +a(5) +s (R′) +�n+1 ++ O +� +a4 +s +� +≡ ∆m , +(2.13) +so that the MSR mass at R is obtained as mMSR +t +(R) = mMSR +t +(mt)−∆m. As far as QCD corrections +are concerned, the formulae above allow to relate MSR and MS top quark mass values at any +(perturbative) scale with a precision of better than 20 MeV. The REvolver library [37] provides +this functionality in user-friendly software package. +In the present work, the MCFM program (version 6.8) [19, 20] is extended to include the im- +plementation of the MSR scheme in the computation of the hadronic tt production cross section for +3In the matching relations in Eqs. (2.8) and (2.9) we have not indicated the 5- or 6-flavor schemes for the strong +coupling, since at the order shown the coefficients are identical in both schemes. +5 + +single-differential kinematics. Based on the procedure presented in Refs. [21, 22], the tt production +cross section differential with respect to an observable X at NLO reads +dσ +dX = (as(µr))2 dσ(0) +dX +� +m, µr, µf +� ++ (as(µr))3 dσ(1) +dX +� +m, µr, µf +� ++ (as(µr))3 ˜R d1 +d +dmt +� +dσ(0)(mt, µr, µf) +dX +� ���� +mt=m +, +(2.14) +where σ(0) is the leading order (LO) and σ(1) the NLO cross section in the pole mass scheme. At +NLO, the derivative term (the third summand in Eq. (2.14)) implements the MS or MSR top quark +mass schemes. In the present work, the observable of interest is the invariant mass of the tt system, +and X = mtt. In particular, we have the following set of parameters in Eq. (2.14)) +� +as(µr), m, d1, ˜R +� += +� +� +� +� +a(5) +s (µr), mMSR +t +(R), dMSR +1 +, R +� +, +R < mt(mt) (MSR regime) , +� +a(5) +s (µr), mt(µm), dMS +1 (µm), mt(µm) +� +, +µm > mt(mt) (MS regime) . +(2.15) +It is important to note that the choice of the renormalization and factorization scales µr and µf +is independent of the mass renormalization scales R or µm in this implementation. We empha- +size that it is essential that the mass scheme correction proportional to d1 is consistently used +at the renormalization scale µr, which yields logarithms ln(R/µr) or ln(µm/µr) beyond NLO to +consistently cancel the pole mass renormalon. Since MCFM is based on renormalization with 5 +dynamical flavors, one has to consistently expand a(6) +s (µr) for the MS top mass scheme corrections +of Eq. (2.1) in powers of a(5) +s (µr) in the cross section formula of Eq. (2.14). At NLO this leads to +Eq. (2.15). +We note that the fixed-order perturbative corrections for the differential cross section in the +pole mass scheme are known at next-to-next-to-leading order (NNLO) accuracy in QCD [38] and at +NLO in the electroweak theory [39, 40]. In addition, an implementation of the MS mass scheme at +NNLO has been provided in Ref. [41]. The conversion of the mass renormalization scheme from the +pole mass to the running or the MSR mass beyond NLO accuracy in QCD (and LO for electroweak +effects as presented here) needs to be performed numerically and requires theory predictions for +differential cross sections with the pole mass at NNLO accuracy for a large array of pole mass +values (typically in a range 150 GeV < m < 180 GeV)), which are currently not readily available in +the literature. +Non-relativistic quasi-bound state QCD corrections are important for the region mtt ∼ 340- +360 GeV, where the strongest top quark mass sensitivity arises in the mtt distribution. In this +threshold region the produced top quarks attain small non-relativistic velocities v ≪ 1 in the tt +center-of-mass frame, and the dynamics of the tt system are hence governed by the mass mt, the +relative momentum mtv, and the kinetic energy mtv2 of the top quark. +Since mt ≫ mtv ≫ +mtv2, the appearance of ratios involving the masses, momenta and kinetic energy of the top quark +renders the standard fixed-order expansion in powers of αs unreliable in this mtt range. +The +6 + +most pronounced quasi-bound state effects arise from the Coulomb corrections due to the exchange +of gluons between the produced t and t yielding a dependence of the prediction on the ratio +mt/(mtv). This leads to a singular (αs/v)n behavior in the fixed-order perturbative QCD correction +at n-loops [42]. These quasi-bound state effects have been considered in Refs. [43, 44], and more +recently again in [45]. These predictions, however, do not provide an adequate description of the +lowest mtt bin in the region between 300 GeV and the quasi-bound state region around 350 GeV, +where the imaginary energy approach and the use of the optical theorem [46] predict a sizeable +and unphysical finite tt production rate, see the results shown in Ref. [45]. +In this region the +differential cross section depends on the experimental cuts on the top and antitop quark decay +products [47, 48], which complicates the theoretical prediction as well as the experimental analysis, +but any sensible choice of cuts leads to a strongly suppressed rate for mtt close to 300 GeV. This +latter aspect is actually better described by the fixed-order predictions for stable top quarks where +the rate vanishes identically for mtt < 2mt (for a correct top mass scheme choice as discussed +below). Furthermore, a systematic treatment of the intermediate region, where the non-relativistic +and relativistic calculations need to be matched, is currently not available with a reliable matching +error estimate.4 +We also mention that for the electroweak corrections different scheme choices +for the MS mass are available related to the definition of the vacuum expectation value [35, 36]. +Their effects concerning the MSR mass and their impact on the use of different mass schemes in +experimental observables is unknown. Overall, there is currently no complete and reliable theory +prediction for the low mtt distribution available for experimental analysis. For the study of the tt +differential cross section as a function of mtt and its dependence on the MSR mass scale R, the NLO +fixed order prediction for stable top quarks based on the MCFM program is appropriate, since it +properly describes the generic size of subleading QCD corrections and vanishes for mtt < 2mt. For +a reliable measurement of the MSR top quark mass, however, a more complete code including the +features mentioned above has to be made available. +3 +First investigation of the R scale dependence +In this section we examine the dependence of the mtt distribution in different representative bins +in the range between 300 and 700 GeV on the scales µr, µf, and R in the MSR mass scheme as +well as µm in the MS scheme using as input the results of the ABMP16 PDF fit at NLO [50] with +α(5) +s (mZ) = 0.11905 at mZ = 91.19 GeV. For the MS mass value mt(mt) = 160.68 GeV has been +chosen close to the fit of Ref. [51]. The latter value corresponds to a MSR masses at R = 1 GeV +and R = 80 GeV of mMSR +t +(1 GeV) = 170.48 GeV and mMSR +t +(80 GeV) = 164.98 GeV, respectively. +In Fig. 1, the cross section for the bin mtt ∈ [300, 333] GeV, i.e. the region below the tt pro- +duction threshold, is shown for different scale choices at LO and NLO. The cross section is zero +for R < 60 GeV, which corresponds to 2mMSR +t +(R) > 333 GeV. Non-zero contributions to the cross +section in the mtt ∈ [300, 333] GeV range appear only at large values of R or when using the MS +4Such a treatment is available only for top quark production in e+e− annihilation, see Ref. [49]. +7 + +mass, which correspond to smaller values of mMSR +t +(R) or mt(µm). The LO contribution to the +cross section is zero or positive throughout the probed range of R and µm. At NLO, however, the +quick decrease of the derivative terms in Eq. (2.14) in comparison to the increase of the positive +contributions would lead to unphysical negative values of the NLO cross section in this kinematic +range, as was also pointed out in Ref. [41], where the MS mass scheme was examined. +Since tt production in the range mtt ∈ [300, 333] GeV is impossible, the results in Fig. 1 also +show that R values above 80 GeV must be avoided. This also implies that the MS mass cannot be +used if the tt cross section in this mtt range is included in the experimental analysis. This conclusion +holds even in the presence of quasi-bound state effects, since these provide a more precise prediction +of the tt production threshold, which is, however, located at mtt values above 333 GeV. A further +feature of the mtt ∈ [300, 333] GeV range, shown in Fig. 1, is the rapid increase of the cross section +at µm ≳ 410 GeV. This occurs when mt(µm) is so small, such that LO tt production is even possible +below 300 GeV. +In Fig. 2, the cross section for the bin mtt ∈ [333, 366] GeV, i.e. the region where the tt produc- +tion threshold is located, is shown as a function of R and µm at NLO in the left panel. The right +panel displays the relative size of the NLO corrections with respect to the LO description. Here, the +quasi-bound state effects are sizeable and our NLO result only provides a qualitative description. +Similar as in the lowest bin, we observe a quite strong dependence on the mass renormalization +scale. We see that for very small values of R the size of the NLO correction increases significantly, +particularly for large µr and µf values, making the use of fixed-order perturbation theory unreliable +for these choices. This shows that the impact of the higher-order QCD corrections, including the +1 +100 +200 +300 +400 +500 +600 + [GeV] +m +µ +R, +6 +− +4 +− +2 +− +0 +2 +4 +6 +8 + [pb/GeV] +tt +dm +σ +d +)=160.68 GeV +t +m +( +t +m +ABMP16_5_nlo + = 13 TeV +s + < 333 GeV +tt +300 GeV < m +) +t +m +( +t +m + = 1/4 +f +µ + = +r +µ +) +t +m +( +t +m + = 1/2 +f +µ + = +r +µ +) +t +m +( +t +m + = +f +µ + = +r +µ +) +t +m +( +t +m + = 2 +f +µ + = +r +µ +) +t +m +( +t +m + = 4 +f +µ + = +r +µ +Total +LO +1 +Figure 1: The mtt ∈ [300, 333] GeV range of the mtt distribution. There is no tt production at +R ≲ 60 GeV, but the region above it suffers from the lack of Coulomb corrections. The discontinuity +at µm ≳ 410 GeV is due to the tt production threshold becoming artificially low, and such high +values of the scale µm should be avoided. +8 + +1 +100 +200 +300 +400 +500 +600 + [GeV] +m +µ +R, +0 +0.5 +1 +1.5 +2 +2.5 +3 +3.5 +4 +4.5 + [pb/GeV] +tt +dm +NLO +σ +d +)=160.68 GeV +t +m +( +t +m +ABMP16_5_nlo + = 13 TeV +s +pp, + < 366 GeV +tt +333 GeV < m +)t +m +(t +m + = 1/4 +f +µ + = +r +µ +)t +m +(t +m + = 1/2 +f +µ + = +r +µ +)t +m +(t +m + = +f +µ + = +r +µ +)t +m +(t +m + = 2 +f +µ + = +r +µ +)t +m +(t +m + = 4 +f +µ + = +r +µ +1 +1 +100 +200 +300 +400 +500 +600 + [GeV] +m +µ +R, +0 +0.2 +0.4 +0.6 +0.8 +1 +1.2 +1.4 +1.6 +1.8 +tt +dm + LO +σ +d + / +tt +dm +NLO +σ +d +)=160.68 GeV +t +m +( +t +m +ABMP16_5_nlo + = 13 TeV +s + < 366 GeV +tt +333 GeV < m +) +t +m +( +t +m + = 1/4 +f +µ + = +r +µ +) +t +m +( +t +m + = 1/2 +f +µ + = +r +µ +) +t +m +( +t +m + = +f +µ + = +r +µ +) +t +m +( +t +m + = 2 +f +µ + = +r +µ +) +t +m +( +t +m + = 4 +f +µ + = +r +µ +1 +Figure 2: The NLO cross section (left) and the ratio of the LO and NLO cross sections (right) for +mtt ∈ [333, 366] GeV. The transition from a region suffering from the missing Coulomb corrections +to a more stable region where the threshold effects become less important is seen at R ≳ 60 GeV +(dashed blue). Further, predictions obtained using small values of µr, µf are observed to stabilize +the prediction quickly as a function of R or µm. +quasi-bound state corrections, is particularly sizeable and essentially maximized in the pole mass +scheme. This is closely mimicked by the result for R = 1 GeV. +We see that the most stable predictions are obtained and that the NLO corrections are signif- +icantly smaller for R in the range of 60 to 80 GeV. This is not accidental, but expected from the +fact that the smaller value of the MSR mass at these R values accounts for the reduced mass of +the tt system due to the Coulomb-binding effects. So also the impact of the (missing) Coulomb +corrections can be expected to be moderate and in particular much smaller than in the pole mass +scheme. Adopting values for µr and µf below the top quark mass further diminishes the size of +the NLO corrections. This is because for this R-range and for these µr and µf values mMSR +t +(R) +captures a sizeable part of the non-relativistic bound state dynamics relevant in this bin.5 +At this point it is also instructive to examine mtt far above threshold. In Figs. 3 and 4, the +results for mtt ∈ [465, 498] GeV and mtt ∈ [663, 696] GeV, respectively, are shown. Here the NLO +predictions provide an appropriate theoretical description. In contrast to the low mtt bins discussed +above, the mass renormalization scale behavior is very smooth. This is partly related to the much +smaller top quark mass sensitivity, but also means that none of the top quark mass schemes (and +values for R or µm) provide any advantage concerning capturing essential QCD corrections. Here, +only the choices of the scales µr and µf are essential for the prediction showing a preference for +values of around mt. This observation applies also to other invariant mass bins covering large mtt +5Due to the integration over the bin range, the R and µr values are expected to be larger than for a description +on the bound state resonance peak, where even lower scale choices are appropriate [46]. +9 + +1 +100 +200 +300 +400 +500 +600 + [GeV] +m +µ +R, +0 +0.5 +1 +1.5 +2 +2.5 +3 +3.5 +4 +4.5 + [pb/GeV] +tt +dm +NLO +σ +d +)=160.68 GeV +t +m +( +t +m +ABMP16_5_nlo + = 13 TeV +s +pp, + < 498 GeV +tt +465 GeV < m +)t +m +(t +m + = 1/4 +f +µ + = +r +µ +)t +m +(t +m + = 1/2 +f +µ + = +r +µ +)t +m +(t +m + = +f +µ + = +r +µ +)t +m +(t +m + = 2 +f +µ + = +r +µ +)t +m +(t +m + = 4 +f +µ + = +r +µ +1 +100 +200 +300 +400 +500 +600 + [GeV] +m +µ +R, +0 +0.2 +0.4 +0.6 +0.8 +1 +1.2 +1.4 +1.6 +1.8 +2 +2.2 +tt +dm + LO +σ +d + / +tt +dm +NLO +σ +d +)=160.68 GeV +t +m +( +t +m +ABMP16_5_nlo + = 13 TeV +s + < 498 GeV +tt +465 GeV < m +) +t +m +( +t +m + = 1/4 +f +µ + = +r +µ +) +t +m +( +t +m + = 1/2 +f +µ + = +r +µ +) +t +m +( +t +m + = +f +µ + = +r +µ +) +t +m +( +t +m + = 2 +f +µ + = +r +µ +) +t +m +( +t +m + = 4 +f +µ + = +r +µ +Figure 3: The NLO cross section (left) and the ratio of the LO and NLO cross sections (right) for +mtt ∈ [465, 498] GeV. +1 +100 +200 +300 +400 +500 +600 + [GeV] +m +µ +R, +0 +0.2 +0.4 +0.6 +0.8 +1 + [pb/GeV] +tt +dm +NLO +σ +d +)=160.68 GeV +t +m +( +t +m +ABMP16_5_nlo + = 13 TeV +s +pp, + < 696 GeV +tt +663 GeV < m +)t +m +(t +m + = 1/4 +f +µ + = +r +µ +)t +m +(t +m + = 1/2 +f +µ + = +r +µ +)t +m +(t +m + = +f +µ + = +r +µ +)t +m +(t +m + = 2 +f +µ + = +r +µ +)t +m +(t +m + = 4 +f +µ + = +r +µ +1 +100 +200 +300 +400 +500 +600 + [GeV] +m +µ +R, +0 +0.2 +0.4 +0.6 +0.8 +1 +1.2 +1.4 +1.6 +1.8 +2 +2.2 +tt +dm + LO +σ +d + / +tt +dm +NLO +σ +d +)=160.68 GeV +t +m +( +t +m +ABMP16_5_nlo + = 13 TeV +s + < 696 GeV +tt +663 GeV < m +) +t +m +( +t +m + = 1/4 +f +µ + = +r +µ +) +t +m +( +t +m + = 1/2 +f +µ + = +r +µ +) +t +m +( +t +m + = +f +µ + = +r +µ +) +t +m +( +t +m + = 2 +f +µ + = +r +µ +) +t +m +( +t +m + = 4 +f +µ + = +r +µ +Figure 4: +Same as Fig. 3 for the bin mtt ∈ [663, 696] GeV. +values, see Ref. [52]. +Overall, our examination suggests that the MSR top quark mass mMSR +t +(R) and the choice for the +central value of R = 80 GeV provide the most reliable theoretical predictions for all mtt bins. For the +scales µr and µf the central values mt(mt) and, in particular mt(mt)/2 for the mtt range containing +the tt threshold, are adequate choices. We note that these findings are also in line with the optimal +scale choices for the total cross section for tt hadro-production, when using the top quark mass in +the MS scheme. In this case, central values for µr and µf of the order mt(mt)/2 ≈ 80 GeV are in the +10 + +region of fastest apparent convergence considering perturbative QCD corrections through NNLO +and also minimize the scale sensitivity of the total cross section [22]. Settings for PDF factorization +scale µf different from µr have been explored in Refs [41, 53], corroborating these findings. On the +other hand, for the total cross section with the top quarks in the pole mass scheme, which is well +modeled by the MSR scheme mass mMSR +t +(1 GeV), the preferred central values for µr and µf, which +minimize scale sensitivity and optimize perturbative convergence through NNLO, are of the order +mpole +t +/4 ≈ 45 GeV, see e.g. Ref. [22]. This is also visible in the ratio plots on the right in Figs. 2–4. +In the following, we demonstrate the impact of the mass scheme and the scale setting on the value +of the top quark mass obtained in fits to the experimental data of Ref. [18]. +4 +Extraction of the top quark MSR mass +The MSR mass mMSR +t +(R) is extracted from the differential tt production cross section measured by +the CMS Collaboration in pp collisions at the LHC at √s = 13 TeV, corresponding to an integrated +luminosity of 35.9 fb−1 [18]. The tt cross section is measured as a function of mtt in the ranges: +mtt < 420 GeV, mtt ∈ [420, 550] GeV, mtt ∈ [550, 810] GeV and mtt > 810 GeV. +The theoretical predictions are obtained using the ABMP16 5-flavor PDF set [51] at NLO. +According to the preferred MSR mass scale settings described in the previous section, the initial +value of the scale R is set to 80 GeV in Eq. (2.14), and the cross section is calculated for a range of +assumed values of mMSR +t +(80 GeV). The function +χ2 = +� +i,j +(σexp +i +− σth +i )C−1 +ij (σexp +j +− σth +j ), +(4.1) +is computed for each mMSR +t +(80 GeV). The indices i, j in Eq. (4.1) run over the bins of the mtt +distribution, while σexp +i +are the experimental data and σth +i +the theoretical predictions. The inverse +covariance matrix C−1 +ij +provided in Ref. [18] is used. +The scales µr and µf are set to mMSR +t +(80 GeV) for all 4 bins of the mtt distribution or, alter- +natively, to mMSR +t +(80 GeV)/2 for mtt < 420 GeV, to stabilize the prediction against the missing +quasi-bound state corrections, and to mMSR +t +(80 GeV) for the remainder. Fig. 5 shows a 4th order +polynomial fit to the χ2 values resulting from each configuration. +The fit uncertainties are obtained via the ∆χ2 = 1 tolerance criterion, while the µr and µf scale +uncertainties are evaluated by varying their central values in each bin up and down by a factor of +2, avoiding the cases where one scale is multiplied by 1/2 and the other by 2, and constructing +an envelope. For comparison with previous analyses, the extracted values of mMSR +t +(80 GeV) are +evolved to the reference scales R of 1 and 3 GeV. Note that determining mMSR +t +(1 GeV) requires +evaluating αs(1 GeV) rather close to the Landau pole, which is expected to lead to an increased +perturbative uncertainty in the MSR mass at R = 1 GeV due to missing higher order corrections. +Reporting the mass value also at R = 3 GeV thus ensures the stability of the result, and the use of +reference scales R > 1 GeV will become increasingly important in future extractions of mMSR +t +(R). +11 + +160 +162 +164 +166 +168 +170 +172 +174 +176 +178 +(80 GeV) [GeV] +MSR +t +m +0 +20 +40 +60 +80 +100 +120 +140 +160 +180 +200 +220 +2 +χ + = 1.86 / 3 +dof + / N +2 +χ +Min. + [GeV] +tt + m +(80 GeV) +MSR +t + = m +f +µ +, +r +µ + < 420 : +(80 GeV) +MSR +t + = m +f +µ +,r +µ + [420, 550] : +(80 GeV) +MSR +t + = m +f +µ +,r +µ + [550, 810] : +(80 GeV) +MSR +t + = m +f +µ +, +r +µ + > 810 : + = 1.86 / 3 +dof + / N +2 +χ +Min. +162 +164 +166 +168 +170 +172 +174 +176 +178 +180 +(80 GeV) [GeV] +MSR +t +m +0 +20 +40 +60 +80 +100 +120 +140 +160 +180 +200 +220 +2 +χ + = 3.03 / 3 +dof + / N +2 +χ +Min. + [GeV] +tt + m +(80 GeV) +MSR +t +m +2 +1 + = +f +µ +,r +µ + < 420 : +(80 GeV) +MSR +t + = m +f +µ +, +r +µ + [420, 550] : +(80 GeV) +MSR +t + = m +f +µ +, +r +µ + [550, 810] : +(80 GeV) +MSR +t + = m +f +µ +,r +µ + > 810 : + = 3.03 / 3 +dof + / N +2 +χ +Min. +Figure 5: A 4th order polynomial fitted to the χ2 resulting from comparing the experimental +data to theory predictions assuming different values of mMSR +t +(80 GeV). +The scales µr and µf +are set to mMSR +t +(80 GeV) considering the whole mtt distribution (left), or to mMSR +t +(80 GeV)/2 for +mtt < 420 GeV and to mMSR +t +(80 GeV) for the remainder (right). The number of degrees of freedom +in the fits is denoted by Ndof. +Table 1: The values of mMSR +t +(R) obtained at different scales R (given in brackets below mMSR +t +), +and the corresponding mt(mt), the χ2 divided by the number of degrees of freedom Ndof in the +fit, along with the fit and scale uncertainties for the mMSR +t +(R) extracted at R = 80 GeV. The +results are shown for the constant µr, µf setting, where the central µr and µf values are set to +mMSR +t +(80 GeV) in the whole mtt distribution, and for the semi-dynamical (SD) setting where they +are set to mMSR +t +(80 GeV)/2 for mtt < 420 GeV and to mMSR +t +(80 GeV) for higher mtt. The fit and +µr, µf uncertainties correspond to the MSR mass extracted at R = 80 GeV. Within the reported +accuracy, the uncertainty in the initial choice of R agrees in all cases when the extracted mMSR +t +(R) +is evolved to the reference R. +mMSR +t +mMSR +t +mMSR +t +mt +Fit +µr, µf +R +µr, µf +χ2/Ndof +(80 GeV) +(1 GeV) +(3 GeV) +(mt) +unc. +unc. +unc. +setting +[ GeV] +[ GeV] +[ GeV] +[ GeV] +[ GeV] +[ GeV] +[ GeV] +Const. +1.86/3 +167.7 +173.2 +172.9 +163.3 ++0.6 +−0.6 ++0.4 +−0.6 ++0.4 +−0.5 +SD +3.03/3 +169.3 +174.8 +174.5 +164.8 ++0.5 +−0.5 ++0.2 +−0.4 ++0.2 +−0.3 +Furthermore, the results are translated into the standard MS mass mt(mt) by iteratively finding +mMSR +t +(mMSR +t +) via the condition R = mMSR +t +(R), and applying the matching formula in Eq. (2.9) +up to O(a3 +s). The uncertainty related to the initial choice of R is assessed by repeating the fits at +R = 60 GeV and R = 100 GeV, and the difference in the resulting masses at the reference scales +to the respective values obtained in the R = 80 GeV fit is taken as the R scale uncertainty. The +resulting values for the top quark mass are listed in Table 1. +In particular, setting the central µr and µf to mMSR +t +(80 GeV) and considering the complete mtt +12 + +distribution yields +mMSR +t +(1 GeV) = 173.2 ± 0.6 (fit)+0.4 +−0.6 (µr, µf)+0.4 +−0.5 (R) GeV . +(4.2) +The value for mMSR +t +(80 GeV) in this fit translates into mt(mt) = 163.3+0.8 +−1.0 GeV. This is compatible +within uncertainties with the value of mt(mt) = 162.1+1.0 +−1.0 GeV obtained at NLO in the ABMP16 +5-flavor PDF set [50]. +In accordance with the results shown in Fig. 1, multiplying the scales µr and µf by 1/2 within +mtt < 420 GeV is observed to increase the NLO cross section at R = 80 GeV. To compensate for +this effect, the fit for mMSR +t +(80 GeV) leads to a somewhat larger value for the top quark MSR mass, +reducing the predicted cross section especially in the vicinity of the tt production threshold. This +results in the value +mMSR +t +(1 GeV) = 174.8 ± 0.5 (fit)+0.2 +−0.4 (µr, µf)+0.2 +−0.3 (R) GeV. +(4.3) +It is expected that the impact of the choices for µr and µf, i.e. the shift of 1.6 GeV in the cen- +tral values between Eqs. (4.2) and (4.3), will be reduced at NNLO accuracy and once a reliable +description of the quasi-bound state effects is available. Nonetheless, as already expected from the +observations in Sec. 3, the scale setting in Eq. (4.3) already increases the robustness against scale +variations, yielding somewhat smaller uncertainties than Eq. (4.2). +In order to illustrate the main conceptual novelty and the phenomenological importance of the +mass scheme choice, we perform the following variant of the fit: Instead of determining the top +quark MSR mass at R = 80 GeV and evolving the extracted mMSR +t +(80 GeV) value to R = 1 GeV, as +in Eqs. (4.2) and (4.3), we perform the fit to data directly with the initial scale set to R = 1 GeV +166 +168 +170 +172 +174 +(1 GeV) [GeV] +MSR +t +m +0 +20 +40 +60 +80 +100 +120 +2 +χ + = 2.16 / 3 +dof + / N +2 +χ +Min. + [GeV] +tt + m +(1 GeV) +MSR +t + = m +f +µ +, +r +µ + < 420 : +(1 GeV) +MSR +t + = m +f +µ +,r +µ + [420, 550] : +(1 GeV) +MSR +t + = m +f +µ +,r +µ + [550, 810] : +(1 GeV) +MSR +t + = m +f +µ +, +r +µ + > 810 : + = 2.16 / 3 +dof + / N +2 +χ +Min. +Figure 6: +Same as Fig. 5, now fitting mMSR +t +(1 GeV) and with the scales µr and µf set to +mMSR +t +(1 GeV) in the whole mtt distribution. +13 + +in NLO cross section of Eq. (2.14). Using also the central scales µr, µf set to mMSR +t +(1 GeV), this +results in +mMSR +t +(1 GeV) = 170.1 ± 0.6 (fit)+1.1 +−0.9 (µr, µf) GeV , +(4.4) +where the corresponding fit to χ2 is shown in Fig. 6. In Eq. (4.4) the µr and µf scale uncertainties +are twice as large as those of Eq. (4.2). The sizeable discrepancy to the results of Eqs. (4.2) and (4.3) +indicates that scale variation does not provide a proper estimate of the theoretical uncertainties +due to the missing higher order and quasi-bound state corrections for the result quoted in Eq. (4.4). +Since using mMSR +t +(1 GeV) closely approximates the outcome using pole mass scheme, this confirms +our conclusions drawn in Sec. 3 that the use of the pole mass scheme (or a very small initial R value +for the MSR mass) leads to less reliable results in a fixed order QCD description at NLO accuracy, +where the quasi-bound state effects are missing. The significant difference of 4.7 GeV between the +central values in Eqs. (4.3) and (4.4) demonstrates the phenomenological relevance of this issue. +This underpins the importance of proper scale setting in future phenomenological analyses. +Let us now comment on other recent extractions of the top-quark mass, which have employed +different methodologies. +Data from the CMS collaboration for the tt production cross section +collected in pp collisions at the LHC at √s = 13 TeV has been used previously for a determination +of the top-quark mass using both, the pole and the MS mass scheme [54, 55]. The emphasis of +those analyses has been on keeping the correlations of the top-quark mass with the strong coupling +αs(mZ) and the PDFs. In a different thread of analyses, the running of top quark MS mass mt(µm) +has been studied at NLO [18] and NNLO [56] with dynamical scales, using data from the CMS +collaboration for the mtt distributions.6 +Of these analyses, the results of Ref. [55] can be compared to the present work, since they are +obtained from normalized multi-differential cross sections which also include the low mtt region +discussed here, and the theoretical predictions have also been based on the NLO MCFM cross +section description. Ref. [55] quotes mpole +t += 170.5±0.8 GeV, which, if interpreted as the asymptotic +pole mass [37], translates into mMSR +t +(1 GeV) = 170.2±0.8 GeV. This is compatible with the variant +of the present study in Eq. (4.4) obtained by directly fitting mMSR +t +(1 GeV) to data, although the +combined fit of mpole +t +, αs(mZ) and PDFs in Ref. [55] reports a smaller value of αs(mZ) than used +in Eq. (4.4) on the basis of the ABMP16 PDF set, and a somewhat different gluon PDF. +The ATLAS collaboration has derived a value for the top quark MSR mass at the reference scale +R = 1 GeV in Ref. [57] by comparing QCD predictions at next-to-leading logarithmic accuracy for +the soft-drop groomed top quark jet mass distribution to parton shower Monte Carlo simulations +for a Monte-Carlo top quark mass mMC +t += 172.5 GeV. Obtained in the Monte Carlo calibration +(following [58]), the result of Ref. [57] is not based on experimental data and hence cannot be +directly compared to the results of the present study. +The value for the top quark MSR mass of mMSR +t +(3 GeV) = 169.6+0.8 +−1.1 GeV has been extracted in +6See also http://cms-results.web.cern.ch/cms-results/public-results/publications/TOP-19-007/index. +html#Figure-aux_001. +14 + +Ref. [53], using the CMS data of Ref. [55] and the same methodology, i.e. using fixed-order QCD +perturbation theory at NLO accuracy, so that mMSR +t +(3 GeV) has been fitted simultaneously with +the PDFs and strong coupling constant. Evolving the result of the present study in Eq. (4.3) to +R = 3 GeV yields +mMSR +t +(3 GeV) = 174.5 ± 0.5 (fit)+0.2 +−0.4 (µr, µf)+0.2 +−0.3 (R) GeV , +(4.5) +which indicates some tension.7 Part of this difference is due to the direct fitting of mMSR +t +(3 GeV) +in Ref. [53] compared to mMSR +t +(80 GeV) in Eq. (4.5). In addition, Ref. [53] has obtained αs(mZ) = +0.1132+0.0023 +−0.0018, which is two standard deviations away from the value of the ABMP16 fit at NLO [50] +used in the extraction of Eq. (4.5). +Notably, neither any of the cited previous top quark mass extractions nor the present work have +included the aforementioned corrections for the quasi-bound state effects. However, the extraction +of the top quark MSR mass using predictions in the MSR scheme at the scale R = 80 GeV profits +from the smaller size of these effects and thus from an improved stability of the cross section. +5 +Summary and Conclusions +We have presented the first comprehensive study of the mtt distribution in its dependence on the +mass renormalization scales R and µm of the MSR and MS top quark mass schemes. Our findings +suggest that the scale setting of R close to 80 GeV improves the robustness of the predictions for +the mtt distribution against scale variations in general and, in particular, against the impact of +quasi-bound state corrections in the region of mtt close to the tt threshold. The theory predictions +are based on the NLO fixed order QCD description provided by the MCFM program, adapted to +the MSR and MS top quark mass schemes. The optimized scale choices for those mass schemes are +characterized by low values of the renormalization and factorization scales µr and µf. This holds +in particular in the vicinity of the tt production threshold region in the mtt distribution, where +values µr ≃ µf ≃ mt/2 are observed to stabilize cross section predictions and to decrease the scale +uncertainty in the determination of the MSR mass. +These settings have been applied in an extractions of the top quark MSR mass at R = 80 GeV, +using tt pair production cross section, measured as a function of mtt in pp collisions at √s = 13 TeV +at the LHC by the CMS collaboration, using fixed-order perturbative QCD predictions at NLO +accuracy and also the semi-dynamical scales for µr, µf in the low-mtt regime. The fitted value of +mMSR +t +(80 GeV) has then been evolved to various low reference scales R, rather than computing the +cross sections directly at low R as performed in earlier analyses. This procedure yields the value +mMSR +t +(3 GeV) = 174.5+0.6 +−0.7 GeV, which is discussed in the context of other recent extractions of the +top quark mass from LHC data. The observed differences are explained in part by the scale choice +7The computations in Ref. [53] rely on the practical MSR (pMSR) definition [13] instead of the natural MSR +(nMSR) scheme used in this work. The difference is at the level of 10 MeV [13] and thus negligible for the uncertainties +quoted. +15 + +of R = 80 GeV for the top quark MSR mass, advocated by the present study. Other reasons for +differences are due to the choice of the value for the strong coupling αs(mZ), which directly affects +the normalisation of the cross section and is anti-correlated with the top quark mass, and, to a +lesser extent, due to the particular PDF sets used. +While we have argued that the implementation of the MSR mass scheme in the tt cross section +calculation and the optimal scale choice for R of 80 GeV provide more robust predictions even at +NLO accuracy, the findings should be corroborated by extending the analysis to NNLO accuracy. In +addition, the proper treatment of both, the quasi-bound state effects, together with a matching to +the relativistic tt region, and the mtt region below the threshold are further important improvements +to be implemented. A final reliable measurement of the top quark MSR mass needs to address those +issues as well as the correlation of the top quark mass with the other theoretical parameters, which +control the cross section predictions. We leave these aspects for future studies. +Acknowledgements +The work of A.H.H was supported in part by FWF Austrian Science Fund under the Project No. +P32383-N27, the work of S.M. in part by the Bundesministerium f¨ur Bildung und Forschung under +contract 05H21GUCCA, the work by T.M. and K. L. is supported by the Helmholtz Association +under the contract W2/W3-123, and T.M. is also supported by the National Science Centre, Poland, +research grant No. 2021/42/E/ST2/00031. +References +[1] +F. Bezrukov et al. “Higgs Boson Mass and New Physics”. In: JHEP 10 (2012), p. 140. arXiv: +1205.2893 [hep-ph]. +[2] +G. Degrassi et al. “Higgs mass and vacuum stability in the Standard Model at NNLO”. In: +JHEP 08 (2012), p. 098. arXiv: 1205.6497 [hep-ph]. +[3] +S. Alekhin, A. Djouadi, and S. Moch. “The top quark and Higgs boson masses and the stability +of the electroweak vacuum”. In: Phys. Lett. B 716 (2012), pp. 214–219. arXiv: 1207.0980 +[hep-ph]. +[4] +A. V. Bednyakov et al. “Stability of the Electroweak Vacuum: Gauge Independence and +Advanced Precision”. In: Phys. Rev. Lett. 115.20 (2015), p. 201802. arXiv: 1507 . 08833 +[hep-ph]. +[5] +I. I. Y. Bigi et al. “The Pole mass of the heavy quark. Perturbation theory and beyond”. In: +Phys. Rev. D 50 (1994), pp. 2234–2246. arXiv: hep-ph/9402360. +[6] +M. Beneke and V. M. Braun. “Heavy quark effective theory beyond perturbation theory: +Renormalons, the pole mass and the residual mass term”. In: Nucl. Phys. B 426 (1994), +pp. 301–343. arXiv: hep-ph/9402364. +[7] +M. C. Smith and S. S. Willenbrock. “Top quark pole mass”. In: Phys. Rev. Lett. 79 (1997), +pp. 3825–3828. arXiv: hep-ph/9612329. +16 + +[8] +S. Ferrario Ravasio, P. Nason, and C. Oleari. “All-orders behaviour and renormalons in top- +mass observables”. In: JHEP 01 (2019), p. 203. arXiv: 1810.10931 [hep-ph]. +[9] +A. H. Hoang. “What is the Top Quark Mass?” In: Ann. Rev. Nucl. Part. Sci. 70 (2020), +pp. 225–255. arXiv: 2004.12915 [hep-ph]. +[10] +G. ’t Hooft. “Dimensional regularization and the renormalization group”. In: Nucl. Phys. B +61 (1973), pp. 455–468. +[11] +W. A. Bardeen et al. “Deep-inelastic scattering beyond the leading order in asymptotically +free gauge theories”. In: Phys. Rev. D 18 (11 Dec. 1978), pp. 3998–4017. url: https:// +link.aps.org/doi/10.1103/PhysRevD.18.3998. +[12] +A. H. Hoang et al. “Infrared Renormalization Group Flow for Heavy Quark Masses”. In: +Phys. Rev. Lett. 101 (2008), p. 151602. arXiv: 0803.4214 [hep-ph]. +[13] +A. H. Hoang et al. “The MSR mass and the O (ΛQCD) renormalon sum rule”. In: JHEP 04 +(2018), p. 003. arXiv: 1704.01580 [hep-ph]. +[14] +A. H. Hoang and I. W. Stewart. “Top Mass Measurements from Jets and the Tevatron Top- +Quark Mass”. In: Nucl. Phys. B Proc. Suppl. 185 (2008). Ed. by G. Bellettini, G. Chiarelli, +and R. Tenchini, pp. 220–226. arXiv: 0808.0222 [hep-ph]. +[15] +A. H. Hoang. “The Top Mass: Interpretation and Theoretical Uncertainties”. In: 7th Inter- +national Workshop on Top Quark Physics. Dec. 2014. arXiv: 1412.3649 [hep-ph]. +[16] +A. H. Hoang, S. Pl¨atzer, and D. Samitz. “On the Cutoff Dependence of the Quark Mass +Parameter in Angular Ordered Parton Showers”. In: JHEP 10 (2018), p. 200. arXiv: 1807. +06617 [hep-ph]. +[17] +A. H. Hoang, C. Lepenik, and M. Preisser. “On the Light Massive Flavor Dependence of the +Large Order Asymptotic Behavior and the Ambiguity of the Pole Mass”. In: JHEP 09 (2017), +p. 099. arXiv: 1706.08526 [hep-ph]. +[18] +A. M. Sirunyan et al. “Running of the top quark mass from proton-proton collisions at √s = +13TeV”. In: Phys. Lett. B 803 (2020), p. 135263. arXiv: 1909.09193 [hep-ex]. +[19] +J. M. Campbell and R. K. Ellis. “MCFM for the Tevatron and the LHC”. In: Nucl. Phys. B +Proc. Suppl. 205-206 (2010). Ed. by J. Bl¨umlein, S.-O. Moch, and T. Riemann, pp. 10–15. +arXiv: 1007.3492 [hep-ph]. +[20] +J. M. Campbell and R. K. Ellis. “Top-Quark Processes at NLO in Production and Decay”. +In: J. Phys. G 42.1 (2015), p. 015005. arXiv: 1204.1513 [hep-ph]. +[21] +U. Langenfeld, S. Moch, and P. Uwer. “Measuring the running top-quark mass”. In: Phys. +Rev. D 80 (2009), p. 054009. arXiv: 0906.5273 [hep-ph]. +[22] +M. Dowling and S. Moch. “Differential distributions for top-quark hadro-production with a +running mass”. In: Eur. Phys. J. C 74.11 (2014), p. 3167. arXiv: 1305.6422 [hep-ph]. +[23] +P. Marquard et al. “Quark Mass Relations to Four-Loop Order in Perturbative QCD”. In: +Phys. Rev. Lett. 114.14 (2015), p. 142002. arXiv: 1502.01030 [hep-ph]. +[24] +N. Gray et al. “Three-loop relation of quark MS and pole masses”. In: Zeitschrift f¨ur Physik +C Particles and Fields 48 (1990), pp. 673–679. +[25] +K. G. Chetyrkin and M. Steinhauser. “The Relation between the MS and the on-shell quark +mass at order αs3”. In: Nucl. Phys. B 573 (2000), pp. 617–651. arXiv: hep-ph/9911434. +[26] +K. Melnikov and T. v. Ritbergen. “The Three loop relation between the MS-bar and the pole +quark masses”. In: Phys. Lett. B 482 (2000), pp. 99–108. arXiv: hep-ph/9912391. +17 + +[27] +P. A. Baikov, K. G. Chetyrkin, and J. H. K¨uhn. “Quark Mass and Field Anomalous Dimen- +sions to O(α5 +s)”. In: JHEP 10 (2014), p. 076. arXiv: 1402.6611 [hep-ph]. +[28] +T. Luthe et al. “Five-loop quark mass and field anomalous dimensions for a general gauge +group”. In: JHEP 01 (2017), p. 081. arXiv: 1612.05512 [hep-ph]. +[29] +K. G. Chetyrkin, J. H. K¨uhn, and M. Steinhauser. “RunDec: A Mathematica package for run- +ning and decoupling of the strong coupling and quark masses”. In: Comput. Phys. Commun. +133 (2000), pp. 43–65. arXiv: hep-ph/0004189. +[30] +R. Tarrach. “The Pole Mass in Perturbative QCD”. In: Nucl. Phys. B 183 (1981), pp. 384– +396. +[31] +O. V. Tarasov. “Anomalous dimensions of quark masses in the three-loop approximation”. +In: Phys. Part. Nucl. Lett. 17.2 (2020), pp. 109–115. arXiv: 1910.12231 [hep-ph]. +[32] +S. A. Larin. “The Renormalization of the axial anomaly in dimensional regularization”. In: +Phys. Lett. B 303 (1993), pp. 113–118. arXiv: hep-ph/9302240. +[33] +K. G. Chetyrkin. “Quark mass anomalous dimension to O(α4 +s)”. In: Phys. Lett. B 404 (1997), +pp. 161–165. arXiv: hep-ph/9703278. +[34] +J. A. M. Vermaseren, S. A. Larin, and T. van Ritbergen. “The four loop quark mass anomalous +dimension and the invariant quark mass”. In: Phys. Lett. B 405 (1997), pp. 327–333. arXiv: +hep-ph/9703284. +[35] +S. Dittmaier and H. Rzehak. “Electroweak renormalization based on gauge-invariant vacuum +expectation values of non-linear Higgs representations. Part I. Standard Model”. In: JHEP +05 (2022), p. 125. arXiv: 2203.07236 [hep-ph]. +[36] +A. L. Kataev and V. S. Molokoedov. “Notes on Interplay between the QCD and EW Pertur- +bative Corrections to the Pole-Running-to-Top-Quark Mass Ratio”. In: JETP Lett. 115.12 +(2022), pp. 704–712. arXiv: 2201.12073 [hep-ph]. +[37] +A. H. Hoang, C. Lepenik, and V. Mateu. “REvolver: Automated running and matching of +couplings and masses in QCD”. In: Comput. Phys. Commun. 270 (2022), p. 108145. arXiv: +2102.01085 [hep-ph]. +[38] +M. Czakon, D. Heymes, and A. Mitov. “High-precision differential predictions for top-quark +pairs at the LHC”. In: Phys. Rev. Lett. 116.8 (2016), p. 082003. arXiv: 1511.00549 [hep-ph]. +[39] +J. H. K¨uhn, A. Scharf, and P. Uwer. “Electroweak effects in top-quark pair production at +hadron colliders”. In: Eur. Phys. J. C 51 (2007), pp. 37–53. arXiv: hep-ph/0610335. +[40] +M. Czakon et al. “Top-pair production at the LHC through NNLO QCD and NLO EW”. In: +JHEP 10 (2017), p. 186. arXiv: 1705.04105 [hep-ph]. +[41] +S. Catani et al. “Top-quark pair hadroproduction at NNLO: differential predictions with the +MS mass”. In: JHEP 08.08 (2020), p. 027. arXiv: 2005.00557 [hep-ph]. +[42] +A. H. Hoang and T. Teubner. “Top quark pair production close to threshold: Top mass, width +and momentum distribution”. In: Phys. Rev. D 60 (1999), p. 114027. arXiv: hep-ph/9904468. +[43] +K. Hagiwara, Y. Sumino, and H. Yokoya. “Bound-state Effects on Top Quark Production at +Hadron Colliders”. In: Phys. Lett. B 666 (2008), pp. 71–76. arXiv: 0804.1014 [hep-ph]. +[44] +Y. Kiyo et al. “Top-quark pair production near threshold at LHC”. In: Eur. Phys. J. C 60 +(2009), pp. 375–386. arXiv: 0812.0919 [hep-ph]. +[45] +W.-L. Ju et al. “Top quark pair production near threshold: single/double distributions and +mass determination”. In: JHEP 06 (2020), p. 158. arXiv: 2004.03088 [hep-ph]. +18 + +[46] +A. H. Hoang et al. “Top - anti-top pair production close to threshold: Synopsis of recent +NNLO results”. In: Eur. Phys. J. direct 2.1 (2000), p. 3. arXiv: hep-ph/0001286. +[47] +A. H. Hoang, C. J. Reisser, and P. Ruiz-Femenia. “Phase Space Matching and Finite Lifetime +Effects for Top-Pair Production Close to Threshold”. In: Phys. Rev. D 82 (2010), p. 014005. +arXiv: 1002.3223 [hep-ph]. +[48] +M. Beneke et al. “Non-resonant and electroweak NNLO correction to the e+e− top anti-top +threshold”. In: JHEP 02 (2018), p. 125. arXiv: 1711.10429 [hep-ph]. +[49] +F. Bach et al. “Fully-differential Top-Pair Production at a Lepton Collider: From Threshold +to Continuum”. In: JHEP 03 (2018), p. 184. arXiv: 1712.02220 [hep-ph]. +[50] +S. Alekhin, J. Bl¨umlein, and S. Moch. “NLO PDFs from the ABMP16 fit”. In: Eur. Phys. J. +C 78.6 (2018), p. 477. arXiv: 1803.07537 [hep-ph]. +[51] +S. Alekhin et al. “Parton distribution functions, αs, and heavy-quark masses for LHC Run +II”. In: Phys. Rev. D 96 (2017), p. 014011. arXiv: 1701.05838 [hep-ph]. +[52] +T. M¨akel¨a. “Towards global interpretation of LHC data: SM and EFT couplings from jet and +top quark measurements at CMS”. Dissertation, Universit¨at Hamburg. PhD thesis. 2022, 213 +pages: Illustrations, figures. url: https://bib-pubdb1.desy.de/record/482499. +[53] +M. V. Garzelli et al. “Heavy-flavor hadro-production with heavy-quark masses renormalized +in the MS, MSR and on-shell schemes”. In: JHEP 04 (2021), p. 043. arXiv: 2009.07763 +[hep-ph]. +[54] +A. M. Sirunyan et al. “Measurement of the tt production cross section, the top quark mass, +and the strong coupling constant using dilepton events in pp collisions at √s = 13 TeV”. In: +Eur. Phys. J. C 79.5 (2019), p. 368. arXiv: 1812.10505 [hep-ex]. +[55] +A. M. Sirunyan et al. “Measurement of t¯t normalised multi-differential cross sections in pp +collisions at √s = 13 TeV, and simultaneous determination of the strong coupling strength, +top quark pole mass, and parton distribution functions”. In: Eur. Phys. J. C 80.7 (2020), +p. 658. arXiv: 1904.05237 [hep-ex]. +[56] +M. M. Defranchis et al. “Running of the top quark mass at NNLO in QCD”. In: (Aug. 2022). +arXiv: 2208.11399 [hep-ph]. +[57] +“A precise interpretation for the top quark mass parameter in ATLAS Monte Carlo sim- +ulation”. In: ATL-PHYS-PUB-2021-034 (2021). url: https://cds.cern.ch/record/ +2777332/. +[58] +M. Butensch¨on et al. “Top Quark Mass Calibration for Monte Carlo Event Generators”. In: +Phys. Rev. Lett. 117.23 (2016), p. 232001. arXiv: 1608.01318 [hep-ph]. +19 + diff --git a/-9E1T4oBgHgl3EQf8gV6/content/tmp_files/load_file.txt b/-9E1T4oBgHgl3EQf8gV6/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..aeb5a9bcdbf804839050b5187bf5d010220660d8 --- /dev/null +++ b/-9E1T4oBgHgl3EQf8gV6/content/tmp_files/load_file.txt @@ -0,0 +1,1151 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf,len=1150 +page_content='DESY 23-001 UWThPh-2023-1 Investigation of the scale dependence in the MSR and MS top quark mass schemes for the tt invariant mass differential cross section using LHC data Toni M¨akel¨a∗a,b, Andr´e H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Hoang†c,d, Katerina Lipka‡a,e, and Sven-Olaf Moch§f aDeutsches Elektronen-Synchrotron, Notkestr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 85, 22607 Hamburg, Germany bNational Centre for Nuclear Research, Pasteura 7, PL-02-093 Warsaw, Poland cFaculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria dErwin Schr¨odinger Institute for Mathematics and Physics, University of Vienna, Boltzmanngasse 9, A-1090 Vienna, Austria eFakult¨at f¨ur Mathematik und Naturwissenschaften, Bergische Universit¨at Wuppertal, Gaußstrassse 20, D-42119 Wuppertal, Germany fII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Institut f¨ur Theoretische Physik, Universit¨at Hamburg, Luruper Chaussee 149, D-22761 Hamburg, Germany January 10, 2023 Abstract The computation of the single-differential top quark-antiquark pair (tt) production cross section at NLO in the fixed-order expansion is examined consistently using the MSR and MS short-distance top quark mass schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' A thorough investigation of the dependence of the tt invariant mass spectrum on the renormalization scales R and µm of the MSR mass mMSR t (R) and MS mass mt(µm), respectively, is carried out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' We demonstrate that a scale choice of R ∼ 80 GeV is important for the stability of the cross-section predictions for the low tt invariant mass range, which is important for a reliable extraction of the top quark mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Furthermore, a choice of semi- dynamical renormalization and factorization scales is preferred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' These findings are expected to remain valid once non-relativistic quasi-bound state effects are included in the low invariant mass region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' ∗toni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='makela@cern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='ch †andre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='hoang@univie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='at ‡katerina.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='lipka@desy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='de §sven-olaf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='moch@desy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='de 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='03546v1 [hep-ph] 9 Jan 2023 1 Introduction The top quark mass mt is a fundamental parameter of the Standard Model and has an important role in many predictions, both directly and via higher-order corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' For instance, together with the values of the strong coupling constant αs and the mass of the Higgs boson, it determines the stability of the electroweak vacuum [1–4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Yet, the formal definition of quark masses makes them renormalization scheme dependent quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The frequently used pole mass mpole t , which is based on the picture that real and virtual radiation can be resolved at arbitrarily small energy scales, suffers from the renormalon ambiguity, a spurious linear infrared (IR) sensitivity of the order of the QCD scale ΛQCD [5–7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1 In contrast, short-distance mass schemes such as the modified minimal subtraction (MS) scheme [10, 11] mass mt(µm), or the MSR scheme [12, 13] mass mMSR t (R), do not have this issue, and their renormalization scales µm and R, respectively, act as a finite resolution scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This means that real and virtual radiation are treated inclusively for scales below µm and R, which provides a more suitable description for realistic physical observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The absence of the O(ΛQCD) renormalon problem and the additional freedom to adopt suitable scale choices can be very useful to achieve higher precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Moreover, the MSR scheme can be related to quark mass definitions used in parton shower Monte Carlo programs, as worked out conceptually in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [14– 16], see also Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [13, 17] for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' For small, but still perturbative R values at around 2 GeV the MSR mass serves as a viable and renormalon-free proxy for the pole mass concept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The sensitivity of an observable to mt is always associated to a dynamical physics scale, such as the inverse Bohr radius ⟨1/rB⟩ ∼ mtαs for the impact of the top quark-antiquark (tt) quasi-bound state on the tt cross section at the threshold, or the top quark width Γt for the single top resonance mass distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Thus, the scale dependence of mt(µm) and mMSR t (R) allows to properly adapt to these dynamical scales for an observable under consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The respective renormalization group equations (RGEs) and matching relations provide the tool to unambiguously relate the top quark mass extracted at different dynamical scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This concept is well known for the running strong coupling αs and applies to the quark masses as well, particularly for increasing precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In this work, the dependence of the invariant mass of the tt pair, mtt, on the MSR mass scale R and the MS mass scale µm is investigated concurrently for the first time accounting for QCD corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Using experimental measurements of tt production at the LHC at √s = 13 TeV [18], the next-to-leading order (NLO) prediction of the mtt differential cross section from Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [19, 20] and the scheme implementation procedure of Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [21, 22], we demonstrate that the proper scheme choice is of key importance and affects the size of higher-order corrections as well as the resulting value of the extracted top quark mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 2, we review the MS and MSR top quark mass schemes and the formulae to implement them, and in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 3 we carry out a detailed investigation concerning the best choice of the MSR renormalization scale R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 4 we quote the results for 1We note that linear IR sensitivities arise in cross sections whenever cuts on soft radiation are imposed, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' These are associated to nonperturbative corrections in contrast to the pole mass, where the IR sensitivity arises purely from the choice of scheme [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 2 mMSR t (R = 1 GeV) and higher R values from the fits to the LHC measurements, demonstrating the impact of the renormalization scale choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' We close in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 5 with a summary and an outlook on future improvements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 2 Running mt and the tt pair production cross section at NLO In terms of a general mass renormalization scale µm, the pole and MS masses are related in perturbative QCD as mpole t = mt(µm) � 1 + � n=1 dMS n (µm) � a(6) s (µm) �n � , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1) where as ≡ αs/π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Here and everywhere else in this study, we explicitly indicate by the superscript whether we use the strong coupling α(5) s in the 5-flavor or α(6) s in the 6-flavor scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' For the parton distribution functions (PDFs) only the 5-flavor scheme is employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' All quarks except for the top quark are treated as massless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The coefficients dMS n (µm) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1) are known up to four loops [23] and the first few orders read [24–26] dMS 1 (µm) = 4/3 + L , dMS 2 (µm) = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1952 + 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6806L + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4167L2 , dMS 3 (µm) = 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='161 + 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='776L + 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2026L2 + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='7940L3 , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2) where the expansion uses α(6) s in the 6-flavor scheme and L = log((µm/m(µm))2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The running of the MS mass is described by the RGE µ2 m dmt(µm) dµ2m = − mt(µm) � i=0 γm i � a(6) s (µ) �i+1 , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3) where the anomalous dimensions γm i are known to five loops [27, 28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The first few orders [29–34] are given by γm 0 = 1 , γm 1 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3750 , γm 2 = 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8387 , γm 3 = −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5082 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4) Electroweak corrections (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [35, 36]) are not considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The RGE in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3) has the solution mt(µ1) = mt(µ0) exp � −2 � i=0 � µ1 µ0 dµ µ γm i � a(6) s (µ) �i+1 � , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5) yielding the MS mass at a scale µ1 via evolution from the known mass at a reference scale µ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Here and below we quote relations at O(α3 s) and evolution equations at O(α4 s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' We have also 3 used these relations in our analysis for determining numerical values for the quark masses (and the strong coupling), even though our cross section analysis is based on a fixed-order theory description at NLO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Since the mass (and strong coupling) matching relations and RGE equations are well convergent series and no subtle cancellations between the different ingredients need to be taken care of (which would be the case for the PDFs) this approach is fully consistent and has the advantage that the theoretical uncertainties in the numerical values of the masses (and the strong coupling) are eliminated entirely from our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' We recommend this approach also for future phenomenological analyses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' For implementing different mass schemes in the analytic expression for the differential mtt cross sections at NLO, see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='14) below, only the O(αs) coefficients from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6) are used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The MS mass is by construction a 6-flavor quantity and should only be used in observables where the dynamical scale of the top-quark mass sensitivity is of order mt or larger, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' µm ≳ mt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The MSR mass is, like the MS mass mass, determined from top-quark self-energy corrections [13, 17], but designed such that all virtual and off-shell top-quark quantum fluctuations are integrated out in the on-shell limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 The MSR mass mMSR t (R) is therefore a 5-flavor quantity and its R- dependence properly captures all radiation off the top quark that is soft in the top quark rest frame, which is not the case for the MS mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The MSR mass is the proper choice if the dynamical scale of the top quark mass sensitivity is below mt, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' R ≲ mt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The pole and MSR masses are related as mpole t = mMSR t (R) + R ∞ � n=1 dMSR n � a(5) s (R) �n , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6) where the coefficients dMSR n read [13] dMSR 1 = 4/3 , dMSR 2 = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1330 dMSR 3 = 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='602 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='7) In the limit R → mt(mt), mMSR t (R) approaches the MS mass mt(mt) and matches on it in analogy to the 5-flavor and 6-flavor strong coupling, see below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In contrast to the logarithmic µm evolution of mt(µm), the R-evolution of mMSR t (R) is linear and captures the correct physical logarithms for observables with mt dependence, generated at dynamical scales R < mt, such as resonances, thresholds, and low-energy endpoints [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The mass renormalization constant of the MSR mass only contains the on-shell self-energy corrections for scales larger than R in contrast to the pole mass which contains self-energy corrections at all scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' So while the MSR mass is numerically close to the pole mass for small R at low orders, it is free of the pole mass renormalon problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Formally the MSR mass approaches the pole mass for R → 0, but the Landau pole prevents taking 2We are using the natural MSR mass definition (MSRn), where virtual top-quark loops are integrated out consis- tently, see [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 4 this limit in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' For small R values in the range of 1 to 2 GeV the MSR mass captures the kinematic particle mass interpretation commonly associated of the pole mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Within perturbative uncertainties at NLO, where we can still ignore the pole mass renormalon problem, the scheme choice mMSR t (R = 1 GeV) is therefore a proxy for the pole mass scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The matching of the 5-flavor MSR mass to the 6-flavor MS mass at the scale R = mt(mt) reads [13] mMSR t (mt) = mt(mt) � 1 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='10357 � a(5) s (mt) �2 + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8308 � a(5) s (mt) �3 � , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8) and the inverse at the scale R = mMSR t (mMSR t ) reads [13] mt(mt) = mMSR t � mMSR t � � 1 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='10357 � a(5) s (mMSR t ) �2 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6927 � a(5) s (mMSR t ) �3 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='9) The matching starts at O(α2 s), where virtual top quark loops first appear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3 These relations are in close analogy to the corresponding strong coupling matching relation which reads a(6) s (mt) = a(5) s (mt) � 1 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='15278 � a(5) s (mt) �2 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='54881 � a(5) s (mt) �3 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='10) The MSR mass at an arbitrary scale R is then obtained from a given MS mass, applying Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8), and evolving the scale R from mt(mt) to the desired value by solving the RGE R d dRmMSR t (R) = −R � n γR n � a(5) s (R) �n+1 , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='11) where the anomalous dimensions γR n are given by [17] γR 0 = 4/3 γR 1 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='0219 , γR 2 = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8047 , γR 3 = −73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='257 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='12) The solution of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='11) yields mMSR t (mt) − mMSR t (R) = − � n=0 γR n � mt R dR′ � a(5) s (R′) �n+1 + O � a4 s � ≡ ∆m , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='13) so that the MSR mass at R is obtained as mMSR t (R) = mMSR t (mt)−∆m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' As far as QCD corrections are concerned, the formulae above allow to relate MSR and MS top quark mass values at any (perturbative) scale with a precision of better than 20 MeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The REvolver library [37] provides this functionality in user-friendly software package.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In the present work, the MCFM program (version 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8) [19, 20] is extended to include the im- plementation of the MSR scheme in the computation of the hadronic tt production cross section for 3In the matching relations in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8) and (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='9) we have not indicated the 5- or 6-flavor schemes for the strong coupling, since at the order shown the coefficients are identical in both schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 5 single-differential kinematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Based on the procedure presented in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [21, 22], the tt production cross section differential with respect to an observable X at NLO reads dσ dX = (as(µr))2 dσ(0) dX � m, µr, µf � + (as(µr))3 dσ(1) dX � m, µr, µf � + (as(µr))3 ˜R d1 d dmt � dσ(0)(mt, µr, µf) dX � ���� mt=m , (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='14) where σ(0) is the leading order (LO) and σ(1) the NLO cross section in the pole mass scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' At NLO, the derivative term (the third summand in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='14)) implements the MS or MSR top quark mass schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In the present work, the observable of interest is the invariant mass of the tt system, and X = mtt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In particular, we have the following set of parameters in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='14)) � as(µr), m, d1, ˜R � = � � � � a(5) s (µr), mMSR t (R), dMSR 1 , R � , R < mt(mt) (MSR regime) , � a(5) s (µr), mt(µm), dMS 1 (µm), mt(µm) � , µm > mt(mt) (MS regime) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='15) It is important to note that the choice of the renormalization and factorization scales µr and µf is independent of the mass renormalization scales R or µm in this implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' We empha- size that it is essential that the mass scheme correction proportional to d1 is consistently used at the renormalization scale µr, which yields logarithms ln(R/µr) or ln(µm/µr) beyond NLO to consistently cancel the pole mass renormalon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Since MCFM is based on renormalization with 5 dynamical flavors, one has to consistently expand a(6) s (µr) for the MS top mass scheme corrections of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1) in powers of a(5) s (µr) in the cross section formula of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' At NLO this leads to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' We note that the fixed-order perturbative corrections for the differential cross section in the pole mass scheme are known at next-to-next-to-leading order (NNLO) accuracy in QCD [38] and at NLO in the electroweak theory [39, 40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In addition, an implementation of the MS mass scheme at NNLO has been provided in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The conversion of the mass renormalization scheme from the pole mass to the running or the MSR mass beyond NLO accuracy in QCD (and LO for electroweak effects as presented here) needs to be performed numerically and requires theory predictions for differential cross sections with the pole mass at NNLO accuracy for a large array of pole mass values (typically in a range 150 GeV < m < 180 GeV)), which are currently not readily available in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Non-relativistic quasi-bound state QCD corrections are important for the region mtt ∼ 340- 360 GeV, where the strongest top quark mass sensitivity arises in the mtt distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In this threshold region the produced top quarks attain small non-relativistic velocities v ≪ 1 in the tt center-of-mass frame, and the dynamics of the tt system are hence governed by the mass mt, the relative momentum mtv, and the kinetic energy mtv2 of the top quark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Since mt ≫ mtv ≫ mtv2, the appearance of ratios involving the masses, momenta and kinetic energy of the top quark renders the standard fixed-order expansion in powers of αs unreliable in this mtt range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The 6 most pronounced quasi-bound state effects arise from the Coulomb corrections due to the exchange of gluons between the produced t and t yielding a dependence of the prediction on the ratio mt/(mtv).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This leads to a singular (αs/v)n behavior in the fixed-order perturbative QCD correction at n-loops [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' These quasi-bound state effects have been considered in Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [43, 44], and more recently again in [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' These predictions, however, do not provide an adequate description of the lowest mtt bin in the region between 300 GeV and the quasi-bound state region around 350 GeV, where the imaginary energy approach and the use of the optical theorem [46] predict a sizeable and unphysical finite tt production rate, see the results shown in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In this region the differential cross section depends on the experimental cuts on the top and antitop quark decay products [47, 48], which complicates the theoretical prediction as well as the experimental analysis, but any sensible choice of cuts leads to a strongly suppressed rate for mtt close to 300 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This latter aspect is actually better described by the fixed-order predictions for stable top quarks where the rate vanishes identically for mtt < 2mt (for a correct top mass scheme choice as discussed below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Furthermore, a systematic treatment of the intermediate region, where the non-relativistic and relativistic calculations need to be matched, is currently not available with a reliable matching error estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4 We also mention that for the electroweak corrections different scheme choices for the MS mass are available related to the definition of the vacuum expectation value [35, 36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Their effects concerning the MSR mass and their impact on the use of different mass schemes in experimental observables is unknown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Overall, there is currently no complete and reliable theory prediction for the low mtt distribution available for experimental analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' For the study of the tt differential cross section as a function of mtt and its dependence on the MSR mass scale R, the NLO fixed order prediction for stable top quarks based on the MCFM program is appropriate, since it properly describes the generic size of subleading QCD corrections and vanishes for mtt < 2mt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' For a reliable measurement of the MSR top quark mass, however, a more complete code including the features mentioned above has to be made available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 3 First investigation of the R scale dependence In this section we examine the dependence of the mtt distribution in different representative bins in the range between 300 and 700 GeV on the scales µr, µf, and R in the MSR mass scheme as well as µm in the MS scheme using as input the results of the ABMP16 PDF fit at NLO [50] with α(5) s (mZ) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='11905 at mZ = 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='19 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' For the MS mass value mt(mt) = 160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='68 GeV has been chosen close to the fit of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The latter value corresponds to a MSR masses at R = 1 GeV and R = 80 GeV of mMSR t (1 GeV) = 170.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='48 GeV and mMSR t (80 GeV) = 164.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='98 GeV, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 1, the cross section for the bin mtt ∈ [300, 333] GeV, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' the region below the tt pro- duction threshold, is shown for different scale choices at LO and NLO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The cross section is zero for R < 60 GeV, which corresponds to 2mMSR t (R) > 333 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Non-zero contributions to the cross section in the mtt ∈ [300, 333] GeV range appear only at large values of R or when using the MS 4Such a treatment is available only for top quark production in e+e− annihilation, see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 7 mass, which correspond to smaller values of mMSR t (R) or mt(µm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The LO contribution to the cross section is zero or positive throughout the probed range of R and µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' At NLO, however, the quick decrease of the derivative terms in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='14) in comparison to the increase of the positive contributions would lead to unphysical negative values of the NLO cross section in this kinematic range, as was also pointed out in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [41], where the MS mass scheme was examined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Since tt production in the range mtt ∈ [300, 333] GeV is impossible, the results in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 1 also show that R values above 80 GeV must be avoided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This also implies that the MS mass cannot be used if the tt cross section in this mtt range is included in the experimental analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This conclusion holds even in the presence of quasi-bound state effects, since these provide a more precise prediction of the tt production threshold, which is, however, located at mtt values above 333 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' A further feature of the mtt ∈ [300, 333] GeV range, shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 1, is the rapid increase of the cross section at µm ≳ 410 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This occurs when mt(µm) is so small, such that LO tt production is even possible below 300 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 2, the cross section for the bin mtt ∈ [333, 366] GeV, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' the region where the tt produc- tion threshold is located, is shown as a function of R and µm at NLO in the left panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The right panel displays the relative size of the NLO corrections with respect to the LO description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Here, the quasi-bound state effects are sizeable and our NLO result only provides a qualitative description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Similar as in the lowest bin, we observe a quite strong dependence on the mass renormalization scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' We see that for very small values of R the size of the NLO correction increases significantly, particularly for large µr and µf values, making the use of fixed-order perturbation theory unreliable for these choices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This shows that the impact of the higher-order QCD corrections, including the 1 100 200 300 400 500 600 [GeV] m µ R, 6 − 4 − 2 − 0 2 4 6 8 [pb/GeV] tt dm σ d )=160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='68 GeV t m ( t m ABMP16_5_nlo = 13 TeV s < 333 GeV tt 300 GeV < m ) t m ( t m = 1/4 f µ = r µ ) t m ( t m = 1/2 f µ = r µ ) t m ( t m = f µ = r µ ) t m ( t m = 2 f µ = r µ ) t m ( t m = 4 f µ = r µ Total LO 1 Figure 1: The mtt ∈ [300, 333] GeV range of the mtt distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' There is no tt production at R ≲ 60 GeV, but the region above it suffers from the lack of Coulomb corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The discontinuity at µm ≳ 410 GeV is due to the tt production threshold becoming artificially low, and such high values of the scale µm should be avoided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 8 1 100 200 300 400 500 600 [GeV] m µ R, 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 3 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 4 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 [pb/GeV] tt dm NLO σ d )=160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='68 GeV t m ( t m ABMP16_5_nlo = 13 TeV s pp, < 366 GeV tt 333 GeV < m )t m (t m = 1/4 f µ = r µ )t m (t m = 1/2 f µ = r µ )t m (t m = f µ = r µ )t m (t m = 2 f µ = r µ )t m (t m = 4 f µ = r µ 1 1 100 200 300 400 500 600 [GeV] m µ R, 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8 tt dm LO σ d / tt dm NLO σ d )=160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='68 GeV t m ( t m ABMP16_5_nlo = 13 TeV s < 366 GeV tt 333 GeV < m ) t m ( t m = 1/4 f µ = r µ ) t m ( t m = 1/2 f µ = r µ ) t m ( t m = f µ = r µ ) t m ( t m = 2 f µ = r µ ) t m ( t m = 4 f µ = r µ 1 Figure 2: The NLO cross section (left) and the ratio of the LO and NLO cross sections (right) for mtt ∈ [333, 366] GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The transition from a region suffering from the missing Coulomb corrections to a more stable region where the threshold effects become less important is seen at R ≳ 60 GeV (dashed blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Further, predictions obtained using small values of µr, µf are observed to stabilize the prediction quickly as a function of R or µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' quasi-bound state corrections, is particularly sizeable and essentially maximized in the pole mass scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This is closely mimicked by the result for R = 1 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' We see that the most stable predictions are obtained and that the NLO corrections are signif- icantly smaller for R in the range of 60 to 80 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This is not accidental, but expected from the fact that the smaller value of the MSR mass at these R values accounts for the reduced mass of the tt system due to the Coulomb-binding effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' So also the impact of the (missing) Coulomb corrections can be expected to be moderate and in particular much smaller than in the pole mass scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Adopting values for µr and µf below the top quark mass further diminishes the size of the NLO corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This is because for this R-range and for these µr and µf values mMSR t (R) captures a sizeable part of the non-relativistic bound state dynamics relevant in this bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 At this point it is also instructive to examine mtt far above threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 3 and 4, the results for mtt ∈ [465, 498] GeV and mtt ∈ [663, 696] GeV, respectively, are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Here the NLO predictions provide an appropriate theoretical description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In contrast to the low mtt bins discussed above, the mass renormalization scale behavior is very smooth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This is partly related to the much smaller top quark mass sensitivity, but also means that none of the top quark mass schemes (and values for R or µm) provide any advantage concerning capturing essential QCD corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Here, only the choices of the scales µr and µf are essential for the prediction showing a preference for values of around mt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This observation applies also to other invariant mass bins covering large mtt 5Due to the integration over the bin range, the R and µr values are expected to be larger than for a description on the bound state resonance peak, where even lower scale choices are appropriate [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 9 1 100 200 300 400 500 600 [GeV] m µ R, 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 3 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 4 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 [pb/GeV] tt dm NLO σ d )=160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='68 GeV t m ( t m ABMP16_5_nlo = 13 TeV s pp, < 498 GeV tt 465 GeV < m )t m (t m = 1/4 f µ = r µ )t m (t m = 1/2 f µ = r µ )t m (t m = f µ = r µ )t m (t m = 2 f µ = r µ )t m (t m = 4 f µ = r µ 1 100 200 300 400 500 600 [GeV] m µ R, 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 tt dm LO σ d / tt dm NLO σ d )=160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='68 GeV t m ( t m ABMP16_5_nlo = 13 TeV s < 498 GeV tt 465 GeV < m ) t m ( t m = 1/4 f µ = r µ ) t m ( t m = 1/2 f µ = r µ ) t m ( t m = f µ = r µ ) t m ( t m = 2 f µ = r µ ) t m ( t m = 4 f µ = r µ Figure 3: The NLO cross section (left) and the ratio of the LO and NLO cross sections (right) for mtt ∈ [465, 498] GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 1 100 200 300 400 500 600 [GeV] m µ R, 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8 1 [pb/GeV] tt dm NLO σ d )=160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='68 GeV t m ( t m ABMP16_5_nlo = 13 TeV s pp, < 696 GeV tt 663 GeV < m )t m (t m = 1/4 f µ = r µ )t m (t m = 1/2 f µ = r µ )t m (t m = f µ = r µ )t m (t m = 2 f µ = r µ )t m (t m = 4 f µ = r µ 1 100 200 300 400 500 600 [GeV] m µ R, 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 tt dm LO σ d / tt dm NLO σ d )=160.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='68 GeV t m ( t m ABMP16_5_nlo = 13 TeV s < 696 GeV tt 663 GeV < m ) t m ( t m = 1/4 f µ = r µ ) t m ( t m = 1/2 f µ = r µ ) t m ( t m = f µ = r µ ) t m ( t m = 2 f µ = r µ ) t m ( t m = 4 f µ = r µ Figure 4: Same as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 3 for the bin mtt ∈ [663, 696] GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' values, see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Overall, our examination suggests that the MSR top quark mass mMSR t (R) and the choice for the central value of R = 80 GeV provide the most reliable theoretical predictions for all mtt bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' For the scales µr and µf the central values mt(mt) and, in particular mt(mt)/2 for the mtt range containing the tt threshold, are adequate choices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' We note that these findings are also in line with the optimal scale choices for the total cross section for tt hadro-production, when using the top quark mass in the MS scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In this case, central values for µr and µf of the order mt(mt)/2 ≈ 80 GeV are in the 10 region of fastest apparent convergence considering perturbative QCD corrections through NNLO and also minimize the scale sensitivity of the total cross section [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Settings for PDF factorization scale µf different from µr have been explored in Refs [41, 53], corroborating these findings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' On the other hand, for the total cross section with the top quarks in the pole mass scheme, which is well modeled by the MSR scheme mass mMSR t (1 GeV), the preferred central values for µr and µf, which minimize scale sensitivity and optimize perturbative convergence through NNLO, are of the order mpole t /4 ≈ 45 GeV, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This is also visible in the ratio plots on the right in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 2–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In the following, we demonstrate the impact of the mass scheme and the scale setting on the value of the top quark mass obtained in fits to the experimental data of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 4 Extraction of the top quark MSR mass The MSR mass mMSR t (R) is extracted from the differential tt production cross section measured by the CMS Collaboration in pp collisions at the LHC at √s = 13 TeV, corresponding to an integrated luminosity of 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='9 fb−1 [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The tt cross section is measured as a function of mtt in the ranges: mtt < 420 GeV, mtt ∈ [420, 550] GeV, mtt ∈ [550, 810] GeV and mtt > 810 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The theoretical predictions are obtained using the ABMP16 5-flavor PDF set [51] at NLO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' According to the preferred MSR mass scale settings described in the previous section, the initial value of the scale R is set to 80 GeV in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='14), and the cross section is calculated for a range of assumed values of mMSR t (80 GeV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The function χ2 = � i,j (σexp i − σth i )C−1 ij (σexp j − σth j ), (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1) is computed for each mMSR t (80 GeV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The indices i, j in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1) run over the bins of the mtt distribution, while σexp i are the experimental data and σth i the theoretical predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The inverse covariance matrix C−1 ij provided in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [18] is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The scales µr and µf are set to mMSR t (80 GeV) for all 4 bins of the mtt distribution or, alter- natively, to mMSR t (80 GeV)/2 for mtt < 420 GeV, to stabilize the prediction against the missing quasi-bound state corrections, and to mMSR t (80 GeV) for the remainder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 5 shows a 4th order polynomial fit to the χ2 values resulting from each configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The fit uncertainties are obtained via the ∆χ2 = 1 tolerance criterion, while the µr and µf scale uncertainties are evaluated by varying their central values in each bin up and down by a factor of 2, avoiding the cases where one scale is multiplied by 1/2 and the other by 2, and constructing an envelope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' For comparison with previous analyses, the extracted values of mMSR t (80 GeV) are evolved to the reference scales R of 1 and 3 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Note that determining mMSR t (1 GeV) requires evaluating αs(1 GeV) rather close to the Landau pole, which is expected to lead to an increased perturbative uncertainty in the MSR mass at R = 1 GeV due to missing higher order corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Reporting the mass value also at R = 3 GeV thus ensures the stability of the result, and the use of reference scales R > 1 GeV will become increasingly important in future extractions of mMSR t (R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 11 160 162 164 166 168 170 172 174 176 178 (80 GeV) [GeV] MSR t m 0 20 40 60 80 100 120 140 160 180 200 220 2 χ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='86 / 3 dof / N 2 χ Min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [GeV] tt m (80 GeV) MSR t = m f µ , r µ < 420 : (80 GeV) MSR t = m f µ ,r µ [420, 550] : (80 GeV) MSR t = m f µ ,r µ [550, 810] : (80 GeV) MSR t = m f µ , r µ > 810 : = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='86 / 3 dof / N 2 χ Min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 162 164 166 168 170 172 174 176 178 180 (80 GeV) [GeV] MSR t m 0 20 40 60 80 100 120 140 160 180 200 220 2 χ = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='03 / 3 dof / N 2 χ Min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [GeV] tt m (80 GeV) MSR t m 2 1 = f µ ,r µ < 420 : (80 GeV) MSR t = m f µ , r µ [420, 550] : (80 GeV) MSR t = m f µ , r µ [550, 810] : (80 GeV) MSR t = m f µ ,r µ > 810 : = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='03 / 3 dof / N 2 χ Min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Figure 5: A 4th order polynomial fitted to the χ2 resulting from comparing the experimental data to theory predictions assuming different values of mMSR t (80 GeV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The scales µr and µf are set to mMSR t (80 GeV) considering the whole mtt distribution (left), or to mMSR t (80 GeV)/2 for mtt < 420 GeV and to mMSR t (80 GeV) for the remainder (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The number of degrees of freedom in the fits is denoted by Ndof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Table 1: The values of mMSR t (R) obtained at different scales R (given in brackets below mMSR t ), and the corresponding mt(mt), the χ2 divided by the number of degrees of freedom Ndof in the fit, along with the fit and scale uncertainties for the mMSR t (R) extracted at R = 80 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The results are shown for the constant µr, µf setting, where the central µr and µf values are set to mMSR t (80 GeV) in the whole mtt distribution, and for the semi-dynamical (SD) setting where they are set to mMSR t (80 GeV)/2 for mtt < 420 GeV and to mMSR t (80 GeV) for higher mtt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The fit and µr, µf uncertainties correspond to the MSR mass extracted at R = 80 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Within the reported accuracy, the uncertainty in the initial choice of R agrees in all cases when the extracted mMSR t (R) is evolved to the reference R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' mMSR t mMSR t mMSR t mt Fit µr, µf R µr, µf χ2/Ndof (80 GeV) (1 GeV) (3 GeV) (mt) unc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' unc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' unc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' setting [ GeV] [ GeV] [ GeV] [ GeV] [ GeV] [ GeV] [ GeV] Const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='86/3 167.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='7 173.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 172.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='9 163.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3 +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 SD 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='03/3 169.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3 174.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8 174.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 164.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8 +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4 +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3 Furthermore, the results are translated into the standard MS mass mt(mt) by iteratively finding mMSR t (mMSR t ) via the condition R = mMSR t (R), and applying the matching formula in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='9) up to O(a3 s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The uncertainty related to the initial choice of R is assessed by repeating the fits at R = 60 GeV and R = 100 GeV, and the difference in the resulting masses at the reference scales to the respective values obtained in the R = 80 GeV fit is taken as the R scale uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The resulting values for the top quark mass are listed in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In particular, setting the central µr and µf to mMSR t (80 GeV) and considering the complete mtt 12 distribution yields mMSR t (1 GeV) = 173.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 (fit)+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 (µr, µf)+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 (R) GeV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2) The value for mMSR t (80 GeV) in this fit translates into mt(mt) = 163.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='0 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This is compatible within uncertainties with the value of mt(mt) = 162.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='0 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='0 GeV obtained at NLO in the ABMP16 5-flavor PDF set [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In accordance with the results shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 1, multiplying the scales µr and µf by 1/2 within mtt < 420 GeV is observed to increase the NLO cross section at R = 80 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' To compensate for this effect, the fit for mMSR t (80 GeV) leads to a somewhat larger value for the top quark MSR mass, reducing the predicted cross section especially in the vicinity of the tt production threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This results in the value mMSR t (1 GeV) = 174.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 (fit)+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4 (µr, µf)+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3 (R) GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3) It is expected that the impact of the choices for µr and µf, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' the shift of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 GeV in the cen- tral values between Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3), will be reduced at NNLO accuracy and once a reliable description of the quasi-bound state effects is available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Nonetheless, as already expected from the observations in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 3, the scale setting in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3) already increases the robustness against scale variations, yielding somewhat smaller uncertainties than Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In order to illustrate the main conceptual novelty and the phenomenological importance of the mass scheme choice, we perform the following variant of the fit: Instead of determining the top quark MSR mass at R = 80 GeV and evolving the extracted mMSR t (80 GeV) value to R = 1 GeV, as in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3), we perform the fit to data directly with the initial scale set to R = 1 GeV 166 168 170 172 174 (1 GeV) [GeV] MSR t m 0 20 40 60 80 100 120 2 χ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='16 / 3 dof / N 2 χ Min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [GeV] tt m (1 GeV) MSR t = m f µ , r µ < 420 : (1 GeV) MSR t = m f µ ,r µ [420, 550] : (1 GeV) MSR t = m f µ ,r µ [550, 810] : (1 GeV) MSR t = m f µ , r µ > 810 : = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='16 / 3 dof / N 2 χ Min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Figure 6: Same as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 5, now fitting mMSR t (1 GeV) and with the scales µr and µf set to mMSR t (1 GeV) in the whole mtt distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 13 in NLO cross section of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Using also the central scales µr, µf set to mMSR t (1 GeV), this results in mMSR t (1 GeV) = 170.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 (fit)+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='9 (µr, µf) GeV , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4) where the corresponding fit to χ2 is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4) the µr and µf scale uncertainties are twice as large as those of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The sizeable discrepancy to the results of Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3) indicates that scale variation does not provide a proper estimate of the theoretical uncertainties due to the missing higher order and quasi-bound state corrections for the result quoted in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Since using mMSR t (1 GeV) closely approximates the outcome using pole mass scheme, this confirms our conclusions drawn in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 3 that the use of the pole mass scheme (or a very small initial R value for the MSR mass) leads to less reliable results in a fixed order QCD description at NLO accuracy, where the quasi-bound state effects are missing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The significant difference of 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='7 GeV between the central values in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3) and (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4) demonstrates the phenomenological relevance of this issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This underpins the importance of proper scale setting in future phenomenological analyses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Let us now comment on other recent extractions of the top-quark mass, which have employed different methodologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Data from the CMS collaboration for the tt production cross section collected in pp collisions at the LHC at √s = 13 TeV has been used previously for a determination of the top-quark mass using both, the pole and the MS mass scheme [54, 55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The emphasis of those analyses has been on keeping the correlations of the top-quark mass with the strong coupling αs(mZ) and the PDFs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In a different thread of analyses, the running of top quark MS mass mt(µm) has been studied at NLO [18] and NNLO [56] with dynamical scales, using data from the CMS collaboration for the mtt distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 Of these analyses, the results of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [55] can be compared to the present work, since they are obtained from normalized multi-differential cross sections which also include the low mtt region discussed here, and the theoretical predictions have also been based on the NLO MCFM cross section description.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [55] quotes mpole t = 170.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8 GeV, which, if interpreted as the asymptotic pole mass [37], translates into mMSR t (1 GeV) = 170.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This is compatible with the variant of the present study in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4) obtained by directly fitting mMSR t (1 GeV) to data, although the combined fit of mpole t , αs(mZ) and PDFs in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [55] reports a smaller value of αs(mZ) than used in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4) on the basis of the ABMP16 PDF set, and a somewhat different gluon PDF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The ATLAS collaboration has derived a value for the top quark MSR mass at the reference scale R = 1 GeV in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [57] by comparing QCD predictions at next-to-leading logarithmic accuracy for the soft-drop groomed top quark jet mass distribution to parton shower Monte Carlo simulations for a Monte-Carlo top quark mass mMC t = 172.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Obtained in the Monte Carlo calibration (following [58]), the result of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [57] is not based on experimental data and hence cannot be directly compared to the results of the present study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The value for the top quark MSR mass of mMSR t (3 GeV) = 169.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1 GeV has been extracted in 6See also http://cms-results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='cern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='ch/cms-results/public-results/publications/TOP-19-007/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' html#Figure-aux_001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 14 Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [53], using the CMS data of Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [55] and the same methodology, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' using fixed-order QCD perturbation theory at NLO accuracy, so that mMSR t (3 GeV) has been fitted simultaneously with the PDFs and strong coupling constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Evolving the result of the present study in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3) to R = 3 GeV yields mMSR t (3 GeV) = 174.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 (fit)+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4 (µr, µf)+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3 (R) GeV , (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5) which indicates some tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='7 Part of this difference is due to the direct fitting of mMSR t (3 GeV) in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [53] compared to mMSR t (80 GeV) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In addition, Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [53] has obtained αs(mZ) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1132+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='0023 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='0018, which is two standard deviations away from the value of the ABMP16 fit at NLO [50] used in the extraction of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Notably, neither any of the cited previous top quark mass extractions nor the present work have included the aforementioned corrections for the quasi-bound state effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' However, the extraction of the top quark MSR mass using predictions in the MSR scheme at the scale R = 80 GeV profits from the smaller size of these effects and thus from an improved stability of the cross section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 5 Summary and Conclusions We have presented the first comprehensive study of the mtt distribution in its dependence on the mass renormalization scales R and µm of the MSR and MS top quark mass schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Our findings suggest that the scale setting of R close to 80 GeV improves the robustness of the predictions for the mtt distribution against scale variations in general and, in particular, against the impact of quasi-bound state corrections in the region of mtt close to the tt threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The theory predictions are based on the NLO fixed order QCD description provided by the MCFM program, adapted to the MSR and MS top quark mass schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The optimized scale choices for those mass schemes are characterized by low values of the renormalization and factorization scales µr and µf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This holds in particular in the vicinity of the tt production threshold region in the mtt distribution, where values µr ≃ µf ≃ mt/2 are observed to stabilize cross section predictions and to decrease the scale uncertainty in the determination of the MSR mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' These settings have been applied in an extractions of the top quark MSR mass at R = 80 GeV, using tt pair production cross section, measured as a function of mtt in pp collisions at √s = 13 TeV at the LHC by the CMS collaboration, using fixed-order perturbative QCD predictions at NLO accuracy and also the semi-dynamical scales for µr, µf in the low-mtt regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The fitted value of mMSR t (80 GeV) has then been evolved to various low reference scales R, rather than computing the cross sections directly at low R as performed in earlier analyses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' This procedure yields the value mMSR t (3 GeV) = 174.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='7 GeV, which is discussed in the context of other recent extractions of the top quark mass from LHC data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The observed differences are explained in part by the scale choice 7The computations in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [53] rely on the practical MSR (pMSR) definition [13] instead of the natural MSR (nMSR) scheme used in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' The difference is at the level of 10 MeV [13] and thus negligible for the uncertainties quoted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 15 of R = 80 GeV for the top quark MSR mass, advocated by the present study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Other reasons for differences are due to the choice of the value for the strong coupling αs(mZ), which directly affects the normalisation of the cross section and is anti-correlated with the top quark mass, and, to a lesser extent, due to the particular PDF sets used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' While we have argued that the implementation of the MSR mass scheme in the tt cross section calculation and the optimal scale choice for R of 80 GeV provide more robust predictions even at NLO accuracy, the findings should be corroborated by extending the analysis to NNLO accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In addition, the proper treatment of both, the quasi-bound state effects, together with a matching to the relativistic tt region, and the mtt region below the threshold are further important improvements to be implemented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' A final reliable measurement of the top quark MSR mass needs to address those issues as well as the correlation of the top quark mass with the other theoretical parameters, which control the cross section predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' We leave these aspects for future studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Acknowledgements The work of A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='H was supported in part by FWF Austrian Science Fund under the Project No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' P32383-N27, the work of S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' in part by the Bundesministerium f¨ur Bildung und Forschung under contract 05H21GUCCA, the work by T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' is supported by the Helmholtz Association under the contract W2/W3-123, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' is also supported by the National Science Centre, Poland, research grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 2021/42/E/ST2/00031.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' References [1] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Bezrukov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Higgs Boson Mass and New Physics”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: JHEP 10 (2012), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2893 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [2] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Degrassi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Higgs mass and vacuum stability in the Standard Model at NNLO”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: JHEP 08 (2012), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 098.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6497 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [3] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Alekhin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Djouadi, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Moch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “The top quark and Higgs boson masses and the stability of the electroweak vacuum”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' B 716 (2012), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 214–219.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='0980 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Bednyakov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='20 (2015), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 201802.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1507 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 08833 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [5] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Bigi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “The Pole mass of the heavy quark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Perturbation theory and beyond”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' D 50 (1994), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 2234–2246.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: hep-ph/9402360.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [6] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Beneke and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Braun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Heavy quark effective theory beyond perturbation theory: Renormalons, the pole mass and the residual mass term”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' B 426 (1994), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 301–343.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: hep-ph/9402364.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [7] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Smith and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Willenbrock.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Top quark pole mass”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 79 (1997), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 3825–3828.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: hep-ph/9612329.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 16 [8] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Ferrario Ravasio, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Nason, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Oleari.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “All-orders behaviour and renormalons in top- mass observables”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: JHEP 01 (2019), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='10931 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Hoang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “What is the Top Quark Mass?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 70 (2020), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 225–255.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='12915 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [10] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' ’t Hooft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Dimensional regularization and the renormalization group”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' B 61 (1973), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 455–468.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [11] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Bardeen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Deep-inelastic scattering beyond the leading order in asymptotically free gauge theories”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' D 18 (11 Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 1978), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 3998–4017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' url: https:// link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='aps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='org/doi/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1103/PhysRevD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Hoang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Infrared Renormalization Group Flow for Heavy Quark Masses”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 101 (2008), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 151602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 0803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='4214 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [13] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Hoang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “The MSR mass and the O (ΛQCD) renormalon sum rule”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: JHEP 04 (2018), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1704.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='01580 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Hoang and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Stewart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Top Mass Measurements from Jets and the Tevatron Top- Quark Mass”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' B Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Suppl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 185 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' by G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Bellettini, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Chiarelli, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Tenchini, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 220–226.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 0808.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='0222 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [15] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Hoang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “The Top Mass: Interpretation and Theoretical Uncertainties”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: 7th Inter- national Workshop on Top Quark Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Dec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3649 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [16] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Hoang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Pl¨atzer, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Samitz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “On the Cutoff Dependence of the Quark Mass Parameter in Angular Ordered Parton Showers”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: JHEP 10 (2018), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 06617 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [17] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Hoang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Lepenik, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Preisser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “On the Light Massive Flavor Dependence of the Large Order Asymptotic Behavior and the Ambiguity of the Pole Mass”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: JHEP 09 (2017), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 099.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='08526 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [18] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Sirunyan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Running of the top quark mass from proton-proton collisions at √s = 13TeV”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' B 803 (2020), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 135263.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='09193 [hep-ex].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [19] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Campbell and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Ellis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “MCFM for the Tevatron and the LHC”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' B Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Suppl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 205-206 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' by J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Bl¨umlein, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='-O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Moch, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Riemann, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 10–15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3492 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [20] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Campbell and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Ellis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Top-Quark Processes at NLO in Production and Decay”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' G 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1 (2015), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 015005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1513 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [21] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Langenfeld, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Moch, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Uwer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Measuring the running top-quark mass”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' D 80 (2009), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 054009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 0906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5273 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [22] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Dowling and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Moch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Differential distributions for top-quark hadro-production with a running mass”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' C 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='11 (2014), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 3167.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6422 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [23] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Marquard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Quark Mass Relations to Four-Loop Order in Perturbative QCD”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='14 (2015), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 142002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='01030 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [24] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Gray et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Three-loop relation of quark MS and pole masses”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Zeitschrift f¨ur Physik C Particles and Fields 48 (1990), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 673–679.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [25] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Chetyrkin and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Steinhauser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “The Relation between the MS and the on-shell quark mass at order αs3”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' B 573 (2000), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 617–651.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: hep-ph/9911434.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [26] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Melnikov and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Ritbergen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “The Three loop relation between the MS-bar and the pole quark masses”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' B 482 (2000), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 99–108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: hep-ph/9912391.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 17 [27] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Baikov, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Chetyrkin, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' K¨uhn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Quark Mass and Field Anomalous Dimen- sions to O(α5 s)”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: JHEP 10 (2014), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 076.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6611 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [28] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Luthe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Five-loop quark mass and field anomalous dimensions for a general gauge group”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: JHEP 01 (2017), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 081.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1612.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='05512 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [29] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Chetyrkin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' K¨uhn, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Steinhauser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “RunDec: A Mathematica package for run- ning and decoupling of the strong coupling and quark masses”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 133 (2000), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 43–65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: hep-ph/0004189.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [30] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Tarrach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “The Pole Mass in Perturbative QCD”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' B 183 (1981), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 384– 396.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [31] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Tarasov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Anomalous dimensions of quark masses in the three-loop approximation”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='2 (2020), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 109–115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1910.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='12231 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [32] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Larin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “The Renormalization of the axial anomaly in dimensional regularization”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' B 303 (1993), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 113–118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: hep-ph/9302240.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [33] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Chetyrkin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Quark mass anomalous dimension to O(α4 s)”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' B 404 (1997), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 161–165.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: hep-ph/9703278.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [34] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Vermaseren, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Larin, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' van Ritbergen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “The four loop quark mass anomalous dimension and the invariant quark mass”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' B 405 (1997), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 327–333.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: hep-ph/9703284.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [35] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Dittmaier and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Rzehak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Electroweak renormalization based on gauge-invariant vacuum expectation values of non-linear Higgs representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Part I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Standard Model”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: JHEP 05 (2022), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='07236 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [36] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Kataev and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Molokoedov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Notes on Interplay between the QCD and EW Pertur- bative Corrections to the Pole-Running-to-Top-Quark Mass Ratio”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: JETP Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='12 (2022), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 704–712.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='12073 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [37] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Hoang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Lepenik, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Mateu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “REvolver: Automated running and matching of couplings and masses in QCD”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 270 (2022), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 108145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='01085 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [38] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Czakon, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Heymes, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Mitov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “High-precision differential predictions for top-quark pairs at the LHC”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 116.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='8 (2016), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 082003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='00549 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [39] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' K¨uhn, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Scharf, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Uwer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Electroweak effects in top-quark pair production at hadron colliders”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' C 51 (2007), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 37–53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: hep-ph/0610335.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [40] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Czakon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Top-pair production at the LHC through NNLO QCD and NLO EW”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: JHEP 10 (2017), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 186.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='04105 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [41] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Catani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Top-quark pair hadroproduction at NNLO: differential predictions with the MS mass”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: JHEP 08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='08 (2020), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 027.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='00557 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [42] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Hoang and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Teubner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Top quark pair production close to threshold: Top mass, width and momentum distribution”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' D 60 (1999), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 114027.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: hep-ph/9904468.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [43] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Hagiwara, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Sumino, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Yokoya.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Bound-state Effects on Top Quark Production at Hadron Colliders”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' B 666 (2008), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 71–76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 0804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1014 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [44] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Kiyo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Top-quark pair production near threshold at LHC”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' C 60 (2009), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 375–386.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 0812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='0919 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [45] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Ju et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Top quark pair production near threshold: single/double distributions and mass determination”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: JHEP 06 (2020), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 158.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='03088 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 18 [46] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Hoang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Top - anti-top pair production close to threshold: Synopsis of recent NNLO results”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' direct 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='1 (2000), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: hep-ph/0001286.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [47] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Hoang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Reisser, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Ruiz-Femenia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Phase Space Matching and Finite Lifetime Effects for Top-Pair Production Close to Threshold”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' D 82 (2010), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 014005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='3223 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [48] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Beneke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Non-resonant and electroweak NNLO correction to the e+e− top anti-top threshold”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: JHEP 02 (2018), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 125.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='10429 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [49] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Bach et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Fully-differential Top-Pair Production at a Lepton Collider: From Threshold to Continuum”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: JHEP 03 (2018), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1712.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='02220 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [50] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Alekhin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Bl¨umlein, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Moch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “NLO PDFs from the ABMP16 fit”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' C 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='6 (2018), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 477.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='07537 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [51] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Alekhin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Parton distribution functions, αs, and heavy-quark masses for LHC Run II”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' D 96 (2017), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 014011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1701.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='05838 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [52] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' M¨akel¨a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Towards global interpretation of LHC data: SM and EFT couplings from jet and top quark measurements at CMS”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Dissertation, Universit¨at Hamburg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' PhD thesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 2022, 213 pages: Illustrations, figures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' url: https://bib-pubdb1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='desy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='de/record/482499.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [53] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Garzelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Heavy-flavor hadro-production with heavy-quark masses renormalized in the MS, MSR and on-shell schemes”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: JHEP 04 (2021), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 043.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='07763 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [54] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Sirunyan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Measurement of the tt production cross section, the top quark mass, and the strong coupling constant using dilepton events in pp collisions at √s = 13 TeV”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' C 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='5 (2019), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 368.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='10505 [hep-ex].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [55] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Sirunyan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Measurement of t¯t normalised multi-differential cross sections in pp collisions at √s = 13 TeV, and simultaneous determination of the strong coupling strength, top quark pole mass, and parton distribution functions”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' C 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='7 (2020), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 658.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1904.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='05237 [hep-ex].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [56] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Defranchis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Running of the top quark mass at NNLO in QCD”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: (Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='11399 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [57] “A precise interpretation for the top quark mass parameter in ATLAS Monte Carlo sim- ulation”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: ATL-PHYS-PUB-2021-034 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' url: https://cds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='cern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='ch/record/ 2777332/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' [58] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Butensch¨on et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' “Top Quark Mass Calibration for Monte Carlo Event Generators”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' In: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 117.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='23 (2016), p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 232001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' arXiv: 1608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content='01318 [hep-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} +page_content=' 19' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/-9E1T4oBgHgl3EQf8gV6/content/2301.03546v1.pdf'} diff --git a/.gitattributes b/.gitattributes index d6cde4f8df428a37bfe7ee1cb1180529f777c92e..0a8b6f606e16b852b1b2c5db3edbecc8e1eae0cf 100644 --- a/.gitattributes +++ b/.gitattributes @@ -3922,3 +3922,68 @@ SdE2T4oBgHgl3EQfWgfj/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -tex iNFJT4oBgHgl3EQfWSzz/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text ydE2T4oBgHgl3EQfMQZF/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text 79E1T4oBgHgl3EQfnQTu/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +YNE5T4oBgHgl3EQfCw5O/content/2301.05398v1.pdf filter=lfs diff=lfs merge=lfs -text +3NFQT4oBgHgl3EQf3DZF/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +SdE2T4oBgHgl3EQfCAaW/content/2301.03609v1.pdf filter=lfs diff=lfs merge=lfs -text +B9AzT4oBgHgl3EQfTfz1/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +mNFIT4oBgHgl3EQfsyss/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +hNE3T4oBgHgl3EQf4AvA/content/2301.04769v1.pdf filter=lfs diff=lfs merge=lfs -text +uNAzT4oBgHgl3EQfc_zP/content/2301.01414v1.pdf filter=lfs diff=lfs merge=lfs -text +cdE4T4oBgHgl3EQfpA0g/content/2301.05188v1.pdf filter=lfs diff=lfs merge=lfs -text +MdE2T4oBgHgl3EQfBQZc/content/2301.03600v1.pdf filter=lfs diff=lfs merge=lfs -text +oNFRT4oBgHgl3EQfbzf_/content/2301.13562v1.pdf filter=lfs diff=lfs merge=lfs -text +jdE1T4oBgHgl3EQfNQNY/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +ydE0T4oBgHgl3EQfcgDn/content/2301.02365v1.pdf filter=lfs diff=lfs merge=lfs -text +x9FST4oBgHgl3EQfSzhz/content/2301.13767v1.pdf filter=lfs diff=lfs merge=lfs -text +b9FPT4oBgHgl3EQfBTTg/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +S9E2T4oBgHgl3EQfswjv/content/2301.04064v1.pdf filter=lfs diff=lfs merge=lfs -text +KNAyT4oBgHgl3EQff_hn/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +ldE3T4oBgHgl3EQfiAoP/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +3NFST4oBgHgl3EQfYjhQ/content/2301.13788v1.pdf filter=lfs diff=lfs merge=lfs -text +oNE_T4oBgHgl3EQf8RxN/content/2301.08374v1.pdf filter=lfs diff=lfs merge=lfs -text +oNFRT4oBgHgl3EQfbzf_/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +VtAzT4oBgHgl3EQfJ_ud/content/2301.01090v1.pdf filter=lfs diff=lfs merge=lfs -text +ydE0T4oBgHgl3EQfcgDn/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +r9E2T4oBgHgl3EQfLQZF/content/2301.03711v1.pdf filter=lfs diff=lfs merge=lfs -text +ktAyT4oBgHgl3EQfyPnx/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +ktAyT4oBgHgl3EQfyPnx/content/2301.00682v1.pdf filter=lfs diff=lfs merge=lfs -text +ndA0T4oBgHgl3EQfJv-v/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +HNE4T4oBgHgl3EQfgg1T/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +KNAyT4oBgHgl3EQff_hn/content/2301.00350v1.pdf filter=lfs diff=lfs merge=lfs -text +o9E1T4oBgHgl3EQfPAM1/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +ddAyT4oBgHgl3EQfjPi0/content/2301.00412v1.pdf filter=lfs diff=lfs merge=lfs -text +NNFRT4oBgHgl3EQfGTcp/content/2301.13484v1.pdf filter=lfs diff=lfs merge=lfs -text +o9E1T4oBgHgl3EQfPAM1/content/2301.03021v1.pdf filter=lfs diff=lfs merge=lfs -text +WdE5T4oBgHgl3EQfCA5G/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +odA0T4oBgHgl3EQfJ__J/content/2301.02099v1.pdf filter=lfs diff=lfs merge=lfs -text +cdE4T4oBgHgl3EQfpA0g/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +zNE4T4oBgHgl3EQfAQs4/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +YNE5T4oBgHgl3EQfCw5O/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +oNE_T4oBgHgl3EQf8RxN/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +CNE1T4oBgHgl3EQfVwTa/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +BtE4T4oBgHgl3EQfeA0g/content/2301.05095v1.pdf filter=lfs diff=lfs merge=lfs -text +odA0T4oBgHgl3EQfJ__J/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +h9AzT4oBgHgl3EQfMvvr/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +GNAyT4oBgHgl3EQfSvfA/content/2301.00093v1.pdf filter=lfs diff=lfs merge=lfs -text +VtAzT4oBgHgl3EQfJ_ud/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +VtAyT4oBgHgl3EQfV_ek/content/2301.00155v1.pdf filter=lfs diff=lfs merge=lfs -text +q9AzT4oBgHgl3EQfA_op/content/2301.00934v1.pdf filter=lfs diff=lfs merge=lfs -text +ydE2T4oBgHgl3EQf3wjf/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +JdAyT4oBgHgl3EQfsPlo/content/2301.00573v1.pdf filter=lfs diff=lfs merge=lfs -text +tdE1T4oBgHgl3EQfQQPo/content/2301.03039v1.pdf filter=lfs diff=lfs merge=lfs -text +S9E2T4oBgHgl3EQfswjv/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +tdE1T4oBgHgl3EQfQQPo/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +8NE2T4oBgHgl3EQflQeg/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +FtE1T4oBgHgl3EQfXARM/content/2301.03121v1.pdf filter=lfs diff=lfs merge=lfs -text +9tFST4oBgHgl3EQfbTje/content/2301.13799v1.pdf filter=lfs diff=lfs merge=lfs -text +Y9AyT4oBgHgl3EQf9frR/content/2301.00877v1.pdf filter=lfs diff=lfs merge=lfs -text +ANE3T4oBgHgl3EQfsQvt/content/2301.04667v1.pdf filter=lfs diff=lfs merge=lfs -text +a9FLT4oBgHgl3EQfXi8l/content/2301.12061v1.pdf filter=lfs diff=lfs merge=lfs -text +ddAzT4oBgHgl3EQfn_0r/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +w9E_T4oBgHgl3EQf_xxJ/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +ddAyT4oBgHgl3EQfjPi0/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +GNE0T4oBgHgl3EQfhQF8/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +q9AzT4oBgHgl3EQfA_op/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +NNFRT4oBgHgl3EQfGTcp/vector_store/index.faiss filter=lfs diff=lfs merge=lfs -text +UtAzT4oBgHgl3EQfX_xg/content/2301.01327v1.pdf filter=lfs diff=lfs merge=lfs -text +69AzT4oBgHgl3EQfEvpR/content/2301.00998v1.pdf filter=lfs diff=lfs merge=lfs -text diff --git a/29E1T4oBgHgl3EQfAQI2/content/tmp_files/load_file.txt b/29E1T4oBgHgl3EQfAQI2/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..04fed6aee5a6d4639efb6fb92420733c98ce1037 --- /dev/null +++ b/29E1T4oBgHgl3EQfAQI2/content/tmp_files/load_file.txt @@ -0,0 +1,1149 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf,len=1148 +page_content='Dynamic Local Feature Aggregation for Learning on Point Clouds Zihao Lia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Pan Gaoa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Hui Yuanb,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Ran Weic aNanjing University of Aeronautics and Astronautics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Nanjing ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='China bShandong University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Jinan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' China cScience and Technology on Electro-optic Control Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Luoyang,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' China Abstract Existing point cloud learning methods aggregate features from neighbouring points relying on constructing graph in the spatial domain,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' which results in feature update for each point based on spatially-fixed neighbours throughout layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In this paper, we propose a dynamic feature aggregation (DFA) method that can transfer information by constructing local graphs in the feature domain without spatial constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' By finding k-nearest neighbors in the feature domain, we perform relative position encoding and semantic feature encoding to explore latent position and feature similarity information, respectively, so that rich local features can be learned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' At the same time, we also learn low-dimensional global features from the original point cloud for enhancing feature representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Between DFA layers, we dynamically update the constructed local graph structure, so that we can learn richer information, which greatly improves adaptability and efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We demonstrate the superiority of our method by conducting extensive experiments on point cloud classification and segmentation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Implementation code is available: https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='com/jiamang/DFA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Keywords: dynamic feature aggregation, point cloud, relative position encoding, semantic feature encoding, classification, segmentation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Introduction The collection of points that express the spatial distri- bution and surface features of the target is called point cloud data, which represents the 3D target in an unstruc- tured form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The point cloud obtained by combining the laser principle and the photography principle mainly con- tains three-dimensional position coordinates (X, Y, Z), laser reflection intensity and color information (R, G, B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Common point cloud data formats include RGB-D dual- modality format and Point Cloud space format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' RGB- D dual-modality data records the color information and depth information of the surface of the target object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The Email addresses: pride_19@163.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='com (Zihao Li), Pan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='Gao@nuaa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='cn (Pan Gao), huiyuan@sdu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='cn (Hui Yuan), 115946873@qq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='com (Ran Wei) Point Cloud space format records three-dimensional coor- dinates of the sampling points on the surface of the object, reflecting the spatial contour information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Learning features from point clouds often requires a lot of advanced processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Traditional methods proposed to solve these problems include capturing the geometric characteristics of point clouds by using the hand-crafted features [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' With the breakthrough of convolution neu- ral network and deep learning, significantly better perfor- mance is achieved in various tasks of point cloud process- ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' However, standard deep neural network needs nor- mative input data, but the point cloud data does not need to be irregular, and operations such as translation and rotation will not change its own nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Some methods consider converting to a normative 3D grid and then send the grid into the network for training, but it will cause ad- Preprint submitted to Journal of LATEX Templates January 10, 2023 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='02836v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='CV] 7 Jan 2023 ditional memory occupation and information loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Point- net proposed by [2] creates a precedent for learning and processing directly on the original point cloud, where the multi-layer perceptron is applied to each point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' However, since Pointnet [2] cannot capture the contex- tual information, many recent studies have introduced dif- ferent modules to learn more abundant local structures, which can be divided into the following categories: 1) Feature update based on constructing graph structure [3][4][5][6][7];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 2) Feature pooling based on neighboring points [8][9][10][11][12];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 3) Convolution based on a series of kernels [13][14][15][16][17][15][18][19];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 4) Learning based on attention mechanism [20][21][22][23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' These methods have achieved good results in classification and segmen- tation, but the construction of local feature learners and calculation of attention weight have very expensive com- puting cost and memory occupation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In addition, the fea- ture extractors proposed by some methods are not efficient enough, and there are many parts worth improving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The goal of this paper is to design an efficient local feature extractor without adding much complexity, and then use the learned efficient features to represent objects, which will improve the point cloud classification and seg- mentation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' So we propose a dynamic feature ag- gregation (DFA) module, which extracts and learns latent features by finding k-nearest neighbors in the feature do- main, encoding location information and semantic feature information simultaneously, and concatenating these two parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In the classification and segmentation task, this module is stacked to extract rich local features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Using the network structure like Pointnet [2], we extract low- dimensional global features from the initial point cloud, and then concatenate them with local features extracted by multiple DFAs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Finally, high-dimensional global fea- tures are obtained for classification and segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' For segmentation, we concatenate the high-dimensional global features again with local features, and perform the MLP operation to predict the category of each point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In general, we design an efficient local feature extrac- tor that utilizes multi-level and multi-source features to effectively characterize objects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Multi-level features are reflected in that by stacking several layers of DFA, we can gradually obtain deeper contextual features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Multi-source features are reflected in that we combine multiple types of features of location information, feature differences, fea- tures themselves, and low-dimensional global features to perform deeper and higher-dimensional feature learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In order to test its efficiency, we have done relevant tests on the ModelNet40 [24], shapeNet [25] and S3DIS [26] datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Furthermore, we also do many visualization re- sults and ablation experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Our main contributions are summarized as follows: We propose a new operation DFA, which finds k- nearest neighbors in the feature domain to construct a local graph structure for feature aggregation at each time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The graph between DFA layers is dynamically updated, which is more adaptable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In each DFA layer, we can learn rich latent position and feature difference information through proposed relative position encoding and semantic feature en- coding, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' To the best of our knowledge, simultaneously aggregating the relative position and feature information in the feature domain has not been studied before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We make full use of the learned local features and low- dimensional global features for point cloud classifica- tion and segmentation tasks, and test on benchmark datasets with outstanding quantitative and qualita- tive results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Related work 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Voxel-based Network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Converting point cloud data into regular voxel structure can preserve and express spatial distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In 2016, Qi 2 et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [27] improved voxel CNN and proposed two differ- ent voxel CNN network structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Afterwards, Tchapmi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [28] jointly proposed segcloud based on voxel-based 3D full convolution neural network and point based con- ditional random field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [29] proposed O-CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Its core idea is to use octree to represent 3D shapes, and only the sparse octree occupied by the shape boundary is subject to CNN operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In order to effectively en- code the distribution of voxel midpoint, Meng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [30] proposed the voxel variational self encoder network VV- net, and the point distribution in each voxel is captured by the self encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In 2020, Shao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [31] proposed the data structure of opportunity space hash, designed hash2col and col2hash, so that CNN operations such as convolution and pooling can be parallelized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' View-based Network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Usually, the point cloud is projected into the 2D image first, and then the 2D CNN is used to extract the image features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Due to the limitations of the existing deep learn- ing network, this kind of method can only recognize the point cloud model from a specific angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In 2017, Lawin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [32] generated images with different pitch angles and translation distances by controlling the equidistant angle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Snapnet-r proposed by Gueery et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [33] can use 2D im- ages and 3D as spatial structure information at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The mvpnet proposed by Jaritz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [34] in 2019 can aggregate 2D image features into 3D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The relationship network proposed by Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [35] comprehensively con- siders the relationship between different views and regions, and also uses the attention mechanism to generate scores to reflect the relative discrimination ability of views.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Point-based Network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Direct processing of point clouds contains complete orig- inal information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Qi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [2] proposed Pointnet network, which is the first deep neural network to directly process disordered point clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Since it does not consider local features, they [36] further proposed Pointnet++ to extract local features at multiple levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Later Atzmon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [37] proposed point convolution neural network, which uses ex- pansion operator and constraint operator to generate con- volution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In response to the problem of inflexibility of fixed grids, Thomas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [19] proposed KPconv, which is lo- cated in Euclidean space and is very effective in classifying point clouds with different densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In addition, Point- Conv [15] and PointCNN [38] use 3D convolution kernels to extract features instead of sharing MLP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The PointConv [15] can be extended to deconvolution to achieve better segmentation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' And PointCNN [38] introduced the x-transform to rearrange the points into a potentially regu- lar order, and then use convolution to extract local features from the point cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Graph-based Methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' By constructing a local or global graph structure to update delivery messages and learn fea- tures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In general, the graph structure of the spatial domain relies on finding k-nearest neighbors for message passing, and the graph structure of the spectral domain needs to be realized by methods such as Laplace matrix spectral decomposition and Chebyshev polynomial approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' KCNet [4] defines a point set kernel as a set of learnable 3D points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' It aggregates repetitive features at 3D locations on the nearest neighbor graph based on geometric rela- tionships and local high-dimensional features measured by kernel correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [5] proposed DGCNN to learn the embedding of edges by constructing local graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Unlike DGCNN [5], 3DGCN [39] defines learnable ker- nels using graph max pooling mechanism, and introduces shift invariance and scale invariance into deep learning net- works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' DeepGCNs [40] uses residual connections and di- lated convolutions to train deeper graph structures, and experiments confirm the positive effect of depth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Transformer-based Methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Since the great success of transformers in the NLP field, a lot of work has also in- troduced attention mechanisms to related tasks in point clouds recently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' PCT [41] adopts a similar architecture to 3 Concat 𝑓�′ Pool 𝑥��,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 𝑓�� 𝑥�,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 𝑓� 𝑥��,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 𝑓�� 𝑥��,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 𝑓�� 𝑥��,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 𝑓�� 𝑥��,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 𝑓�� ℎ��� ℎ��� ℎ��� ℎ��� ℎ��� Feature Potential Encoding(FeaPE) Concat MLP shared ℎ��� ℎ��� ℎ��� ℎ��� ℎ��� ℎ�� shared 𝐸�� 𝑥�- 𝑥�� 𝑥� 𝑥�� MLP 𝐸��� 𝑥�- 𝑥�� 𝑥� 𝑥�� 𝐸�� 𝑥�- 𝑥�� 𝑥� 𝑥�� ℎ�� ℎ�� Relative position encoding ℎ�� Concat (𝑓�- 𝑓��) 𝑓� (𝑓�- 𝑓��) 𝑓� (𝑓�- 𝑓��) 𝑓� ℎ�� ℎ�� Semantic feature encoding ℎ�� ℎ�� ℎ�� ℎ�� ℎ�� ℎ�� ℎ�� ℎ�� ℎ�� ℎ�� Figure 1: Illustration of feature extraction by DFA layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The color closeness represents the adjacent points in the feature domain rather than the spatial neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Rich information is obtained through relative position encoding and semantic feature encoding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The edge features of each adjacent point are obtained by sharing MLP, and finally the features of the central point are updated by maximum pooling operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The subscript j1 · · · j5 index the feature-domain neighbors for center xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' pointnet [2], using neighbor information embedding, and improved offset transformer for feature learning, so that it has achieved good results in classification and segmenta- tion tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Similarly, there are also some research works based on the pointnet++ [36] network, such as PT [42] and BL-Net [43] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The PT [42] proposed by Zhao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' is to add a layer of transformer to extract features after each downsampling or upsampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The transformer has been modified to measure the difference between the cor- responding channels between two eigenvectors (Q and K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' BL-Net [43] newly designed position feedback module to perform feature-guided point shifting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In addition, Yan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [44] also used the attention mechanism and proposed PointASNL that can effectively process point clouds with noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Methodology Extracting and utilizing effective features is crucial in point cloud tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We construct a local graph structure through dynamic updating, and the information can dif- fuse nonlocally in the whole point cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Based on the graph structure, we explore both the latent location and semantic features of different layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Further, we make full use of global features and local features containing detailed information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We describe the operation called Dynamic Feature Aggregation (DFA) in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1, and then the network structure is introduced in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Dynamic Feature Aggregation We define the input point cloud as X = {xi|i = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=', N} ∈ RN×3 with the corresponding features defined as F = {fi|i = 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='N} ∈ RN×D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Here xi represents the three-dimensional coordinates (x, y, z) of the i-th point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' As the input point cloud only contain three-dimensional coordinates, the geometry coordinates can also be regarded as its initial feature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' When extracting features at each layer, a local graph needs to be dynamically constructed, which is defined as G = (V, E), where V = {1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='n} and E ⊆ V × V are the vertices and edges, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We construct a local graph structure by finding k-nearest neighbors in the feature domain, including self-loops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Suppose that xi is the center point of the graph structure, and then N(i) = {j : (i, j) ∈ E} is the neighboring point in the fea- ture domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Specifically,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' the similarity of features is cal- culated and measured in the same way as Euclidean space 4 DFA (64) DFA (64) DFA (64) DFA (64) N ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 3 N ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 64 N ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 64 N ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 64 N ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 64 ⊕ N ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 1024 Pool 1024 ⊕ N ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 1024 1024 Pool Pointnet(64) Pointnet(64) N ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 1280 ⊕ repeat ⊕ Classification Segmentation Model Architecture ⊕ Categorical vector MLP MLP (N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='192) (N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='256) Spatial transform (64) MLP MLP (512,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='256,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='c) (512,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='256,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='p) Figure 2: DFA based network architectures for classification and segmentation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' ⊕ stands for concatenated operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The spatial transformation is designed to compute a 3 × 3 matrix to align the input point cloud to the canonical space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' By concatenating local features and low-dimensional global features through MLP and max pooling, 1D global descriptors can be generated for classification tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' For part segmentation, we generate 1024-dimensional global features, fuse the category feature vectors, and then concatenate the detailed local features again to output the category score of each point through MLP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' distance in each feature dimension, and the k points with the smallest value are selected as the nearest neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Then retrieve the 3D coordinates of each nearest neigh- bor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Given the input three-dimensional coordinates and D-dimensional features, our purpose is to learn and output M-dimensional features with the same number of points through the DFA layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Because we establish the connection between the center point and the surrounding k-nearest neighbors by build- ing a local graph structure, so we define the feature of the edge as eij = hΘ(fi, fj) , where hΘ : RD × RD → RM is a nonlinear function with a set of learnable parameters Θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Finally, we aggregate the edge features of the k near- est neighbors along each channel, and obtain the result for each center point fi that enters the DFA layer feature extraction, which is defined as follows: f ′ i = Π j∈N(i)hΘ(fi, fj) (1) Semantic Feature Encoding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We choose to find k- nearest neighbors in the feature domain, which means that the points sharing the same class will have high probabil- ity to be connected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Then we concatenate the feature of the center point and the feature differences with its neigh- bors as semantic feature information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Because this not only includes the features of all the original center points, but also transmits information to the surrounding points through the feature difference with the neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' And we define the encoding as follows: hfj = fi ⊕ (fi − fj), j ∈ N(i) (2) Here, ⊕ is the concatenate operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We calculate and concatenate the feature differences and its own features along each dimension, aiming to encode semantically sim- ilar features and explore their latent information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Relative Position Encoding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We first need to store the original 3-dimensional position coordinate, and then find the latent position information of the corresponding nearest neighbors in the feature domain for each center point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We use the relative position information of the neighboring points to encode as follows: hxj = MLP(xi⊕xj⊕(xi−xj)⊕ ∥ xi−xj ∥), j ∈ N(i) (3) where xi and xj represent the original three-dimensional coordinates, (xi − xj) calculate the relative coordinates of the center point and the k-nearest neighbors of the fea- ture domain , ⊕ is the concatenate operation, and ∥ · ∥ 5 calculates the Euclidean distance between the neighbours and center point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Unlike finding the nearest neighbors in the space restricted by geometry distance, we can discover more latent location information in the feature domain that may have similar semantic feature but with larger geometry distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' When obtaining the position and semantic embedding, we can concatenate these two parts first and then extract the edge features through the MLP operation: hij = MLP(hxj ⊕ hfj), j ∈ N(i) (4) Finally, we need to consider how to aggregate the fea- tures of the neighboring edges, that is Π in (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We have three options for the over-aggregation Π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The first is to maximize the pool of edge features learned by all nearest neighbors to obtain the features of the center point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The second is to add all edge features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The third is to perform softmax on the neighbors to obtain a weight coefficient Wij, and then multiply it with each edge feature, that is, Wij × hij to obtain the attentive edge feature, and fi- nally add and update the features of the center point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The experimental results show that the first maximum pool- ing has the best performance, so we choose the maximum pooling to aggregate all edge features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Network Architecture We use the proposed DFA layer to design two network architectures for the point cloud classification and segmen- tation task as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We send the initial point cloud into a spatial transformation network similar to the Pointnet [2] network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' By learning the position information of the point cloud itself, we can learn a rotation matrix that is most conducive to the classification or segmenta- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The point clouds are multiplied and fed into our stacked DFA layer to extract features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Local and Global Information Aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Fo- cusing only on the global features obtained by pooling on each point ignores the local interaction between points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Or only focusing on local features of surrounding points is one-sided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Therefore, we choose a combination of local features and global features to comprehensively learn the information contained in the point cloud, so that it can be better used in classification and segmentation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Our local features are learned by several layers of DFA, and the lower-dimensional global features is obtained similarly to Pointnet [2] by using shared MLP and max pooling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Our ablation experiments have also confirmed that integration with global feature is beneficial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' On the other hand, we set several local features and low-dimensional global fea- tures to the same dimension (64) because we think they are equally important, which is also confirmed in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Classification Network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Our classification network is shown in the upper part of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 2, and the point cloud through the spatial transformation network is sequentially passed through four DFA to extract local features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The input of each layer is the output of the previous layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We concatenate these four local features and the global fea- tures extracted from the initial point cloud, and then con- vert them to higher dimensions through MLP operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Finally, global features are obtained by max pooling for classification prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Segmentation Network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Our segmentation network is similar to the classification network, as shown in the lower part of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We pass the transformed point cloud through three DFA layers in sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The three local features and low-dimensional global features are also concatenated to obtain a 1024-dimensional global features through MLP and max pooling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' If it is part segmenta- tion, then we add a category feature vector (64).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' If it is semantic segmentation, it will not be added.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Finally we use the shared MLP to resize the features and predict the semantic label for each point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Dynamic Graph Update.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Depending on the spa- tial interaction of the point cloud, locally adjacent parts can form subsets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' However, considering the spatial neigh- bors for graph update sometimes leads to failure of fea- 6 ture aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' For example, for the point clouds of air plane, the aircraft wing and fuselage are adjacent in space, the mutually updated features are useless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' So we use the point of finding k-nearest neighbors on the feature domain, which means that these points can constitute meaningful parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Each time we find neighbors in the feature domain to reconstruct the local graph structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' It can be said that our graph is dynamically updated, so we can explore more latent location information, which is also a limitation that cannot be achieved by doing k-nearest neighbors in space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Experiments In this section, we evaluate our models using DFA for point cloud classification and part segmentation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Methods Input point mAcc OA Pointnet[2] xyz 1k 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 Pointnet++[36] xyz 1k 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 Pointnet++[36] xyz,normal 5k 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 SpiderCNN[45] xyz,normal 1k 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 PointWeb[12] xyz,normal 1k 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 PointCNN[38] xyz 1k 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 DGCNN[5] xyz 1k 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 Point2Sequence[46] xyz 1k 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 FPConv[47] xyz,normal 1k 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 PointConv[15] xyz,normal 1k 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 KPConv[19] xyz 6k 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 Point2Node [48] xyz 1k 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 PointASNL[44] xyz 1k 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 PointASNL[44] xyz,normal 1k 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 PCT[41] xyz 1k 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 SO-Net[8] xyz,normal 5k 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 BL-Net[43] xyz 1k 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 AG-conv[49] xyz 1k 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 PointStack[50] xyz 1k 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 Ours(1024 points) xyz 1k 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 Ours(2048 points) xyz 2k 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 Table 1: Classification results on ModelNet40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Classification Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We evaluate our point cloud classification model on the ModelNet40 [24] dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' This dataset contains 12311 mesh CAD models from 40 categories, where 9843 models are used for training and 2468 models are used for testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We follow the experimental setting of [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We uni- formly sample 1024 or 2048 points for each model, each using only 3D coordinates (x, y, z) as input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Data aug- mentation operations include point shifting, scaling and perturbing of the points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Network Configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The network architecture is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' At each layer we recompute the graph based on feature similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' For the 1024 points we set the number of nearest neighbors k value to 20, and to maintain the same density, we set k to 40 for the 2048 points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We use four DFA layers to extract local geometric features and a Pointnet-like structure to extract low-dimensional global features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' These are implemented using fully connected lay- ers (64).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We connect the extracted multi-layer features to obtain 64×5 = 320-dimensional features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Then the global features are obtained, and then two fully connected layers are used to transform the global features for classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' All layers use LeakyReLU and batch normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We use the SGD optimizer with momentum of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The initial learning rate is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1, and the random drop rate of the fully connected layer is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 to prevent overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The batch size is set to 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We use Pytorch implementation and train the network on two RTX 2080Ti GPUs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Table 1 shows the results of the classification task, and the evaluation metrics we use on this dataset are the average class accuracy and overall accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Our network only feeds 3D coordinates into training, which contains less raw information, but achieves the best re- sults on this dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The test result of 2048 sampling points is better than that of 1024 points, indicating that when more original information is included, our network can learn more features and have better performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 7 PointNet DGCNN AG-conv ours ground truth Figure 3: Visual comparison of four methods for part segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Methods mIou air.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' bag cap car cha.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' ear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' gui.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' kni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' lam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' lap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' mot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' mug pis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' roc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' ska.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' NUM 2690 76 55 898 3758 69 787 392 1547 451 202 184 283 66 152 5271 Pointnet[2] 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 Pointnet++[36] 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 SO-Net[8] 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 RGCNN[51] 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 DGCNN[5] 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 PCNN[37] 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 3D-GCN[39] 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 PointASNL[44] 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 PRA-Net[52] 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 Ours 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 Table 2: Part segmentation results on ShapeNet dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Metric is mIoU(%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Part Segmentation Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We test our model on the ShapeNet dataset [25] for point cloud part segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' This dataset contains 16881 shapes in 16 categories, of which 14006 are used for training and 2874 are used for testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' There are 50 parts tags in total, and each model includes 2-6 parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We follow the experimental setup of [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 2048 points are sampled from each shape, and the input consists only of the 3D coordinates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Network Configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We use three DFA layers to extract features, and operate the same as classification to obtain 1024-dimensional global features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Following [5], we also add a one-hot vector representing the category type to each point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Then we concatenate global features and category vectors as new global features with 1024 + 64 = 1088-dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We re-concatenate the previous three local features and convert them into the features of each point through three fully connected layers (512, 256, 128) for segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The settings of our training parameters are the same as in the classification task, except that the batch size is changed to 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We evaluate the performance of part segmen- tation by the mIou metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The Iou of a shape is computed by averaging of each part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The mean Iou (mIou) is calcu- lated by averaging the Ious of all testing instances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' From the experimental results in table 2, it can be seen that 8 Methods mAcc mIou ceiling floor wall beam column windows door chair table bookcase sofa board clutter Pointnet[2] 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='98 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='09 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='80 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='33 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='05 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='92 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='26 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='76 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='93 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='61 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='85 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='28 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='38 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='22 SEGCloud[28] 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='35 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='92 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='06 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='05 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='86 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='00 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='37 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='35 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='12 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='40 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='89 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='88 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='42 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='96 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='60 PointCNN[38] 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='86 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='26 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='31 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='24 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='41 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='00 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='60 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='77 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='09 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='39 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='59 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='67 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='67 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='05 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='74 PointWeb[12] 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='64 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='28 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='95 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='48 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='39 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='00 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='11 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='72 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='81 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='33 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='27 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='89 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='30 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='91 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='46 SPG[53] 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='50 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='04 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='35 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='87 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='00 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='81 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='93 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='58 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='66 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='41 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='84 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='60 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='10 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='22 PCNN[37] 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='01 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='27 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='26 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='20 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='89 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='27 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='98 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='49 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='45 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='87 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='63 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='28 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='91 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='10 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='22 PCT[41] 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='65 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='33 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='54 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='42 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='63 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='00 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='35 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='64 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='00 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='58 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='20 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='22 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='71 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='93 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='29 Ours 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='96 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='18 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='68 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='50 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='05 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='72 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='45 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='18 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='36 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='77 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='52 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='59 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='02 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='12 Table 3: Semantic segmentation results on S3DIS dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Pointnet DGCNN ours ground truth Figure 4: Visual comparison of three methods for semantic segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' in some categories with a small number of samples, the segmentation effect is not good due to too few training samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' But overall, our method has better performance, especially with the highest mIou in many categories such as airplane, car, chair, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' This benefits from these cat- egories having sufficient samples so that our network can learn rich features for part segmentation tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 3 shows the visual differences between us and several other mainstream methods on some categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' These methods are roughly capable of distinguishing different parts of an object, and the difference lies in the identification of de- tails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Looking closely at the tail section of the airplane, the fence section below the chair, the top of the car, and the connection between different parts in the guitar, our method is closer to the ground truth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Semantic Segmentation Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We further test our model on the Stanford Large- Scale 3D Indoor Spaces Dataset (S3DIS) dataset [26] for point cloud semantic scene segmentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' This dataset is taken from 271 rooms in 6 different areas in 3 differ- ent buildings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The point cloud data of each scene has 9-dimensional data including xyz three-dimensional coor- dinates, RGB color information, and the normalized posi- tion coordinates x′y′z′ of each point relative to the room where it is located.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' At the same time, each point cloud in the scene is assigned a semantic label from 13 categories 9 (such as ceiling, table, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Network Configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Our semantic segmentation network configuration is the same as for part segmentation, the only difference is that no feature vector is added.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We divide each room into 1m × 1m blocks and sample 4096 points in each block during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' And we use area5 as the test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' For evaluation metrics, we use mean class accuracy (mAcc) and mean class intersection (mIou).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The experimental results are shown in the table 3, and the visualization is shown in the fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Ablation Studies In this subsection, we explore the effect of using different choices in the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The effectiveness of our module and parameter selection is demonstrated in these ablation experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Number of neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The k value of constructing the local graph structure has a great influence on the ex- tracted features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Therefore, it is very important to choose an appropriate value of k in the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We conducted 4 sets of experiments to explore the impact of choosing dif- ferent k values on the classification results of 2048 points, which is also shown in the table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' When the value of k is 10 and 20, the neighborhood of each center point is small and cannot fully interact with the neighbor points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Appro- priately increasing the value of k can also have room for improvement, which also shows that DFA can effectively use the features of neighborhood points to learn local fea- tures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' By further increasing the value of k, it can be found that increasing the value of k all the time will not increase the accuracy of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Because when the value of k is too large, there will be many noise points that are very different from the center point features, which is useless or even burdensome for updating the center point features, and will also increase the amount of parameters and net- work training time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Choosing a neighbor k value of 40 can obtain the best average class accuracy and overall accu- racy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' k mAcc OA 10 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 20 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7 40 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 60 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 Table 4: Number of neighbors(k) Selection of aggregate functions Π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' It can be seen in many previous works[2][36][41] that some symmetric pool- ing functions such as max/sum/mean are often used to overcome the disordered characteristics of point clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In our DFA layer, we also need to aggregate edge features to update features for each center point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We experimented with different aggregation functions such as max, sum, or sum with attention weights which first do softmax on k- nearest neighbors dimension to get the attention weights and then multiply and accumulate them accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The max function is to select the largest feature of points in the local neighborhood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The sum function is to add the features of all points in the neighborhood, and the mean function is to divide by the k value after the sum func- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Table 5 shows the results of our selection of differ- ent aggregation functions on a classification experiment of 2048 points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Although the maximum pooling function will lose the non-largest part of the features, it will retain the largest part of the most significant features, and the ex- perimental results show that it is the most effective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We finally choose the best-performing max function to aggre- gate the edge features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Π mAcc OA max 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 sum 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 mean 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 attention sum 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5 Table 5: Choice of different aggregation functions Π 10 Feature or space domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Further, we explore in which domain is better to compute k-nearest neighbors, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=', the feature domain or the spatial domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' If we choose to do k-nearest neighbors in the spatial domain, it means that the graph structure is fixed each time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' On the one hand, the relative position coding will be the same, on the other hand, it is very limited to exchange information with fixed neighbor points each time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' If we choose to do k-nearest neighbors on the feature domain, it means that the local graph structure is dynamically updated, and the neighbors of the graph are different each time but the fea- tures are similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We can make better use of DFA layers to discover efficient features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We choose to compare the ex- perimental results in the classification task of 2048 points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' As can be seen from the table 6, our way of exchanging information with neighbor updates in the feature domain is better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Because the k-nearest neighbors obtained in this way are more homogeneous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Especially for part segmen- tation, spatially adjacent points are not necessarily of the same class, so it is useless or even redundant to exchange information with these points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' spatial or feature domain mAcc OA feature 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 spatial 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 Table 6: Comparison of k-nearest neighbors in feature domain and space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Relative position information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' By computing the k-nearest neighbors of the feature domain, we are able to discover latent-location feature information that is not lim- ited by space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In this way, the relative position encoding in each DFA layer is different because the neighborhood points are changing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' This allows us to connect points that may not be in close spatial locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' So we explore its ef- fectiveness by whether incorporating this part in the clas- sification task of 2048 points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The experimental results in table 7 show that adding location information encoding can have better performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' This also shows that the po- tential position information obtained by relative position encoding is crucial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Position information mAcc OA w 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 w/o 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='3 Table 7: Whether to add position information Low-dimensional global features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Inspired by Pointnet [2] and Pointnet++ [36], it is not advisable to only focus on global features or local features, so we adopt a fusion of both.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Global features can provide overall direc- tion control, while local features can provide more detailed information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' We believe that these are equally important in network learning, so after extracting local features of different depths, we concatenate these local features and low-dimensional global features together through MLP op- erations to upgrade to high-dimensional for subsequent tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' To this end, we compare the classification results of 2048 points with or without adding low-dimensional global features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The table 8 confirms the effectiveness of our way of concatenating the learned local features and low-dimensional global features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Low-global features mAcc OA w 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0 w/o 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1 Table 8: Whether to add low-dimensional global features 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Model Complexity We use the stat package in pytorch to output some quan- titative results of the network model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' It includes the total number of parameters of the network model, the number of floating-point operations required for network opera- tion, and the memory occupied by node inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The experimental results are all tested based on the classifi- cation model on 1024 points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' At the same time, we test 11 other mainstream methods for comparison as shown in the following table 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' It can be seen that our model has fewer parameters and does not occupy a large amount of memory, indicating that our network structure is lightweight, and not complicated and easy to implement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' In networks based on graph meth- ods, the amount of computation is generally too large due to the need to interact with neighbors to update features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Compared with other methods of this type, our floating- point operations are also much less.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' At the same time the performance is still the best.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Method Pparams Flops Memory OA Pointnet[2] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='7M 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5M 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5M 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 Pointnet++[36] 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2M 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1M 231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5M 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 DGCNN[5] 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='8M 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='89G 123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0M 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9 AG-conv[49] 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9M 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9G 202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='0M 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='4 PCT[41] 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='9M 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='32G 187.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6M 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='2 ours 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='1M 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='17G 154.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='5M 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='6 Table 9: Quantitative evaluation of classification on ModelNet40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Conclusion This paper proposes a new operation for point cloud learning and also demonstrates its performance in differ- ent tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' The main contribution of our method is to ag- gregate local feature in the feature domain, explore the la- tent relative position information and semantic feature in- formation, and learn to obtain higher-dimensional features by concatenating local features and low-dimensional global features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Our DFA can dynamically construct graphs that are not spatially correlated and exchange information be- tween points with semantically similar features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Exper- imental results show that our network outperforms the state-of-the-art on several public datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Further, our DFA module is simple and efficient, and can be seamlessly integrated into other network models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' References [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Biasotti, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Cerri, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Bronstein, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Bronstein, Recent trends, applications, and perspectives in 3d shape similarity assessment, in: Computer graphics forum, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 35, Wiley Online Library, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 87–119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [2] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Qi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Su, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Mo, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Guibas, Pointnet: Deep learning on point sets for 3d classification and segmentation, in: Proceed- ings of the IEEE conference on computer vision and pattern recognition, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 652–660.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [3] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Samari, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Siddiqi, Local spectral graph convolu- tion for point set feature learning, in: Proceedings of the Euro- pean conference on computer vision (ECCV), 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 52–66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [4] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Shen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Feng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Tian, Mining point cloud local structures by kernel correlation and graph pooling, in: Proceed- ings of the IEEE conference on computer vision and pattern recognition, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 4548–4557.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [5] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Sun, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Sarma, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Bronstein, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Solomon, Dynamic graph cnn for learning on point clouds, Acm Transactions On Graphics (tog) 38 (5) (2019) 1–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [6] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Huang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Hou, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Shan, Graph at- tention convolution for point cloud semantic segmentation, in: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 10296–10305.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [7] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Liu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Ni, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Tian, Dynamic points agglom- eration for hierarchical point sets learning, in: Proceedings of the IEEE/CVF International Conference on Computer Vision, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 7546–7555.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [8] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Li, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Lee, So-net: Self-organizing network for point cloud analysis, in: Proceedings of the IEEE conference on computer vision and pattern recognition, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 9397–9406.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [9] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Mnih, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Gregor, Neural variational inference and learn- ing in belief networks, in: International Conference on Machine Learning, PMLR, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 1791–1799.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [10] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Huang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wang, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Neumann, Recurrent slice networks for 3d segmentation of point clouds, in: Proceedings of the IEEE conference on computer vision and pattern recognition, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 2626–2635.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [11] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Hua, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yeung, Shellnet: Efficient point cloud convolutional neural networks using concentric shells statistics, in: Proceedings of the IEEE/CVF international con- ference on computer vision, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 1607–1616.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [12] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Zhao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Jiang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Fu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Jia, Pointweb: Enhancing lo- cal neighborhood features for point cloud processing, in: Pro- ceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 5565–5573.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [13] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Su, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Jampani, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Sun, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Maji, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Kalogerakis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Kautz, Splatnet: Sparse lattice networks for point 12 cloud processing, in: Proceedings of the IEEE conference on computer vision and pattern recognition, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 2530–2539.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [14] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Hua, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Tran, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yeung, Pointwise convolutional neural networks, in: Proceedings of the IEEE conference on computer vision and pattern recognition, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 984–993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [15] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Qi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Fuxin, Pointconv: Deep convolutional net- works on 3d point clouds, in: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 9621–9630.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [16] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Lan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Davis, Modeling local geometric structure of 3d point clouds using geo-cnn, in: Proceedings of the IEEE/cvf conference on computer vision and pattern recog- nition, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 998–1008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [17] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Komarichev, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Zhong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Hua, A-cnn: Annularly convolu- tional neural networks on point clouds, in: Proceedings of the IEEE/CVF conference on computer vision and pattern recog- nition, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 7421–7430.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [18] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Mao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Li, Interpolated convolutional networks for 3d point cloud understanding, in: Proceedings of the IEEE/CVF international conference on computer vision, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 1578–1587.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [19] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Thomas, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Qi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Deschaud, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Marcotegui, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Goulette, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Guibas, Kpconv: Flexible and deformable convolution for point clouds, in: Proceedings of the IEEE/CVF international conference on computer vision, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 6411– 6420.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [20] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Paigwar, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Erkent, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wolf, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Laugier, Attentional point- net for 3d-object detection in point clouds, in: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 0–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [21] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Xie, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Chen, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Tu, Attentional shapecontextnet for point cloud recognition, in: Proceedings of the IEEE conference on computer vision and pattern recognition, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 4606– 4615.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [22] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Zhang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Xiao, Pcan: 3d attention map learning using contextual information for point cloud based retrieval, in: Pro- ceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 12436–12445.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [23] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Ni, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Zhou, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Tian, Modeling point clouds with self-attention and gumbel subset sampling, in: Proceedings of the IEEE/CVF conference on com- puter vision and pattern recognition, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 3323–3332.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [24] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Song, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Khosla, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Tang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Xiao, 3d shapenets: A deep representation for volumetric shapes, in: Proceedings of the IEEE conference on computer vision and pattern recognition, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 1912–1920.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [25] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Kim, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Ceylan, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Shen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Su, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Lu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Huang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Sheffer, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Guibas, A scalable active framework for region annotation in 3d shape collections, ACM Transactions on Graphics (ToG) 35 (6) (2016) 1–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [26] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Armeni, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Sener, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Zamir, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Jiang, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Brilakis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Fis- cher, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Savarese, 3d semantic parsing of large-scale indoor spaces, in: Proceedings of the IEEE conference on computer vision and pattern recognition, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 1534–1543.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [27] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Qi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Su, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Nießner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Dai, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Guibas, Vol- umetric and multi-view cnns for object classification on 3d data, in: Proceedings of the IEEE conference on computer vision and pattern recognition, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 5648–5656.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [28] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Tchapmi, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Choy, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Armeni, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Gwak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Savarese, Seg- cloud: Semantic segmentation of 3d point clouds, in: 2017 in- ternational conference on 3D vision (3DV), IEEE, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 537–547.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [29] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Guo, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Sun, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Tong, O-cnn: Octree-based convolutional neural networks for 3d shape analy- sis, ACM Transactions On Graphics (TOG) 36 (4) (2017) 1–11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [30] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Meng, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Gao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Lai, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Manocha, Vv-net: Voxel vae net with group convolutions for point cloud segmentation, in: Proceedings of the IEEE/CVF international conference on computer vision, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 8500–8508.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [31] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Shao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Weng, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Hou, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Zhou, H-cnn: Spatial hashing based cnn for 3d shape analysis, IEEE transactions on visualization and computer graphics 26 (7) (2018) 2403–2416.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [32] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Lawin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Danelljan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Tosteberg, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Bhat, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Khan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Felsberg, Deep projective 3d semantic segmentation, in: In- ternational Conference on Computer Analysis of Images and Patterns, Springer, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 95–107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [33] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Guerry, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Boulch, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Le Saux, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Moras, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Plyer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Fil- liat, Snapnet-r: Consistent 3d multi-view semantic labeling for robotics, in: Proceedings of the IEEE international conference on computer vision workshops, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 669–678.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [34] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Jaritz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Gu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Su, Multi-view pointnet for 3d scene un- derstanding, in: Proceedings of the IEEE/CVF International Conference on Computer Vision Workshops, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 0–0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [35] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wang, Learning relationships for multi-view 3d ob- ject recognition, in: Proceedings of the IEEE/CVF Interna- tional Conference on Computer Vision, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 7505–7514.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [36] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Qi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Su, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Guibas, Pointnet++: Deep hierar- chical feature learning on point sets in a metric space, Advances in neural information processing systems 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [37] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Atzmon, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Maron, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Lipman, Point convolutional neural networks by extension operators, arXiv preprint arXiv:1803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='10091.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [38] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Li, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Bu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Sun, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Di, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Chen, Pointcnn: Convo- lution on x-transformed points, Advances in neural information processing systems 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [39] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Lin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Huang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wang, Convolution in the 13 cloud: Learning deformable kernels in 3d graph convolution networks for point cloud analysis, in: Proceedings of the IEEE/CVF conference on computer vision and pattern recog- nition, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 1800–1809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [40] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Li, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Muller, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Thabet, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Ghanem, Deepgcns: Can gcns go as deep as cnns?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=', in: Proceedings of the IEEE/CVF inter- national conference on computer vision, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 9267–9276.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [41] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Guo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Cai, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Mu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Martin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Hu, Pct: Point cloud transformer, Computational Visual Media 7 (2) (2021) 187–199.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [42] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Zhao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Jiang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Jia, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Torr, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Koltun, Point trans- former, in: Proceedings of the IEEE/CVF International Con- ference on Computer Vision, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 16259–16268.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [43] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Han, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Li, Blnet: Bidirectional learning network for point clouds, Computational Visual Media (2022) 1–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [44] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Zheng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Cui, Pointasnl: Robust point clouds processing using nonlocal neural networks with adaptive sampling, in: Proceedings of the IEEE/CVF Confer- ence on Computer Vision and Pattern Recognition, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 5589–5598.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [45] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Xu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Fan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Xu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Zeng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Qiao, Spidercnn: Deep learning on point sets with parameterized convolutional filters, in: Proceedings of the European Conference on Computer Vi- sion (ECCV), 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 87–102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [46] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Han, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Liu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Zwicker, Point2sequence: Learn- ing the shape representation of 3d point clouds with an attention-based sequence to sequence network, in: Proceedings of the AAAI Conference on Artificial Intelligence, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 33, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 8778–8785.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [47] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Lin, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Yan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Huang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Du, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Liu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Cui, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Han, Fp- conv: Learning local flattening for point convolution, in: Pro- ceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 4293–4302.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [48] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Han, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Li, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Li, Point2node: Correla- tion learning of dynamic-node for point cloud feature modeling, in: Proceedings of the AAAI Conference on Artificial Intelli- gence, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 34, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 10925–10932.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [49] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Zhou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Feng, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Fang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wei, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Qin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Lu, Adaptive graph convolution for point cloud analysis, in: Proceedings of the IEEE/CVF International Conference on Computer Vision, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 4965–4974.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [50] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Wijaya, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Paek, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Kong, Advanced feature learn- ing on point clouds using multi-resolution features and learnable pooling, arXiv preprint arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content='09962.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [51] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Te, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Hu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Zheng, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Guo, Rgcnn: Regularized graph cnn for point cloud segmentation, in: Proceedings of the 26th ACM international conference on Multimedia, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 746–754.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [52] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Cheng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' He, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Bai, Pra-net: Point relation-aware network for 3d point cloud analysis, IEEE Trans- actions on Image Processing PP (99).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' [53] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Landrieu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' Simonovsky, Large-scale point cloud semantic segmentation with superpoint graphs, in: Proceedings of the IEEE conference on computer vision and pattern recognition, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 4558–4567.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} +page_content=' 14' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/29E1T4oBgHgl3EQfAQI2/content/2301.02836v1.pdf'} diff --git a/2NE0T4oBgHgl3EQfdwA8/content/tmp_files/2301.02380v1.pdf.txt b/2NE0T4oBgHgl3EQfdwA8/content/tmp_files/2301.02380v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..7d60af6a3345097a312f34b9316a4cef415b3e37 --- /dev/null +++ b/2NE0T4oBgHgl3EQfdwA8/content/tmp_files/2301.02380v1.pdf.txt @@ -0,0 +1,1565 @@ +Spectrum Monitoring and Analysis in Urban and +Rural Environments at Different Altitudes +Amir Hossein Fahim Raouf∗, Sung Joon Maeng∗, Ismail Guvenc∗, ¨Ozg¨ur ¨Ozdemir∗, and Mihail Sichitiu∗ +∗Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC +amirh.fraouf@ieee.org, {smaeng,iguvenc,oozdemi,mlsichit}@ncsu.edu +Abstract—Due to the scarcity of spectrum resources, the emer- +gence of new technologies and ever-increasing number of wireless +devices operating in the radio frequency spectrum lead to data +congestion and interference. In this work, we study the effect of +altitude on sub-6 GHz spectrum measurement results obtained at +a Helikite flying over two distinct scenarios; i.e., urban and rural +environments. Specifically, we aim at investigating the spectrum +occupancy of various long-term evolution (LTE), 5th generation +(5G) and citizens broadband radio service (CBRS) bands utilized +in the United States for both uplink and downlink at altitudes +up to 180 meters. Our results reveal that generally the mean +value of the measured power increases as the altitude increases +where the line-of-sight links with nearby base stations is more +available. SigMF-compliant spectrum measurement datasets used +in this paper covering all the bands between 100 MHz to 6 GHz +are also provided. +Index Terms—5G, C-Band, CBRS, helikite, LTE, spectrum +monitoring, unmanned aerial vehicles (UAV). +I. INTRODUCTION +Wireless communication services and the emergence of new +technologies have created a huge demand for radio frequency +spectrum [1]. One prominent problem is the availability of the +spectrum and the increase in interference in the current wire- +less networks [2]. In addition, more aggressive frequency reuse +is gaining interest recently for achieving higher link capacity +in networks without introducing additional spectrum [3]. It +is necessary to conduct occupancy studies using spectrum +sensing techniques to understand and characterize interference +problems and identify spectrum sharing opportunities. +There are various recent examples that highlight the im- +portance of understanding spectrum occupancy characteristics, +including non-terrestrial scenarios, for developing effective +spectrum sharing mechanisms. The launch of 5th generation +(5G) cellular service in the United States was a concern for +the commercial airline and private aircraft communities who +used the radar altimeters of the aircraft industry. Although +the assigned spectrum band for the altimeters is between +4.2-4.4 GHz, due to their poor design the current versions +suffer from out-of-band leakage problem; i.e., they ignore their +assigned spectrum boundaries [4]. More specifically, Verizon +and AT&T have recently begun operating in the 3.7 GHz to +3.8 GHz spectrum range which is 400 MHz away from the +altimeter band. However, this gap may not be sufficient for +some aircraft to land safely. Moreover, while both Verizon +and AT&T have been delaying switching on portions of their +This research is supported in part by the NSF award CNS-1939334 and its +supplement for studying NRDZs. +respective 5G C-band wireless networks until July 2023, it is +expected after that day that the whole 3.7-3.98 GHz C-band +may be used for 5G transmissions [5], introducing additional +concerns. There is a similar coexistence concern for spectrum +sharing between the 5G networks to be deployed in the 3.1- +3.55 GHz band in the future and the existing airborne radars +using the same spectrum. In another recent debate, there is a +concern in using terrestrial nationwide network in the L-Band +(i.e., 1-2 GHz) and its potential interference with GPS [6]. +Some existing academic studies on spectrum occupancy +are summarized in [7]. In more recent works, [8] presents a +framework that captures and models the short-time spectrum +occupancy to determine the existing interference for Internet- +of-things (IoT) applications. In another study [9], current +state-of-the-art artificial intelligence techniques are reviewed +for channel forecasting, spectrum sensing, signal detection, +network optimization, and security in mega-satellite networks. +In [10], authors investigate and characterize the performance +of coexisting aerial radar and communication networks for +spectrum overlay and time-division multiple access by uti- +lizing stochastic geometry. In [11], the effect of interference +coming from coexisting ground networks on the aerial link +is studied, which could be the uplink (UL) of an aerial cell +served by a drone base station. By considering a Poisson field +of ground interferers, they characterize aggregate interference +experienced by the drone. +In this paper, by post-processing the measurements from +the experiments conducted by the NSF AERPAW platform in +Raleigh, NC [12] at urban and rural environments, we analyze +the spectrum occupancy in different U.S. cellular network +bands as well as the citizens broadband radio service (CBRS) +band. In addition, we study the effect of Helikite altitude +on the signal strength pattern. In Section II, we describe the +data structure and the overall information of the measurement +campaign. Section III and Section IV present the spectrum +monitoring results for various sub-6 Ghz bands in the urban +and rural environments, respectively. Section V studies the +time dependency of the spectrum occupancy for the frequency +bands under consideration. Finally, Section VI highlights the +conclusions of this work. +II. DATA STRUCTURE +The experiment for the urban environment was conducted +by a Helikite flying up to 140 m on August 27, 2022. For +the rural environment, the Helikite flew up to 180 m altitude +on May 5, 2022. An NI USRP B205mini SDR was mounted +arXiv:2301.02380v1 [eess.SP] 6 Jan 2023 + +13:00 +14:00 +15:00 +16:00 +17:00 +18:00 +19:00 +20:00 +Measurement time +0 +50 +100 +150 +Height (m) +(a) Experiment scenario in NC State Main Campus (urban). +0 +10 +20 +30 +40 +50 +60 +70 +80 +90 +100 +110 +120 +130 +140 +Measurement time (min) +0 +50 +100 +150 +200 +Height (m) +(b) Experiment scenario in NC State Lake Wheeler Field (rural). +Fig. 1: Helikite altitude and experiment scenario for: (a) urban +environment, and (b) rural environment. +TABLE I: Summary of LTE and 5G bands in United States. +Technology +Band +No +Duplex +Mode +Uplink Band +(MHz) +DL Band +(MHz) +Operators +LTE +12 +FDD +698 - 716 +728 - 746 +AT&T, Verizon, +T-Mobile +13 +FDD +777 - 787 +746 - 756 +Verizon +14 +FDD +788 - 798 +758 - 768 +AT&T, FirstNet +411 +TDD +2496 - 2690 +2496 - 2690 +T-Mobile +5G +n5 +FDD +824 - 849 +869 - 894 +AT&T, Verizon +n71 +FDD +663 - 698 +617 - 652 +T-Mobile +n77 +TDD +3700 - 3980 +3700 - 3980 +AT&T, Verizon, +T-Mobile +CBRS +n48 +TDD +3550 - 3700 +3550 - 3700 +North America +on the Helikite which enables executing a Python script to +collect samples at the desired center frequency with the desired +sampling rate. The datasets are SigMF compliant and include +information on spectrum usage in frequency bands ranging +from 89 MHz up to 6 GHz for different altitudes [13], [14]. +The data consist of time, altitude, power and Helikite location. +A detailed description of the measurement setups can be found +in [15]. Fig. 1 illustrates the height of the Helikite during the +operation time. +III. URBAN SPECTRUM OCCUPANCY RESULTS +In this section, we present the spectrum occupancy results +for several LTE, 5G and CBRS bands. Table I summarizes the +spectrum allocations for some major cellular providers based +on the technology exploited in the United States [16]. In this +work, we investigate the aggregate in-band power for UL and +downlink (DL) spectrum of various bands. +A. LTE Bands - Uplink +Fig. 2 presents the measured power for LTE bands 13, 14, +15 and 41 considering the UL frequency spectrum ranges. +As it can be seen, the spectrum of LTE 12 and LTE 41 +bands are more crowded compared with LTE 13 and LTE 14 +bands. It is worth mentioning that, unlike other LTE bands +1It is worth mentioning that T-Mobile 5G n41 also uses the same spectrum. +700 +705 +710 +715 +Frequency (MHz) +20 +40 +60 +80 +100 +120 +140 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(a) LTE band 12 (UL). +778 +780 +782 +784 +786 +Frequency (MHz) +20 +40 +60 +80 +100 +120 +140 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(b) LTE band 13 (UL). +788 +790 +792 +794 +796 +798 +Frequency (MHz) +20 +40 +60 +80 +100 +120 +140 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(c) LTE band 14 (UL). +2500 +2550 +2600 +2650 +Frequency (MHz) +20 +40 +60 +80 +100 +120 +140 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(d) LTE band 41 (TDD UL/DL). +Fig. 2: Measured LTE UL power for urban environment. +40 +60 +80 +100 +120 +140 +Altitude (m) +-30 +-20 +-10 +0 +Power (dB) +LTE Band-12 (AT&T, T-Mobile) +LTE Band-13 (Verizon) +LTE Band 14 (AT&T, FirstNet) +LTE Band 41 (T-Mobile) +(a) Mean. +40 +60 +80 +100 +120 +140 +Altitude (m) +0 +50 +100 +150 +200 +Power (dB) +LTE Band-12 (AT&T, T-Mobile) +LTE Band-13 (Verizon) +LTE Band 14 (AT&T, FirstNet) +LTE Band 41 (T-Mobile) +(b) Variance. +Fig. 3: Spectrum occupancy versus altitude in LTE bands 12, +13, 14 and 41 (UL) for urban environment. +under consideration, LTE 41 works in time-division duplexing +(TDD) mode and includes both UL and DL transmissions. +The mean and variance of the measured power for various +LTE bands are presented in Fig. 3. As it can be observed +from Fig. 3a, generally the mean value of the measured power +increases as the altitude increases. The mean power value for +LTE bands 12 and 41 are almost identical and much higher +than the other two bands under consideration. Note that band +41 has significantly larger bandwidth than band 12 and it +includes both UL and DL transmission. From Fig. 3b, it can +be observed that the fluctuation of variance for LTE band 13 +is much lower than the other ones. Although the mean value +of LTE 12 and 41 show similar behaviour, the variance of LTE +41 is lower than LTE band 12. +B. LTE Bands - Downlink +Considering the DL frequency range for different LTE +bands, Fig. 4 illustrates the measured power for the bands un- +der consideration. It can be readily checked that the spectrum +of DL frequency ranges are more crowded compared with the +UL ones. Although the occupied spectrum for LTE 13 and 14 +expand the whole range, the main frequency usage of LTE 12 +is between 735 - 745 MHz. +Fig. 5 shows the mean and variance of the measured power +versus altitude. As it can be observed from Fig. 5a, the mean + +730 +735 +740 +745 +Frequency (MHz) +20 +40 +60 +80 +100 +120 +140 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(a) LTE band 12 (DL). +746 +748 +750 +752 +754 +756 +Frequency (MHz) +20 +40 +60 +80 +100 +120 +140 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(b) LTE band 13 (DL). +758 +760 +762 +764 +766 +768 +Frequency (MHz) +20 +40 +60 +80 +100 +120 +140 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(c) LTE band 14 (DL). +2500 +2550 +2600 +2650 +Frequency (MHz) +20 +40 +60 +80 +100 +120 +140 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(d) LTE band 41 (TDD UL/DL). +Fig. 4: Measured LTE DL power for urban environment. +40 +60 +80 +100 +120 +140 +Altitude (m) +-30 +-20 +-10 +0 +10 +20 +Power (dB) +LTE Band-12 (AT&T, T-Mobile) +LTE Band-13 (Verizon) +LTE Band 14 (AT&T, FirstNet) +LTE Band 41 (T-Mobile) +(a) Mean. +40 +60 +80 +100 +120 +140 +Altitude (m) +0 +100 +200 +300 +Power (dB) +LTE Band-12 (AT&T, T-Mobile) +LTE Band-13 (Verizon) +LTE Band 14 (AT&T, FirstNet) +LTE Band 41 (T-Mobile) +(b) Variance. +Fig. 5: Spectrum occupancy versus altitude in LTE bands 12, +13, 14 and 41 (DL) for urban environment. +value of the measured power increases as the altitude increases +up to almost 80 m. This is due to the fact that at high +altitudes the probability of receiving signal from neighbor +cells increases as the obstacles decrease, which results in the +availability of the line of sight (LoS). For higher altitudes +(i.e., higher than 80 m), the mean values for LTE bands +under consideration remain almost constant. As it is shown +in Fig. 5b, the variance of the measured power for LTE bands +13, 14 and 41 show relatively smaller variation over different +altitudes compared to LTE band 12. The main reason for this +behavior can be found by observing the measured power for +LTE band 12 shown in Fig. 4a. It seems that some portion of +the LTE band 12 is not fully utilized. +C. 5G Bands - Uplink +Fig. 6 presents the measured power for 5G bands n5, n71 +and n77 considering the UL frequency spectrum ranges. This +result reveals that the spectrum of n77 is mainly occupied +between 3700-3800 MHz. One should also note that 5G band +n5 and n71 utilize the frequency-division duplexing (FDD), +while 5G band n77 exploit TDD mode. The performance +of mean and variance of the measured power for 5G bands +(uplink) are presented in Fig. 7. As it can be observed from +Fig. 7a, the mean value of the measured power increases as the +altitude increases up to almost 80 m due to the same argument +825 +830 +835 +840 +845 +Frequency (MHz) +20 +40 +60 +80 +100 +120 +140 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(a) 5G band n5 (UL). +670 +680 +690 +Frequency (MHz) +20 +40 +60 +80 +100 +120 +140 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(b) 5G band n71 (UL) +3750 3800 3850 3900 3950 +Frequency (MHz) +20 +40 +60 +80 +100 +120 +140 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(c) 5G band n77 (TDD UL/DL). +Fig. 6: Measured 5G UL power for urban environment. +40 +60 +80 +100 +120 +140 +Altitude (m) +-35 +-30 +-25 +-20 +-15 +-10 +Power (dB) +5G Band-n5 (AT&T, Verizon) +5G Band-n71 (T-Mobile) +5G Band-n77 (AT&T, Verizon, T-Mobile) +(a) Mean. +40 +60 +80 +100 +120 +140 +Altitude (m) +0 +50 +100 +150 +200 +Power (dB) +5G Band-n5 (AT&T, Verizon) +5G Band-n71 (T-Mobile) +5G Band-n77 (AT&T, Verizon, T-Mobile) +(b) Variance. +Fig. 7: Spectrum occupancy versus altitude in 5G n5, n71 and +n77 bands (UL) for urban environment. +870 +875 +880 +885 +890 +Frequency (MHz) +20 +40 +60 +80 +100 +120 +140 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(a) 5G band n5 (DL). +620 +630 +640 +650 +Frequency (MHz) +20 +40 +60 +80 +100 +120 +140 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(b) 5G band n71 (DL). +Fig. 8: Measured 5G DL power for urban environment. +mentioned earlier. The mean value of 5G band n5 shows higher +value compared with n71 and n77. As it is shown in Fig. 7b, +the variance of the measured power for 5G bands n5 and n77 +intersect with each other around the altitude of 60 m. The +variance of n77 band keeps increasing as the altitude increases. +D. 5G Bands - Downlink +Fig. 8 illustrates the measured power for 5G n5 and n71 +bands by considering the DL frequency range. It can be seen +that the measured power for 870 - 880 MHz and 885-894 MHz +are higher than the rest of spectrum. Fig. 9 shows the mean and +variance of the measured power versus altitude. As it can be +observed from Fig. 9a, the mean value of the measured power +for n5 and n71 are similar and significantly higher than n77. + +40 +60 +80 +100 +120 +140 +Altitude (m) +-40 +-20 +0 +20 +Power (dB) +5G Band-n5 (AT&T, Verizon) +5G Band-n71 (T-Mobile) +5G Band-n77 (AT&T, Verizon, T-Mobile) +(a) Mean. +40 +60 +80 +100 +120 +140 +Altitude (m) +0 +50 +100 +150 +200 +Power (dB) +5G Band-n5 (AT&T, Verizon) +5G Band-n71 (T-Mobile) +5G Band-n77 (AT&T, Verizon, T-Mobile) +(b) Variance. +Fig. 9: Spectrum occupancy versus altitude in 5G bands n5 +and n77 (DL) for urban environment. +(a) +3550 +3600 +3650 +Frequency (MHz) +20 +40 +60 +80 +100 +120 +140 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(b) +Fig. 10: (a) CBRS spectrum and tiers; and (b) Measured CBRS +band n48 power for urban environment (TDD UL/DL). +40 +60 +80 +100 +120 +140 +Altitude (m) +-34 +-32 +-30 +-28 +-26 +-24 +Power (dB) +CBRS Band-n48 (3550-3600 MHz) +CBRS Band-n48 (3600-3650 MHz) +CBRS Band-n48 (3650-3700 MHz) +(a) Mean. +40 +60 +80 +100 +120 +140 +Altitude (m) +0 +10 +20 +30 +40 +50 +Power (dB) +CBRS Band-n48 (3550-3600 MHz) +CBRS Band-n48 (3600-3650 MHz) +CBRS Band-n48 (3650-3700 MHz) +(b) Variance. +Fig. 11: Spectrum occupancy versus altitude in CBRS band +for urban environment. +For the bands under consideration, the mean value increases +as the altitude increases up to almost 80 m. As it is shown in +Fig. 9b, the variance of the measured power for n77 starts with +a small value, while it climes up to near those of n5 values +as the altitude increases. The variance of n71 band depicts +a higher value for all the measured altitudes compared with +those others 5G bands. +E. CBRS Band +Fig. 10a illustrates the CBRS spectrum which it lays out +three tiers of users. Fig. 10b presents the measured power +for CBRS n48 band. Similar to LTE 41 and 5G n77 bands, +n48 also exploits TDD mode. As it can be seen, the spectrum +is mainly occupied within the range of 3610-3690 MHz. In +Fig. 11, we study the mean and variance of the measured +power versus altitude whereas the CBRS band is divided into +three equal portions. As it can be observed, the mean and +variance of the measured power for the first portion (i.e., +3550-3600 MHz) are lower than the other parts. The mean +value of the third portion (i.e., 3650-3700 MHz) increases +700 +705 +710 +715 +Frequency (MHz) +50 +100 +150 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(a) LTE band 12 (UL). +778 +780 +782 +784 +786 +Frequency (MHz) +50 +100 +150 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(b) LTE band 13 (UL). +788 +790 +792 +794 +796 +798 +Frequency (MHz) +50 +100 +150 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(c) LTE band 14 (UL). +2500 +2550 +2600 +2650 +Frequency (MHz) +50 +100 +150 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(d) LTE band 41 (TDD UL/DL). +Fig. 12: Measured LTE UL power for rural environment. +50 +100 +150 +Altitude (m) +-30 +-20 +-10 +0 +Power (dB) +LTE Band-12 (AT&T, T-Mobile) +LTE Band-13 (Verizon) +LTE Band 14 (AT&T, FirstNet) +LTE Band 41 (T-Mobile) +(a) Mean. +50 +100 +150 +Altitude (m) +0 +100 +200 +300 +Power (dB) +LTE Band-12 (AT&T, T-Mobile) +LTE Band-13 (Verizon) +LTE Band 14 (AT&T, FirstNet) +LTE Band 41 (T-Mobile) +(b) Variance. +Fig. 13: Spectrum occupancy versus altitude in LTE bands 12, +13, 14 and 41 (UL) for rural environment. +as the altitude increases up to 60 m and then it drops +afterwards. However, the man value of the second part (i.e., +3600-3650 MHz) keeps increasing as the altitude increases. +IV. RURAL SPECTRUM OCCUPANCY RESULTS +In this section, we study the spectrum occupancy and its +characteristic for the similar bands as previous section by +considering the experimental results for the rural environment. +A. LTE Bands - Uplink +Fig. 12 illustrates the measured power for for LTE bands +13, 14, 15 and 41 considering the UL frequency spectrum. +As it can be seen, LTE bands 12 and 41 show more crowded +spectrum compared with LTE bands 13 and 14. The mean and +variance of the measured power for various LTE bands are +presented in Fig. 13. As opposed to the urban environment +(cf. Fig. 3a), the mean value for LTE bands 13 and 14 are +much higher than the other two bands under consideration. +B. LTE Bands - Downlink +Considering the DL frequency range for different LTE +bands, Fig. 14 illustrates the measured power for the bands +under consideration. Same as the urban results, the spectrum +of DL frequency range are more crowded compared with the +UL ones in the rural environment. Fig. 15 shows the mean + +3550 MHz +3600 MHz +3650 MHz +3700 MHz +Tier 1 +Incumbent Users +(e.g. the Navy) +Tier 2 +Priority Access Licensees +(e.g. private organizations) +Tier 3 +General Authorized Access +(e.g. unlicensed users)730 +735 +740 +745 +Frequency (MHz) +50 +100 +150 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(a) LTE band 12 (DL). +746 +748 +750 +752 +754 +756 +Frequency (MHz) +50 +100 +150 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(b) LTE band 13 (DL). +758 +760 +762 +764 +766 +768 +Frequency (MHz) +50 +100 +150 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(c) LTE band 14 (DL). +2500 +2550 +2600 +2650 +Frequency (MHz) +50 +100 +150 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(d) LTE band 41 (TDD UL/DL). +Fig. 14: Measured LTE DL power for rural environment. +50 +100 +150 +Altitude (m) +-30 +-20 +-10 +0 +10 +20 +Power (dB) +LTE Band-12 (AT&T, T-Mobile) +LTE Band-13 (Verizon) +LTE Band 14 (AT&T, FirstNet) +LTE Band 41 (T-Mobile) +(a) Mean. +50 +100 +150 +Altitude (m) +0 +100 +200 +300 +Power (dB) +LTE Band-12 (AT&T, T-Mobile) +LTE Band-13 (Verizon) +LTE Band 14 (AT&T, FirstNet) +LTE Band 41 (T-Mobile) +(b) Variance. +Fig. 15: Spectrum occupancy versus altitude in LTE bands 12, +13, 14 and 41 (DL) for rural environment. +and variance of the measured power versus altitude. As it can +be observed from Fig. 15a, the mean value of the measured +power increases as the altitude increases up to 80 m and it +remains almost constant for the higher altitudes. The variance +of LTE bands 13, 14, and 41 show similar behaviour, while +the corresponded plot for LTE band 12 starts with increasing +for the altitude up to 40 m and then it drops afterwards. +C. 5G Bands - Uplink +Fig. 16 illustrates the measured power for 5G bands n5, n71 +and n77 considering the UL frequency spectrum ranges. This +result reveals that the spectrum of n77 is less crowded than +those of n5 and n71. The performance of mean and variance +of the measured power for 5G bands (uplink) are presented in +Fig. 17. As it can be observed from Fig. 17a, while the mean +value of the measured power for n77 is almost independent of +the altitude, it increases for n5 and n71 bands as the altitude +increases. As it is shown in Fig. 17b, the variance of the +measured power for n71 depicts higher value compared with +the other 5G bands. +D. 5G Bands - Downlink +Fig. 18 illustrates the measured power for 5G n5 and n71 +bands by considering the DL frequency range. Similar to the +urban case, it can be seen that the measured power for 870 +825 +830 +835 +840 +845 +Frequency (MHz) +50 +100 +150 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(a) 5G band n5 (UL). +670 +680 +690 +Frequency (MHz) +50 +100 +150 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(b) 5G band n71 (UL). +3750 3800 3850 3900 3950 +Frequency (MHz) +50 +100 +150 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(c) 5G band n77 (TDD UL/DL). +Fig. 16: Measured 5G UL power for rural environment. +50 +100 +150 +Altitude (m) +-30 +-25 +-20 +-15 +-10 +Power (dB) +5G Band-n5 (AT&T, Verizon) +5G Band-n71 (T-Mobile) +5G Band-n77 (AT&T, Verizon, T-Mobile) +(a) Mean. +50 +100 +150 +Altitude (m) +0 +50 +100 +150 +200 +250 +Power (dB) +5G Band-n5 (AT&T, Verizon) +5G Band-n71 (T-Mobile) +5G Band-n77 (AT&T, Verizon, T-Mobile) +(b) Variance. +Fig. 17: Spectrum occupancy versus altitude in 5G n5 and n77 +bands (UL) for rural environment. +870 +875 +880 +885 +890 +Frequency (MHz) +50 +100 +150 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(a) 5G band n5 (DL). +620 +630 +640 +650 +Frequency (MHz) +50 +100 +150 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +(b) 5G band n71 (DL). +Fig. 18: Measured 5G DL power for rural environment. +- 880 MHz and 885-894 MHz are higher than the rest of +spectrum in the rural environment. Fig. 19 depicts the mean +and variance of the measured power versus altitude. As it can +be observed from Fig. 19a, the mean value of the measured +power for n77 band remains almost constant for different +altitudes, while it increases as the altitude increases up to +almost 80 m for n5 and n71 bands. As it is shown in Fig. 19b, +the variance of the measured power for 5G band n71 shows +higher values compared with n5 and n77. +E. CBRS Band +Fig. 20 present the measured power for CBRS n48 band +for rural environment. As it can be seen, the spectrum is less + +50 +100 +150 +Altitude (m) +-40 +-20 +0 +20 +Power (dB) +5G Band-n5 (AT&T, Verizon) +5G Band-n71 (T-Mobile) +5G Band-n77 (AT&T, Verizon, T-Mobile) +(a) Mean. +50 +100 +150 +Altitude (m) +0 +100 +200 +300 +400 +Power (dB) +5G Band-n5 (AT&T, Verizon) +5G Band-n71 (T-Mobile) +5G Band-n77 (AT&T, Verizon, T-Mobile) +(b) Variance. +Fig. 19: Spectrum occupancy versus altitude in 5G bands n5 +and n77 (DL) for rural environment. +3550 +3600 +3650 +Frequency (MHz) +50 +100 +150 +Altitude (m) +-40 +-20 +0 +20 +40 +dB +Fig. 20: Measured power during Helikite operation over rural +environment for CBRS band n48 (TDD UL/DL). +50 +100 +150 +Altitude (m) +-30 +-25 +-20 +-15 +-10 +Power (dB) +CBRS Band-n48 (3550-3600 MHz) +CBRS Band-n48 (3600-3650 MHz) +CBRS Band-n48 (3650-3700 MHz) +(a) Mean. +50 +100 +150 +Altitude (m) +0 +1 +2 +3 +4 +Power (dB) +CBRS Band-n48 (3550-3600 MHz) +CBRS Band-n48 (3600-3650 MHz) +CBRS Band-n48 (3650-3700 MHz) +(b) Variance. +Fig. 21: Spectrum occupancy versus altitude in CBRS band +for rural environment. +crowded compared with the rural environment. In Fig. 21, we +study the mean and variance of the measured power versus +altitude. As it can be observed, the mean value of the measured +power for all three considered portions are almost similar +and remain constant as the altitude increases. In addition, the +variance also shows slight fluctuations compared to the other +bands under consideration. +V. TIME DOMAIN ANALYSIS OF SPECTRUM OCCUPENCY +In this section, we focus on the spectrum occupancy of +LTE and NR signals in time, while we describe the altitude +dependency of the spectrum in the previous section. For +around 8 hours of measurement duration by the Helikite in +the urban environment, we observe signal strength changes. +This section focuses exclusively on those urban environment +measurements. +Fig. 22 shows the spectrum monitoring results by the +Helikite. The x-axis is the monitored spectrum range and the +y-axis is the measured time stamp, which is indicated by hours +and minutes. In Fig. 22a, we capture the frequency range from +700 MHz to 800 MHz, which contains LTE FDD bands 12, +13, 14 (see Table I). First of all, we can clearly observe a +series of occupied 10 MHz bandwidth 12, 13, and, 14 DL +bands. On the other hand, the signal strength of UL bands is +lower than DL bands, and UL bands 13 and 14 are scarcely +occupied. We also observe that there are time periods when +signal strength becomes low for the whole observed frequency +range, which coincides with the periods where the altitude of +the Helikite stays low in Fig. 1. It implies that received signal +strength is abruptly reduced by the blockage when the altitude +of the Helikite is lower than a certain height. In addition, +this tendency is observed in other frequency bands as well in +Fig. 22b and Fig. 22c. In Fig 22b, we capture the frequency +range 2500 MHz - 2700 MHz, which contains LTE TDD +41 band. Since carrier frequency is higher than Fig. 22a, we +observe that this LTE band covers wider bandwidth: 20 MHz, +40 MHz, and 100 MHz. It is also observed that the received +signal strength is lower than the frequency range in Fig. 22a. +This is due to the fact that as carrier frequency increases a +received signal suffers higher path loss, which is also observed +in a much higher carrier frequency range in Fig. 22c. In +particular, Fig. 22c shows spectrum occupancy of NR TDD +n77 band, 3700 MHz - 3800 MHz. We can observe 40 MHz +and 60 MHz bandwidth signals. +Fig. 23 shows the received signal strength changes during +the measurement time for the captured LTE and NR bands. In +Fig. 23a, we observe the LTE FDD UL/DL 12 band shown +in Fig. 22a. Mean value of the received signal strength across +the frequency band is represented by lines and half of the +standard deviation (std) of signal strength is described by the +shaded area around lines. It is observed that the signal strength +of UL is lower than DL, while the variation of the signal +strength of UL inside the band is higher than DL, which can +be observed from higher std values. Fig. 23b and Fig. 23b +show the received signal strength changes of LTE TDD 41 +and NR TDD 77 bands which can be shown in Fig. 22b and +Fig. 22c. It is observed that the signal strength fluctuation of +NR TDD 77 band is higher than other bands such as LTE 12 +and 41 bands. +VI. CONCLUSION +Using the data measured by a Helikite flying over an urban +and rural environments, in this paper we studied spectrum +measurements in various sub-6 GHz 4G, 5G and CBRS bands. +Both UL and DL spectrum occupancy has been investigated. +Our results revealed that generally the mean value of measured +power tends to increase as the altitude increases due to higher +probability of line-of-sight, at least for the considered max- +imum altitude range. Further, the spectrum of DL frequency +ranges showed to be more crowded compared with the uplink +ones for both environments. It has been also seen that for the +rural environment the mean value for LTE bands 13 and 14 +are much higher than the other two bands under considera- +tion, as opposed to the urban environment. Furthermore, the +performance of CBRS band for urban environment indicates +more activity compared with the rural condition. + +(a) 700 MHz - 800 MHz. +(b) 2500 MHz - 2700 MHz. +(c) 3700 MHz - 3800 MHz. +Fig. 22: Spectrum monitoring during the measurement time. We observe different LTE and NR bands’ occupancy and the +received signal strength is strong when the Helikite floats at a high altitude. +12:00 +14:00 +16:00 +18:00 +20:00 +Time +-30 +-25 +-20 +-15 +-10 +-5 +0 +5 +10 +15 +20 +Power (dBm) +std/2 | LTE DL 12 +mean | LTE DL 12 +std/2 | LTE UL 12 +mean | LTE UL 12 +(a) LTE FDD 12 band. +12:00 +14:00 +16:00 +18:00 +20:00 +Time +-30 +-25 +-20 +-15 +-10 +-5 +0 +Power (dBm) +std/2 | LTE TDD 41 +mean | LTE TDD 41 +(b) LTE TDD 41 band. +14:00 +16:00 +18:00 +20:00 +Time +-35 +-30 +-25 +-20 +-15 +-10 +Power (dBm) +std/2 | NR TDD n77 +maen | NR TDD n77 +(c) NR TDD 77 band. +Fig. 23: Received power of different LTE and NR bands during the measurement time. The solid lines represent the mean value +of signal power and shaded areas indicate half of the standard deviation (std) of signal strength, which shows the variation of +signal strength inside the specific bands. +REFERENCES +[1] M. H. Islam, C. L. Koh, S. W. Oh, X. Qing, Y. Y. Lai, C. Wang, Y.- +C. Liang, B. E. Toh, F. Chin, G. L. Tan et al., “Spectrum survey in +Singapore: Occupancy measurements and analyses,” in Proc. IEEE Int. +conf. Cognitive Radio Oriented Wireless Networks and Communications, +2008, pp. 1–7. +[2] F. Adelantado, X. Vilajosana, P. Tuset-Peiro, B. Martinez, J. Melia- +Segui, and T. Watteyne, “Understanding the limits of LoRaWAN,” IEEE +Commun. Mag., vol. 55, no. 9, pp. 34–40, 2017. +[3] Ericsson, +“Frequency +reuse +in +limited +spectrum +networks,” +Oct. +2022, +accessed: +2023-01-04. +[Online]. +Available: +https://www.ericsson.com/en/reports-and-papers/microwave-outlook/ +articles/maximizing-capacity-in-spectrum-limited-networks +[4] D. +Roberson, +“The +5G/aviation +crisis +that +never +should +have +happened,” +https://www.linkedin.com/pulse/ +5g-aviation-crisis-never-should-have-happened-dennis-roberson/, +2022, accessed: 2023-01-04. +[5] W. Bellamy, “US Airlines Begin Installing 5G C-Band Filter for +Radio Altimeters on Airbus A320s,” Sep. 2022, accessed: 2023- +01-04. [Online]. Available: https://www.aviationtoday.com/2022/09/14/ +us-airlines-begin-installing-5g-c-band-filter-radio-altimeters-airbus-a320s/ +[6] K. +Dennehy, +“Ligado +scraps +5G +network +launch +amid +interference +flap,” +2022, +accessed: +2023-01-04. +[Online]. +Available: +https://locationbusinessnews.substack.com/p/ +ligado-scraps-5g-network-launch-amid +[7] Y. Chen and H.-S. Oh, “A survey of measurement-based spectrum +occupancy modeling for cognitive radios,” IEEE Commun. Surv. Tuts., +vol. 18, no. 1, pp. 848–859, 2014. +[8] B. Al Homssi, A. Al-Hourani, Z. Krusevac, and W. S. Rowe, “Machine +learning framework for sensing and modeling interference in IoT fre- +quency bands,” IEEE Internet Things J., vol. 8, no. 6, pp. 4461–4471, +2020. +[9] B. A. Homssi, K. Dakic, K. Wang, T. Alpcan, B. Allen, S. Kandeepan, +A. Al-Hourani, and W. Saad, “Artificial intelligence techniques for next- +generation mega satellite networks,” arXiv preprint arXiv:2207.00414, +2022. +[10] S. J. Maeng, J. Park, and I. Guvenc, “Analysis of UAV radar and commu- +nication network coexistence with different multiple access protocols,” +arXiv preprint arXiv:2211.16614, 2022. +[11] M. M. Azari, F. Rosas, A. Chiumento, A. Ligata, and S. Pollin, “Uplink +performance analysis of a drone cell in a random field of ground +interferers,” in Proc. IEEE Wireless Commun. and Netw. Conf. (WCNC), +2018, pp. 1–6. +[12] V. Marojevic, I. Guvenc, R. Dutta, M. L. Sichitiu, and B. A. Floyd, +“Advanced wireless for unmanned aerial systems: 5G standardization, +research challenges, and AERPAW architecture,” IEEE Vehicular Tech- +nology Magazine, vol. 15, no. 2, pp. 22–30, 2020. +[13] AERPAW, +“Helikite +spectrum +measurements +(pack- +apalooza),” +Aug. +2022, +accessed: +2023-01-04. +[Online]. +Available: +https://sites.google.com/ncsu.edu/ +aerpaw-wiki/aerpaw-user-manual/4-sample-experiments-repository/ +4-4-data-repository/aerpaw-nrdz-research/ +august-2022-helikite-spectrum-measurements-packapalooza +[14] ——, +“Helikite +spectrum +measurements,” +May. +2022, +accessed: +2023-01-04. +[Online]. +Available: +https://sites.google.com/ncsu.edu/aerpaw-wiki/aerpaw-user-manual/ +4-sample-experiments-repository/4-4-data-repository/ +aerpaw-nrdz-research/may-2022-helikite-spectrum-measurements +[15] S. J. Maeng, O. Ozdemir, H. Nandakumar, I. Guvenc, M. Sichitiu, +R. Dutta, and M. Mushi, “Spectrum Activity Monitoring and Analysis +for Sub-6 GHz Bands Using a Helikite,” in Proc Int. Conf. Commun. +Syst. Netw. (COMSNETS), Bengaluru, India, Jan. 2023. +[16] S. J. Maeng, I. G¨uvenc¸, M. Sichitiu, B. A. Floyd, R. Dutta, T. Zajkowski, +¨O. ¨Ozdemir, and M. J. Mushi, “National radio dynamic zone concept +with autonomous aerial and ground spectrum sensors,” in IEEE Int. Conf. +Communications Workshops (ICC Workshops), 2022, pp. 687–692. + +18:00 +17:00 +Time +16:00 +15:00 +111 +14:00 +12 +13 +14 +DL +DL +DL +13:00 +12:00 +710 +720 +730 +740 +750 +760 +770 +780 +790 +Freq (MHz)20 +10 +0 +dBr +-10 +-20 +-30 +-4020:00 +19:0040 +3018:00 +17:00 +Time +16:00 +15:00 +14:00 +LTETDD.41 +13:00 +12:00 +2520 +25402560258026002620 +2640 +2660 +2680 +Freg (MHz)20 +10 +0 +dBr +-10 +-20 +-30 +-4020:00 +19:0040 +3018:00 +17:00 +Time +16:00 +15:00 +14:00 +NRTDD +0n77 +13:00 +12:00 +3790 +Freg (MHz)20 +10 +0 +dBi +-10 +-20 +-30 +-4020:00 +19:0040 +30 \ No newline at end of file diff --git a/2NE0T4oBgHgl3EQfdwA8/content/tmp_files/load_file.txt b/2NE0T4oBgHgl3EQfdwA8/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..e7cd4a59681d6c2fcd229105d903849dd01d92b8 --- /dev/null +++ b/2NE0T4oBgHgl3EQfdwA8/content/tmp_files/load_file.txt @@ -0,0 +1,514 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf,len=513 +page_content='Spectrum Monitoring and Analysis in Urban and Rural Environments at Different Altitudes Amir Hossein Fahim Raouf∗, Sung Joon Maeng∗, Ismail Guvenc∗, ¨Ozg¨ur ¨Ozdemir∗, and Mihail Sichitiu∗ ∗Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC amirh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='fraouf@ieee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='org, {smaeng,iguvenc,oozdemi,mlsichit}@ncsu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='edu Abstract—Due to the scarcity of spectrum resources, the emer- gence of new technologies and ever-increasing number of wireless devices operating in the radio frequency spectrum lead to data congestion and interference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In this work, we study the effect of altitude on sub-6 GHz spectrum measurement results obtained at a Helikite flying over two distinct scenarios;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=', urban and rural environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Specifically, we aim at investigating the spectrum occupancy of various long-term evolution (LTE), 5th generation (5G) and citizens broadband radio service (CBRS) bands utilized in the United States for both uplink and downlink at altitudes up to 180 meters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Our results reveal that generally the mean value of the measured power increases as the altitude increases where the line-of-sight links with nearby base stations is more available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' SigMF-compliant spectrum measurement datasets used in this paper covering all the bands between 100 MHz to 6 GHz are also provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Index Terms—5G, C-Band, CBRS, helikite, LTE, spectrum monitoring, unmanned aerial vehicles (UAV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' INTRODUCTION Wireless communication services and the emergence of new technologies have created a huge demand for radio frequency spectrum [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' One prominent problem is the availability of the spectrum and the increase in interference in the current wire- less networks [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In addition, more aggressive frequency reuse is gaining interest recently for achieving higher link capacity in networks without introducing additional spectrum [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' It is necessary to conduct occupancy studies using spectrum sensing techniques to understand and characterize interference problems and identify spectrum sharing opportunities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' There are various recent examples that highlight the im- portance of understanding spectrum occupancy characteristics, including non-terrestrial scenarios, for developing effective spectrum sharing mechanisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' The launch of 5th generation (5G) cellular service in the United States was a concern for the commercial airline and private aircraft communities who used the radar altimeters of the aircraft industry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Although the assigned spectrum band for the altimeters is between 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='2-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='4 GHz, due to their poor design the current versions suffer from out-of-band leakage problem;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=', they ignore their assigned spectrum boundaries [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' More specifically, Verizon and AT&T have recently begun operating in the 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='7 GHz to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='8 GHz spectrum range which is 400 MHz away from the altimeter band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' However, this gap may not be sufficient for some aircraft to land safely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Moreover, while both Verizon and AT&T have been delaying switching on portions of their This research is supported in part by the NSF award CNS-1939334 and its supplement for studying NRDZs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' respective 5G C-band wireless networks until July 2023, it is expected after that day that the whole 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='7-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='98 GHz C-band may be used for 5G transmissions [5], introducing additional concerns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' There is a similar coexistence concern for spectrum sharing between the 5G networks to be deployed in the 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='1- 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='55 GHz band in the future and the existing airborne radars using the same spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In another recent debate, there is a concern in using terrestrial nationwide network in the L-Band (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=', 1-2 GHz) and its potential interference with GPS [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Some existing academic studies on spectrum occupancy are summarized in [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In more recent works, [8] presents a framework that captures and models the short-time spectrum occupancy to determine the existing interference for Internet- of-things (IoT) applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In another study [9], current state-of-the-art artificial intelligence techniques are reviewed for channel forecasting, spectrum sensing, signal detection, network optimization, and security in mega-satellite networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In [10], authors investigate and characterize the performance of coexisting aerial radar and communication networks for spectrum overlay and time-division multiple access by uti- lizing stochastic geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In [11], the effect of interference coming from coexisting ground networks on the aerial link is studied, which could be the uplink (UL) of an aerial cell served by a drone base station.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' By considering a Poisson field of ground interferers, they characterize aggregate interference experienced by the drone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In this paper, by post-processing the measurements from the experiments conducted by the NSF AERPAW platform in Raleigh, NC [12] at urban and rural environments, we analyze the spectrum occupancy in different U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' cellular network bands as well as the citizens broadband radio service (CBRS) band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In addition, we study the effect of Helikite altitude on the signal strength pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In Section II, we describe the data structure and the overall information of the measurement campaign.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Section III and Section IV present the spectrum monitoring results for various sub-6 Ghz bands in the urban and rural environments, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Section V studies the time dependency of the spectrum occupancy for the frequency bands under consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Finally, Section VI highlights the conclusions of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' DATA STRUCTURE The experiment for the urban environment was conducted by a Helikite flying up to 140 m on August 27, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' For the rural environment, the Helikite flew up to 180 m altitude on May 5, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' An NI USRP B205mini SDR was mounted arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='02380v1 [eess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='SP] 6 Jan 2023 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 Measurement time 0 50 100 150 Height (m) (a) Experiment scenario in NC State Main Campus (urban).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 Measurement time (min) 0 50 100 150 200 Height (m) (b) Experiment scenario in NC State Lake Wheeler Field (rural).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 1: Helikite altitude and experiment scenario for: (a) urban environment, and (b) rural environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' TABLE I: Summary of LTE and 5G bands in United States.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Technology Band No Duplex Mode Uplink Band (MHz) DL Band (MHz) Operators LTE 12 FDD 698 - 716 728 - 746 AT&T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Verizon,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' T-Mobile 13 FDD 777 - 787 746 - 756 Verizon 14 FDD 788 - 798 758 - 768 AT&T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' FirstNet 411 TDD 2496 - 2690 2496 - 2690 T-Mobile 5G n5 FDD 824 - 849 869 - 894 AT&T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Verizon n71 FDD 663 - 698 617 - 652 T-Mobile n77 TDD 3700 - 3980 3700 - 3980 AT&T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Verizon,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' T-Mobile CBRS n48 TDD 3550 - 3700 3550 - 3700 North America on the Helikite which enables executing a Python script to collect samples at the desired center frequency with the desired sampling rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' The datasets are SigMF compliant and include information on spectrum usage in frequency bands ranging from 89 MHz up to 6 GHz for different altitudes [13], [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' The data consist of time, altitude, power and Helikite location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' A detailed description of the measurement setups can be found in [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 1 illustrates the height of the Helikite during the operation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' URBAN SPECTRUM OCCUPANCY RESULTS In this section, we present the spectrum occupancy results for several LTE, 5G and CBRS bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Table I summarizes the spectrum allocations for some major cellular providers based on the technology exploited in the United States [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In this work, we investigate the aggregate in-band power for UL and downlink (DL) spectrum of various bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' LTE Bands - Uplink Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 2 presents the measured power for LTE bands 13, 14, 15 and 41 considering the UL frequency spectrum ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it can be seen, the spectrum of LTE 12 and LTE 41 bands are more crowded compared with LTE 13 and LTE 14 bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' It is worth mentioning that, unlike other LTE bands 1It is worth mentioning that T-Mobile 5G n41 also uses the same spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 700 705 710 715 Frequency (MHz) 20 40 60 80 100 120 140 Altitude (m) 40 20 0 20 40 dB (a) LTE band 12 (UL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 778 780 782 784 786 Frequency (MHz) 20 40 60 80 100 120 140 Altitude (m) 40 20 0 20 40 dB (b) LTE band 13 (UL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 788 790 792 794 796 798 Frequency (MHz) 20 40 60 80 100 120 140 Altitude (m) 40 20 0 20 40 dB (c) LTE band 14 (UL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 2500 2550 2600 2650 Frequency (MHz) 20 40 60 80 100 120 140 Altitude (m) 40 20 0 20 40 dB (d) LTE band 41 (TDD UL/DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 2: Measured LTE UL power for urban environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 40 60 80 100 120 140 Altitude (m) 30 20 10 0 Power (dB) LTE Band-12 (AT&T, T-Mobile) LTE Band-13 (Verizon) LTE Band 14 (AT&T, FirstNet) LTE Band 41 (T-Mobile) (a) Mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 40 60 80 100 120 140 Altitude (m) 0 50 100 150 200 Power (dB) LTE Band-12 (AT&T, T-Mobile) LTE Band-13 (Verizon) LTE Band 14 (AT&T, FirstNet) LTE Band 41 (T-Mobile) (b) Variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 3: Spectrum occupancy versus altitude in LTE bands 12, 13, 14 and 41 (UL) for urban environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' under consideration, LTE 41 works in time-division duplexing (TDD) mode and includes both UL and DL transmissions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' The mean and variance of the measured power for various LTE bands are presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it can be observed from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 3a, generally the mean value of the measured power increases as the altitude increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' The mean power value for LTE bands 12 and 41 are almost identical and much higher than the other two bands under consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Note that band 41 has significantly larger bandwidth than band 12 and it includes both UL and DL transmission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 3b, it can be observed that the fluctuation of variance for LTE band 13 is much lower than the other ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Although the mean value of LTE 12 and 41 show similar behaviour, the variance of LTE 41 is lower than LTE band 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' LTE Bands - Downlink Considering the DL frequency range for different LTE bands, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 4 illustrates the measured power for the bands un- der consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' It can be readily checked that the spectrum of DL frequency ranges are more crowded compared with the UL ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Although the occupied spectrum for LTE 13 and 14 expand the whole range, the main frequency usage of LTE 12 is between 735 - 745 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 5 shows the mean and variance of the measured power versus altitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it can be observed from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 5a, the mean 730 735 740 745 Frequency (MHz) 20 40 60 80 100 120 140 Altitude (m) 40 20 0 20 40 dB (a) LTE band 12 (DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 746 748 750 752 754 756 Frequency (MHz) 20 40 60 80 100 120 140 Altitude (m) 40 20 0 20 40 dB (b) LTE band 13 (DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 758 760 762 764 766 768 Frequency (MHz) 20 40 60 80 100 120 140 Altitude (m) 40 20 0 20 40 dB (c) LTE band 14 (DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 2500 2550 2600 2650 Frequency (MHz) 20 40 60 80 100 120 140 Altitude (m) 40 20 0 20 40 dB (d) LTE band 41 (TDD UL/DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 4: Measured LTE DL power for urban environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 40 60 80 100 120 140 Altitude (m) 30 20 10 0 10 20 Power (dB) LTE Band-12 (AT&T, T-Mobile) LTE Band-13 (Verizon) LTE Band 14 (AT&T, FirstNet) LTE Band 41 (T-Mobile) (a) Mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 40 60 80 100 120 140 Altitude (m) 0 100 200 300 Power (dB) LTE Band-12 (AT&T, T-Mobile) LTE Band-13 (Verizon) LTE Band 14 (AT&T, FirstNet) LTE Band 41 (T-Mobile) (b) Variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 5: Spectrum occupancy versus altitude in LTE bands 12, 13, 14 and 41 (DL) for urban environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' value of the measured power increases as the altitude increases up to almost 80 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' This is due to the fact that at high altitudes the probability of receiving signal from neighbor cells increases as the obstacles decrease, which results in the availability of the line of sight (LoS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' For higher altitudes (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=', higher than 80 m), the mean values for LTE bands under consideration remain almost constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 5b, the variance of the measured power for LTE bands 13, 14 and 41 show relatively smaller variation over different altitudes compared to LTE band 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' The main reason for this behavior can be found by observing the measured power for LTE band 12 shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 4a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' It seems that some portion of the LTE band 12 is not fully utilized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 5G Bands - Uplink Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 6 presents the measured power for 5G bands n5, n71 and n77 considering the UL frequency spectrum ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' This result reveals that the spectrum of n77 is mainly occupied between 3700-3800 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' One should also note that 5G band n5 and n71 utilize the frequency-division duplexing (FDD), while 5G band n77 exploit TDD mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' The performance of mean and variance of the measured power for 5G bands (uplink) are presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it can be observed from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 7a, the mean value of the measured power increases as the altitude increases up to almost 80 m due to the same argument 825 830 835 840 845 Frequency (MHz) 20 40 60 80 100 120 140 Altitude (m) 40 20 0 20 40 dB (a) 5G band n5 (UL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 670 680 690 Frequency (MHz) 20 40 60 80 100 120 140 Altitude (m) 40 20 0 20 40 dB (b) 5G band n71 (UL) 3750 3800 3850 3900 3950 Frequency (MHz) 20 40 60 80 100 120 140 Altitude (m) 40 20 0 20 40 dB (c) 5G band n77 (TDD UL/DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 6: Measured 5G UL power for urban environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 40 60 80 100 120 140 Altitude (m) 35 30 25 20 15 10 Power (dB) 5G Band-n5 (AT&T, Verizon) 5G Band-n71 (T-Mobile) 5G Band-n77 (AT&T, Verizon, T-Mobile) (a) Mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 40 60 80 100 120 140 Altitude (m) 0 50 100 150 200 Power (dB) 5G Band-n5 (AT&T, Verizon) 5G Band-n71 (T-Mobile) 5G Band-n77 (AT&T, Verizon, T-Mobile) (b) Variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 7: Spectrum occupancy versus altitude in 5G n5, n71 and n77 bands (UL) for urban environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 870 875 880 885 890 Frequency (MHz) 20 40 60 80 100 120 140 Altitude (m) 40 20 0 20 40 dB (a) 5G band n5 (DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 620 630 640 650 Frequency (MHz) 20 40 60 80 100 120 140 Altitude (m) 40 20 0 20 40 dB (b) 5G band n71 (DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 8: Measured 5G DL power for urban environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' mentioned earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' The mean value of 5G band n5 shows higher value compared with n71 and n77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 7b, the variance of the measured power for 5G bands n5 and n77 intersect with each other around the altitude of 60 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' The variance of n77 band keeps increasing as the altitude increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 5G Bands - Downlink Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 8 illustrates the measured power for 5G n5 and n71 bands by considering the DL frequency range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' It can be seen that the measured power for 870 - 880 MHz and 885-894 MHz are higher than the rest of spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 9 shows the mean and variance of the measured power versus altitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it can be observed from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 9a, the mean value of the measured power for n5 and n71 are similar and significantly higher than n77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 40 60 80 100 120 140 Altitude (m) 40 20 0 20 Power (dB) 5G Band-n5 (AT&T, Verizon) 5G Band-n71 (T-Mobile) 5G Band-n77 (AT&T, Verizon, T-Mobile) (a) Mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 40 60 80 100 120 140 Altitude (m) 0 50 100 150 200 Power (dB) 5G Band-n5 (AT&T, Verizon) 5G Band-n71 (T-Mobile) 5G Band-n77 (AT&T, Verizon, T-Mobile) (b) Variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 9: Spectrum occupancy versus altitude in 5G bands n5 and n77 (DL) for urban environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' (a) 3550 3600 3650 Frequency (MHz) 20 40 60 80 100 120 140 Altitude (m) 40 20 0 20 40 dB (b) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 10: (a) CBRS spectrum and tiers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' and (b) Measured CBRS band n48 power for urban environment (TDD UL/DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 40 60 80 100 120 140 Altitude (m) 34 32 30 28 26 24 Power (dB) CBRS Band-n48 (3550-3600 MHz) CBRS Band-n48 (3600-3650 MHz) CBRS Band-n48 (3650-3700 MHz) (a) Mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 40 60 80 100 120 140 Altitude (m) 0 10 20 30 40 50 Power (dB) CBRS Band-n48 (3550-3600 MHz) CBRS Band-n48 (3600-3650 MHz) CBRS Band-n48 (3650-3700 MHz) (b) Variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 11: Spectrum occupancy versus altitude in CBRS band for urban environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' For the bands under consideration, the mean value increases as the altitude increases up to almost 80 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 9b, the variance of the measured power for n77 starts with a small value, while it climes up to near those of n5 values as the altitude increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' The variance of n71 band depicts a higher value for all the measured altitudes compared with those others 5G bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' CBRS Band Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 10a illustrates the CBRS spectrum which it lays out three tiers of users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 10b presents the measured power for CBRS n48 band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Similar to LTE 41 and 5G n77 bands, n48 also exploits TDD mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it can be seen, the spectrum is mainly occupied within the range of 3610-3690 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 11, we study the mean and variance of the measured power versus altitude whereas the CBRS band is divided into three equal portions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it can be observed, the mean and variance of the measured power for the first portion (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=', 3550-3600 MHz) are lower than the other parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' The mean value of the third portion (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=', 3650-3700 MHz) increases 700 705 710 715 Frequency (MHz) 50 100 150 Altitude (m) 40 20 0 20 40 dB (a) LTE band 12 (UL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 778 780 782 784 786 Frequency (MHz) 50 100 150 Altitude (m) 40 20 0 20 40 dB (b) LTE band 13 (UL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 788 790 792 794 796 798 Frequency (MHz) 50 100 150 Altitude (m) 40 20 0 20 40 dB (c) LTE band 14 (UL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 2500 2550 2600 2650 Frequency (MHz) 50 100 150 Altitude (m) 40 20 0 20 40 dB (d) LTE band 41 (TDD UL/DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 12: Measured LTE UL power for rural environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 50 100 150 Altitude (m) 30 20 10 0 Power (dB) LTE Band-12 (AT&T, T-Mobile) LTE Band-13 (Verizon) LTE Band 14 (AT&T, FirstNet) LTE Band 41 (T-Mobile) (a) Mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 50 100 150 Altitude (m) 0 100 200 300 Power (dB) LTE Band-12 (AT&T, T-Mobile) LTE Band-13 (Verizon) LTE Band 14 (AT&T, FirstNet) LTE Band 41 (T-Mobile) (b) Variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 13: Spectrum occupancy versus altitude in LTE bands 12, 13, 14 and 41 (UL) for rural environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' as the altitude increases up to 60 m and then it drops afterwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' However, the man value of the second part (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=', 3600-3650 MHz) keeps increasing as the altitude increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' RURAL SPECTRUM OCCUPANCY RESULTS In this section, we study the spectrum occupancy and its characteristic for the similar bands as previous section by considering the experimental results for the rural environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' LTE Bands - Uplink Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 12 illustrates the measured power for for LTE bands 13, 14, 15 and 41 considering the UL frequency spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it can be seen, LTE bands 12 and 41 show more crowded spectrum compared with LTE bands 13 and 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' The mean and variance of the measured power for various LTE bands are presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As opposed to the urban environment (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 3a), the mean value for LTE bands 13 and 14 are much higher than the other two bands under consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' LTE Bands - Downlink Considering the DL frequency range for different LTE bands, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 14 illustrates the measured power for the bands under consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Same as the urban results, the spectrum of DL frequency range are more crowded compared with the UL ones in the rural environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 15 shows the mean 3550 MHz 3600 MHz 3650 MHz 3700 MHz Tier 1 Incumbent Users (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' the Navy) Tier 2 Priority Access Licensees (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' private organizations) Tier 3 General Authorized Access (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' unlicensed users)730 735 740 745 Frequency (MHz) 50 100 150 Altitude (m) 40 20 0 20 40 dB (a) LTE band 12 (DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 746 748 750 752 754 756 Frequency (MHz) 50 100 150 Altitude (m) 40 20 0 20 40 dB (b) LTE band 13 (DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 758 760 762 764 766 768 Frequency (MHz) 50 100 150 Altitude (m) 40 20 0 20 40 dB (c) LTE band 14 (DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 2500 2550 2600 2650 Frequency (MHz) 50 100 150 Altitude (m) 40 20 0 20 40 dB (d) LTE band 41 (TDD UL/DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 14: Measured LTE DL power for rural environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 50 100 150 Altitude (m) 30 20 10 0 10 20 Power (dB) LTE Band-12 (AT&T, T-Mobile) LTE Band-13 (Verizon) LTE Band 14 (AT&T, FirstNet) LTE Band 41 (T-Mobile) (a) Mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 50 100 150 Altitude (m) 0 100 200 300 Power (dB) LTE Band-12 (AT&T, T-Mobile) LTE Band-13 (Verizon) LTE Band 14 (AT&T, FirstNet) LTE Band 41 (T-Mobile) (b) Variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 15: Spectrum occupancy versus altitude in LTE bands 12, 13, 14 and 41 (DL) for rural environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' and variance of the measured power versus altitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it can be observed from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 15a, the mean value of the measured power increases as the altitude increases up to 80 m and it remains almost constant for the higher altitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' The variance of LTE bands 13, 14, and 41 show similar behaviour, while the corresponded plot for LTE band 12 starts with increasing for the altitude up to 40 m and then it drops afterwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 5G Bands - Uplink Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 16 illustrates the measured power for 5G bands n5, n71 and n77 considering the UL frequency spectrum ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' This result reveals that the spectrum of n77 is less crowded than those of n5 and n71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' The performance of mean and variance of the measured power for 5G bands (uplink) are presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it can be observed from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 17a, while the mean value of the measured power for n77 is almost independent of the altitude, it increases for n5 and n71 bands as the altitude increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 17b, the variance of the measured power for n71 depicts higher value compared with the other 5G bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 5G Bands - Downlink Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 18 illustrates the measured power for 5G n5 and n71 bands by considering the DL frequency range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Similar to the urban case, it can be seen that the measured power for 870 825 830 835 840 845 Frequency (MHz) 50 100 150 Altitude (m) 40 20 0 20 40 dB (a) 5G band n5 (UL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 670 680 690 Frequency (MHz) 50 100 150 Altitude (m) 40 20 0 20 40 dB (b) 5G band n71 (UL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 3750 3800 3850 3900 3950 Frequency (MHz) 50 100 150 Altitude (m) 40 20 0 20 40 dB (c) 5G band n77 (TDD UL/DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 16: Measured 5G UL power for rural environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 50 100 150 Altitude (m) 30 25 20 15 10 Power (dB) 5G Band-n5 (AT&T, Verizon) 5G Band-n71 (T-Mobile) 5G Band-n77 (AT&T, Verizon, T-Mobile) (a) Mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 50 100 150 Altitude (m) 0 50 100 150 200 250 Power (dB) 5G Band-n5 (AT&T, Verizon) 5G Band-n71 (T-Mobile) 5G Band-n77 (AT&T, Verizon, T-Mobile) (b) Variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 17: Spectrum occupancy versus altitude in 5G n5 and n77 bands (UL) for rural environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 870 875 880 885 890 Frequency (MHz) 50 100 150 Altitude (m) 40 20 0 20 40 dB (a) 5G band n5 (DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 620 630 640 650 Frequency (MHz) 50 100 150 Altitude (m) 40 20 0 20 40 dB (b) 5G band n71 (DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 18: Measured 5G DL power for rural environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 880 MHz and 885-894 MHz are higher than the rest of spectrum in the rural environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 19 depicts the mean and variance of the measured power versus altitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it can be observed from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 19a, the mean value of the measured power for n77 band remains almost constant for different altitudes, while it increases as the altitude increases up to almost 80 m for n5 and n71 bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 19b, the variance of the measured power for 5G band n71 shows higher values compared with n5 and n77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' CBRS Band Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 20 present the measured power for CBRS n48 band for rural environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it can be seen, the spectrum is less 50 100 150 Altitude (m) 40 20 0 20 Power (dB) 5G Band-n5 (AT&T, Verizon) 5G Band-n71 (T-Mobile) 5G Band-n77 (AT&T, Verizon, T-Mobile) (a) Mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 50 100 150 Altitude (m) 0 100 200 300 400 Power (dB) 5G Band-n5 (AT&T, Verizon) 5G Band-n71 (T-Mobile) 5G Band-n77 (AT&T, Verizon, T-Mobile) (b) Variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 19: Spectrum occupancy versus altitude in 5G bands n5 and n77 (DL) for rural environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 3550 3600 3650 Frequency (MHz) 50 100 150 Altitude (m) 40 20 0 20 40 dB Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 20: Measured power during Helikite operation over rural environment for CBRS band n48 (TDD UL/DL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 50 100 150 Altitude (m) 30 25 20 15 10 Power (dB) CBRS Band-n48 (3550-3600 MHz) CBRS Band-n48 (3600-3650 MHz) CBRS Band-n48 (3650-3700 MHz) (a) Mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 50 100 150 Altitude (m) 0 1 2 3 4 Power (dB) CBRS Band-n48 (3550-3600 MHz) CBRS Band-n48 (3600-3650 MHz) CBRS Band-n48 (3650-3700 MHz) (b) Variance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 21: Spectrum occupancy versus altitude in CBRS band for rural environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' crowded compared with the rural environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 21, we study the mean and variance of the measured power versus altitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' As it can be observed, the mean value of the measured power for all three considered portions are almost similar and remain constant as the altitude increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In addition, the variance also shows slight fluctuations compared to the other bands under consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' TIME DOMAIN ANALYSIS OF SPECTRUM OCCUPENCY In this section, we focus on the spectrum occupancy of LTE and NR signals in time, while we describe the altitude dependency of the spectrum in the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' For around 8 hours of measurement duration by the Helikite in the urban environment, we observe signal strength changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' This section focuses exclusively on those urban environment measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 22 shows the spectrum monitoring results by the Helikite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' The x-axis is the monitored spectrum range and the y-axis is the measured time stamp, which is indicated by hours and minutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 22a, we capture the frequency range from 700 MHz to 800 MHz, which contains LTE FDD bands 12, 13, 14 (see Table I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' First of all, we can clearly observe a series of occupied 10 MHz bandwidth 12, 13, and, 14 DL bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' On the other hand, the signal strength of UL bands is lower than DL bands, and UL bands 13 and 14 are scarcely occupied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' We also observe that there are time periods when signal strength becomes low for the whole observed frequency range, which coincides with the periods where the altitude of the Helikite stays low in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' It implies that received signal strength is abruptly reduced by the blockage when the altitude of the Helikite is lower than a certain height.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In addition, this tendency is observed in other frequency bands as well in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 22b and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 22c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In Fig 22b, we capture the frequency range 2500 MHz - 2700 MHz, which contains LTE TDD 41 band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Since carrier frequency is higher than Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 22a, we observe that this LTE band covers wider bandwidth: 20 MHz, 40 MHz, and 100 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' It is also observed that the received signal strength is lower than the frequency range in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 22a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' This is due to the fact that as carrier frequency increases a received signal suffers higher path loss, which is also observed in a much higher carrier frequency range in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 22c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In particular, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 22c shows spectrum occupancy of NR TDD n77 band, 3700 MHz - 3800 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' We can observe 40 MHz and 60 MHz bandwidth signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 23 shows the received signal strength changes during the measurement time for the captured LTE and NR bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 23a, we observe the LTE FDD UL/DL 12 band shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 22a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Mean value of the received signal strength across the frequency band is represented by lines and half of the standard deviation (std) of signal strength is described by the shaded area around lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' It is observed that the signal strength of UL is lower than DL, while the variation of the signal strength of UL inside the band is higher than DL, which can be observed from higher std values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 23b and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 23b show the received signal strength changes of LTE TDD 41 and NR TDD 77 bands which can be shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 22b and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 22c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' It is observed that the signal strength fluctuation of NR TDD 77 band is higher than other bands such as LTE 12 and 41 bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' CONCLUSION Using the data measured by a Helikite flying over an urban and rural environments, in this paper we studied spectrum measurements in various sub-6 GHz 4G, 5G and CBRS bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Both UL and DL spectrum occupancy has been investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Our results revealed that generally the mean value of measured power tends to increase as the altitude increases due to higher probability of line-of-sight, at least for the considered max- imum altitude range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Further, the spectrum of DL frequency ranges showed to be more crowded compared with the uplink ones for both environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' It has been also seen that for the rural environment the mean value for LTE bands 13 and 14 are much higher than the other two bands under considera- tion, as opposed to the urban environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Furthermore, the performance of CBRS band for urban environment indicates more activity compared with the rural condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' (a) 700 MHz - 800 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' (b) 2500 MHz - 2700 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' (c) 3700 MHz - 3800 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 22: Spectrum monitoring during the measurement time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' We observe different LTE and NR bands’ occupancy and the received signal strength is strong when the Helikite floats at a high altitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 12:00 14:00 16:00 18:00 20:00 Time 30 25 20 15 10 5 0 5 10 15 20 Power (dBm) std/2 | LTE DL 12 mean | LTE DL 12 std/2 | LTE UL 12 mean | LTE UL 12 (a) LTE FDD 12 band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 12:00 14:00 16:00 18:00 20:00 Time 30 25 20 15 10 5 0 Power (dBm) std/2 | LTE TDD 41 mean | LTE TDD 41 (b) LTE TDD 41 band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 14:00 16:00 18:00 20:00 Time 35 30 25 20 15 10 Power (dBm) std/2 | NR TDD n77 maen | NR TDD n77 (c) NR TDD 77 band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 23: Received power of different LTE and NR bands during the measurement time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' The solid lines represent the mean value of signal power and shaded areas indicate half of the standard deviation (std) of signal strength, which shows the variation of signal strength inside the specific bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' REFERENCES [1] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Islam, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Koh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Oh, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Qing, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Lai, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='- C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Liang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Toh, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Chin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Tan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=', “Spectrum survey in Singapore: Occupancy measurements and analyses,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' IEEE Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Cognitive Radio Oriented Wireless Networks and Communications, 2008, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 1–7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' [2] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Adelantado, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Vilajosana, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Tuset-Peiro, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Martinez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Melia- Segui, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Watteyne, “Understanding the limits of LoRaWAN,” IEEE Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Mag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 55, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 34–40, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' [3] Ericsson, “Frequency reuse in limited spectrum networks,” Oct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 2022, accessed: 2023-01-04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Available: https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='ericsson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='com/en/reports-and-papers/microwave-outlook/ articles/maximizing-capacity-in-spectrum-limited-networks [4] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Roberson, “The 5G/aviation crisis that never should have happened,” https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='linkedin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='com/pulse/ 5g-aviation-crisis-never-should-have-happened-dennis-roberson/, 2022, accessed: 2023-01-04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' [5] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Bellamy, “US Airlines Begin Installing 5G C-Band Filter for Radio Altimeters on Airbus A320s,” Sep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 2022, accessed: 2023- 01-04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Available: https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='aviationtoday.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='com/2022/09/14/ us-airlines-begin-installing-5g-c-band-filter-radio-altimeters-airbus-a320s/ [6] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Dennehy, “Ligado scraps 5G network launch amid interference flap,” 2022, accessed: 2023-01-04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Available: https://locationbusinessnews.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='substack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='com/p/ ligado-scraps-5g-network-launch-amid [7] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Chen and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Oh, “A survey of measurement-based spectrum occupancy modeling for cognitive radios,” IEEE Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Surv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Tuts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 18, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 848–859, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' [8] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Al Homssi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Al-Hourani, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Krusevac, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Rowe, “Machine learning framework for sensing and modeling interference in IoT fre- quency bands,” IEEE Internet Things J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 8, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 4461–4471, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' [9] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Homssi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Dakic, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Wang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Alpcan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Allen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Kandeepan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Al-Hourani, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Saad, “Artificial intelligence techniques for next- generation mega satellite networks,” arXiv preprint arXiv:2207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='00414, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' [10] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Maeng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Park, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Guvenc, “Analysis of UAV radar and commu- nication network coexistence with different multiple access protocols,” arXiv preprint arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='16614, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' [11] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Azari, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Rosas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Chiumento, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Ligata, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Pollin, “Uplink performance analysis of a drone cell in a random field of ground interferers,” in Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' IEEE Wireless Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' and Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' (WCNC), 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' [12] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Marojevic, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Guvenc, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Dutta, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Sichitiu, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Floyd, “Advanced wireless for unmanned aerial systems: 5G standardization, research challenges, and AERPAW architecture,” IEEE Vehicular Tech- nology Magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 15, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 22–30, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' [13] AERPAW, “Helikite spectrum measurements (pack- apalooza),” Aug.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 2022, accessed: 2023-01-04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Available: https://sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='com/ncsu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='edu/ aerpaw-wiki/aerpaw-user-manual/4-sample-experiments-repository/ 4-4-data-repository/aerpaw-nrdz-research/ august-2022-helikite-spectrum-measurements-packapalooza [14] ——, “Helikite spectrum measurements,” May.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 2022, accessed: 2023-01-04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' [Online].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Available: https://sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='google.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='com/ncsu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='edu/aerpaw-wiki/aerpaw-user-manual/ 4-sample-experiments-repository/4-4-data-repository/ aerpaw-nrdz-research/may-2022-helikite-spectrum-measurements [15] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Maeng, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Ozdemir, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Nandakumar, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Guvenc, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Sichitiu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Dutta, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Mushi, “Spectrum Activity Monitoring and Analysis for Sub-6 GHz Bands Using a Helikite,” in Proc Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Netw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' (COMSNETS), Bengaluru, India, Jan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' [16] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Maeng, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' G¨uvenc¸, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Sichitiu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Floyd, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Dutta, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Zajkowski, ¨O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' ¨Ozdemir, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Mushi, “National radio dynamic zone concept with autonomous aerial and ground spectrum sensors,” in IEEE Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' Communications Workshops (ICC Workshops), 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 687–692.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content=' 18:00 17:00 Time 16:00 15:00 111 14:00 12 13 14 DL DL DL 13:00 12:00 710 720 730 740 750 760 770 780 790 Freq (MHz)20 10 0 dBr 10 20 30 4020:00 19:0040 3018:00 17:00 Time 16:00 15:00 14:00 LTETDD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} +page_content='41 13:00 12:00 2520 25402560258026002620 2640 2660 2680 Freg (MHz)20 10 0 dBr 10 20 30 4020:00 19:0040 3018:00 17:00 Time 16:00 15:00 14:00 NRTDD 0n77 13:00 12:00 3790 Freg (MHz)20 10 0 dBi 10 20 30 4020:00 19:0040 30' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE0T4oBgHgl3EQfdwA8/content/2301.02380v1.pdf'} diff --git a/2NE2T4oBgHgl3EQfjAcm/content/tmp_files/2301.03963v1.pdf.txt b/2NE2T4oBgHgl3EQfjAcm/content/tmp_files/2301.03963v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..76827ab4f1a55aa23f2b4b11796d2de8a12c8b96 --- /dev/null +++ b/2NE2T4oBgHgl3EQfjAcm/content/tmp_files/2301.03963v1.pdf.txt @@ -0,0 +1,787 @@ +Genetic optimization of Brillouin scattering gain in +subwavelength-structured silicon membrane +waveguides +Paula Nuño Ruano∗, Jianhao Zhang1, Daniele Melati, +David González-Andrade, Xavier Le Roux, Eric Cassan, +Delphine Marris-Morini, Laurent Vivien, Daniel Lanzillotti-Kimura, +Carlos Alonso-Ramos∗ +aCentre de Nanosciences et de Nanotechnologies, Université Paris-Saclay, CNRS, 10 +boulevard Thomas Gobert, 91120, Palaiseau, France +Abstract +On-chip Brillouin optomechanics has great potential for applications in com- +munications, sensing, and quantum technologies. Tight confinement of near- +infrared photons and gigahertz phonons in integrated waveguides remains a +key challenge to achieving strong on-chip Brillouin gain. Here, we propose +a new strategy to harness Brillouin gain in silicon waveguides, based on the +combination of genetic algorithm optimization and periodic subwavelength +structuration to engineer photonic and phononic modes simultaneously. The +proposed geometry is composed of a waveguide core and a lattice of anchoring +arms with a subwavelength period requiring a single etch step. The waveguide +geometry is optimized to maximize the Brillouin gain using a multi-physics +genetic algorithm. Our simulation results predict a remarkable Brillouin gain +exceeding 3300 W−1m−1, for a mechanical frequency near 15 GHz. +Keywords: +Brillouin scattering, subwavelength, genetic optimization +∗Corresponding author +Email addresses: paula.nuno-ruano@c2n.upsaclay.fr (Paula Nuño Ruano), +carlos.ramos@c2n.upsaclay.fr (Carlos Alonso-Ramos) +1Present address: National Research Council Canada, 1200 Montreal Road, Bldg. M50, +Ottawa, Ontario K1A 0R6, Canada +arXiv:2301.03963v1 [physics.optics] 10 Jan 2023 + +1. Introduction +Brillouin scattering (BS) refers to the nonlinear interaction between opti- +cal and mechanical fields inside a material. BS has been widely exploited in +optical fibers to implement a wide range of devices, including optical ampli- +fiers, ultra-narrow linewidth lasers, radio-frequency (RF) signal generators, +and distributed sensors [1]. +Brillouin scattering was for long thought to be mediated by electrostric- +tive forces only. Thus, its spectrum was considered to be governed by ma- +terial properties [2]. In 2006, microstructuration of optical fibers enabled +shaping the BS spectrum [3], opening a new path for geometric control of +this effect [4]. In 2012, a new theory [5] predicted that Brillouin interactions +could be greatly magnified by strong radiation pressure on the boundaries +of suspended silicon waveguides with nanometric-scale core sizes [6, 7]. The +simultaneous confinement of optical and mechanical modes is challenging in +silicon-on-insulator (SOI) waveguides due to a strong phonon leakage towards +the silica cladding [8–10]. However, this limitation can be circumvented by +isolating the silicon waveguide core by complete or partial removal of the silica +cladding [5, 11, 12]. Suspended or quasi-suspended structures such as silicon +membrane rib waveguides [13] and fully suspended silicon nanowires [12] have +demonstrated large Brillouin gain. These results generated a great scientific +interest for its potential for laser sources [14], microwave signal generation +[15] and processing [16], sensing applications [17, 18] and non-reciprocal op- +tical devices [19]. In particular, pedestal waveguides [20] yield an experi- +mental Brillouin gain of 3000 W−1m−1. However, the need for narrow-width +pedestals to optimize the Brillouin gain complicates the fabrication process +and may compromise the mechanical stability of the structures. On the other +hand, a lower experimental Brillouin gain (1000 W−1m−1) was obtained for +silicon membrane rib waveguides due to the very different confinement of +optical and mechanical modes [13]. Still, this comparatively modest Bril- +louin gain was compensated by achieving ultra-low optical propagation loss, +allowing the demonstration of lasing effect [14]. The use of photonic crystals +with simultaneous photonic and phononic bandgaps [21] (also referred to as +phoxonic crystals) has been proposed to maximize the Brillouin gain in silicon +membrane waveguides, achieving calculated values up to 8000 W−1m−1. Yet, +the narrow bandwidth and high optical propagation loss, typically linked to +bandgap confinement [22], may compromise the performance of these phox- +onic crystals. +2 + +Subwavelength grating silicon waveguides, with periods shorter than half +of the wavelength of the guided light, exploit index-contrast confinement to +yield low optical loss and wideband operation [23, 24]. Interestingly, near- +infrared photons and GHz phonons in nanoscale Si waveguides have compara- +ble wavelengths (near 1 µm) [10]. Thus, the same periodic structuration could +operate in the subwavelength regime for both, photons and phonons. In addi- +tion, forward Brillouin scattering (FBS), used to demonstrate Brillouin gain +in Si, relies on longitudinally propagating photons and transversally propa- +gating phonons [8–10]. Hence, engineering the longitudinal and transversal +subwavelength geometries would allow independent control of photonic and +phononic modes. Brillouin optimization in silicon membranes has been pro- +posed based on index-contrast confinement of photons (longitudinal subwave- +length grating) and bandgap confinement of phonons (transversal phononic +crystal) [25], achieving a calculated gain of 1750 W−1m−1. More recently, +the combination of subwavelength index-contrast and subwavelength soften- +ing has been proposed to optimize Brillouin gain in suspended Si waveguides, +achieving a calculated value of 3000 W−1m−1, for a minimum feature size of +50 nm [26]. Still, these two approaches require several etch steps of the silicon +core, complicating the device’s fabrication. In this work, we propose a novel +subwavelength-structured Si membrane, illustrated in Fig. 1, requiring only +one etch step of silicon. We develop an optimization method to design the +waveguide geometry, combining multi-physics optical and mechanical simu- +lations with a genetic algorithm (GA) capable of handling a large number of +parameters [27]. The optimized geometry yields a calculated Brillouin gain +of 3300 W−1m−1, with a minimum feature size of 50 nm, compatible with +electron-beam lithography. +2. Design and Results +The proposed optomechanical waveguide geometry, depicted in Fig. 1, +comprises a suspended central strip of width Wg = 400 nm that is anchored +to the lateral silicon slabs by a lattice of arms with a longitudinal period +(z-direction) of Λ = 300 nm. This period is shorter than half of the optical +wavelength, ensuring optical operation in the subwavelength regime. The +anchoring arms are symmetric with respect to the waveguide center. We +split the arms into five different sections with widths and lengths of Wi (x- +direction) and Li (z-direction), respectively. The index i = 1 refers to the +section adjacent to the waveguide core, while the index i = 5 refers to the +3 + +outermost section (see Fig. 1, inset). The fifth section has a fixed width +of W5 = 500 nm and length of L5 = 50 nm to ensure proper guidance and +localization of the optical mode. The widths and lengths of sections 1 to 4 +are optimized using the genetic algorithm. The whole waveguide has a fixed +silicon thickness of t = 220 nm, allowing fabrication in a single-etch step. +Figure 1: Proposed optomechanical waveguide. In the inset, the different sections of the +anchoring arms are numbered from 1 to 5. The width of the waveguide core (Wg = 400 +nm), the period (Λ = 300 nm), and the dimensions of the outermost section (L5 = 50 nm, +W5 = 500 nm) remain fixed throughout the optimization process. The thickness of the +silicon slab is t = 220 nm. +We focus on FBS, where only near-cut-off acoustic modes are involved. +In the absence of optical absorption, which is the case of silicon at near- +infrared wavelengths, the optical and mechanical mode equations describing +FBS decouple and can be solved separately [10]. +We use here COMSOL +Multiphysics software for the optomechanical simulations. For the calculation +of optical and mechanical modes in the optimization process, we reduce the +3D structure to an equivalent 2D geometry. The effective index method [28] +is considered for the computation of the transverse-electric (TE) polarized +4 + +Wg +Wi +Anchoring arms: sections +2 +3 +4 +5optical modes while the in-plane mechanical modes are calculated assuming +the plane stress approximation [29]. We compute the Brillouin gain, GB, as +[9] +GB(Ωm) = Qm +2ωp +meff Ω2 +m +���� +� +fMB dℓ + +� +fPE dA +���� +2 +, +(1) +where ωp is the frequency of the optical pump, Ωm is the mechanical fre- +quency, Qm is the mechanical quality factor, meff = +� +ρ |um|2/ max |um|2 dA +is the effective linear mass density of the mechanical mode with displacement +profile um, and fMB and fPE are the linear and surface overlap of optical force +density and deformation representing the moving boundaries effect (MB) and +the photoelastic effect (PE), respectively, +fMB = u∗ +m · n +� +δεMB E∗ +p,t · Es,t − δε−1 +MB D∗ +p,n · Ds,n +� +max |um| Pp Ps +and +fPE = E∗ +p · δε∗ +PE · Es +max |um| Pp Ps +, +(2) +where the permittivity differences due to the moving boundaries effects are +given by δεMB = ε1 − ε2 and δε−1 +MB = 1/ε1 − 1/ε2, with εi = ε0n2 +i being +the permittivities of the silicon (i = 1) and air (i = 2). The photoelastic +tensor perturbation in the material permittivity is δεPE = −ε0 n4 p : S, with +n being the material refractive index, p the photoelastic tensor, and S the +mechanical stress tensor induced by the mechanical mode. The term um · n +is the normal component of the mechanical displacement and Ej,t and Dj,n +are the tangential electric field and normal dielectric displacement for the +pump (j = p) and the scattered field (j = s). The denominator represents +the power normalization given by Pj = [2ℜ( +� +[Ej × H∗ +j] · z dA)]1/2. +The symmetry directions [100], [010], and [001] of the crystalline silicon +are set to coincide with the x, y, and z simulation axis, respectively. With this +orientation, the photoelastic tensor [6, 30] is [p11, p12, p44] = [−0.094, 0.017, −0.051]. +The refractive index of silicon is n = 3.45 and its density ρ = 2329 kg m−3 +while the corresponding values for the air are n = 1 and ρ = 1.293 kg m−3. +The quality factor of the mechanical mode, Qm, is related to the full width +at half maximum (FWHM) of the gain spectrum, γm, through Qm = Ωm/γm +and it is limited by different loss mechanisms, +1 +Qm += +1 +QTE ++ 1 +QL ++ +1 +Qair +. +(3) +5 + +Here, we consider the thermoelastic loss (QTE), the mechanical leakage to- +wards the silica under-cladding (QL), and the viscous loss from surround- +ing air (Qair). The thermoelastic loss yields mechanical quality factors of +QTE ∼ 6 · 105 [31] for silicon nanostructures while the leakage loss is mainly +governed by the geometries of the waveguide and the arms anchoring it to +the lateral silicon slab. +These two effects are directly considered in the +mechanical-mode simulations performed in COMSOL Multiphysics. The vis- +cous loss induced by the surrounding air is considered here by imposing a +limiting value to the mechanical quality factor of Qm = 4 · 103, which is the +highest expected value at atmospheric pressure and room temperature for +phonon frequency in the order of GHz [32]. +Based on the resulting optomechanical coupling calculations, a genetic +algorithm [33] is used to maximize the FBS gain. Starting with randomly +generated combinations of parameters Wi and Li (individuals), optomechan- +ical simulations are carried out and the individuals are ranked according to +their Brillouin gain. Recombination is used to produce a successor set of +individuals, the next generation. The best-performing individuals directly +become part of the next generation (elitism). A large number of individuals +of the new generation is obtained by combining the parameter of pairs of +individuals from the current generation (crossover). Finally, the remaining +individuals of the new generation are produced by randomly modifying the +parameters of single individuals of the current generation (mutation). This +process continues until the convergence criterion has been reached. +In our particular optimization problem, an individual is a possible geome- +try, represented by a set of 8 parameters (width and length of each of the arm +sections). Each generation is composed of 50 individuals and the successive +generations are obtained applying a rate of elitism and crossover of 6% and +80%, respectively, with the remaining elements obtained through mutation. +The convergence criterion was defined in terms of the difference between the +best and the average performance, GB − ⟨GB⟩ < 10 W−1m−1, over 10 gener- +ations. For this work, we have used a standard computer with the following +specifications: a 64-bit operating system with an x64-based processor Intel® +Core™ i7-4790 (4 total cores, 8 total threads, base-frequency of 3.60 GHz), +and an installed RAM of 8.00 GB. Under these conditions, the optimiza- +tion process was completed in 12h 35 min, comprising 1500 optomechanical +simulations of 30 seconds each. +The method we propose here relies on a defined geometry whose pa- +rameters are allowed to vary within a specific range of values. Hence, the +6 + +optimized structure will depend strongly on our initial guess. +In Fig. 2, we present the optimization process. Figures 2a and 2b show +the Brillouin gain and mechanical frequency, respectively, as a function of +the generation number. As a result of the evolution of the geometry, we +observe an increase in the gain and a variation in the mechanical frequency. +This result should be expected as the Brillouin shift in FBS is particularly +sensitive to the waveguide dimensions. The optimum performance is achieved +after 10 generations while 30 generations are required for convergence. The +optimized geometry, whose dimensions are listed in Table 1, is characterized +by a Brillouin gain of GB = 3350 W−1m−1 for a mechanical mode with +frequency of Ωm = 14.357 GHz and mechanical quality factor of Qm ≈ 3.2 · +103. The optical mode has a mode effective index of 2.36 and wavelength in +vacuum of λ = 1556.5 nm (ωp = 2π · 192.6 THz in (1)). +Figure 2: Optimization process. a) Best (in blue) and average (in orange) Brillouin gain +as a function of the number of generations during genetic optimization. +b) Evolution +of the mechanical frequency as a function of the number of generations. +During the +optimization process, all possible mechanical losses are considered, including thermoelastic +loss, mechanical leakage, and viscous loss due to air (operation in air ambient at room +temperature). +In terms of geometry, the first and fourth sections, with considerably +larger widths, generate reflections that help localize the mechanical mode +in the waveguide core. The frequency of the mechanical mode is governed +by the interplay between the waveguide width and the length of the partial +cavity formed by the fourth section on each side. +Full 3D simulations are realized to verify the performance of the optimized +geometry. This structure provides a Brillouin gain of GB = 3310 W−1m−1 for +a mechanical mode with a frequency of Ωm = 14.579 GHz. The optical mode +7 + +a) +b) +4000 +16.0 +[GHz] +Brillouin Gain [(Wm)-1] +3000 +Frequency +15.5 +2000 +15.0 +Mechanical +1000 +14.5 +Best +Average +0 +14.0 +0 +5 +10 +15 +20 +25 +30 +35 +0 +5 +10 +15 +20 +25 +30 +35 +Number of + generation +Number of + generationTable 1: Dimensions for the GA-optimized geometry when operating in air ambient at +room temperature. In the table above, Si stands for section i in Fig. 1. +S1 +S2 +S3 +S4 +Width +170 nm +320 nm +330 nm +100 nm +Length +130 nm +60 nm +60 nm +190 nm +has a mode effective index of 2.23 and wavelength in vacuum of λ = 1557.2 +nm (ωp = 2π · 192.52 THz in (1)). +Figure 3 shows the calculated field +distribution for the mechanical and optical modes in the optimized geometry. +Figure 3: Optical and mechanical modes of the optimized geometry operating in air ambi- +ent and room temperature (table 1): a) Approximated 2D structure. The upper structure +corresponds to the normalized mechanical displacement at 14.357 GHz and the lower fig- +ure to the x-component of the electric field at 1556.5 nm (mode effective index 2.36). b) +Full 3D device. On the bottom left, x-component of the electric field at 1557.2 nm (mode +effective index 2.23), and on the top right, normalized mechanical displacement at 14.579 +GHz. +These results show a good agreement between the approximated 2D ge- +ometry used for the optimization and the full 3D structure. The small dis- +crepancies in the optical mode index and mechanical frequency are due to +the influence of the thickness. +Finally, we study the fabrication tolerance of the proposed structure us- +ing again 3D simulations. We consider under- and over-etching errors that +we model by a variation of all the waveguide lengths and widths by a factor +∆, measured in nm (Fig. 4a). Figure 4c shows the variation of the Bril- +louin gain (in blue) and mechanical frequency (in orange) as a function of ∆. +8 + +b) +a) +[ul / max|ul +u/max|u +E.The Brillouin gain remains above 2000 W−1m−1 for geometry variations of +±10 nm. It should be noted that for the over-etch case (∆ < 0 in Fig. 4c), +the Brillouin gain is larger than the optimized case due to the larger optome- +chanical coupling resulting from a better overlap of the mechanical mode +with the optical field. However, these smaller structures are incompatible +with the target minimum feature size of 50 nm that was chosen to guarantee +fabrication reliability. The mechanical frequency varies less than 2% (Fig.4c, +in orange) and the mechanical profile is not modified significantly. +We also study the effect of stitching errors, modeled by a deviation ζ (in +nm) of the arm axis at both sides of the waveguide core, hence breaking the +symmetry of the structure (Fig. 4b). Figure 4d shows the variation of the +Brillouin gain (in blue) and mechanical frequency (in orange) as a function of +ζ. A non-perfectly symmetric structure is slightly detrimental to the Brillouin +gain but does not affect the mechanical frequency or profile. Interestingly, +both parameters (Brillouin gain and mechanical frequency) remain constant +over a large range of stitching errors. +Lastly, we examine the effect of random fabrication errors affecting each +section independently (Table 2). We consider deviations of 5 to 20 nm, both +in positive (enlargement) or negative (shrinking) directions. Our geometry +exhibits a robust performance despite these errors with Brillouin gains above +2000 W−1m−1 (Fig. 4e, blue) and mechanical frequencies between 14 and 15 +GHz (Fig. 4e, orange). It should be noted that the period remains constant, +Λ = 300 nm since it is controlled with high precision (±2 nm) in terms of +fabrication. +3. Conclusions +In summary, we have proposed a new approach to optimizing Brillouin +gain in silicon membrane waveguides. We exploit genetic optimization to +maximize Brillouin gain in subwavelength-structured Si waveguides, requir- +ing only one etch step. +Genetic algorithm is a well-known optimization +technique capable of handling design spaces of moderate dimension [33]. +It has the main advantage over gradient-based algorithms in its capabil- +ity to search the design space in many directions simultaneously. On the +other hand, the genetic algorithms cannot guarantee a global optimum so- +lution, being the final result strongly dependent on the initial population. +Based on this strategy, a calculated Brillouin gain up to 3310 W−1m−1 is +achieved for air environment. This result compares favorably to previously +9 + +Figure 4: Fabrication tolerance of the optimized geometry. a) and b) Variation of the +geometry due to fabrication errors. The solid black line corresponds to optimized geometry, +dotted (solid) blue depicts a positive deviation from the nominal design, and dotted orange +refers to a negative deviation from the expected design. c) and d) Evolution of the Brillouin +gain (in blue, left axis) and the mechanical frequency (in orange, right axis) for different +values of under- and over-etching (c), different values of stitching errors (d), and different +structures with randomized geometrical parameters (e). In e), N stands for the nominal +design obtained after the optimization problem and i for the different geometries listed in +Table 2. +10 + +a) +b) +Wg/2 +Si Slab +Si Slab +W. +Si Slab +c) +d) +6000 +15.0 +3500 +15.0 +[(Wm)- +(Wm) +14.8 +ZH +14.8 +3250 +GH +4000 +Brillouin Gain +'requency +requency +3000 +14.4 +14.4 +2000 +2750 +14.2 +14.0 +2500 +14.0 +-10 +-5 +0 +5 +10 +0 +5 +10 +15 +20 +25 +30 +35 +Fabrication error, △ [nm +Stiching error, S[nm] +e) +6000 +16 +4000 +15 +[2H)] +Brillouin Gain +2000 +14 +13 +N +1 +2 +3 +4 +5 +6 +7 +8 +9 +GeometryTable 2: Dimensions for the different geometries used for studying the effect of random- +ization of the design parameters. In the table, Si stands for section i in Fig. 1, N stands +for the nominal design as obtained from the optimization (Table 1), and i stands for the +different geometries in Fig. 4e. In all cases, the period, Λ = 300 nm, remains constant. +Geometry +S1 +S2 +S3 +S4 +S5 +Wg +N +Width +170 nm +320 nm +330 nm +100 nm +500 nm +400 nm +Length +130 nm +60 nm +60 nm +190 nm +50 nm +1 +Width +165 nm +305 nm +345 nm +90 nm +510 nm +405 nm +Length +130 nm +45 nm +65 nm +180 nm +60 nm +2 +Width +165 nm +320 nm +340 nm +115 nm +495 nm +400 nm +Length +110 nm +45 nm +55 nm +170 nm +35 nm +3 +Width +155 nm +340 nm +340 nm +100 nm +485 nm +405 nm +Length +150 nm +40 nm +70 nm +200 nm +55 nm +4 +Width +185 nm +300 nm +325 nm +95 nm +480 nm +385 nm +Length +140 nm +65 nm +75 nm +185 nm +60 nm +5 +Width +160 nm +320 nm +330 nm +95 nm +510 nm +390 nm +Length +140 nm +65 nm +55 nm +210 nm +60 nm +6 +Width +185 nm +340 nm +315 nm +120 nm +520 nm +420 nm +Length +135 nm +40 nm +50 nm +190 nm +35 nm +7 +Width +185 nm +340 nm +340 nm +110 nm +480 nm +410 nm +Length +140 nm +55 nm +65 nm +175 nm +40 nm +8 +Width +150 nm +300 nm +345 nm +110 nm +510 nm +395 nm +Length +120 nm +80 nm +40 nm +175 nm +65 nm +9 +Width +170 nm +340 nm +325 nm +105 nm +520 nm +410 nm +Length +120 nm +70 nm +50 nm +190 nm +70 nm +11 + +reported subwavelength-based Brillouin waveguides requiring several etch- +ing steps [25, 26], with calculated Brillouin gain of 1750 W−1m−1 and 3000 +W−1m−1. Our results show the potential of optimization for obtaining novel +designs with improved performance in the context of Brillouin scattering. +Moreover, they show the reliability of computationally efficient optimizations +based on approximated 2D simulations. +Declaration of Competing Interest +The authors declare that they have no known competing financial inter- +ests or personal relationships that could have appeared to influence the work +reported in this paper. +Author Statement +Paula Nuño Ruano, Jianhao Zhang, and Carlos Alonso Ramos proposed +the concept. Paula Nuño Ruano, Jianhao Zhang, and Daniele Melati devel- +oped the simulation framework. Paula Nuño Ruano, Jianhao Zhang, Daniele +Melati, David González Andrade, and Carlos Alonso Ramos optimized and +analyzed the results. All authors contributed to the manuscript. +Data Availability Statement +The data supporting this study’s findings are available from the corre- +sponding author upon reasonable request. +Acknowledgements +The authors want to thank the Agence Nationale de la Recherche for sup- +porting this work through BRIGHT ANR-18-CE24-0023-01 and MIRSPEC +ANR-17-CE09-0041. P.N.R. acknowledges the support of Erasmus Mundus +Grant: Erasmus+ Erasmus Mundus Europhotonics Master program (599098- +EPP-1-2018-1-FR-EPPKA1-JMD-MOB) of the European Union. This project +has received funding from the European Union’s Horizon Europe research and +innovation program under the Marie Sklodowska-Curie grant agreement Nº +101062518. +12 + +References +[1] E. Garmire, Perspectives on stimulated brillouin scattering, New Journal +of Physics 19 (1) (2017) 011003. doi:10.1088/1367-2630/aa5447. +[2] G. S. Wiederhecker, L. Chen, A. Gondarenko, M. Lipson, Controlling +photonic structures using optical forces, Nature 462 (7273) (2009) 633– +636. doi:10.1038/nature08584. +[3] P. Dainese, P. S. J. Russell, N. Joly, J. Knight, G. Wiederhecker, H. L. +Fragnito, V. Laude, A. Khelif, Stimulated brillouin scattering from +multi-ghz-guided acoustic phonons in nanostructured photonic crystal +fibres, Nature Physics 2 (6) (2006) 388–392. doi:10.1038/nphys315. +[4] J.-C. Beugnot, T. Sylvestre, H. Maillotte, G. Mélin, V. Laude, Guided +acoustic wave brillouin scattering in photonic crystal fibers, Optics let- +ters 32 (1) (2007) 17–19. doi:10.1364/ol.32.000017. +[5] Peter T. Rakich, Charles Reinke, Ryan Camacho, Paul Davids, Zheng +Wang, Giant enhancement of stimulated brillouin scattering in the +subwavelength limit, Physical Review X 2 (1) (2012) 011008. +doi: +10.1103/PhysRevX.2.011008. +[6] W. Qiu, P. T. Rakich, H. Shin, H. Dong, M. Soljačić, Z. Wang, Stim- +ulated brillouin scattering in nanoscale silicon step-index waveguides: +a general framework of selection rules and calculating sbs gain, Optics +Express 21 (25) (2013) 31402–31419. doi:10.1364/OE.21.031402. +[7] C. Wolff, M. J. Steel, B. J. Eggleton, C. G. Poulton, Stimulated brillouin +scattering in integrated photonic waveguides: Forces, scattering mech- +anisms, and coupled-mode analysis, Physical Review A 92 (1) (2015) +013836. doi:10.1103/PhysRevA.92.013836. +[8] B. J. Eggleton, C. G. Poulton, P. T. Rakich, M. J. Steel, G. Bahl, +Brillouin integrated photonics, Nature Photonics 13 (10) (2019) 664– +677. doi:10.1038/s41566-019-0498-z. +[9] G. S. Wiederhecker, P. Dainese, T. P. Mayer Alegre, Brillouin optome- +chanics in nanophotonic structures, APL Photonics 4 (7) (2019) 071101. +doi:10.1063/1.5088169. +13 + +[10] A. H. Safavi-Naeini, D. V. Thourhout, R. Baets, R. V. Laer, Control- +ling phonons and photons at the wavelength scale: integrated photon- +ics meets integrated phononics, Optica 6 (2) (2019) 213–232. +doi: +10.1364/OPTICA.6.000213. +[11] H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, +Z. Wang, P. T. Rakich, Tailorable stimulated Brillouin scattering in +nanoscale silicon waveguides, Nature Communications 4 (1) (2013) 1944. +doi:10.1038/ncomms2943. +[12] R. V. Laer, A. Bazin, B. Kuyken, R. Baets, D. V. Thourhout, Net +on-chip brillouin gain based on suspended silicon nanowires, New Jour- +nal of Physics 17 (11) (2015) 115005. doi:10.1088/1367-2630/17/11/ +115005. +[13] E. A. Kittlaus, H. Shin, P. T. Rakich, Large brillouin amplification in sil- +icon, Nature Photonics 10 (7) (2016) 463–467. doi:10.1038/nphoton. +2016.112. +[14] N. T. Otterstrom, R. O. Behunin, E. A. Kittlaus, Z. Wang, P. T. Rakich, +A silicon brillouin laser, Science 360 (6393) (2018) 1113–1116. +doi: +10.1126/science.aar6113. +[15] J. Li, H. Lee, K. J. Vahala, Microwave synthesizer using an on-chip +brillouin oscillator, Nature Communications 4 (1) (2013) 2097. doi: +10.1038/ncomms3097. +[16] Y. Liu, A. Choudhary, D. Marpaung, B. J. Eggleton, Chip-based bril- +louin Processing for phase control of rf signals, IEEE Journal of Quan- +tum Electronics 54 (3) (2018) 1–13. doi:10.1109/JQE.2018.2823323. +[17] D. M. Chow, Z. Yang, M. A. Soto, L. Thévenaz, Distributed forward +brillouin sensor based on local light phase recovery, Nature Communi- +cations 9 (1) (2018) 2990. doi:10.1038/s41467-018-05410-2. +[18] Y.-H. Lai, M.-G. Suh, Y.-K. Lu, B. Shen, Q.-F. Yang, H. Wang, J. Li, +S. H. Lee, K. Y. Yang, K. Vahala, Earth rotation measured by a chip- +scale ring laser gyroscope, Nature Photonics 14 (2020) 345–349. doi: +10.1038/s41566-020-0588-y. +14 + +[19] E. A. Kittlaus, N. T. Otterstrom, P. Kharel, S. Gertler, P. T. Ra- +kich, Non-reciprocal interband brillouin modulation, Nature Photonics +12 (10) (2018) 613–619. doi:10.1038/s41566-018-0254-9. +[20] R. Van Laer, B. Kuyken, D. Van Thourhout, R. Baets, Interaction +between light and highly confined hypersound in a silicon photonic +nanowire, Nature Photonics 9 (3) (2015) 199–203. +doi:10.1038/ +nphoton.2015.11. +[21] R. Zhang, J. Sun, Design of silicon phoxonic crystal waveguides for +slow light enhanced forward stimulated brillouin scattering, Journal of +Lightwave Technology 35 (14) (2017) 2917–2925. doi:10.1109/JLT. +2017.2704615. +[22] T. Baba, Slow light in photonic crystals, Nature Photonics 2 (8) (2008) +465–473. doi:10.1038/nphoton.2008.146. +[23] R. Halir, P. J. Bock, P. Cheben, A. Ortega-Moñux, C. Alonso- +Ramos, J. H. Schmid, J. Lapointe, D.-X. Xu, J. G. Wangüemert-Pérez, +Í. Molina-Fernández, S. Janz, Waveguide sub-wavelength structures: a +review of principles and applications, Laser & Photonics Reviews 9 (1) +(2015) 25–49. doi:https://doi.org/10.1002/lpor.201400083. +[24] P. Cheben, R. Halir, J. H. Schmid, H. A. Atwater, D. R. Smith, Sub- +wavelength integrated photonics, Nature 560 (7720) (2018) 565–572. +doi:10.1038/s41586-018-0421-7. +[25] M. K. Schmidt, C. G. Poulton, G. Z. Mashanovich, G. T. Reed, B. J. +Eggleton, M. Steel, Suspended mid-infrared waveguides for stimulated +brillouin scattering, Optics express 27 (4) (2019) 4976–4989. doi:10. +1364/OE.27.004976. +[26] J. Zhang, O. Ortiz, X. L. Roux, E. Cassan, L. Vivien, D. Marris- +Morini, N. D. Lanzillotti-Kimura, C. Alonso-Ramos, C. Alonso-Ramos, +Subwavelength engineering for brillouin gain optimization in silicon +optomechanical waveguides, Optics Letters 45 (13) (2020) 3717–3720. +doi:10.1364/OL.397081. +[27] J. Håkansson, D. Van Thourhout, Generating novel waveguides for stim- +ulated brillouin scattering with genetic algorithms, APL Photonics 4 (1) +(2019) 010803. doi:10.1063/1.5063783. +15 + +[28] C. L. Chen, Foundations for Guided-Wave Optics, John Wiley & Sons, +Inc, 2005. +[29] B. Auld, Acoustic Fields And Waves In Solids, Vol. I & II, John Wiley +& Sons, 1973. +[30] P. T. Rakich, P. Davids, Z. Wang, Tailoring optical forces in waveguides +through radiation pressure and electrostrictive forces, Optics Express +18 (14) (2010) 14439–14453. doi:10.1364/OE.18.014439. +[31] COMSOL multiphysics® reference manual v.5.4 (2018). +[32] S. Ghaffari, S. A. Chandorkar, S. Wang, E. J. Ng, C. H. Ahn, V. Hong, +Y. Yang, T. W. Kenny, Quantum limit of quality Factor in silicon micro +and nano mechanical resonators, Scientific Reports 3 (1) (2013) 3244. +doi:10.1038/srep03244. +[33] X.-S. Yang, Chapter 5 - genetic algorithms, in: +X.-S. Yang (Ed.), +Nature-Inspired Optimization Algorithms, Elsevier, 2014, pp. 77–87. +doi:10.1016/B978-0-12-416743-8.00005-1. +16 + diff --git a/2NE2T4oBgHgl3EQfjAcm/content/tmp_files/load_file.txt b/2NE2T4oBgHgl3EQfjAcm/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..cdbd691ba23e867570f5a5fd9626cafce2c006cc --- /dev/null +++ b/2NE2T4oBgHgl3EQfjAcm/content/tmp_files/load_file.txt @@ -0,0 +1,730 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf,len=729 +page_content='Genetic optimization of Brillouin scattering gain in subwavelength-structured silicon membrane waveguides Paula Nuño Ruano∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Jianhao Zhang1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Daniele Melati,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' David González-Andrade,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Xavier Le Roux,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Eric Cassan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Delphine Marris-Morini,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Laurent Vivien,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Daniel Lanzillotti-Kimura,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Carlos Alonso-Ramos∗ aCentre de Nanosciences et de Nanotechnologies,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Université Paris-Saclay,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' CNRS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 10 boulevard Thomas Gobert,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 91120,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Palaiseau,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' France Abstract On-chip Brillouin optomechanics has great potential for applications in com- munications,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' sensing,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' and quantum technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Tight confinement of near- infrared photons and gigahertz phonons in integrated waveguides remains a key challenge to achieving strong on-chip Brillouin gain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Here, we propose a new strategy to harness Brillouin gain in silicon waveguides, based on the combination of genetic algorithm optimization and periodic subwavelength structuration to engineer photonic and phononic modes simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The proposed geometry is composed of a waveguide core and a lattice of anchoring arms with a subwavelength period requiring a single etch step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The waveguide geometry is optimized to maximize the Brillouin gain using a multi-physics genetic algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Our simulation results predict a remarkable Brillouin gain exceeding 3300 W−1m−1, for a mechanical frequency near 15 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Keywords: Brillouin scattering, subwavelength, genetic optimization ∗Corresponding author Email addresses: paula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='nuno-ruano@c2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='upsaclay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='fr (Paula Nuño Ruano), carlos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='ramos@c2n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='upsaclay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='fr (Carlos Alonso-Ramos) 1Present address: National Research Council Canada, 1200 Montreal Road, Bldg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' M50, Ottawa, Ontario K1A 0R6, Canada arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='03963v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='optics] 10 Jan 2023 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Introduction Brillouin scattering (BS) refers to the nonlinear interaction between opti- cal and mechanical fields inside a material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' BS has been widely exploited in optical fibers to implement a wide range of devices, including optical ampli- fiers, ultra-narrow linewidth lasers, radio-frequency (RF) signal generators, and distributed sensors [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Brillouin scattering was for long thought to be mediated by electrostric- tive forces only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Thus, its spectrum was considered to be governed by ma- terial properties [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' In 2006, microstructuration of optical fibers enabled shaping the BS spectrum [3], opening a new path for geometric control of this effect [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' In 2012, a new theory [5] predicted that Brillouin interactions could be greatly magnified by strong radiation pressure on the boundaries of suspended silicon waveguides with nanometric-scale core sizes [6, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The simultaneous confinement of optical and mechanical modes is challenging in silicon-on-insulator (SOI) waveguides due to a strong phonon leakage towards the silica cladding [8–10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' However, this limitation can be circumvented by isolating the silicon waveguide core by complete or partial removal of the silica cladding [5, 11, 12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Suspended or quasi-suspended structures such as silicon membrane rib waveguides [13] and fully suspended silicon nanowires [12] have demonstrated large Brillouin gain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' These results generated a great scientific interest for its potential for laser sources [14], microwave signal generation [15] and processing [16], sensing applications [17, 18] and non-reciprocal op- tical devices [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' In particular, pedestal waveguides [20] yield an experi- mental Brillouin gain of 3000 W−1m−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' However, the need for narrow-width pedestals to optimize the Brillouin gain complicates the fabrication process and may compromise the mechanical stability of the structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' On the other hand, a lower experimental Brillouin gain (1000 W−1m−1) was obtained for silicon membrane rib waveguides due to the very different confinement of optical and mechanical modes [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Still, this comparatively modest Bril- louin gain was compensated by achieving ultra-low optical propagation loss, allowing the demonstration of lasing effect [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The use of photonic crystals with simultaneous photonic and phononic bandgaps [21] (also referred to as phoxonic crystals) has been proposed to maximize the Brillouin gain in silicon membrane waveguides, achieving calculated values up to 8000 W−1m−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Yet, the narrow bandwidth and high optical propagation loss, typically linked to bandgap confinement [22], may compromise the performance of these phox- onic crystals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 2 Subwavelength grating silicon waveguides, with periods shorter than half of the wavelength of the guided light, exploit index-contrast confinement to yield low optical loss and wideband operation [23, 24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Interestingly, near- infrared photons and GHz phonons in nanoscale Si waveguides have compara- ble wavelengths (near 1 µm) [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Thus, the same periodic structuration could operate in the subwavelength regime for both, photons and phonons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' In addi- tion, forward Brillouin scattering (FBS), used to demonstrate Brillouin gain in Si, relies on longitudinally propagating photons and transversally propa- gating phonons [8–10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Hence, engineering the longitudinal and transversal subwavelength geometries would allow independent control of photonic and phononic modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Brillouin optimization in silicon membranes has been pro- posed based on index-contrast confinement of photons (longitudinal subwave- length grating) and bandgap confinement of phonons (transversal phononic crystal) [25], achieving a calculated gain of 1750 W−1m−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' More recently, the combination of subwavelength index-contrast and subwavelength soften- ing has been proposed to optimize Brillouin gain in suspended Si waveguides, achieving a calculated value of 3000 W−1m−1, for a minimum feature size of 50 nm [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Still, these two approaches require several etch steps of the silicon core, complicating the device’s fabrication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' In this work, we propose a novel subwavelength-structured Si membrane, illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 1, requiring only one etch step of silicon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' We develop an optimization method to design the waveguide geometry, combining multi-physics optical and mechanical simu- lations with a genetic algorithm (GA) capable of handling a large number of parameters [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The optimized geometry yields a calculated Brillouin gain of 3300 W−1m−1, with a minimum feature size of 50 nm, compatible with electron-beam lithography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Design and Results The proposed optomechanical waveguide geometry, depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 1, comprises a suspended central strip of width Wg = 400 nm that is anchored to the lateral silicon slabs by a lattice of arms with a longitudinal period (z-direction) of Λ = 300 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' This period is shorter than half of the optical wavelength, ensuring optical operation in the subwavelength regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The anchoring arms are symmetric with respect to the waveguide center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' We split the arms into five different sections with widths and lengths of Wi (x- direction) and Li (z-direction), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The index i = 1 refers to the section adjacent to the waveguide core, while the index i = 5 refers to the 3 outermost section (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 1, inset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The fifth section has a fixed width of W5 = 500 nm and length of L5 = 50 nm to ensure proper guidance and localization of the optical mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The widths and lengths of sections 1 to 4 are optimized using the genetic algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The whole waveguide has a fixed silicon thickness of t = 220 nm, allowing fabrication in a single-etch step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Figure 1: Proposed optomechanical waveguide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' In the inset, the different sections of the anchoring arms are numbered from 1 to 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The width of the waveguide core (Wg = 400 nm), the period (Λ = 300 nm), and the dimensions of the outermost section (L5 = 50 nm, W5 = 500 nm) remain fixed throughout the optimization process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The thickness of the silicon slab is t = 220 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' We focus on FBS, where only near-cut-off acoustic modes are involved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' In the absence of optical absorption, which is the case of silicon at near- infrared wavelengths, the optical and mechanical mode equations describing FBS decouple and can be solved separately [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' We use here COMSOL Multiphysics software for the optomechanical simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' For the calculation of optical and mechanical modes in the optimization process, we reduce the 3D structure to an equivalent 2D geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The effective index method [28] is considered for the computation of the transverse-electric (TE) polarized 4 Wg Wi Anchoring arms: sections 2 3 4 5optical modes while the in-plane mechanical modes are calculated assuming the plane stress approximation [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' We compute the Brillouin gain,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' GB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' as [9] GB(Ωm) = Qm 2ωp meff Ω2 m ���� � fMB dℓ + � fPE dA ���� 2 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' (1) where ωp is the frequency of the optical pump,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Ωm is the mechanical fre- quency,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Qm is the mechanical quality factor,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' meff = � ρ |um|2/ max |um|2 dA is the effective linear mass density of the mechanical mode with displacement profile um,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' and fMB and fPE are the linear and surface overlap of optical force density and deformation representing the moving boundaries effect (MB) and the photoelastic effect (PE),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' respectively,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' fMB = u∗ m · n � δεMB E∗ p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='t · Es,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='t − δε−1 MB D∗ p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='n · Ds,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='n � max |um| Pp Ps and fPE = E∗ p · δε∗ PE · Es max |um| Pp Ps ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' (2) where the permittivity differences due to the moving boundaries effects are given by δεMB = ε1 − ε2 and δε−1 MB = 1/ε1 − 1/ε2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' with εi = ε0n2 i being the permittivities of the silicon (i = 1) and air (i = 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The photoelastic tensor perturbation in the material permittivity is δεPE = −ε0 n4 p : S, with n being the material refractive index, p the photoelastic tensor, and S the mechanical stress tensor induced by the mechanical mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The term um · n is the normal component of the mechanical displacement and Ej,t and Dj,n are the tangential electric field and normal dielectric displacement for the pump (j = p) and the scattered field (j = s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The denominator represents the power normalization given by Pj = [2ℜ( � [Ej × H∗ j] · z dA)]1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The symmetry directions [100], [010], and [001] of the crystalline silicon are set to coincide with the x, y, and z simulation axis, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' With this orientation, the photoelastic tensor [6, 30] is [p11, p12, p44] = [−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='094, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='017, −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='051].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The refractive index of silicon is n = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='45 and its density ρ = 2329 kg m−3 while the corresponding values for the air are n = 1 and ρ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='293 kg m−3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The quality factor of the mechanical mode, Qm, is related to the full width at half maximum (FWHM) of the gain spectrum, γm, through Qm = Ωm/γm and it is limited by different loss mechanisms, 1 Qm = 1 QTE + 1 QL + 1 Qair .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' (3) 5 Here, we consider the thermoelastic loss (QTE), the mechanical leakage to- wards the silica under-cladding (QL), and the viscous loss from surround- ing air (Qair).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The thermoelastic loss yields mechanical quality factors of QTE ∼ 6 · 105 [31] for silicon nanostructures while the leakage loss is mainly governed by the geometries of the waveguide and the arms anchoring it to the lateral silicon slab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' These two effects are directly considered in the mechanical-mode simulations performed in COMSOL Multiphysics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The vis- cous loss induced by the surrounding air is considered here by imposing a limiting value to the mechanical quality factor of Qm = 4 · 103, which is the highest expected value at atmospheric pressure and room temperature for phonon frequency in the order of GHz [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Based on the resulting optomechanical coupling calculations, a genetic algorithm [33] is used to maximize the FBS gain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Starting with randomly generated combinations of parameters Wi and Li (individuals), optomechan- ical simulations are carried out and the individuals are ranked according to their Brillouin gain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Recombination is used to produce a successor set of individuals, the next generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The best-performing individuals directly become part of the next generation (elitism).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' A large number of individuals of the new generation is obtained by combining the parameter of pairs of individuals from the current generation (crossover).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Finally, the remaining individuals of the new generation are produced by randomly modifying the parameters of single individuals of the current generation (mutation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' This process continues until the convergence criterion has been reached.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' In our particular optimization problem, an individual is a possible geome- try, represented by a set of 8 parameters (width and length of each of the arm sections).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Each generation is composed of 50 individuals and the successive generations are obtained applying a rate of elitism and crossover of 6% and 80%, respectively, with the remaining elements obtained through mutation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The convergence criterion was defined in terms of the difference between the best and the average performance, GB − ⟨GB⟩ < 10 W−1m−1, over 10 gener- ations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' For this work, we have used a standard computer with the following specifications: a 64-bit operating system with an x64-based processor Intel® Core™ i7-4790 (4 total cores, 8 total threads, base-frequency of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='60 GHz), and an installed RAM of 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='00 GB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Under these conditions, the optimiza- tion process was completed in 12h 35 min, comprising 1500 optomechanical simulations of 30 seconds each.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The method we propose here relies on a defined geometry whose pa- rameters are allowed to vary within a specific range of values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Hence, the 6 optimized structure will depend strongly on our initial guess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 2, we present the optimization process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Figures 2a and 2b show the Brillouin gain and mechanical frequency, respectively, as a function of the generation number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' As a result of the evolution of the geometry, we observe an increase in the gain and a variation in the mechanical frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' This result should be expected as the Brillouin shift in FBS is particularly sensitive to the waveguide dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The optimum performance is achieved after 10 generations while 30 generations are required for convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The optimized geometry, whose dimensions are listed in Table 1, is characterized by a Brillouin gain of GB = 3350 W−1m−1 for a mechanical mode with frequency of Ωm = 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='357 GHz and mechanical quality factor of Qm ≈ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='2 · 103.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The optical mode has a mode effective index of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='36 and wavelength in vacuum of λ = 1556.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='5 nm (ωp = 2π · 192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='6 THz in (1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Figure 2: Optimization process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' a) Best (in blue) and average (in orange) Brillouin gain as a function of the number of generations during genetic optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' b) Evolution of the mechanical frequency as a function of the number of generations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' During the optimization process, all possible mechanical losses are considered, including thermoelastic loss, mechanical leakage, and viscous loss due to air (operation in air ambient at room temperature).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' In terms of geometry, the first and fourth sections, with considerably larger widths, generate reflections that help localize the mechanical mode in the waveguide core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The frequency of the mechanical mode is governed by the interplay between the waveguide width and the length of the partial cavity formed by the fourth section on each side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Full 3D simulations are realized to verify the performance of the optimized geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' This structure provides a Brillouin gain of GB = 3310 W−1m−1 for a mechanical mode with a frequency of Ωm = 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='579 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The optical mode 7 a) b) 4000 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='0 [GHz] Brillouin Gain [(Wm)-1] 3000 Frequency 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='5 2000 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='0 Mechanical 1000 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='5 Best Average 0 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='0 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 Number of generation Number of generationTable 1: Dimensions for the GA-optimized geometry when operating in air ambient at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' In the table above, Si stands for section i in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' S1 S2 S3 S4 Width 170 nm 320 nm 330 nm 100 nm Length 130 nm 60 nm 60 nm 190 nm has a mode effective index of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='23 and wavelength in vacuum of λ = 1557.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='2 nm (ωp = 2π · 192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='52 THz in (1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Figure 3 shows the calculated field distribution for the mechanical and optical modes in the optimized geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Figure 3: Optical and mechanical modes of the optimized geometry operating in air ambi- ent and room temperature (table 1): a) Approximated 2D structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The upper structure corresponds to the normalized mechanical displacement at 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='357 GHz and the lower fig- ure to the x-component of the electric field at 1556.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='5 nm (mode effective index 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='36).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' b) Full 3D device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' On the bottom left, x-component of the electric field at 1557.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='2 nm (mode effective index 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='23), and on the top right, normalized mechanical displacement at 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='579 GHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' These results show a good agreement between the approximated 2D ge- ometry used for the optimization and the full 3D structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The small dis- crepancies in the optical mode index and mechanical frequency are due to the influence of the thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Finally, we study the fabrication tolerance of the proposed structure us- ing again 3D simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' We consider under- and over-etching errors that we model by a variation of all the waveguide lengths and widths by a factor ∆, measured in nm (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 4a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Figure 4c shows the variation of the Bril- louin gain (in blue) and mechanical frequency (in orange) as a function of ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 8 b) a) [ul / max|ul u/max|u E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='The Brillouin gain remains above 2000 W−1m−1 for geometry variations of ±10 nm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' It should be noted that for the over-etch case (∆ < 0 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 4c), the Brillouin gain is larger than the optimized case due to the larger optome- chanical coupling resulting from a better overlap of the mechanical mode with the optical field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' However, these smaller structures are incompatible with the target minimum feature size of 50 nm that was chosen to guarantee fabrication reliability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The mechanical frequency varies less than 2% (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='4c, in orange) and the mechanical profile is not modified significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' We also study the effect of stitching errors, modeled by a deviation ζ (in nm) of the arm axis at both sides of the waveguide core, hence breaking the symmetry of the structure (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 4b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Figure 4d shows the variation of the Brillouin gain (in blue) and mechanical frequency (in orange) as a function of ζ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' A non-perfectly symmetric structure is slightly detrimental to the Brillouin gain but does not affect the mechanical frequency or profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Interestingly, both parameters (Brillouin gain and mechanical frequency) remain constant over a large range of stitching errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Lastly, we examine the effect of random fabrication errors affecting each section independently (Table 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' We consider deviations of 5 to 20 nm, both in positive (enlargement) or negative (shrinking) directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Our geometry exhibits a robust performance despite these errors with Brillouin gains above 2000 W−1m−1 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 4e, blue) and mechanical frequencies between 14 and 15 GHz (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 4e, orange).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' It should be noted that the period remains constant, Λ = 300 nm since it is controlled with high precision (±2 nm) in terms of fabrication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Conclusions In summary, we have proposed a new approach to optimizing Brillouin gain in silicon membrane waveguides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' We exploit genetic optimization to maximize Brillouin gain in subwavelength-structured Si waveguides, requir- ing only one etch step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Genetic algorithm is a well-known optimization technique capable of handling design spaces of moderate dimension [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' It has the main advantage over gradient-based algorithms in its capabil- ity to search the design space in many directions simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' On the other hand, the genetic algorithms cannot guarantee a global optimum so- lution, being the final result strongly dependent on the initial population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Based on this strategy, a calculated Brillouin gain up to 3310 W−1m−1 is achieved for air environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' This result compares favorably to previously 9 Figure 4: Fabrication tolerance of the optimized geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' a) and b) Variation of the geometry due to fabrication errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' The solid black line corresponds to optimized geometry, dotted (solid) blue depicts a positive deviation from the nominal design, and dotted orange refers to a negative deviation from the expected design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' c) and d) Evolution of the Brillouin gain (in blue, left axis) and the mechanical frequency (in orange, right axis) for different values of under- and over-etching (c), different values of stitching errors (d), and different structures with randomized geometrical parameters (e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' In e), N stands for the nominal design obtained after the optimization problem and i for the different geometries listed in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 10 a) b) Wg/2 Si Slab Si Slab W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Si Slab c) d) 6000 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='0 3500 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='0 [(Wm)- (Wm) 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='8 ZH 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content="8 3250 GH 4000 Brillouin Gain 'requency requency 3000 14." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='4 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='4 2000 2750 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='2 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='0 2500 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='0 10 5 0 5 10 0 5 10 15 20 25 30 35 Fabrication error, △ [nm Stiching error, S[nm] e) 6000 16 4000 15 [2H)] Brillouin Gain 2000 14 13 N 1 2 3 4 5 6 7 8 9 GeometryTable 2: Dimensions for the different geometries used for studying the effect of random- ization of the design parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' In the table, Si stands for section i in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 1, N stands for the nominal design as obtained from the optimization (Table 1), and i stands for the different geometries in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 4e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' In all cases, the period, Λ = 300 nm, remains constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Geometry ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='S1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='S2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='S3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='S4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='S5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Wg ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='N ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Width ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='170 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='320 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='330 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='100 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='500 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='400 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Length ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='130 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='60 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='60 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='190 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='50 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Width ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='165 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='305 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='345 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='90 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='510 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='405 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Length ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='130 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='45 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='65 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='180 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='60 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Width ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='165 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='320 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='340 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='115 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='495 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='400 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Length ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='110 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='45 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='55 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='170 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='35 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Width ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='155 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='340 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='340 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='100 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='485 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='405 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Length ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='150 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='40 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='70 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='200 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='55 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Width ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='185 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='300 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='325 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='95 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='480 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='385 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Length ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='140 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='65 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='75 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='185 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='60 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Width ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='160 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='320 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='330 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='95 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='510 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='390 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Length ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='140 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='65 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='55 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='210 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='60 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Width ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='185 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='340 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='315 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='120 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='520 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='420 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Length ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='135 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='40 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='50 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='190 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='35 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Width ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='185 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='340 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='340 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='110 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='480 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='410 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Length ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='140 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='55 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='65 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='175 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='40 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Width ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='150 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='300 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='345 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='110 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='510 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='395 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Length ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='120 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='80 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='40 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='175 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='65 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Width ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='170 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='340 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='325 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='105 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='520 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='410 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='Length ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='120 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='70 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='50 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='190 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='70 nm ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='11 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='reported subwavelength-based Brillouin waveguides requiring several etch- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='ing steps [25,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 26],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' with calculated Brillouin gain of 1750 W−1m−1 and 3000 W−1m−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Our results show the potential of optimization for obtaining novel designs with improved performance in the context of Brillouin scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Moreover, they show the reliability of computationally efficient optimizations based on approximated 2D simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Declaration of Competing Interest The authors declare that they have no known competing financial inter- ests or personal relationships that could have appeared to influence the work reported in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Author Statement Paula Nuño Ruano, Jianhao Zhang, and Carlos Alonso Ramos proposed the concept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Paula Nuño Ruano, Jianhao Zhang, and Daniele Melati devel- oped the simulation framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Paula Nuño Ruano, Jianhao Zhang, Daniele Melati, David González Andrade, and Carlos Alonso Ramos optimized and analyzed the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' All authors contributed to the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Data Availability Statement The data supporting this study’s findings are available from the corre- sponding author upon reasonable request.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Acknowledgements The authors want to thank the Agence Nationale de la Recherche for sup- porting this work through BRIGHT ANR-18-CE24-0023-01 and MIRSPEC ANR-17-CE09-0041.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' acknowledges the support of Erasmus Mundus Grant: Erasmus+ Erasmus Mundus Europhotonics Master program (599098- EPP-1-2018-1-FR-EPPKA1-JMD-MOB) of the European Union.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' This project has received funding from the European Union’s Horizon Europe research and innovation program under the Marie Sklodowska-Curie grant agreement Nº 101062518.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 12 References [1] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Garmire, Perspectives on stimulated brillouin scattering, New Journal of Physics 19 (1) (2017) 011003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1088/1367-2630/aa5447.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [2] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Wiederhecker, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Chen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Gondarenko, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Lipson, Controlling photonic structures using optical forces, Nature 462 (7273) (2009) 633– 636.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1038/nature08584.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [3] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Dainese, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Russell, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Joly, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Knight, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Wiederhecker, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Fragnito, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Laude, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Khelif, Stimulated brillouin scattering from multi-ghz-guided acoustic phonons in nanostructured photonic crystal fibres, Nature Physics 2 (6) (2006) 388–392.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1038/nphys315.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [4] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Beugnot, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Sylvestre, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Maillotte, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Mélin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Laude, Guided acoustic wave brillouin scattering in photonic crystal fibers, Optics let- ters 32 (1) (2007) 17–19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1364/ol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='000017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [5] Peter T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Rakich, Charles Reinke, Ryan Camacho, Paul Davids, Zheng Wang, Giant enhancement of stimulated brillouin scattering in the subwavelength limit, Physical Review X 2 (1) (2012) 011008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1103/PhysRevX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='011008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [6] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Qiu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Rakich, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Shin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Dong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Soljačić, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Wang, Stim- ulated brillouin scattering in nanoscale silicon step-index waveguides: a general framework of selection rules and calculating sbs gain, Optics Express 21 (25) (2013) 31402–31419.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1364/OE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='031402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [7] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Wolff, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Steel, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Eggleton, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Poulton, Stimulated brillouin scattering in integrated photonic waveguides: Forces, scattering mech- anisms, and coupled-mode analysis, Physical Review A 92 (1) (2015) 013836.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='013836.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [8] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Eggleton, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Poulton, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Rakich, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Steel, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Bahl, Brillouin integrated photonics, Nature Photonics 13 (10) (2019) 664– 677.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1038/s41566-019-0498-z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [9] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Wiederhecker, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Dainese, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Mayer Alegre, Brillouin optome- chanics in nanophotonic structures, APL Photonics 4 (7) (2019) 071101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='5088169.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 13 [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Safavi-Naeini, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Thourhout, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Baets, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Laer, Control- ling phonons and photons at the wavelength scale: integrated photon- ics meets integrated phononics, Optica 6 (2) (2019) 213–232.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1364/OPTICA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='000213.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [11] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Shin, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Qiu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Jarecki, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Cox, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Olsson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Starbuck, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Wang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Rakich, Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides, Nature Communications 4 (1) (2013) 1944.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1038/ncomms2943.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [12] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Laer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Bazin, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Kuyken, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Baets, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Thourhout, Net on-chip brillouin gain based on suspended silicon nanowires, New Jour- nal of Physics 17 (11) (2015) 115005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1088/1367-2630/17/11/ 115005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [13] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Kittlaus, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Shin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Rakich, Large brillouin amplification in sil- icon, Nature Photonics 10 (7) (2016) 463–467.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1038/nphoton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [14] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Otterstrom, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Behunin, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Kittlaus, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Wang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Rakich, A silicon brillouin laser, Science 360 (6393) (2018) 1113–1116.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='aar6113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Vahala, Microwave synthesizer using an on-chip brillouin oscillator, Nature Communications 4 (1) (2013) 2097.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1038/ncomms3097.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [16] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Liu, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Choudhary, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Marpaung, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Eggleton, Chip-based bril- louin Processing for phase control of rf signals, IEEE Journal of Quan- tum Electronics 54 (3) (2018) 1–13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1109/JQE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='2823323.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [17] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Chow, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Yang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Soto, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Thévenaz, Distributed forward brillouin sensor based on local light phase recovery, Nature Communi- cations 9 (1) (2018) 2990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1038/s41467-018-05410-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [18] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Lai, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Suh, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Lu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Shen, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Yang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Yang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Vahala, Earth rotation measured by a chip- scale ring laser gyroscope, Nature Photonics 14 (2020) 345–349.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1038/s41566-020-0588-y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 14 [19] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Kittlaus, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Otterstrom, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Kharel, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Gertler, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Ra- kich, Non-reciprocal interband brillouin modulation, Nature Photonics 12 (10) (2018) 613–619.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1038/s41566-018-0254-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [20] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Van Laer, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Kuyken, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Van Thourhout, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Baets, Interaction between light and highly confined hypersound in a silicon photonic nanowire, Nature Photonics 9 (3) (2015) 199–203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1038/ nphoton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [21] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Sun, Design of silicon phoxonic crystal waveguides for slow light enhanced forward stimulated brillouin scattering, Journal of Lightwave Technology 35 (14) (2017) 2917–2925.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1109/JLT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='2704615.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [22] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Baba, Slow light in photonic crystals, Nature Photonics 2 (8) (2008) 465–473.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1038/nphoton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='146.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [23] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Halir, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Bock, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Cheben, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Ortega-Moñux, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Alonso- Ramos, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Schmid, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Lapointe, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Xu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Wangüemert-Pérez, Í.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Molina-Fernández, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Janz, Waveguide sub-wavelength structures: a review of principles and applications, Laser & Photonics Reviews 9 (1) (2015) 25–49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1002/lpor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='201400083.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [24] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Cheben, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Halir, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Schmid, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Atwater, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Smith, Sub- wavelength integrated photonics, Nature 560 (7720) (2018) 565–572.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1038/s41586-018-0421-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [25] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Schmidt, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Poulton, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Mashanovich, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Reed, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Eggleton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Steel, Suspended mid-infrared waveguides for stimulated brillouin scattering, Optics express 27 (4) (2019) 4976–4989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 1364/OE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='004976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [26] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Zhang, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Ortiz, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Roux, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Cassan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Vivien, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Marris- Morini, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Lanzillotti-Kimura, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Alonso-Ramos, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Alonso-Ramos, Subwavelength engineering for brillouin gain optimization in silicon optomechanical waveguides, Optics Letters 45 (13) (2020) 3717–3720.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1364/OL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='397081.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [27] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Håkansson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Van Thourhout, Generating novel waveguides for stim- ulated brillouin scattering with genetic algorithms, APL Photonics 4 (1) (2019) 010803.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='5063783.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 15 [28] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Chen, Foundations for Guided-Wave Optics, John Wiley & Sons, Inc, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [29] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Auld, Acoustic Fields And Waves In Solids, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' I & II, John Wiley & Sons, 1973.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [30] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Rakich, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Davids, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Wang, Tailoring optical forces in waveguides through radiation pressure and electrostrictive forces, Optics Express 18 (14) (2010) 14439–14453.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1364/OE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='014439.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [31] COMSOL multiphysics® reference manual v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='4 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [32] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Ghaffari, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Chandorkar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Wang, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Ng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Ahn, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Hong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Yang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Kenny, Quantum limit of quality Factor in silicon micro and nano mechanical resonators, Scientific Reports 3 (1) (2013) 3244.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1038/srep03244.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' [33] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Yang, Chapter 5 - genetic algorithms, in: X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' Yang (Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' ), Nature-Inspired Optimization Algorithms, Elsevier, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 77–87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='1016/B978-0-12-416743-8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content='00005-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} +page_content=' 16' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/2NE2T4oBgHgl3EQfjAcm/content/2301.03963v1.pdf'} diff --git a/3NAyT4oBgHgl3EQfo_gV/vector_store/index.pkl b/3NAyT4oBgHgl3EQfo_gV/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..de41258d83aba3075d13bd5aa10ddc093b2943e3 --- /dev/null +++ b/3NAyT4oBgHgl3EQfo_gV/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2bdb1dcaa050387ecd3d3ac78085e7aadbf48c9d26b1f973bef8c214202b085c +size 159314 diff --git a/3NFQT4oBgHgl3EQf3DZF/vector_store/index.faiss b/3NFQT4oBgHgl3EQf3DZF/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..6dfa7fd6d00e01ab9697bb40e86d0750c5b2326e --- /dev/null +++ b/3NFQT4oBgHgl3EQf3DZF/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:10b313251882e2787c7af355a9f6b14923fbb7cba56a4ac1150e8aaf2d97e198 +size 917549 diff --git a/3NFST4oBgHgl3EQfYjhQ/content/2301.13788v1.pdf b/3NFST4oBgHgl3EQfYjhQ/content/2301.13788v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..eb22a9e8e6db025e4774cd7b683ba7f75bf2fac6 --- /dev/null +++ b/3NFST4oBgHgl3EQfYjhQ/content/2301.13788v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:80a6f0eb4e9ec38ef160354e879bb51b61af0885127a49a26a75ea18a8b17582 +size 1467235 diff --git a/3NFST4oBgHgl3EQfYjhQ/vector_store/index.pkl b/3NFST4oBgHgl3EQfYjhQ/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..3e0a4c1498c6e931f82189909d97133bcea918ff --- /dev/null +++ b/3NFST4oBgHgl3EQfYjhQ/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d5972601904815e359914af348f9e07d48222447a977958f6fff94518c3c57f1 +size 117984 diff --git a/3tAyT4oBgHgl3EQfb_f6/vector_store/index.pkl b/3tAyT4oBgHgl3EQfb_f6/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..1d05f634ac42a7d8a80c4a5e9e63e69f0cde5c7b --- /dev/null +++ b/3tAyT4oBgHgl3EQfb_f6/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:66440a4fe9de050b4c76f3e019e4a61fd0af1d09cf65ae7277fdb5a5c8a1f188 +size 184359 diff --git a/49E4T4oBgHgl3EQfBAv2/content/tmp_files/2301.04849v1.pdf.txt b/49E4T4oBgHgl3EQfBAv2/content/tmp_files/2301.04849v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..ee13391b96cc5f2efca751d6f081965fcae2f4a2 --- /dev/null +++ b/49E4T4oBgHgl3EQfBAv2/content/tmp_files/2301.04849v1.pdf.txt @@ -0,0 +1,1823 @@ +Exit options sustain altruistic punishment and decrease the second-order free-riders, +but it is not a panacea +Chen Shen1,2, Zhao Song3, Lei Shi2,∗ Jun Tanimoto1, and Zhen Wang3,4† +1. Faculty of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan +2. School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China +3. School of Mechanical Engineering,Northwestern Polytechnical University, Xi’an 710072, China +4. School of Artifcial Intelligence, OPtics and ElectroNics (iOPEN), +Northwestern Polytechnical University, Xi’an 710072, China +(Dated: January 13, 2023) +The emergence and maintenance of altruistic punishment remains an open question and this +conundrum is shared across diverse fields. In this study, we evaluated the evolution of altruistic +punishment in a two-stage prisoner’s dilemma game in which cooperators and defectors interact with +another two actors called altruistic punishers and exiters. Traditionally cooperators and defectors, +in the first stage, choose to cooperate and defect with their opponent, respectively, but they do not +punish in the second stage; the altruistic punishers cooperate in the first stage and punish defectors +in the second stage, and the exiters who simply exit the game in favor of a small payoff. +We +found that exiters did not provide any substantial assistance to altruistic punishment in well-mixed +populations, they destabilize defection and finally replace them. In the finite population, although +the exit option enables the coexistence of altruistic punishers, defectors, and exiters through cyclic +dominance. Altruistic punishers never dominate the finite population and the exit option provides +another alternative cyclic dominance route for the emergence of non-punishing cooperators. +In +networked populations, however, adding the exit option allows for the establishment of altruistic +punishment, and enables the coexistence of altruistic punishers, defectors, and exiters through cyclic +dominance. However, this type of cyclic dominance is not always stable, with adjustments to the +exit payoff, this type of cyclic dominance is replaced by the cyclic dominance of non-punishing +cooperators, defectors, and exiters or a bi-stable state between these two types of cyclic dominance. +Our results indicate that although the exit option can help explain altruistic punishment, it is +certainly not a panacea. +Keywords: Evolutionary game theory; Cooperation; Coexistence; Cyclic dominance; Bi-stable +INTRODUCTION +Costly punishment is ubiquitous in many animal +species including humans [1–3]. +Unlike other animals, +humans often show altruistic traits, i.e., humans punish +other individuals who have harmed others even at the ex- +pense of their own interest [3, 4], however, the emergence +and maintenance of altruistic punishment is an evolu- +tionary conundrum as costly punishment is unlikely to +evolve according to natural selection. Costly punishment +reduces the payoff for both the punisher and the pun- +ished. If it is the fittest who survive, the second-order +free riders that cooperate but do not punish are better +off than punishers, and defectors should eventually take +over the whole population. Therefore, the understanding +of whether and how costly punishment can evolve is a +crucial issue in the study of human cooperation. Fehr +and G¨achter pointed out that the evolutionary study of +human cooperation in large groups of unrelated individ- +uals should include a focus on explaining altruistic pun- +ishment [4]. In addition, they argued that negative emo- +tions may be a potential explanation for the emergence +of costly punishment. +∗ shi lei65@hotmail.com +† w-zhen@nwpu.edu.cn +To resolve this evolutionary puzzle, many scholars have +explored how and why costly punishment can emerge in +humans both from a theoretical and experimental per- +spective. Egas Martijn and Riedl Arno experimentally +explored the boundary conditions that altruistic punish- +ment can promote cooperation. +They found that the +maintenance of cooperation is subject to the cost-to- +effect ratio of altruistic punishment, and cooperation is +maintained if the conditions for altruistic punishment are +relatively favorable [5]. It has been well established that +voluntary participation plays a vital role in sustaining the +prevalence of costly punishment both in finite and infinite +populations [6–11]. The main idea behind established al- +truistic punishment is that a loner itself is sufficient to +maintain cooperation through cyclic dominance even in a +one-shot game. Other reciprocity mechanisms including +indirect reciprocity [12–16], group selection [17–19], spa- +tial interaction [20–23], prior commitment [24–27], and +so on [28], that can explain the emergence of cooperation +have been applied to explain costly punishment, and its +effect on costly punishment has previously been widely +explored. +To avoid the exploitation of defectors, exiters simply +exit the game in favor of a small-but-positive payoff and +generate nothing for their opponent. While loners can +receive a small-but-positive payoff by opting out but gen- +erates the same payoff for its opponent. Although these +arXiv:2301.04849v1 [q-bio.PE] 12 Jan 2023 + +2 +two mechanisms seem materially similar, such a subtle +difference leads to completely different outcomes [29, 30]. +On one hand, exit means a potential punishment for their +opponent, although the exiters can avoid being exploited +by the defectors through opting out, they also hurt the +cooperators. However, loners enable the coexistence with +cooperators and defectors through cyclic dominance in a +one-shot game [31], while exiters allow cooperation to +flourish only if they adhere to either direct, indirect or +network reciprocity [32]. Given these differences, an in- +teresting question arises: to what extent do exiters help +explain altruistic punishment. To this end, we introduce +the exit option and altruistic punishment in a two-stage +prisoner’s dilemma game, and we start our analysis in +well-mixed populations in which the extended prisoner’s +dilemma game in both finite and infinite populations are +considered. Then, we turn our attention to a networked +population. +In doing so, we found that the exit op- +tion does not bring any substantial benefit to altruistic +punishment in well-mixed populations, but enables the +existence of altruistic punishment in networked popula- +tions. +In addition, multiple dynamical phenomena in- +cluding cyclic dominance and a bi-stable state can be +observed in networked populations. +METHODS +We studied the evolution of altruistic punishment in +a two-stage prisoner’s dilemma game by introducing two +other action types, altruistic punishment and exit. In the +first stage, each individual must make a choice simulta- +neously between cooperation (C), defection (D), and exit +(E). In the second stage, cooperators decide whether to +punish the defectors at a personal cost to themselves γ. +To the defectors, this means an imposed fine β. +This +process results in four possible actions: +• AP, cooperate and punish defectors. Those who +cooperate and punish are altruistic punishers be- +cause they punish free riders even at the expense +of its own interests . +• NC, +cooperate but do not punish defectors. +These non-punishing cooperators are also known +as second-order free riders because by free-riding +on punishment save the the cost of punishing the +defectors. +• D, defect but do not punish. These are also known +as first-order free riders. +• E, exit the game in favor of a small but positive +payoff ϵ irrespective of whom they encounter. They +do not participate in these two stages. +In a typical prisoner’s dilemma game, mutual cooper- +ation (defection) generates the reward (punishment) R +(P). If one player cooperates and the other defects, the +cooperative player gets the sucker’s payoff S, and the de- +fected player obtains the temptation to defect T. +For +simplicity, we choose the weak prisoner’s dilemma game +as our base model by setting R = 1, P = S = 0, T = b. +TABLE I. +Payoff matrix for the weak prisoner’s dilemma +game with altruistic punishment and an exit option. +AP +NC +D +E +AP +1 +1 +−γ +0 +NC +1 +1 +0 +0 +D +b − β +b +0 +0 +E +ϵ +ϵ +ϵ +ϵ +The extended weak prisoner’s dilemma game contains four +competing action types: altruistic punishers who cooperate +and punish defectors(AP), non-punishing cooperators who +cooperate but do not punish defectors (NC), defectors who +free ride on the non-punishing cooperators and do not punish +(D), and exiters who exit the game irrespective of whom they +encounter (E). The first row indicates that when an altruis- +tic punisher, AP, meets another altruistic punisher AP, non- +punishing cooperator NC, defector D, or exiter E, they earn +a payoff equal to 1, 1, −γ, or 0, respectively. When a non- +punishing cooperator meets another altruistic punisher, non- +punishing cooperator, defector, or exiter, they earn a payoff +equal to 1, 1, 0, or 0, respectively. Analogously, when a de- +fector meets an altruistic punisher, non-punishing cooperator, +defector, or exiter, they earn a payoff equal to b−β, b, 0, or 0, +respectively. Finally, exiters earn a payoff equal to ϵ ∈ [0, 1), +irrespective of whom they meet, and their opponent receives +nothing. +To make exiting less valuable than cooperating, and to +ensure that the weak prisoner’s dilemma game satisfied +the payoff ranking of the strict prisoner’s dilemma game, +T > R > P > S was used. Additional limits placed on +the parameters were 1 ≤ b < 2 and ϵ < 1. The described +above is summarized in table I. Altruistic punishment +maintains cooperation only when its effectiveness is rel- +atively large [5, 33], thus to investigate the effect of the +exit option on the explanation of altruistic punishment, +throughout this study, the cost of punishment γ and the +fine of the defectors was set as 0.1 and 0.3, respectively. +Finite population +We first considered a finite and well-mixed population +of N individuals. +Each individual adopted the Moran +process, also known as frequently dependent process, to +select their action. At each time step, a randomly se- +lected player i with fitness fi = esΠi (Πi is the actual +payoff of the individual i obtained through their interac- +tion) updates its action by imitating the action of player +j with fitness fj = esΠj who is selected with a proba- +bility proportional to its fitness. Here, s is the selection +strength, the condition of s → 0 corresponds to the weak +selection and evolution proceeds as neutral drift. +We +further assumed that with a small probability µ, players +randomly select their action from the rest of the other +actions.This small mutation ensures that the population +is homogeneous most of the time. +Suppose that there are only two actors in the popula- +tion, i.e., action A and B, and these actions can be one + +3 +of the four actions among the full action set {a, b, c, d}. +Here, the symbols a, b, c, d represent AP, NC, D and E, +respectively. In a finite population of size N with x A +and y = N − x B actions, the average payoff of Πxy and +Πyx to players with A and B actions are the following: +ΠAB = (x−1)PAA+(N−x)PAB +N−1 +ΠBA = xPBA+(N−x−1)PBB +N−1 +, +(1) +where PAB is the payoff obtained from the single en- +counter of actors A and B, and so does payoffs PAA, PBA, +and PBB. This allows us to describe the evolutionary dy- +namics of the population in terms of a reduced Markov +Chain of size 4 [34–37]. Given the above assumptions, +the probability to change the number of x individuals +with action A in a population of y = N − x individuals +with action B by ±1, T ± +AB is: +T + +AB = +xfi +xfi+yfj +y +N +T − +AB = +yfj +xfi+yfj +x +N +, +(2) +and hence the fixation probability ρAB of a single mutant +actor A within a population of N − 1 B actors can be +derived as [38, 39]: +ρAB = +1 +N−1 +� +k=0 +k� +x=1 +T − +AB +T + +AB += +1 +N−1 +� +k=0 +k� +x=1 +esΠBA +esΠAB +. +(3) +The fixation probabilities ρAB define the transition prob- +abilities of the reduced Markov Chain, with the following +associated transition matrix: +� +� +� +AP +NC +D +E +AP +ρaa +ρab +ρac +ρad +NC +ρba +ρbb +ρbc +ρbd +D +ρca +ρcb +ρcc +ρcd +E +ρda +ρdb +ρdc +ρdd +� +� +�. +(4) +Here, ρAA = 1 − � +A̸=B +ρAB, A, B ∈ {a, b, c, d}. The nor- +malized right eigenvector to the largest eigenvalue deter- +mines the stationary distribution of each strategy. For +any pair of strategies A and B in the finite population, +natural selection favors B replacing A only if ρAB > 1 +N . +Infinite population +We then employed replicator dynamics to analyze the +evolutionary outcomes in an infinite and well-mixed pop- +ulation. Let x, y, z, w denote the fractions of altruistic +punishers (AP), non-punishing cooperators (NC), de- +fectors (D), and exiters (E) in the population. Where +0 ≤ x, y, z, w ≤ 1, and x + y + z + w = 1. The replicator +equations are: +˙x = x +� +ΠAP − Π +� +, +˙y = y +� +ΠNC − Π +� +, +˙z = z +� +ΠD − Π +� +, +˙w = w +� +ΠE − Π +� +. +(5) +The symbols ΠAP , ΠNC, ΠD, and ΠE denote the average +payoff of altruistic punishers, non-punishing cooperators, +defectors, and exiters. Whereas Π = xΠAP + yΠNC + +zΠD+wΠE is the average payoff of the whole population. +According to the defined payoffs in table I, we obtained +the following equation: +ΠAP = x + y − zγ +ΠNC = x + y +ΠD = x(b − β) + yb +ΠE = ϵ +. +(6) +Using the constraint w = 1 − x − y − z, we obtained: +� +� +� +� +� +� +� +� +� +� +� +� +� +˙x = f (x, y, z) += x [(1 − x) (ΠAP − ΠE) − y (ΠNC − ΠE) − z (ΠD − ΠE)] +˙y = g (x, y, z) += y [(1 − y) (ΠNC − ΠE) − x (ΠAP − ΠE) − z (ΠD − ΠE)] +˙z = h (x, y, z) += z [(1 − z) (ΠD − ΠE) − y (ΠNC − ΠE) − x (ΠAP − ΠE)] +(7) +For the detailed stability analysis of each equilibria, +please refer to the Appendix. +Networked population +Different with well-mixed populations, global interac- +tions in which an individual can interact with any other +individual are no longer possible in the networked pop- +ulation. Instead, networks only allow local interactions, +which means that individuals can only interact with their +direct neighbors. Our basic network structure is a two +dimensional regular lattice with periodic boundary con- +ditions, each node was occupied by one individual, and +each individual can only interact with its neighbors along +its links. Our simulation contained the following steps. +Initially, each individual was designed as either an altru- +istic punisher (AP), a non-punishing cooperator (NC), +a defector (D), or an exiter (E) with equal probability. +Each player acquires their total payoff by playing with +all their direct neighbors according to the payoff matrix +defined in table I. A randomly selected player i decides +to imitate the strategy of player j who is also randomly +selected from all the direct neighbors of player i by com- +paring their payoff difference with the following proba- +bility: +Wi←j = +1 +1 + exp ((Πi − Πj) /K), +(8) +where Πi and Πj is the acquired total payoff of the focal +player i and its randomly selected neighbor j, respec- +tively. K denotes the noise in the imitation process, and +we fixed the value of K to be 0.1 throughout the study. +A full Monte Carlo step is to repeat the above proce- +dure L2 times, and L2 is the number of nodes in the given +network. Each individual update their strategy once on + +4 +FIG. 1. +Exiters establish altruistic punishment in a +finite population, but altruistic punishers struggle to +dominate the population. A. Stationary probability dis- +tributions of each actors independence on the exiters’ payoff +ϵ. +B. Transition probabilities for each pair of actors when +the exiters’ payoff is negative (left) and positive (right). The +parameter values are b = 1.5, β = 0.3, γ = 0.1, s = 0.2, +N = 100. +average. To subside the transient dynamics and avoid the +finite-size effect, we ran simulations for 50,000 steps on a +regular lattice with size ranging from 200*200 to 800*800. +The final fraction of each strategy was obtained after up +to 45,000 steps. The presented data was averaged over +20 independent runs. +RESULTS +Well-mixed populations +We started our analysis in a well-mixed and finite pop- +ulation, then we turned our attention to a well-mixed and +infinite population, and finally, we investigated the evo- +lution of altruistic punishment in networked population. +Finite population. +In the prisoner’s dilemma game +with altruistic punishment, cooperation can only be +maintained if the cost-to-fine ratio of altruistic punish- +ment is relatively small [5]. +The favorable conditions +for altruistic punishment imply the small enough pun- +ishment cost or high enough punishment fine. Although +altruistic punishment can establish the cooperation even +in a one-shot game, punishment reduces the social wel- +fare [40, 41]. If the cost-to-fine ratio of altruistic pun- +ishment is high, altruistic punishment does not support +the survival of cooperation, and thus defectors take over +the whole population. As previously mentioned, nega- +tive values of exiters’ payoff revert the extended model +to the traditional weak prisoner’s dilemma game with al- +truistic punishment, and in this case, selection favors the +dominance of the defectors (refer to the left panel in fig- +ure.1B and figure.A1A). A small but positive exiters’ pay- +off enables the coexistence of altruistic punishers through +cyclic dominance with defectors and exiters (refer to the +right panel in figure.1B and figure.A1B). However, ex- +iters also enable the survival of non-punishing cooper- +ators, and allows the coexistence of non-punishing co- +operators, defectors, and exiters through an alternative +route of cyclic dominance. With increasing ϵ, the fac- +tion of altruistic punishers first reaches its peak, where +the maximum faction of altruistic punishers is less than +0.2, and then decreases until its extinction. (figure.1A). +The exiters facilitate the evolution of altruistic punishers +in a finite population, but also allow for the survival of +second-order free riders. Importantly, altruistic punish- +ers never dominate the whole population. +Infinite population. +The situation changes greatly +when the finite population is replaced by the infinite pop- +ulation. Stability analysis shows that, (i), when b−β > 1 +and ϵ < 0, the monomorphic defecting equilibrium is sta- +ble, and the others are unstable (figure.A2A); (ii), when +b−β > 1 and ϵ > 0, the monomorphic exiting equilibrium +is stable, and the others are unstable (figure.A2B); (iii), +when b − β < 1 and ϵ < 0, the evolutionary dynamics +result in either the mixed equilibrium of altruistic pun- +ishers and non-punishing cooperators or the monomor- +phic defecting equilibrium (figure.A2C); and (iv), when +b − β < 1 and ϵ > 0, the evolutionary dynamics result in +either the mixed equilibrium of altruistic punishers and +non-punishing cooperators or the monomorphic exiting +equilibrium (figure.A2D). In other words, exiters support +the emergence of altruistic punishment only when the +cost-to-fine ratio of punishment is favorable for coopera- +tors in the infinite population. Nevertheless, the exiters +destabilize the defection and eventually replace them re- +gardless of whether altruistic punishment can establish +cooperation. +In a word, our results show that when the exit option +was introduced in well-mixed populations, there was little +additional benefit to the dominance of altruistic punish- +ment. Rather by adding the exit option the equilibrium +was either monomorphic exiting in the infinite popula- +tion or joint dominance between the defectors and ex- +iters in the finite population. Given the above conclusion, +the natural question arises: does a networked population +support the dominance of altruistic punishment in the +extended model? +Networked population +Figure.2 shows the full ϵ − b phase diagram obtained +by the extensive Monte Carlo simulations. It is noted + +1.0 +A +AP +0.8 +NC +么 +Fractions +D +0.6 +A +E +V +0.4 +7 +0.2 +0.0 ++ +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Exit pay-off, E +B +AP +NC +NC +AP +P=0.01 +p=0.01 +4% +1% +8% +16% +p=0.015 +=0.07 +=0. +=0. +=0.04 +=0.04 +=0.07 +=0.015 +E +D +E +D +p=0.04 +p=0.04 +0% +95% +44% +32% +E =-0.2 +E =0.25 +FIG. 2. Adding exit option establishes altruistic pun- +ishment in networked population. Presented is the full +ϵ − b phase diagram obtained by Monte Carlo simulations of +the extended weak prisoner’s dilemma game on a regular lat- +tice. Exiters dominate the whole population when the incen- +tives to the exiters are large, ϵ ≳ 0.51. Fewer exit option in- +centives lead to six possible outcomes. If b is relatively small, +b ≲ 1.19, the effectiveness of altruistic punishment ensures +the dominance of cooperators, and, altruistic punishers can +coexist with defectors when 1.19 ≲ b ≲ 1.29. For large temp- +tation b, b ≳ 1.29, negative ϵ leads to full defection, whereas, +positive ϵ ensures the coexistence of altruistic punishers with +defectors and exiters, the coexistence of second-order free rid- +ers with defectors and exiters, or the bi-stable state of these +two coexistence types. +that the addition of the simple exit option leads to com- +plicated evolutionary outcomes. Initially, when the in- +centives to exiters are sufficiently large, ϵ ≳ 0.51, the +exiters outcompete other action types and dominate the +whole population (the E phase in figure.2), and this is +consistent with previous findings [32]. Less incentives to +exiters, ϵ ≲ 1.51, lead to six different possible outcomes. +In detail, if the temptation to defect is relatively small, +b ≲ 1.29, altruistic punishment together with network +reciprocity are sufficient to maintain prosocial behavior +(the All C phase and the AP + D phase in figure.2). +When b ≲ 1.19, defectors can be completely eliminated +by altruistic punishers, and thus altruistic punishers and +non-punishing cooperators can coexist in a regular lat- +tice. +In the absence of defectors, non-punishing coop- +erators and altruistic punishers cannot be distinguished, +and whether the evolutionary dynamics lead to the full +AP state, the full NC state or the mixed AP +NC state +are determined by the initial conditions (the All C phase +in figure.2). With increasing b, 1.19 ≲ b ≲ 1.29, the effec- +tiveness of altruistic punishment is greatly reduced, and +defectors cannot be completely eliminated by altruistic +punishers, and they coexist with the altruistic punish- +ers in the population (the AP + D phase in figure.2). +It is well established that altruistic punishment together +with network reciprocity promotes cooperation even in +the presence of antisocial punishment or second-order +free-riders when the cost-to-fine ratio of punishment is +low +[14, 21, 22]. +The results of this study confirmed +this conclusion. If b is sufficiently large, altruistic pun- +ishment loses its effectiveness in sustaining prosocial be- +havior, and defectors dominate the entire population for +negative ϵ (the D phase in figure.2). When exit options +are added, this undesirable outcome is solved and leads +to three possible outcomes. These outcomes can be either +(i) the coexistence of AP, D and E (the AP +D+E phase +in figure.2), (ii) the coexistence of NC, D, and E (the +NC +D +E phase in figure.2), or (iii) the bi-stable state +between these two types of coexistences (the B phase in +figure.2). When the cost-to-fine ratio of punishment is +relatively large, the exiters sustain cooperation in a net- +worked population in that it facilitates its coexistence +of two different routes for altruistic punishers and non- +punishing cooperators, but interestingly, these two types +of cooperators cannot coexist in the networked popula- +tion. +To gain a better understanding of how these actors +coexist in the population, the evolution features of the +fractions of each actors was examined and the results +are presented in figure.3. +In the bi-stable phase, it is +the cooperators (altruistic punishers or non-punishing +cooperators) start giving way to the defectors and with +fewer cooperators around, defectors then giving way to +the exiters. With large numbers of exiters, both the al- +truistic punishers and non-punishing cooperators com- +pete for the exiters as they can only survive by adhering +to the exiters. The described phenomenon is the cyclic +dominance in which these actors dominate one another. +Here, the cyclic dominance routes can be either (i) al- +truistic punishers that dominate exiters, who dominate +defectors, who in turn dominate the altruistic punishers; +or (ii) non-punishing cooperators that dominate the ex- +iters, who dominate the defectors, who then dominate +the non-punishing cooperators. +As a key mechanism, +researchers have verified the efficiency of cyclic domi- +nance in sustaining bio-diversity or promoting cooper- +ation [42, 43]. Although we started with random initial +conditions, the evolutionary outcomes are different by +implementing more independent simulations under same +parameter combinations. For example, in the NC+D+E +attractor (figure.3A), the fraction of altruistic punishers +is temporarily much larger than that of non-punishing co- +operators at around 100th step, then the faction of altru- +istic punishers gradually decreases until it is eliminated +and the fraction of second-order free riders increases un- +til it reaches a stable state. However, in the AP + D + E +attractor (figure.3B), the fraction of altruistic punishers +is always comparable to that of non-punishing cooper- +ators up to around 1000th step, after this critical time +step, the fraction of non-punishing cooperators gradually +decreases until it is eliminated, and altruistic punishers +gradually increase to reach a stable state. Thus, it is the +initial distributions of the actors which determines the + +1.0 +0.8 +E +3 +Exit's payoff, +0.6 +0.4 +NC+D+E +All C +AP+D+E +0.2 +AP+D +B +0.0 +D +1.0 +1.2 +1.4 +1.6 +1.8 +2.0 +Temptation, b6 +FIG. 3. +Time dependence of actor abundances exhibits complicated evolutionary dynamics. +In the bi-stable +phase, starting from random initial conditions, small incentives to exit option lead the system to either NC + D + E or +AP + D + E attractor but the coexistence of these four actors is not possible. During the evolution, if the abundance of +altruistic punishers in the initial stage is much larger than that of the non-punishing cooperators, then altruistic punishers are +eliminated and non-punishing cooperators coexist with defectors and exiters through cyclic dominance (figure.3A). However, +if the abundance of altruistic punishers in the initial stage is comparable to that of non-punishing cooperators, then the +non-punishing cooperators are eliminated and altruistic punishers coexist with defectors and exiters through cyclic dominance +(figure.3B). Larger incentives to exiters turn the bi-stability to monostability and the evolutionary outcomes are determined +by the incentives that were presented to exiters. The parameters were fixed as b = 1.8, ϵ = 0.05 (top rows), ϵ = 0.2 (bottom +left), and ϵ = 0.4(bottom right). +fate of altruistic punishers and non-punishing coopera- +tors. +The phenomenon of bi-stability disappears by increas- +ing the incentives for exiters. +Evolutionary dynamics +lead to either a NC + D + E phase or a AP + D + E +phase depending on the incentives for exiters. Although +both altruistic punishers and non-punishing cooperators +can dominate exiters when the fraction of exiters reaches +its peak. However, it is non-punishing cooperators who +dominate the exiters when the incentives for exiters are +intermediate, ϵ = 0.2. +Altruistic punishers lose when +in indirect competition with the non-punishing cooper- +ators and it is eliminated with simulation proceeds. Fi- +nally, the non-punishing cooperators coexist with the de- +fectors and exiters through cyclic dominance in the net- +worked population(figure.3C). If the incentives for exiters +are larger, ϵ = 0.4, it is the altruistic punishers start to +dominate the exiters, and the non-punishing cooperators +cannot exceed the exiters and is eventually eliminated. +Finally, the altruistic punishers coexist with defectors +and exiters through cyclic dominance in the system (fig- +ure.3D). +To understand the quantitative power relationships at +the equilibria abundances of these actors, we present the +two representative cross sections of the phase diagram in +figure.4. Along the vertical transect of the ϵ − b phase +plane, figure.4A shows the stationary fractions of the four +competing actors in dependence on the exit payoff ϵ at +b = 1.8. In the traditional weak prisoner’s dilemma game +with only cooperators and defectors, a high temptation +leads to the complete dominance of defectors and the net- +work reciprocity loses its efficiency to support the coexis- +tence of cooperators and defectors [44]. Although adding +altruistic punishment in the weak prisoner’s dilemma +game can avoid this unfavorable outcome, its efficiency +to decrease defection is at the expanse of social welfare. + +A +B +B phase: NC+D+E attractor +B phase: AP+D+E attractor +1.0 +1.0 += 0.05 +0.8 +0.8 += 0.05 - +Fractions +0.6 +0.6 +0.4 +0.4 +0.2 +0.2 +0.0 +0.0 +10-2 10-1 100101 102 103 +104 +10-2 + 10-1 100 101102 103104 +C +D +NC+D+E phase +AP+D+E phase +1.0 +1.0 +AP += 0.2 +8= 0.4 +0.8 +0.8 +NC +Fractions +0.6 +D +0.6 +E +0.4 +0.4 +0.2 +0.2 +0.0 +0.0 +2 10-1 100 101 102 103 104 +10-2 10-1 100 101 102 103 104 +10-2 +time steps +time steps7 +FIG. 4. Power relations between altruistic punishers, second-order free riders, defectors, and exiters exhibiting +complicated equilibra. A. Along the vertical transect of ϵ − b phase at b = 1.8. When ϵ ≲ 0.06, the networked population +falls into the bi-stable state between the coexistence type of altruistic punishers, defectors, and exiters and the coexistence +type of second-order free riders, defectors and exiters. In the range 0.06 ≲ ϵ ≲ 0.16, altruistic punishment outcompetes the +second-order free riders, and coexists with the defectors and exiters. Whereas, in the range 0.16 ≲ ϵ ≲ 0.17, there is narrow +dominance of the bi-stable state. In the range 0.17 ≲ ϵ ≲ 0.25, the second-order free riders outcompete the altruistic punishers, +and coexist with the defectors and exiters. When 0.25 ≲ ϵ ≲ 0.51, the coexistence of altruistic punishers, defectors, and exiters +again dominates the population. Finally the eixters dominate the population when 0.51 ≲ ϵ. B. Along the horizontal transect +of ϵ−b phase plane at ϵ = 0.2, the effectiveness of altruistic punishment together with network reciprocity is sufficient to secure +prosocial behavior when b ≲ 1.29. With increasing b, altruistic punishment loses its efficiency to sustain prosocial behavior, +and adding exit option enables the networked population to first enter a coexistence state of altruistic punishers, defectors, and +exiters in the temptation range of 1.29 ≲ b ≲ 1.73, and reaches a coexistence state between second-order free riders, defectors, +and exiters when b ≳ 1.73. +That is the decreasing defection can be realized only if +the cost-to-fine ratio of altruistic punishment is relatively +low, i.e., small punishment cost γ or large punishment +fine β [5, 20–22]. If the cost-to-fine ratio of altruistic pun- +ishment is relatively large, the altruistic punishment to- +gether with network reciprocity cannot provide sufficient +benefit for cooperators, and the complete dominance of +defectors is still as per the Nash equilibrium. Adding the +exit option to the weak prisoner’s dilemma game with +altruistic punishment changes the equilibrium dramati- +cally even if the conditions to support cooperation for +altruistic punishment are unfavorable. +When exit is costly (ϵ < 0), the defectors dominate the +whole population (the D phase in figure.2). As shown +in figure.4A, if the incentives to exiters are small but +positive, the D phase gives way to the B phase, where +the system converges to either the AP +D +E attractor +or the NC +D +E attractor depending on the results of +the indirect competition between the altruistic punishers +and non-punishing cooperators. +By further increasing +the ϵ, the NC + D + E phase is reached at ϵ ≈ 0.17, and +there are two narrow strips that AP + D + E phase and +B phase can dominate separately during this increment. +The AP + D + E phase dominates in the range 0.06 ≲ +ϵ ≲ 0.16, and the B phase is short-lived again in the +range 0.16 ≲ ϵ ≲ 0.17. As ϵ continues to increase, the +NC + D + E phase gives way to AP + D + E phase +via discontinuous phase transition at ϵ ≈ 0.25. When +incentives to exiters are sufficiently large, the AP +D+E +phase is finally replaced by the E phase at the critical +point ϵ ≈ 0.51. +Figure.4B shows the horizontal transect of ϵ − b at +ϵ = 0.2, it also reveals the power relations between these +competing actors, but it is dependent on the temptation +level, b. When b is small, 1 ≤ b ≲ 1.29, the altruistic pun- +ishment together with the network reciprocity are able to +support prosocial behavior. When 1 ≤ b ≲ 1.23, the al- +truistic punishers can completely eliminate the defectors, +the elimination of the defectors also negatively affects the +exiters, and thus altruistic punishers coexist with non- +punishing cooperators as they cannot be distinguished in +the absence of defectors. The All C phase gives way to +the AP + D phase through continuous phase transition. +Although the advantages of cooperators decreases with + +A +B +NC+D+E +B +E +AP+D+E +NC+D+E +1.0 +1.0 +0.8 +0.8 +AP +口 +ractions +NC +0.6 +0.6 +ID +-E +0.4 +0.4 +M +0.2 +0.2 +0.0 +0.0 +15888888888 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +1.0 +1.2 +1.4 +1.6 +1.8 +2.0 +Exit pay-off, +temptation, b8 +FIG. 5. Evolutionary snapshots reveal the detailed dominance modes between all actors. Shown are evolutionary +snapshots at different time steps (column) and for different temptations for defection (rows). When the temptation is small +(top row), both altruistic punishers and second-order free riders dominate the exiters, who take over the defectors. However, +the decrease of exiters is much fast than its increase, and they are eliminated first. The defectors are then eliminated by the +altruistic punishers, and finally the altruistic punishers coexist with second-order free riders in the population, and these two +actors cannot separately be distinguished. When the temptation is larger (second row), the fate of exiters is the same as in the +first row, however, the larger temptation leads more competitive defectors. Therefore, instead of completely dominating the +defectors, the altruistic punishers coexist with defectors who replace the second-order free-riders until second-order free-riders +they are eliminated. When the temptation is even larger (third row), more competitive defectors can encroach on both, the +altruistic punishers and second-order free riders can only survive when they adhere to exiters. The indirect competition between +altruistic punishers and second-order free riders with exiters determine the outcome for these two actors. Compared with non- +punishing cooperators, altruistic punishers have greater fitness when compared to defectors and have greater probability to +endure, therefore non-punishing cooperators are eliminated, and altruistic punishers coexist with defectors and exiters through +cyclic dominance. When the temptation is at its largest (bottom row), exiters dominate and non-punishing cooperators have +a larger probability to endure than altruistic punishers as it avoids the cost of punishment. Finally altruistic punishers are +eliminated and non-punishing cooperators coexist with defectors and exiters. Results were obtained with ϵ = 0.2 after the +30000th step to generate the final snapshots (rightmost column). The intermediate snapshots (second to fourth columns) were +taken at different time steps across rows to ensure that the figure as illustrative as possible. +increasing b, the cooperators who punish defectors gain +a greater advantage when compared against defectors, +and thus network reciprocity supports the coexistence of +altruistic punishers and defectors in this instance. If the +conditions to support cooperation with altruistic punish- +ment are unfavorable, adding an exit option can promote +the system to the AP +D+E phase when b ≲ 1.73. How- +ever, with increasing b, the AP + D + E phase gives way +to the NC + D + E phase through discontinuous phase +transition at the critical point, b ≈ 1.73. +To reexamine the evolutionary dynamics and further +check the indirect competition between altruistic punish- +ers and non-punishing cooperators in both spatial and +temporal dimensions,. We plotted the evolutionary snap- +shots for varying b at ϵ = 0.2, and the results are pre- +sented in figure.5. When the temptation is small (top row +in figure.5), the exiters were eliminated first by altruistic +punishers and non-punishing cooperators, and the de- +fectors experienced the same fate shortly after. The al- +truistic punishers coexist with non-punishing cooperators +eventually as they cannot be distinguished and the sys- +tem falls into frozen state. A larger temptation makes the +defectors more competitive (second row in figure.5), and +instead of being eliminated by the altruistic punishers, + +Temptation, b +NC +D +b=1.04 +AP +E +b=1.25 +b=1.5 +b=1.8 +timesteps9 +FIG. 6. Initial conditions determine the outcome of +altruistic punishers and non-punishing cooperators in +the bi-stable phase. Shown are the evolutionary outcomes +after implementing 100 independent simulations for each pa- +rameter combination under four different initial conditions. +The initial conditions were (i) 97% of players were initially +assigned as AP, (ii) 97% of players were initially assigned as +NC, (iii) 97% of players were initially assigned as D, and (iv) +97% of players were initially assigned as E. The rest of the +other action types were assigned to the other players with +equal probability in these different initial conditions. Param- +eters were fixed as b = 1.8, from left to right, ϵ = 0.05, 0.4, 0.6, +respectively. +they can coexist. However, the coexistence of defectors +cannot ensure the survival of exiters, who are eliminated +in situations with small temptation. The non-punishing +cooperators are eliminated by defectors and finally, the +altruistic punishers coexist with defectors in the popula- +tion. When the temptation is even larger, the coexistence +of defectors and altruistic punishers was no longer pos- +sible, instead, defectors can invade both altruistic pun- +ishers and non-punishing cooperators. The competitive +defectors allow for the survival of exiters. In turn, altru- +istic punishers and non-punishing cooperators can sur- +vive by adhering to the survived exiters. It is therefore, +both altruistic punishers and non-punishing cooperators +can coexist with defectors and exiters through different +cyclic dominance routes. +However, these two types of +cyclic dominance cannot coexist in the population, and +the indirect competition to the territories of exiters be- +tween altruistic punishers and non-punishing cooperators +determine the outcome of the competitors. Competitive +defectors more easily negatively affexct non-punishing co- +operators than altruistic punishers (third row and second +column in figure.5), and therefore, non-punishing cooper- +ators are eliminated first, and the altruistic punishers, de- +fectors, and exiters coexist within the population. When +the temptation is the largest (bottom row in figure.5), +defectors are the most competitive, altruistic punishers +and non-punishing cooperators are exploited by defectors +at almost the same speed, and the exiters dominate by +eliminating the defectors. In the indirect competition of +exiters with the non-punishing cooperators, the altruis- +tic punishers loses its advantages due to the existence of +punishment cost, and non-punishing cooperators coexist +with defectors and exiters. +Our results have shown that by adding an exit option +results in the bi-stable dynamics and it is the initial dis- +tribution of actors determines the outcome of altruistic +punishers and non-punishing cooperators. It is generally +accepted that the initial conditions are crucial for evolu- +tionary outcomes in agent-based models [45]. We further +assessed whether the initial fractions of actors is a poten- +tial reason that the system exhibits bi-stability. Figure.6 +presents the evolutionary outcomes with ϵ = 0.05, 0.4, +and 0.6 under four different initial conditions. The four +different conditions are: (i) 97% of players were initially +assigned as AP, (ii) 97% of players were initially assigned +as NC, (iii) 97% of players were initially assigned as D, +and (iv) 97% of players were initially assigned as E. The +other players were assigned one of the other three actions +with equal probability in these conditions. The results +were obtained by implementing 100 independent simula- +tions. We found that when ϵ = 0.05 (left column in fig- +ure.6), the evolutionary outcome was always AP +D+E +if the majority of players initially had action AP or action +D. However, if the majority of players initially had NC +action, then the system reached the attractor NC+D+E +with 95% probability. If the majority of players were E, +then the system reached the attractor AP + D + E or +NC +D+E with 36% and 62% probability, respectively. +Larger incentives to exiters switched the bi-stability to +monostability (middle and right column in figure.6). In +the monostability state, evolutionary dynamics lead to +either the AP + D + E or the E phase depending on the +incentives to the exiters, and evolutionary outcomes are +independent on the initial conditions. The finite-size ef- +fects are a potential pitfall that may generate misleading +results when implementing agent-based models in struc- +tured populations [45]. Thus, it is crucial to choose a +sufficiently large network size or to employ the method of +subsystem solutions to avoid this potential issue [46, 47]. +It is noteworthy that the system has 23% probability to +fall into the full E phase when most players initially had +D action at ϵ = 0.4 (middle column in figure.6). +We +do believe that the counterintuitive E phase is the prod- +uct of the finite-size effect, and the pure AP + D + E +phase can be expected as long as a larger network size +was implemented. +DISCUSSION +To discuss, we have shown that by adding an exit op- +tion to the two-stage prisoner’s dilemma game results in +complicated dynamics. Particularly, in the infinite and +well-mixed population, it was observed that exiters pro- + +NC+D+E +E +AP+D+E +62% +100% +100% +E +36% +1 +1 +1 +2% +/ +1 +1 +- +I +100% +77% +100% +D +23% +I +1 +1 +1 +/ +95% +1 +100% +100% +NC +/ +5% +1 +1 +1 +1 +/ +100% +100% +I +100% +AP +1 +I +1 +-- +1 += 0.05 +=0.4 +=0.610 +vide little benefit to cooperation. When the effectiveness +of altruistic punishment is sufficient to support cooper- +ation, adding an exit option turns the bi-stable equilib- +rium between the mixed AP −NC and pure D to another +bi-stable equilibrium, whereby the mixed AP − NC and +pure E coexists (panel C and D in the figure.A2). When +altruistic punishment itself cannot establishes coopera- +tion, the monomorphic defecting equilibrium is replaced +by the monomorphic exiting equilibrium (panel A and B +in the figure.A2). In the finite and well-mixed popula- +tion, although the availability of exit options maintains +the survival of both altruistic punishers and second-order +free riders through two types of cyclic dominance, the +altruistic punishers never dominate the population. In +contrast with the well-mixed populations, combining the +exit option with network reciprocity produces greatly dif- +ferent outcomes. We determined that the domination of +altruistic punishment is possible in a networked popula- +tion. Altruistic punishers can coexist with defectors and +exiters through cyclic dominance in a majority of the ϵ−b +phase plane. When the temptation is large, b ≳ 1.71, ex- +iters enable the survival of second-order free riders. De- +pending on the incentives to exiters, the system also fall +into a bi-stable phase or single NC+D+E phase. There- +fore the exit option is certainly not a panacea in solving +social dilemmas. +Previous studies have shown that introduced voluntary +participation is capable of establishing altruistic punish- +ment in both finite and infinite populations [6–10]. In the +infinite population, evolutionary dynamics can result in +either a Nash equilibrium of punishing and non-punishing +cooperators or to an oscillating state without punish- +ers [6]. +If a single cooperator (either a non-punishing +cooperator or a punisher) can participate in the game, +and a punisher can punish the non-punishing cooperator +even in the absence of defectors, the evolutionary dynam- +ics result in the stable coexistence of altruistic punishers +and non-punishing cooperators [9]. In a finite population, +with the assistance of loners, altruistic punishers can pre- +vail and even dominate the whole population for most +of the time when mutations are rare [8]. If loners can +escape punishment, altruistic punishment prevails even +under the threat of anti-social punishment [11]. Exiters +produce outcomes that differ greatly from these in lon- +ers. In the infinite and well-mixed population, adding +an exit option can also result in a bi-stable outcome, in +which the Nash equilibrium can be either the coexistence +of altruistic punishers and non-punishing cooperators or +a monomorphic exiting equilibrium. +However, this bi- +stable outcome is only possible when the punishment it- +self is sufficient to maintain cooperation, otherwise, the +bi-stable outcome can be replaced with a monomorphic +exiting equilibrium. In other words, exiters just simply +destabilize the defectors and eventually replaces them in +the infinite population. In the finite population, although +exiters allow the survival of altruistic punishment when +the exiter’s payoff is moderate, altruistic punishers never +dominate the whole population (e.g. figure.1A). The di- +rect comparison between exiters and loners in a finite +and infinite population lead us to conclude that loners +are more effective than exiters in supporting the preva- +lence of altruistic punishment. +The effectiveness of altruistic punishment is not only +challenged by second-order free riders but also by anti- +social punishment. It has been experimentally reported +that the existence of antisocial punishment is widespread +in different human cultures [48–50]. Recent theoretical +studies have shown that the existence of antisocial pun- +ishment can prevent the successful coevolution of pun- +ishment and cooperation [51, 52]. Furthermore, if pun- +ishment is available for loners, punishment does not in- +creases cooperation and altruistic punishment becomes a +self-interested tool for protecting itself against potential +competitors [53]. As discussed above, exiters are a po- +tential spiteful punishment as it harms both cooperators +and defectors, while loners generate a small-but-positive +payoff for its opponent. This tiny difference leads to to- +tally different equilibrium in a one-shot game. Exiters +can destabilize defectors and finally replace them, while +loners can sustain cooperation through cyclic dominance. +If we extend our model by considering all punishment sets +where actors can be punished by each other and exiters +cannot escape potential punishment by both cooperators +and defectors. By restricting the analysis to a one-shot +game, we determine how this setup influenced the stabil- +ity of punishment, and whether and how this setup gen- +erates outcomes that differ from that of loners. These +undoubtedly invite future considerations. +Exiters established the prevalence of altruistic punish- +ers and eliminated the second-order free riders when it +adheres to network reciprocity in a certain parameter +range (e.g. figure.2 and figure.4). However exiters allow +for the survival of second-order free riders, who can not +only survive, but also dominate the population in some +certain areas of the phase plane. The robustness of this +finding needs to be verified in a human behavior exper- +iment. Human behavior experiments may generate con- +trasting or surprising outcomes with theories on many is- +sues. Scale-free topology, for example, is often recognized +theoretically as an optimal structure for the survival of +cooperation, however, this argument cannot be verified +by experiment and the cooperation level among humans +cannot exceed the level established in the lattice [54]. +Similarly, although strong reciprocity theorists believe +that humans are inherently altruistic and cooperators +will sacrifice their personal interests to (i). achieve fair +outcomes and to (ii). punish non-cooperators[55, 56], this +theory cannot be confirmed by experiments. Yamagishi +et al. performed large scale human behavior experiments +and found that there was no correlation between the ten- +dencies to reject unfair offers in the ultimate game and +tendencies to exhibit prosocial behavior in other games +[57]. Although Yamagishi’s finding was challenged due +to its insufficient sample size, Egloff et al. further con- +firmed that there was indeed no correlation between pos- +itive and negative reciprocity through analyzing the pri- + +11 +vate household data from the Socio-Economic Panel of +the German Institute for Economics Research [58]. +A +recent experimental work is of direct relevance for our +model. Introducing punishment into networks has been +proven to be an efficient method to promote cooperation +theoretically [14, 21–23]. However, in a recent large-scale +human behavior experiment, it was concluded that the +introduced peer punishment did not promote coopera- +tion in structured populations, and instead diminished +the benefits of network reciprocity [59]. +Although we +have shown that exiters support the dominance of altru- +istic punishment when it adheres to network reciprocity, +human behavior experiments are needed to further verify +our theory. +ARTICLE INFORMATION +Acknowledgements. +We thank Prof. +Dr. +Marko +Jusup for valuable discussions. This research was sup- +ported by the National Science Fund for Distinguished +Young Scholars (grants no. 62025602). We also acknowl- +edge support from (i) a JSPS Postdoctoral Fellowship +Program for Foreign Researchers (grant no. +P21374), +and an accompanying Grant-in-Aid for Scientific Re- +search from JSPS KAKENHI (grant no. JP 22F31374), +and the National Natural Science Foundation of China +(grant no. 11931015) to C. S. as a co-investigator, (ii) the +National Natural Science Foundation of China (grants +no. 11931015, 12271471 and 11671348) to L. S., (iii) Na- +tional Natural Science Foundation of China (grants no. +U22B2036, 11931015), Key Technology Research and De- +velopment Program of Science and Technology-Scientific +and Technological Innovation Team of Shaanxi Province +(Grant No. 2020TD-013) and the XPLORER PRIZE. +to Z. W, and (iv) the grant-in-Aid for Scientific Research +from JSPS, Japan, KAKENHI (grant No. JP 20H02314) +awarded to J. T. +Author contributions. +C. S. and L. S. conceived re- +search. +C. S. and Z. S. performed simulations. +All co- +authors discussed the results and wrote the manuscript. +Conflict of interest. +Authors declare no conflict of in- +terest. +Appendix +STABILITY ANALYSIS OF THE EQUILIBRIA IN +INFINITE AND WELL-MIXED POPULATION +Solving +Eq.7, +we +obtain +12 +equilibrium +points: +(1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 0, 1), (0, 0, 1, 0), (ϵ, 0, 0, 1 − +ϵ), +(0, ϵ, 0, 1 − ϵ), +(x, 1 − x, 0, 0), +(x, ϵ − x, 0, 1 − +ϵ), ( −1+b +β +, 1−b+β +β +, 0, 0), ( +ϵ +b−β , 0, ϵ−β−ϵβ +(βϵ)γ , 1 − ϵ(γ+1+β−b) +(b−β)γ +), +( (−1+b)ϵ +β +, ϵ−β+βϵ +β +, 0, 1−ϵ), ( +γ +1−b+β+γ , 0, +−1+b−β +−1+b−β+γ , 0). To +examine the stability of these equilibria, we calculate the +0.0 +5.0x104 +1.0x105 +1.5x105 +2.0x105 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Fractions +time steps + AP + NC + D + E +A +B +Fractions +FIG. A1. Numerical simulation further demonstrates +that the survival of altruistic punishment is due to the +cyclic dominance between altruistic punishers, defec- +tors, and exiters. A. Defectors take over the whole popu- +lation even if altruistic punishers initially dominate the pop- +ulation when the exiters’ payoff is negative. +B. Small but +positive exiters’ payoff enables the coexistence of altruistic +punishers, non-punishing cooperators, defectors, and exiters +through cyclic dominance. If defectors initially dominate the +population, the mutated exiters invade the defectors, and af- +ter transient dynamics, the defectors finally give way to the +exiters. +When exiters dominate the population, altruistic +punishment is less costly and cooperating is more valuable +than exiting, and thus altruistic punishers take over the whole +population. Thereafter, non-punishing cooperators dominate +altruistic punishers and take over the whole population since +altruistic punishers are less valuable than non-punishing coop- +erators. This proceeds until the dominance of non-punishing +cooperators gives way to defectors again. The Parameter val- +ues are b = 1.5, β = 0.3, γ = 0.1, µ = 0.001, s = 0.2, ϵ = −0.2 +(A) and ϵ = 0.2 (B). +eigenvalues of Jacobian matrix: +J = +� +�� +∂f(x,y,z) +∂x +∂f(x,y,z) +∂y +∂f(x,y,z) +∂z +∂g(x,y,z) +∂x +∂g(x,y,z) +∂y +∂g(x,y,z) +∂z +∂h(x,y,z) +∂x +∂h(x,y,z) +∂y +∂h(x,y,z) +∂z +� +�� . +(A1) +Then we have the following conclusion. +Theorem 1. When b < 1 + β, and ϵ < 0, the equi- +librium points (x∗, 1 − x∗, 0, 0) and (0, 0, 1, 0) are stable, +while the rest of others are unstable; When b < 1 + β, +and ϵ > 0, the equilibrium points (x∗, 1 − x∗, 0, 0) and +(0, 0, 0, 1) are stable, and the others are unstable; When +b ≥ 1 + β, only the equilibrium point (0, 0, 1, 0) is stable, +and the rest of others are unstable. When ϵ > 0, only +the equilibrium point (0, 0, 0, 1) is stable, and the rest of +others are unstable. +Proof. (1). For K1: (x, y, z, w) = (1, 0, 0, 0), the Jacobian + +12 +FIG. A2. Adding exit option destabilizes defection regardless of whether altruistic punishment can establish +cooperation in an infinite population. When the cost-to-effect ratio of altruistic punishment is insufficient to establish +cooperation (top row), b − β > 1, the monomorphic defecting equilibrium is replaced by the monomorphic exiting equilibrium +for positive values of ϵ. When the cost-to-effect ratio of altruistic punishment is capable of establishing cooperation (bottom +row), b − β < 1, the bi-stable equilibrium of the mixed altruistic punisher and non-punishing cooperator equilibrium and the +monomorphic defecting equilibrium is replaced by the other bi-stable equilibrium between the mixed altruistic punisher and +non-punishing cooperator equilibrium and the monomorphic exiting equilibrium for positive values of ϵ. The dashed line on the +AP − NC edge indicates that all the points on this edge are unstable. The filled black circles, filled gray circles, and unfilled +circles represent stable fixed points, saddle points, and unstable points, respectively. +The parameters values are β = 0.3, +γ = 0.1, ϵ = −0.2 (left column), ϵ = 0.2 (right column), b = 1.5 (top row), and b = 1.2 (bottom row). +matrix J1 is +J1 = +� +� +−1 + ϵ −1 + ϵ −b + β + ϵ +0 +0 +0 +0 +0 +−1 + b − β +� +� +(A2) +and its corresponding eigenvalues are +{λ1, λ2, λ3} = {0, −1 + b − β, −1 + ϵ}. +(A3) +When b > β + 1, K1 is unstable because −1 + b − β is a +positive eigenvalue. Otherwise, there is at least one zero +eigenvalue. Thus, we use the center manifold theorem to +analyze the stability of K1. Using b < β + 1 as an ex- +ample. First, there is an invertible matrix whose column +elements are the eigenvectors of J1 +P = +� +� +−1 −1 1 +1 +0 +0 +0 +1 +0 +� +� +(A4) +and J1 can be diagonalized as +P −1J1P = +� +� +0 +0 +0 +0 −1 + b − β +0 +0 +0 +−1 + ϵ +� +� . +(A5) +Then change of variable: +� +� +x1 +y1 +z1 +� +� = P −1 +� +� +x +y +z +� +� = +� +� +y +z +x + y + z +� +� +(A6) + +A +B +D +E +D +D +E +D +O +AP +NC +AP +NC +D +D +c +D +D +E +D +D +E +D +C +Q +C +AP +NC +AP +NC +D +D13 +and the system becomes +˙x1 =g(z1 − x1 − y1, x1, y1) +=x1((1 − x1)(−ϵ − y1 + z1)− +x1(−ϵ + bx1 + (b − β)(−x1 − y1 + z1))− +y1(−ϵ + bx1 + (b − β)(−x1 − y1 + z1))) +˙y1 =h(z1 − x1 − y1, x1, y1) +=y1(−x1(−ϵ − y1 + z1) − y1(−ϵ − y1 − x1y1 + z1)+ +(1 − y1)(−ϵ + bx1 + (b − β)(−x1 − y1 + z1))) +˙z1 =f(z1 − x1 − y1, x1, y1) + g(z1 − x1 − y1, x1, y1) ++ h(z1 − x1 − y1, x1, y1) +=x1(ϵ(−1 + 2x1 + y1) + (−1 + x1 + bx1 + by1)(y1 − z1)− +β(x1 + y1)(x1 + y1 − z1))+ +y1((−1 + y1)(ϵ + b(y1 − z1) − β(x1 + y1 − z1))+ +x1(ϵ + y1 − z1) + y1(ϵ + y1 + x1y1 − z1))+ +(x1 + y1 − z1)(ϵ + (1 − b + β + x1)y12− +ϵz1 + (−1 + z1)z1 + y1(1 + x2 +1 + x1(1 + β − z1)+ +(−2 + b − β)z1)) +. +(A7) +Put the system into the form +˙X = AX + F(X, Y ) +˙Y = BY + G(X, Y ) , +(A8) +where X = [x1], Y += +� +y1 +z1 +� +, and A = [0], B = +� +−1 + b − β +0 +0 +−1 + ϵ +� +, whose eigenvalues have zero and +negative real parts, respectively. F and G are the func- +tions of X and Y . They satisfy the condition F (0, 0) = +0, F ′(0, 0) = O. According to the existence theorem of +the center manifold, the system has the center manifold +S = {(X, H(X))|H : R1 → R2}. We define a mapping +(Mϕ)(X) =ϕ′(X)(AX + F (X, ϕ(X)) +− Bϕ(X) − G(X, ϕ(X)) +(A9) +Set ϕ(Y ) = O(X2), we obtain +˙x1 = x1(−ϵ(1 − x1) − x1(−ϵ + bx1 − x1(b − β))) + O(x4 +1) +(A10) +Then we define m(x1) = x1(−ϵ(1 − x1) − x1(−ϵ + bx1 + +−x1(b−β))), and m(x1)′ = 2ϵx1−3x2 +1β−ϵ. Since m(0) < +0, then x1 = 0 is asymptotically stable. Accordingly, we +can conclude the point K1 is stable when b < β+1. When +b = β + 1, K1 is unstable in accordance with the center +manifold theorem whose derivation process is similar to +the above analysis. +(2). For K2: (x, y, z, w) = (0, 1, 0, 0), the correspond- +ing eigenvalues of J are +{λ1, λ2, λ3} = {0, −1 + b, −1 + ϵ}. +(A11) +K2 is unstable since −1 + b > 0. +(3). For K3: (x, y, z, w) = (0, 0, 1, 0). Its correspond- +ing eigenvalues of J are +{λ1, λ2, λ3} = {0, ϵ, −γ}. +(A12) +When ϵ < 0, K3 has an eigenvalue with zero real part and +other eigenvalues with negative real part. According to +the center manifold theorem, K3 is stable. When ϵ > 0, +K3 is unstable because the eigenvalue ϵ has a positive +real part. +(4). For K4 : (x, y, z, w) = (0, 0, 0, 1). Its correspond- +ing eigenvalues of J are +{λ1, λ2, λ3} = {−ϵ, −ϵ, −ϵ}. +(A13) +K4 is stable when ϵ > 0 because all eigenvalues have +negative real parts. K4 is unstable when ϵ < 0 because +all eigenvalues have positive real parts. +(5). For K5 : (x, y, z, w) = (ϵ, 0, 0, 1 − ϵ). Its corre- +sponding eigenvalues of J are +{λ1, λ2, λ3} = {0, ϵ(−1 + b − β), ϵ(1 − ϵ)}. +(A14) +When 0 < ϵ < 1 or ϵ < 0 and b < 1 + β, K5 is unstable +because one of its eigenvalues has a positive real part. +When ϵ < 0 and b ≥ 1+β, K5 has at least one eigenvalue +with a zero real part and the others have negative real +parts. According to the center manifold theorem, K5 is +unstable. +(6). For K6 : (x, y, z, w) = (0, ϵ, 0, 1 − ϵ). Its corre- +sponding eigenvalues of J are +{λ1, λ2, λ3} = {0, ϵ(−1 + b), ϵ(1 − ϵ)}. +(A15) +When ϵ > 0, K6 is unstable because eigenvalue ϵ(−1 + +b) >. When ϵ < 0, there is one eigenvalue with a zero +real part and two eigenvalues with negative real parts. +According to the center manifold theorem, K6 is unsta- +ble. +(7). For K7 : (x, y, z, w) = (x∗, 1 − x∗, 0, 0). Its corre- +sponding eigenvalues of J are +{λ1, λ2, λ3} = {0, −1 + ϵ, −1 + b − βx∗}. +(A16) +When x∗ > b−1 +β , namely b < 1 + β, there is one eigen- +value with a zero real part and others with negative real +parts. According to the center manifold theorem, K7 is +stable. When x∗ < b−1 +β , K7 is unstable because one of +its eigenvalues has a positive real part. +(8). For K8 : (x, y, z, w) = (x∗, ϵ − x∗, 0, 1 − ϵ + x∗). +Its corresponding eigenvalues of J are +{λ1, λ2, λ3} = {0, ϵ − ϵ2, −ϵ + β − βx∗}. +(A17) +When ϵ > 0, K8 is unstable because ϵ − ϵ2 > 0. When +ϵ < 0, K8 is unstable because −ϵ + β − βx∗ > 0. +(9). +For K9 : (x, y, z, w) = ( −1+b +β +, 1−b+β +β +, 0, 0). +Its +corresponding eigenvalues of J are +{λ1, λ2, λ3} = {0, 0, −1 + ϵ}. +(A18) + +14 +K9 exists only when b < 1 + β. When K9 exists, there is +one eigenvalue with a negative real part and two eigenval- +ues with zero real parts. According to the center manifold +theorem, k9 is unstable. +(10). +For K10 : (x, y, z, w) = ( +ϵ +b−β , 0, ϵ−β−ϵβ +(b−β)γ , 1 − +ϵ(γ+1+β−b) +(b−β)γ +). Its corresponding eigenvalues of J are +{λ1, λ2, λ3} = +{−ϵ(−1 + b − β) +b − β +,−ϵ(−1 + b − β) +b − β +,ϵ+ ϵ2(−1 + b − β + γ) +(b − β)γ +} +. +(A19) +K10 exists when 1 − ϵ(γ+1+β−b) +(b−β)γ +) < 1, namely b > β + +ϵ 1−γ +γ+ϵ . Then its eigenvalue ϵ + ϵ2(−1+b−β+γ) +(b−β)γ +> 0. Thus, +K10 is unstable. +(11). For K11 : (x, y, z, w) = ( (−1+b)ϵ +β +, ϵ−β+βϵ +β +, 0, 1−ϵ). +Its corresponding eigenvalues of J are +{λ1, λ2, λ3} = {0, 0, ϵ(1 − ϵ)}. +(A20) +K11 exists when ϵ > 0, then eigenvalue ϵ(1 − ϵ) > 0. +Thus, K11 is unstable. +(12). For K12 : (x, y, z, w) = ( +γ +1−b+β+γ , 0, +1−b+β +1−b+β+γ , 0). +Its corresponding eigenvalues of J are +{λ1, λ2, λ3} = +{ (1 − b + β)γ +1 − b + β + γ , (1 − b + β)γ +1 − b + β + γ , ϵ + +(−b + β)γ +1 − b + β + γ }. +(A21) +K12 exists when b < 1+β, then eigenvalue (1−b+β)γ +1−b+β+γ > 0. +Thus K12 is unstable. +[1] Clutton-Brock T H and Parker G A 1995 Nature 373 +209–216 +[2] West S A, Griffin A S and Gardner A 2007 Journal of +evolutionary biology 20 415–432 +[3] Henrich J, McElreath R, Barr A, Ensminger J, Barrett +C, Bolyanatz A, Cardenas J C, Gurven M, Gwako E, +Henrich N et al. 2006 Science 312 1767–1770 +[4] Fehr E and G¨achter S 2002 Nature 415 137–140 +[5] Egas M and Riedl A 2008 Proceedings of the Royal Society +B: Biological Sciences 275 871–878 +[6] Brandt H, Hauert C and Sigmund K 2006 Proceedings of +the National Academy of Sciences 103 495–497 +[7] Mathew S and Boyd R 2009 Proceedings of the Royal +Society B: Biological Sciences 276 1167–1174 +[8] Hauert C, Traulsen A, Brandt H, Nowak M A and Sig- +mund K 2007 science 316 1905–1907 +[9] Fowler J H 2005 Proceedings of the National Academy of +Sciences 102 7047–7049 +[10] Sasaki T, Br¨annstr¨om ˚A, Dieckmann U and Sigmund K +2012 Proceedings of the National Academy of Sciences +109 1165–1169 +[11] Garcia J and Traulsen A 2012 Journal of theoretical bi- +ology 307 168–173 +[12] Santos M d, Rankin D J and Wedekind C 2011 Pro- +ceedings of the Royal Society B: Biological Sciences 278 +371–377 +[13] Rockenbach B and Milinski M 2006 Nature 444 718–723 +[14] Brandt H, Hauert C and Sigmund K 2003 Proceedings of +the royal society of London. Series B: biological sciences +270 1099–1104 +[15] Ohtsuki H, Iwasa Y and Nowak M A 2009 Nature 457 +79–82 +[16] Hilbe C and Traulsen A 2012 Scientific reports 2 1–4 +[17] Boyd R, Gintis H, Bowles S and Richerson P J 2003 Pro- +ceedings of the National Academy of Sciences 100 3531– +3535 +[18] S¨a¨aksvuori L, Mappes T and Puurtinen M 2011 Pro- +ceedings of the Royal Society B: Biological Sciences 278 +3428–3436 +[19] Gavrilets S and Fortunato L 2014 Nature communica- +tions 5 1–11 +[20] Helbing D, Szolnoki A, Perc M and Szab´o G 2010 PLoS +computational biology 6 e1000758 +[21] Szolnoki A and Perc M 2017 Physical Review X 7 041027 +[22] Helbing D, Szolnoki A, Perc M and Szab´o G 2010 New +Journal of Physics 12 083005 +[23] Perc M and Szolnoki A 2012 New Journal of Physics 14 +043013 +[24] Molleman L, K¨olle F, Starmer C and G¨achter S 2019 +Nature Human Behaviour 3 1145–1153 +[25] Boyd R, Gintis H and Bowles S 2010 Science 328 617– +620 +[26] Przepiorka W and Diekmann A 2013 Proceedings of the +Royal Society B: Biological Sciences 280 20130247 +[27] Han T A 2016 Emergence of social punishment and co- +operation through prior commitments Proceedings of the +Thirtieth AAAI Conference on Artificial Intelligence pp +2494–2500 +[28] Eldakar O T and Wilson D S 2008 Proceedings of the +National Academy of Sciences 105 6982–6986 +[29] Orbell J M and Dawes R M 1993 American sociological +review 787–800 +[30] Hauert C, De Monte S, Hofbauer J and Sigmund K 2002 +Science 296 1129–1132 +[31] Hauert C, De Monte S, Hofbauer J and Sigmund K 2002 +Journal of Theoretical Biology 218 187–194 +[32] Shen C, Jusup M, Shi L, Wang Z, Perc M and Holme P +2021 Journal of the Royal Society Interface 18 20200777 +[33] Vukov J, Pinheiro F L, Santos F C and Pacheco J M 2013 +PLoS computational biology 9 e1002868 +[34] Fudenberg D and Imhof L A 2006 Journal of Economic +Theory 131 251–262 +[35] Imhof L A, Fudenberg D and Nowak M A 2005 Proceed- +ings of the National Academy of Sciences 102 10797– +10800 +[36] Santos F C, Pacheco J M and Skyrms B 2011 Journal of +Theoretical Biology 274 30–35 +[37] McAvoy A 2015 Journal of Economic Theory 159 66–69 + +15 +[38] Nowak M A, Sasaki A, Taylor C and Fudenberg D 2004 +Nature 428 646–650 +[39] Traulsen A, Nowak M A and Pacheco J M 2006 Physical +Review E 74 011909 +[40] Dreber A, Rand D G, Fudenberg D and Nowak M A 2008 +Nature 452 348–351 +[41] Wu J J, Zhang B Y, Zhou Z X, He Q Q, Zheng X D, +Cressman R and Tao Y 2009 Proceedings of the National +Academy of Sciences 106 17448–17451 +[42] Reichenbach T, Mobilia M and Frey E 2007 Nature 448 +1046–1049 +[43] Szolnoki A, Mobilia M, Jiang L L, Szczesny B, Ruck- +lidge A M and Perc M 2014 Journal of the Royal Society +Interface 11 20140735 +[44] Szab´o G, Vukov J and Szolnoki A 2005 Physical Review +E 72 047107 +[45] Perc M, Jordan J J, Rand D G, Wang Z, Boccaletti S +and Szolnoki A 2017 Physics Reports 687 1–51 +[46] Szolnoki A and Perc M 2016 New Journal of Physics 18 +083021 +[47] Perc M 2017 European Journal of Physics 39 014001 +[48] Herrmann B, Thoni C and Gachter S 2008 Science 319 +1362–1367 +[49] Denant-Boemont L, Masclet D and Noussair C N 2007 +Economic theory 33 145–167 +[50] G¨achter S and Herrmann B 2011 European economic re- +view 55 193–210 +[51] Rand D G, Ohtsuki H and Nowak M A 2009 Journal of +theoretical biology 256 45–57 +[52] Rand D G, Armao IV J J, Nakamaru M and Ohtsuki H +2010 Journal of theoretical biology 265 624–632 +[53] Rand D G and Nowak M A 2011 Nature communications +2 1–7 +[54] Gracia-L´azaro C, Ferrer A, Ruiz G, Taranc´on A, Cuesta +J A, S´anchez A and Moreno Y 2012 Proceedings of the +National Academy of Sciences 109 12922–12926 +[55] Fehr E, Fischbacher U and G¨achter S 2002 Human nature +13 1–25 +[56] Bowles S and Gintis H 2004 Theoretical population biol- +ogy 65 17–28 +[57] Yamagishi T, Horita Y, Mifune N, Hashimoto H, Li +Y, Shinada M, Miura A, Inukai K, Takagishi H and +Simunovic D 2012 Proceedings of the National Academy +of Sciences 109 20364–20368 +[58] Egloff B, Richter D and Schmukle S C 2013 Proceedings +of the National Academy of Sciences 110 E786–E786 +[59] Li X, Jusup M, Wang Z, Li H, Shi L, Podobnik B, Stanley +H E, Havlin S and Boccaletti S 2018 Proceedings of the +National Academy of Sciences 115 30–35 + diff --git a/49E4T4oBgHgl3EQfBAv2/content/tmp_files/load_file.txt b/49E4T4oBgHgl3EQfBAv2/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..e9364bca7008540ac75c5bc0ad688a73cf0dc826 --- /dev/null +++ b/49E4T4oBgHgl3EQfBAv2/content/tmp_files/load_file.txt @@ -0,0 +1,816 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf,len=815 +page_content='Exit options sustain altruistic punishment and decrease the second-order free-riders, but it is not a panacea Chen Shen1,2, Zhao Song3, Lei Shi2,∗ Jun Tanimoto1, and Zhen Wang3,4† 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Faculty of Engineering Sciences, Kyushu University, Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' School of Mechanical Engineering,Northwestern Polytechnical University, Xi’an 710072, China 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' School of Artifcial Intelligence, OPtics and ElectroNics (iOPEN), Northwestern Polytechnical University, Xi’an 710072, China (Dated: January 13, 2023) The emergence and maintenance of altruistic punishment remains an open question and this conundrum is shared across diverse fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In this study, we evaluated the evolution of altruistic punishment in a two-stage prisoner’s dilemma game in which cooperators and defectors interact with another two actors called altruistic punishers and exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Traditionally cooperators and defectors, in the first stage, choose to cooperate and defect with their opponent, respectively, but they do not punish in the second stage;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' the altruistic punishers cooperate in the first stage and punish defectors in the second stage, and the exiters who simply exit the game in favor of a small payoff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' We found that exiters did not provide any substantial assistance to altruistic punishment in well-mixed populations, they destabilize defection and finally replace them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In the finite population, although the exit option enables the coexistence of altruistic punishers, defectors, and exiters through cyclic dominance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Altruistic punishers never dominate the finite population and the exit option provides another alternative cyclic dominance route for the emergence of non-punishing cooperators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In networked populations, however, adding the exit option allows for the establishment of altruistic punishment, and enables the coexistence of altruistic punishers, defectors, and exiters through cyclic dominance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' However, this type of cyclic dominance is not always stable, with adjustments to the exit payoff, this type of cyclic dominance is replaced by the cyclic dominance of non-punishing cooperators, defectors, and exiters or a bi-stable state between these two types of cyclic dominance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Our results indicate that although the exit option can help explain altruistic punishment, it is certainly not a panacea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Keywords: Evolutionary game theory;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Cooperation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Coexistence;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Cyclic dominance;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Bi-stable INTRODUCTION Costly punishment is ubiquitous in many animal species including humans [1–3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Unlike other animals, humans often show altruistic traits, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=', humans punish other individuals who have harmed others even at the ex- pense of their own interest [3, 4], however, the emergence and maintenance of altruistic punishment is an evolu- tionary conundrum as costly punishment is unlikely to evolve according to natural selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Costly punishment reduces the payoff for both the punisher and the pun- ished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' If it is the fittest who survive, the second-order free riders that cooperate but do not punish are better off than punishers, and defectors should eventually take over the whole population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Therefore, the understanding of whether and how costly punishment can evolve is a crucial issue in the study of human cooperation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Fehr and G¨achter pointed out that the evolutionary study of human cooperation in large groups of unrelated individ- uals should include a focus on explaining altruistic pun- ishment [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In addition, they argued that negative emo- tions may be a potential explanation for the emergence of costly punishment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' ∗ shi lei65@hotmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='com † w-zhen@nwpu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='cn To resolve this evolutionary puzzle, many scholars have explored how and why costly punishment can emerge in humans both from a theoretical and experimental per- spective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Egas Martijn and Riedl Arno experimentally explored the boundary conditions that altruistic punish- ment can promote cooperation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' They found that the maintenance of cooperation is subject to the cost-to- effect ratio of altruistic punishment, and cooperation is maintained if the conditions for altruistic punishment are relatively favorable [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' It has been well established that voluntary participation plays a vital role in sustaining the prevalence of costly punishment both in finite and infinite populations [6–11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The main idea behind established al- truistic punishment is that a loner itself is sufficient to maintain cooperation through cyclic dominance even in a one-shot game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Other reciprocity mechanisms including indirect reciprocity [12–16], group selection [17–19], spa- tial interaction [20–23], prior commitment [24–27], and so on [28], that can explain the emergence of cooperation have been applied to explain costly punishment, and its effect on costly punishment has previously been widely explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' To avoid the exploitation of defectors, exiters simply exit the game in favor of a small-but-positive payoff and generate nothing for their opponent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' While loners can receive a small-but-positive payoff by opting out but gen- erates the same payoff for its opponent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Although these arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='04849v1 [q-bio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='PE] 12 Jan 2023 2 two mechanisms seem materially similar, such a subtle difference leads to completely different outcomes [29, 30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' On one hand, exit means a potential punishment for their opponent, although the exiters can avoid being exploited by the defectors through opting out, they also hurt the cooperators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' However, loners enable the coexistence with cooperators and defectors through cyclic dominance in a one-shot game [31], while exiters allow cooperation to flourish only if they adhere to either direct, indirect or network reciprocity [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Given these differences, an in- teresting question arises: to what extent do exiters help explain altruistic punishment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' To this end, we introduce the exit option and altruistic punishment in a two-stage prisoner’s dilemma game, and we start our analysis in well-mixed populations in which the extended prisoner’s dilemma game in both finite and infinite populations are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Then, we turn our attention to a networked population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In doing so, we found that the exit op- tion does not bring any substantial benefit to altruistic punishment in well-mixed populations, but enables the existence of altruistic punishment in networked popula- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In addition, multiple dynamical phenomena in- cluding cyclic dominance and a bi-stable state can be observed in networked populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' METHODS We studied the evolution of altruistic punishment in a two-stage prisoner’s dilemma game by introducing two other action types, altruistic punishment and exit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In the first stage, each individual must make a choice simulta- neously between cooperation (C), defection (D), and exit (E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In the second stage, cooperators decide whether to punish the defectors at a personal cost to themselves γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' To the defectors, this means an imposed fine β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' This process results in four possible actions: AP, cooperate and punish defectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Those who cooperate and punish are altruistic punishers be- cause they punish free riders even at the expense of its own interests .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' NC, cooperate but do not punish defectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' These non-punishing cooperators are also known as second-order free riders because by free-riding on punishment save the the cost of punishing the defectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' D, defect but do not punish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' These are also known as first-order free riders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' E, exit the game in favor of a small but positive payoff ϵ irrespective of whom they encounter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' They do not participate in these two stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In a typical prisoner’s dilemma game, mutual cooper- ation (defection) generates the reward (punishment) R (P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' If one player cooperates and the other defects, the cooperative player gets the sucker’s payoff S, and the de- fected player obtains the temptation to defect T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' For simplicity, we choose the weak prisoner’s dilemma game as our base model by setting R = 1, P = S = 0, T = b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Payoff matrix for the weak prisoner’s dilemma game with altruistic punishment and an exit option.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' AP NC D E AP 1 1 −γ 0 NC 1 1 0 0 D b − β b 0 0 E ϵ ϵ ϵ ϵ The extended weak prisoner’s dilemma game contains four competing action types: altruistic punishers who cooperate and punish defectors(AP), non-punishing cooperators who cooperate but do not punish defectors (NC), defectors who free ride on the non-punishing cooperators and do not punish (D), and exiters who exit the game irrespective of whom they encounter (E).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The first row indicates that when an altruis- tic punisher, AP, meets another altruistic punisher AP, non- punishing cooperator NC, defector D, or exiter E, they earn a payoff equal to 1, 1, −γ, or 0, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When a non- punishing cooperator meets another altruistic punisher, non- punishing cooperator, defector, or exiter, they earn a payoff equal to 1, 1, 0, or 0, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Analogously, when a de- fector meets an altruistic punisher, non-punishing cooperator, defector, or exiter, they earn a payoff equal to b−β, b, 0, or 0, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Finally, exiters earn a payoff equal to ϵ ∈ [0, 1), irrespective of whom they meet, and their opponent receives nothing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' To make exiting less valuable than cooperating, and to ensure that the weak prisoner’s dilemma game satisfied the payoff ranking of the strict prisoner’s dilemma game, T > R > P > S was used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Additional limits placed on the parameters were 1 ≤ b < 2 and ϵ < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The described above is summarized in table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Altruistic punishment maintains cooperation only when its effectiveness is rel- atively large [5, 33], thus to investigate the effect of the exit option on the explanation of altruistic punishment, throughout this study, the cost of punishment γ and the fine of the defectors was set as 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='1 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Finite population We first considered a finite and well-mixed population of N individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Each individual adopted the Moran process, also known as frequently dependent process, to select their action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' At each time step, a randomly se- lected player i with fitness fi = esΠi (Πi is the actual payoff of the individual i obtained through their interac- tion) updates its action by imitating the action of player j with fitness fj = esΠj who is selected with a proba- bility proportional to its fitness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Here, s is the selection strength, the condition of s → 0 corresponds to the weak selection and evolution proceeds as neutral drift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' We further assumed that with a small probability µ, players randomly select their action from the rest of the other actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='This small mutation ensures that the population is homogeneous most of the time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Suppose that there are only two actors in the popula- tion, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=', action A and B, and these actions can be one 3 of the four actions among the full action set {a, b, c, d}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Here, the symbols a, b, c, d represent AP, NC, D and E, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In a finite population of size N with x A and y = N − x B actions, the average payoff of Πxy and Πyx to players with A and B actions are the following: ΠAB = (x−1)PAA+(N−x)PAB N−1 ΠBA = xPBA+(N−x−1)PBB N−1 , (1) where PAB is the payoff obtained from the single en- counter of actors A and B, and so does payoffs PAA, PBA, and PBB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' This allows us to describe the evolutionary dy- namics of the population in terms of a reduced Markov Chain of size 4 [34–37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Given the above assumptions, the probability to change the number of x individuals with action A in a population of y = N − x individuals with action B by ±1, T ± AB is: T + AB = xfi xfi+yfj y N T − AB = yfj xfi+yfj x N , (2) and hence the fixation probability ρAB of a single mutant actor A within a population of N − 1 B actors can be derived as [38, 39]: ρAB = 1 N−1 � k=0 k� x=1 T − AB T + AB = 1 N−1 � k=0 k� x=1 esΠBA esΠAB .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (3) The fixation probabilities ρAB define the transition prob- abilities of the reduced Markov Chain, with the following associated transition matrix: � � � AP NC D E AP ρaa ρab ρac ρad NC ρba ρbb ρbc ρbd D ρca ρcb ρcc ρcd E ρda ρdb ρdc ρdd � � �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (4) Here, ρAA = 1 − � A̸=B ρAB, A, B ∈ {a, b, c, d}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The nor- malized right eigenvector to the largest eigenvalue deter- mines the stationary distribution of each strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' For any pair of strategies A and B in the finite population, natural selection favors B replacing A only if ρAB > 1 N .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Infinite population We then employed replicator dynamics to analyze the evolutionary outcomes in an infinite and well-mixed pop- ulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Let x, y, z, w denote the fractions of altruistic punishers (AP), non-punishing cooperators (NC), de- fectors (D), and exiters (E) in the population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Where 0 ≤ x, y, z, w ≤ 1, and x + y + z + w = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The replicator equations are: ˙x = x � ΠAP − Π � , ˙y = y � ΠNC − Π � , ˙z = z � ΠD − Π � , ˙w = w � ΠE − Π � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (5) The symbols ΠAP , ΠNC, ΠD, and ΠE denote the average payoff of altruistic punishers, non-punishing cooperators, defectors, and exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Whereas Π = xΠAP + yΠNC + zΠD+wΠE is the average payoff of the whole population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' According to the defined payoffs in table I, we obtained the following equation: ΠAP = x + y − zγ ΠNC = x + y ΠD = x(b − β) + yb ΠE = ϵ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (6) Using the constraint w = 1 − x − y − z, we obtained: � � � � � � � � � � � � � ˙x = f (x, y, z) = x [(1 − x) (ΠAP − ΠE) − y (ΠNC − ΠE) − z (ΠD − ΠE)] ˙y = g (x, y, z) = y [(1 − y) (ΠNC − ΠE) − x (ΠAP − ΠE) − z (ΠD − ΠE)] ˙z = h (x, y, z) = z [(1 − z) (ΠD − ΠE) − y (ΠNC − ΠE) − x (ΠAP − ΠE)] (7) For the detailed stability analysis of each equilibria, please refer to the Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Networked population Different with well-mixed populations, global interac- tions in which an individual can interact with any other individual are no longer possible in the networked pop- ulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Instead, networks only allow local interactions, which means that individuals can only interact with their direct neighbors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Our basic network structure is a two dimensional regular lattice with periodic boundary con- ditions, each node was occupied by one individual, and each individual can only interact with its neighbors along its links.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Our simulation contained the following steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Initially, each individual was designed as either an altru- istic punisher (AP), a non-punishing cooperator (NC), a defector (D), or an exiter (E) with equal probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Each player acquires their total payoff by playing with all their direct neighbors according to the payoff matrix defined in table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' A randomly selected player i decides to imitate the strategy of player j who is also randomly selected from all the direct neighbors of player i by com- paring their payoff difference with the following proba- bility: Wi←j = 1 1 + exp ((Πi − Πj) /K), (8) where Πi and Πj is the acquired total payoff of the focal player i and its randomly selected neighbor j, respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' K denotes the noise in the imitation process, and we fixed the value of K to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='1 throughout the study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' A full Monte Carlo step is to repeat the above proce- dure L2 times, and L2 is the number of nodes in the given network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Each individual update their strategy once on 4 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Exiters establish altruistic punishment in a finite population, but altruistic punishers struggle to dominate the population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Stationary probability dis- tributions of each actors independence on the exiters’ payoff ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Transition probabilities for each pair of actors when the exiters’ payoff is negative (left) and positive (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The parameter values are b = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='5, β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='3, γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='1, s = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2, N = 100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' To subside the transient dynamics and avoid the finite-size effect, we ran simulations for 50,000 steps on a regular lattice with size ranging from 200*200 to 800*800.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The final fraction of each strategy was obtained after up to 45,000 steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The presented data was averaged over 20 independent runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' RESULTS Well-mixed populations We started our analysis in a well-mixed and finite pop- ulation, then we turned our attention to a well-mixed and infinite population, and finally, we investigated the evo- lution of altruistic punishment in networked population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Finite population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In the prisoner’s dilemma game with altruistic punishment, cooperation can only be maintained if the cost-to-fine ratio of altruistic punish- ment is relatively small [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The favorable conditions for altruistic punishment imply the small enough pun- ishment cost or high enough punishment fine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Although altruistic punishment can establish the cooperation even in a one-shot game, punishment reduces the social wel- fare [40, 41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' If the cost-to-fine ratio of altruistic pun- ishment is high, altruistic punishment does not support the survival of cooperation, and thus defectors take over the whole population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' As previously mentioned, nega- tive values of exiters’ payoff revert the extended model to the traditional weak prisoner’s dilemma game with al- truistic punishment, and in this case, selection favors the dominance of the defectors (refer to the left panel in fig- ure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='1B and figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='A1A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' A small but positive exiters’ pay- off enables the coexistence of altruistic punishers through cyclic dominance with defectors and exiters (refer to the right panel in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='1B and figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='A1B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' However, ex- iters also enable the survival of non-punishing cooper- ators, and allows the coexistence of non-punishing co- operators, defectors, and exiters through an alternative route of cyclic dominance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' With increasing ϵ, the fac- tion of altruistic punishers first reaches its peak, where the maximum faction of altruistic punishers is less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2, and then decreases until its extinction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='1A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The exiters facilitate the evolution of altruistic punishers in a finite population, but also allow for the survival of second-order free riders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Importantly, altruistic punish- ers never dominate the whole population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Infinite population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The situation changes greatly when the finite population is replaced by the infinite pop- ulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Stability analysis shows that, (i), when b−β > 1 and ϵ < 0, the monomorphic defecting equilibrium is sta- ble, and the others are unstable (figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='A2A);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (ii), when b−β > 1 and ϵ > 0, the monomorphic exiting equilibrium is stable, and the others are unstable (figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='A2B);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (iii), when b − β < 1 and ϵ < 0, the evolutionary dynamics result in either the mixed equilibrium of altruistic pun- ishers and non-punishing cooperators or the monomor- phic defecting equilibrium (figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='A2C);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' and (iv), when b − β < 1 and ϵ > 0, the evolutionary dynamics result in either the mixed equilibrium of altruistic punishers and non-punishing cooperators or the monomorphic exiting equilibrium (figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='A2D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In other words, exiters support the emergence of altruistic punishment only when the cost-to-fine ratio of punishment is favorable for coopera- tors in the infinite population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Nevertheless, the exiters destabilize the defection and eventually replace them re- gardless of whether altruistic punishment can establish cooperation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In a word, our results show that when the exit option was introduced in well-mixed populations, there was little additional benefit to the dominance of altruistic punish- ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Rather by adding the exit option the equilibrium was either monomorphic exiting in the infinite popula- tion or joint dominance between the defectors and ex- iters in the finite population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Given the above conclusion, the natural question arises: does a networked population support the dominance of altruistic punishment in the extended model?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Networked population Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 shows the full ϵ − b phase diagram obtained by the extensive Monte Carlo simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' It is noted 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 A AP 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8 NC 么 Fractions D 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6 A E V 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 Exit pay-off, E B AP NC NC AP P=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='01 p=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='01 4% 1% 8% 16% p=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='015 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='07 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='04 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='04 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='07 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='015 E D E D p=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='04 p=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='04 0% 95% 44% 32% E =-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 E =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='25 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Adding exit option establishes altruistic pun- ishment in networked population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Presented is the full ϵ − b phase diagram obtained by Monte Carlo simulations of the extended weak prisoner’s dilemma game on a regular lat- tice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Exiters dominate the whole population when the incen- tives to the exiters are large, ϵ ≳ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Fewer exit option in- centives lead to six possible outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' If b is relatively small, b ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='19, the effectiveness of altruistic punishment ensures the dominance of cooperators, and, altruistic punishers can coexist with defectors when 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='19 ≲ b ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' For large temp- tation b, b ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='29, negative ϵ leads to full defection, whereas, positive ϵ ensures the coexistence of altruistic punishers with defectors and exiters, the coexistence of second-order free rid- ers with defectors and exiters, or the bi-stable state of these two coexistence types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' that the addition of the simple exit option leads to com- plicated evolutionary outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Initially, when the in- centives to exiters are sufficiently large, ϵ ≳ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='51, the exiters outcompete other action types and dominate the whole population (the E phase in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2), and this is consistent with previous findings [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Less incentives to exiters, ϵ ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='51, lead to six different possible outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In detail, if the temptation to defect is relatively small, b ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='29, altruistic punishment together with network reciprocity are sufficient to maintain prosocial behavior (the All C phase and the AP + D phase in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When b ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='19, defectors can be completely eliminated by altruistic punishers, and thus altruistic punishers and non-punishing cooperators can coexist in a regular lat- tice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In the absence of defectors, non-punishing coop- erators and altruistic punishers cannot be distinguished, and whether the evolutionary dynamics lead to the full AP state, the full NC state or the mixed AP +NC state are determined by the initial conditions (the All C phase in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' With increasing b, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='19 ≲ b ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='29, the effec- tiveness of altruistic punishment is greatly reduced, and defectors cannot be completely eliminated by altruistic punishers, and they coexist with the altruistic punish- ers in the population (the AP + D phase in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' It is well established that altruistic punishment together with network reciprocity promotes cooperation even in the presence of antisocial punishment or second-order free-riders when the cost-to-fine ratio of punishment is low [14, 21, 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The results of this study confirmed this conclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' If b is sufficiently large, altruistic pun- ishment loses its effectiveness in sustaining prosocial be- havior, and defectors dominate the entire population for negative ϵ (the D phase in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When exit options are added, this undesirable outcome is solved and leads to three possible outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' These outcomes can be either (i) the coexistence of AP, D and E (the AP +D+E phase in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2), (ii) the coexistence of NC, D, and E (the NC +D +E phase in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2), or (iii) the bi-stable state between these two types of coexistences (the B phase in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When the cost-to-fine ratio of punishment is relatively large, the exiters sustain cooperation in a net- worked population in that it facilitates its coexistence of two different routes for altruistic punishers and non- punishing cooperators, but interestingly, these two types of cooperators cannot coexist in the networked popula- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' To gain a better understanding of how these actors coexist in the population, the evolution features of the fractions of each actors was examined and the results are presented in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In the bi-stable phase, it is the cooperators (altruistic punishers or non-punishing cooperators) start giving way to the defectors and with fewer cooperators around, defectors then giving way to the exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' With large numbers of exiters, both the al- truistic punishers and non-punishing cooperators com- pete for the exiters as they can only survive by adhering to the exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The described phenomenon is the cyclic dominance in which these actors dominate one another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Here, the cyclic dominance routes can be either (i) al- truistic punishers that dominate exiters, who dominate defectors, who in turn dominate the altruistic punishers;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' or (ii) non-punishing cooperators that dominate the ex- iters, who dominate the defectors, who then dominate the non-punishing cooperators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' As a key mechanism, researchers have verified the efficiency of cyclic domi- nance in sustaining bio-diversity or promoting cooper- ation [42, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Although we started with random initial conditions, the evolutionary outcomes are different by implementing more independent simulations under same parameter combinations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' For example, in the NC+D+E attractor (figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='3A), the fraction of altruistic punishers is temporarily much larger than that of non-punishing co- operators at around 100th step, then the faction of altru- istic punishers gradually decreases until it is eliminated and the fraction of second-order free riders increases un- til it reaches a stable state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' However, in the AP + D + E attractor (figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='3B), the fraction of altruistic punishers is always comparable to that of non-punishing cooper- ators up to around 1000th step, after this critical time step, the fraction of non-punishing cooperators gradually decreases until it is eliminated, and altruistic punishers gradually increase to reach a stable state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Thus, it is the initial distributions of the actors which determines the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content="8 E 3 Exit's payoff, 0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 NC+D+E All C AP+D+E 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 AP+D B 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 D 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 Temptation, b6 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Time dependence of actor abundances exhibits complicated evolutionary dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In the bi-stable phase, starting from random initial conditions, small incentives to exit option lead the system to either NC + D + E or AP + D + E attractor but the coexistence of these four actors is not possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' During the evolution, if the abundance of altruistic punishers in the initial stage is much larger than that of the non-punishing cooperators, then altruistic punishers are eliminated and non-punishing cooperators coexist with defectors and exiters through cyclic dominance (figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='3A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' However, if the abundance of altruistic punishers in the initial stage is comparable to that of non-punishing cooperators, then the non-punishing cooperators are eliminated and altruistic punishers coexist with defectors and exiters through cyclic dominance (figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='3B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Larger incentives to exiters turn the bi-stability to monostability and the evolutionary outcomes are determined by the incentives that were presented to exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The parameters were fixed as b = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8, ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='05 (top rows), ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 (bottom left), and ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4(bottom right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' fate of altruistic punishers and non-punishing coopera- tors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The phenomenon of bi-stability disappears by increas- ing the incentives for exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Evolutionary dynamics lead to either a NC + D + E phase or a AP + D + E phase depending on the incentives for exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Although both altruistic punishers and non-punishing cooperators can dominate exiters when the fraction of exiters reaches its peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' However, it is non-punishing cooperators who dominate the exiters when the incentives for exiters are intermediate, ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Altruistic punishers lose when in indirect competition with the non-punishing cooper- ators and it is eliminated with simulation proceeds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Fi- nally, the non-punishing cooperators coexist with the de- fectors and exiters through cyclic dominance in the net- worked population(figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='3C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' If the incentives for exiters are larger, ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4, it is the altruistic punishers start to dominate the exiters, and the non-punishing cooperators cannot exceed the exiters and is eventually eliminated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Finally, the altruistic punishers coexist with defectors and exiters through cyclic dominance in the system (fig- ure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='3D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' To understand the quantitative power relationships at the equilibria abundances of these actors, we present the two representative cross sections of the phase diagram in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Along the vertical transect of the ϵ − b phase plane, figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4A shows the stationary fractions of the four competing actors in dependence on the exit payoff ϵ at b = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In the traditional weak prisoner’s dilemma game with only cooperators and defectors, a high temptation leads to the complete dominance of defectors and the net- work reciprocity loses its efficiency to support the coexis- tence of cooperators and defectors [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Although adding altruistic punishment in the weak prisoner’s dilemma game can avoid this unfavorable outcome, its efficiency to decrease defection is at the expanse of social welfare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' A B B phase: NC+D+E attractor B phase: AP+D+E attractor 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='05 - Fractions 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 10-2 10-1 100101 102 103 104 10-2 10-1 100 101102 103104 C D NC+D+E phase AP+D+E phase 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 AP = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 8= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8 NC Fractions 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6 D 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6 E 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 2 10-1 100 101 102 103 104 10-2 10-1 100 101 102 103 104 10-2 time steps time steps7 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Power relations between altruistic punishers, second-order free riders, defectors, and exiters exhibiting complicated equilibra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Along the vertical transect of ϵ − b phase at b = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When ϵ ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='06, the networked population falls into the bi-stable state between the coexistence type of altruistic punishers, defectors, and exiters and the coexistence type of second-order free riders, defectors and exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In the range 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='06 ≲ ϵ ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='16, altruistic punishment outcompetes the second-order free riders, and coexists with the defectors and exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Whereas, in the range 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='16 ≲ ϵ ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='17, there is narrow dominance of the bi-stable state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In the range 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='17 ≲ ϵ ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='25, the second-order free riders outcompete the altruistic punishers, and coexist with the defectors and exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='25 ≲ ϵ ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='51, the coexistence of altruistic punishers, defectors, and exiters again dominates the population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Finally the eixters dominate the population when 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='51 ≲ ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Along the horizontal transect of ϵ−b phase plane at ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2, the effectiveness of altruistic punishment together with network reciprocity is sufficient to secure prosocial behavior when b ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' With increasing b, altruistic punishment loses its efficiency to sustain prosocial behavior, and adding exit option enables the networked population to first enter a coexistence state of altruistic punishers, defectors, and exiters in the temptation range of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='29 ≲ b ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='73, and reaches a coexistence state between second-order free riders, defectors, and exiters when b ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' That is the decreasing defection can be realized only if the cost-to-fine ratio of altruistic punishment is relatively low, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=', small punishment cost γ or large punishment fine β [5, 20–22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' If the cost-to-fine ratio of altruistic pun- ishment is relatively large, the altruistic punishment to- gether with network reciprocity cannot provide sufficient benefit for cooperators, and the complete dominance of defectors is still as per the Nash equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Adding the exit option to the weak prisoner’s dilemma game with altruistic punishment changes the equilibrium dramati- cally even if the conditions to support cooperation for altruistic punishment are unfavorable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When exit is costly (ϵ < 0), the defectors dominate the whole population (the D phase in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' As shown in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4A, if the incentives to exiters are small but positive, the D phase gives way to the B phase, where the system converges to either the AP +D +E attractor or the NC +D +E attractor depending on the results of the indirect competition between the altruistic punishers and non-punishing cooperators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' By further increasing the ϵ, the NC + D + E phase is reached at ϵ ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='17, and there are two narrow strips that AP + D + E phase and B phase can dominate separately during this increment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The AP + D + E phase dominates in the range 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='06 ≲ ϵ ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='16, and the B phase is short-lived again in the range 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='16 ≲ ϵ ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' As ϵ continues to increase, the NC + D + E phase gives way to AP + D + E phase via discontinuous phase transition at ϵ ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When incentives to exiters are sufficiently large, the AP +D+E phase is finally replaced by the E phase at the critical point ϵ ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4B shows the horizontal transect of ϵ − b at ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2, it also reveals the power relations between these competing actors, but it is dependent on the temptation level, b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When b is small, 1 ≤ b ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='29, the altruistic pun- ishment together with the network reciprocity are able to support prosocial behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When 1 ≤ b ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='23, the al- truistic punishers can completely eliminate the defectors, the elimination of the defectors also negatively affects the exiters, and thus altruistic punishers coexist with non- punishing cooperators as they cannot be distinguished in the absence of defectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The All C phase gives way to the AP + D phase through continuous phase transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Although the advantages of cooperators decreases with A B NC+D+E B E AP+D+E NC+D+E 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8 AP 口 ractions NC 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6 ID E 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 M 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 15888888888 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 Exit pay-off, temptation, b8 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Evolutionary snapshots reveal the detailed dominance modes between all actors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Shown are evolutionary snapshots at different time steps (column) and for different temptations for defection (rows).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When the temptation is small (top row), both altruistic punishers and second-order free riders dominate the exiters, who take over the defectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' However, the decrease of exiters is much fast than its increase, and they are eliminated first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The defectors are then eliminated by the altruistic punishers, and finally the altruistic punishers coexist with second-order free riders in the population, and these two actors cannot separately be distinguished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When the temptation is larger (second row), the fate of exiters is the same as in the first row, however, the larger temptation leads more competitive defectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Therefore, instead of completely dominating the defectors, the altruistic punishers coexist with defectors who replace the second-order free-riders until second-order free-riders they are eliminated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When the temptation is even larger (third row), more competitive defectors can encroach on both, the altruistic punishers and second-order free riders can only survive when they adhere to exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The indirect competition between altruistic punishers and second-order free riders with exiters determine the outcome for these two actors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Compared with non- punishing cooperators, altruistic punishers have greater fitness when compared to defectors and have greater probability to endure, therefore non-punishing cooperators are eliminated, and altruistic punishers coexist with defectors and exiters through cyclic dominance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When the temptation is at its largest (bottom row), exiters dominate and non-punishing cooperators have a larger probability to endure than altruistic punishers as it avoids the cost of punishment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Finally altruistic punishers are eliminated and non-punishing cooperators coexist with defectors and exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Results were obtained with ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 after the 30000th step to generate the final snapshots (rightmost column).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The intermediate snapshots (second to fourth columns) were taken at different time steps across rows to ensure that the figure as illustrative as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' increasing b, the cooperators who punish defectors gain a greater advantage when compared against defectors, and thus network reciprocity supports the coexistence of altruistic punishers and defectors in this instance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' If the conditions to support cooperation with altruistic punish- ment are unfavorable, adding an exit option can promote the system to the AP +D+E phase when b ≲ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' How- ever, with increasing b, the AP + D + E phase gives way to the NC + D + E phase through discontinuous phase transition at the critical point, b ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' To reexamine the evolutionary dynamics and further check the indirect competition between altruistic punish- ers and non-punishing cooperators in both spatial and temporal dimensions,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' We plotted the evolutionary snap- shots for varying b at ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2, and the results are pre- sented in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When the temptation is small (top row in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='5), the exiters were eliminated first by altruistic punishers and non-punishing cooperators, and the de- fectors experienced the same fate shortly after.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The al- truistic punishers coexist with non-punishing cooperators eventually as they cannot be distinguished and the sys- tem falls into frozen state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' A larger temptation makes the defectors more competitive (second row in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='5), and instead of being eliminated by the altruistic punishers, Temptation, b NC D b=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='04 AP E b=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='25 b=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='5 b=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8 timesteps9 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Initial conditions determine the outcome of altruistic punishers and non-punishing cooperators in the bi-stable phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Shown are the evolutionary outcomes after implementing 100 independent simulations for each pa- rameter combination under four different initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The initial conditions were (i) 97% of players were initially assigned as AP, (ii) 97% of players were initially assigned as NC, (iii) 97% of players were initially assigned as D, and (iv) 97% of players were initially assigned as E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The rest of the other action types were assigned to the other players with equal probability in these different initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Param- eters were fixed as b = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8, from left to right, ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' they can coexist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' However, the coexistence of defectors cannot ensure the survival of exiters, who are eliminated in situations with small temptation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The non-punishing cooperators are eliminated by defectors and finally, the altruistic punishers coexist with defectors in the popula- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When the temptation is even larger, the coexistence of defectors and altruistic punishers was no longer pos- sible, instead, defectors can invade both altruistic pun- ishers and non-punishing cooperators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The competitive defectors allow for the survival of exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In turn, altru- istic punishers and non-punishing cooperators can sur- vive by adhering to the survived exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' It is therefore, both altruistic punishers and non-punishing cooperators can coexist with defectors and exiters through different cyclic dominance routes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' However, these two types of cyclic dominance cannot coexist in the population, and the indirect competition to the territories of exiters be- tween altruistic punishers and non-punishing cooperators determine the outcome of the competitors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Competitive defectors more easily negatively affexct non-punishing co- operators than altruistic punishers (third row and second column in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='5), and therefore, non-punishing cooper- ators are eliminated first, and the altruistic punishers, de- fectors, and exiters coexist within the population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When the temptation is the largest (bottom row in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='5), defectors are the most competitive, altruistic punishers and non-punishing cooperators are exploited by defectors at almost the same speed, and the exiters dominate by eliminating the defectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In the indirect competition of exiters with the non-punishing cooperators, the altruis- tic punishers loses its advantages due to the existence of punishment cost, and non-punishing cooperators coexist with defectors and exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Our results have shown that by adding an exit option results in the bi-stable dynamics and it is the initial dis- tribution of actors determines the outcome of altruistic punishers and non-punishing cooperators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' It is generally accepted that the initial conditions are crucial for evolu- tionary outcomes in agent-based models [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' We further assessed whether the initial fractions of actors is a poten- tial reason that the system exhibits bi-stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6 presents the evolutionary outcomes with ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6 under four different initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The four different conditions are: (i) 97% of players were initially assigned as AP, (ii) 97% of players were initially assigned as NC, (iii) 97% of players were initially assigned as D, and (iv) 97% of players were initially assigned as E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The other players were assigned one of the other three actions with equal probability in these conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The results were obtained by implementing 100 independent simula- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' We found that when ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='05 (left column in fig- ure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6), the evolutionary outcome was always AP +D+E if the majority of players initially had action AP or action D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' However, if the majority of players initially had NC action, then the system reached the attractor NC+D+E with 95% probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' If the majority of players were E, then the system reached the attractor AP + D + E or NC +D+E with 36% and 62% probability, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Larger incentives to exiters switched the bi-stability to monostability (middle and right column in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In the monostability state, evolutionary dynamics lead to either the AP + D + E or the E phase depending on the incentives to the exiters, and evolutionary outcomes are independent on the initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The finite-size ef- fects are a potential pitfall that may generate misleading results when implementing agent-based models in struc- tured populations [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Thus, it is crucial to choose a sufficiently large network size or to employ the method of subsystem solutions to avoid this potential issue [46, 47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' It is noteworthy that the system has 23% probability to fall into the full E phase when most players initially had D action at ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 (middle column in figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' We do believe that the counterintuitive E phase is the prod- uct of the finite-size effect, and the pure AP + D + E phase can be expected as long as a larger network size was implemented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' DISCUSSION To discuss, we have shown that by adding an exit op- tion to the two-stage prisoner’s dilemma game results in complicated dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Particularly, in the infinite and well-mixed population, it was observed that exiters pro- NC+D+E E AP+D+E 62% 100% 100% E 36% 1 1 1 2% / 1 1 I 100% 77% 100% D 23% I 1 1 1 / 95% 1 100% 100% NC / 5% 1 1 1 1 / 100% 100% I 100% AP 1 I 1 -- 1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='05 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 =0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='610 vide little benefit to cooperation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When the effectiveness of altruistic punishment is sufficient to support cooper- ation, adding an exit option turns the bi-stable equilib- rium between the mixed AP −NC and pure D to another bi-stable equilibrium, whereby the mixed AP − NC and pure E coexists (panel C and D in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='A2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When altruistic punishment itself cannot establishes coopera- tion, the monomorphic defecting equilibrium is replaced by the monomorphic exiting equilibrium (panel A and B in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='A2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In the finite and well-mixed popula- tion, although the availability of exit options maintains the survival of both altruistic punishers and second-order free riders through two types of cyclic dominance, the altruistic punishers never dominate the population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In contrast with the well-mixed populations, combining the exit option with network reciprocity produces greatly dif- ferent outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' We determined that the domination of altruistic punishment is possible in a networked popula- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Altruistic punishers can coexist with defectors and exiters through cyclic dominance in a majority of the ϵ−b phase plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When the temptation is large, b ≳ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='71, ex- iters enable the survival of second-order free riders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' De- pending on the incentives to exiters, the system also fall into a bi-stable phase or single NC+D+E phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' There- fore the exit option is certainly not a panacea in solving social dilemmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Previous studies have shown that introduced voluntary participation is capable of establishing altruistic punish- ment in both finite and infinite populations [6–10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In the infinite population, evolutionary dynamics can result in either a Nash equilibrium of punishing and non-punishing cooperators or to an oscillating state without punish- ers [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' If a single cooperator (either a non-punishing cooperator or a punisher) can participate in the game, and a punisher can punish the non-punishing cooperator even in the absence of defectors, the evolutionary dynam- ics result in the stable coexistence of altruistic punishers and non-punishing cooperators [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In a finite population, with the assistance of loners, altruistic punishers can pre- vail and even dominate the whole population for most of the time when mutations are rare [8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' If loners can escape punishment, altruistic punishment prevails even under the threat of anti-social punishment [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Exiters produce outcomes that differ greatly from these in lon- ers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In the infinite and well-mixed population, adding an exit option can also result in a bi-stable outcome, in which the Nash equilibrium can be either the coexistence of altruistic punishers and non-punishing cooperators or a monomorphic exiting equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' However, this bi- stable outcome is only possible when the punishment it- self is sufficient to maintain cooperation, otherwise, the bi-stable outcome can be replaced with a monomorphic exiting equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In other words, exiters just simply destabilize the defectors and eventually replaces them in the infinite population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' In the finite population, although exiters allow the survival of altruistic punishment when the exiter’s payoff is moderate, altruistic punishers never dominate the whole population (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='1A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The di- rect comparison between exiters and loners in a finite and infinite population lead us to conclude that loners are more effective than exiters in supporting the preva- lence of altruistic punishment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The effectiveness of altruistic punishment is not only challenged by second-order free riders but also by anti- social punishment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' It has been experimentally reported that the existence of antisocial punishment is widespread in different human cultures [48–50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Recent theoretical studies have shown that the existence of antisocial pun- ishment can prevent the successful coevolution of pun- ishment and cooperation [51, 52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Furthermore, if pun- ishment is available for loners, punishment does not in- creases cooperation and altruistic punishment becomes a self-interested tool for protecting itself against potential competitors [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' As discussed above, exiters are a po- tential spiteful punishment as it harms both cooperators and defectors, while loners generate a small-but-positive payoff for its opponent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' This tiny difference leads to to- tally different equilibrium in a one-shot game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Exiters can destabilize defectors and finally replace them, while loners can sustain cooperation through cyclic dominance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' If we extend our model by considering all punishment sets where actors can be punished by each other and exiters cannot escape potential punishment by both cooperators and defectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' By restricting the analysis to a one-shot game, we determine how this setup influenced the stabil- ity of punishment, and whether and how this setup gen- erates outcomes that differ from that of loners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' These undoubtedly invite future considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Exiters established the prevalence of altruistic punish- ers and eliminated the second-order free riders when it adheres to network reciprocity in a certain parameter range (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 and figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' However exiters allow for the survival of second-order free riders, who can not only survive, but also dominate the population in some certain areas of the phase plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The robustness of this finding needs to be verified in a human behavior exper- iment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Human behavior experiments may generate con- trasting or surprising outcomes with theories on many is- sues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Scale-free topology, for example, is often recognized theoretically as an optimal structure for the survival of cooperation, however, this argument cannot be verified by experiment and the cooperation level among humans cannot exceed the level established in the lattice [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Similarly, although strong reciprocity theorists believe that humans are inherently altruistic and cooperators will sacrifice their personal interests to (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' achieve fair outcomes and to (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' punish non-cooperators[55, 56], this theory cannot be confirmed by experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Yamagishi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' performed large scale human behavior experiments and found that there was no correlation between the ten- dencies to reject unfair offers in the ultimate game and tendencies to exhibit prosocial behavior in other games [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Although Yamagishi’s finding was challenged due to its insufficient sample size, Egloff et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' further con- firmed that there was indeed no correlation between pos- itive and negative reciprocity through analyzing the pri- 11 vate household data from the Socio-Economic Panel of the German Institute for Economics Research [58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' A recent experimental work is of direct relevance for our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Introducing punishment into networks has been proven to be an efficient method to promote cooperation theoretically [14, 21–23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' However, in a recent large-scale human behavior experiment, it was concluded that the introduced peer punishment did not promote coopera- tion in structured populations, and instead diminished the benefits of network reciprocity [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Although we have shown that exiters support the dominance of altru- istic punishment when it adheres to network reciprocity, human behavior experiments are needed to further verify our theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' ARTICLE INFORMATION Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' We thank Prof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Marko Jusup for valuable discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' This research was sup- ported by the National Science Fund for Distinguished Young Scholars (grants no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' 62025602).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' We also acknowl- edge support from (i) a JSPS Postdoctoral Fellowship Program for Foreign Researchers (grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' P21374), and an accompanying Grant-in-Aid for Scientific Re- search from JSPS KAKENHI (grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' JP 22F31374), and the National Natural Science Foundation of China (grant no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' 11931015) to C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' as a co-investigator, (ii) the National Natural Science Foundation of China (grants no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' 11931015, 12271471 and 11671348) to L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=', (iii) Na- tional Natural Science Foundation of China (grants no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' U22B2036, 11931015), Key Technology Research and De- velopment Program of Science and Technology-Scientific and Technological Innovation Team of Shaanxi Province (Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' 2020TD-013) and the XPLORER PRIZE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' to Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' W, and (iv) the grant-in-Aid for Scientific Research from JSPS, Japan, KAKENHI (grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' JP 20H02314) awarded to J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Author contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' conceived re- search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' performed simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' All co- authors discussed the results and wrote the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Conflict of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Authors declare no conflict of in- terest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Appendix STABILITY ANALYSIS OF THE EQUILIBRIA IN INFINITE AND WELL-MIXED POPULATION Solving Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='7, we obtain 12 equilibrium points: (1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 0, 1), (0, 0, 1, 0), (ϵ, 0, 0, 1 − ϵ), (0, ϵ, 0, 1 − ϵ), (x, 1 − x, 0, 0), (x, ϵ − x, 0, 1 − ϵ), ( −1+b β , 1−b+β β , 0, 0), ( ϵ b−β , 0, ϵ−β−ϵβ (βϵ)γ , 1 − ϵ(γ+1+β−b) (b−β)γ ), ( (−1+b)ϵ β , ϵ−β+βϵ β , 0, 1−ϵ), ( γ 1−b+β+γ , 0, −1+b−β −1+b−β+γ , 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' To examine the stability of these equilibria, we calculate the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0x104 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0x105 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='5x105 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0x105 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='0 Fractions time steps AP NC D E A B Fractions FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Numerical simulation further demonstrates that the survival of altruistic punishment is due to the cyclic dominance between altruistic punishers, defec- tors, and exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Defectors take over the whole popu- lation even if altruistic punishers initially dominate the pop- ulation when the exiters’ payoff is negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Small but positive exiters’ payoff enables the coexistence of altruistic punishers, non-punishing cooperators, defectors, and exiters through cyclic dominance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' If defectors initially dominate the population, the mutated exiters invade the defectors, and af- ter transient dynamics, the defectors finally give way to the exiters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When exiters dominate the population, altruistic punishment is less costly and cooperating is more valuable than exiting, and thus altruistic punishers take over the whole population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Thereafter, non-punishing cooperators dominate altruistic punishers and take over the whole population since altruistic punishers are less valuable than non-punishing coop- erators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' This proceeds until the dominance of non-punishing cooperators gives way to defectors again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The Parameter val- ues are b = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='5, β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='3, γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='1, µ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='001, s = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2, ϵ = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 (A) and ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 (B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' eigenvalues of Jacobian matrix: J = � �� ∂f(x,y,z) ∂x ∂f(x,y,z) ∂y ∂f(x,y,z) ∂z ∂g(x,y,z) ∂x ∂g(x,y,z) ∂y ∂g(x,y,z) ∂z ∂h(x,y,z) ∂x ∂h(x,y,z) ∂y ∂h(x,y,z) ∂z � �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (A1) Then we have the following conclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When b < 1 + β, and ϵ < 0, the equi- librium points (x∗, 1 − x∗, 0, 0) and (0, 0, 1, 0) are stable, while the rest of others are unstable;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When b < 1 + β, and ϵ > 0, the equilibrium points (x∗, 1 − x∗, 0, 0) and (0, 0, 0, 1) are stable, and the others are unstable;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When b ≥ 1 + β, only the equilibrium point (0, 0, 1, 0) is stable, and the rest of others are unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When ϵ > 0, only the equilibrium point (0, 0, 0, 1) is stable, and the rest of others are unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' For K1: (x, y, z, w) = (1, 0, 0, 0), the Jacobian 12 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' A2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Adding exit option destabilizes defection regardless of whether altruistic punishment can establish cooperation in an infinite population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When the cost-to-effect ratio of altruistic punishment is insufficient to establish cooperation (top row), b − β > 1, the monomorphic defecting equilibrium is replaced by the monomorphic exiting equilibrium for positive values of ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When the cost-to-effect ratio of altruistic punishment is capable of establishing cooperation (bottom row), b − β < 1, the bi-stable equilibrium of the mixed altruistic punisher and non-punishing cooperator equilibrium and the monomorphic defecting equilibrium is replaced by the other bi-stable equilibrium between the mixed altruistic punisher and non-punishing cooperator equilibrium and the monomorphic exiting equilibrium for positive values of ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The dashed line on the AP − NC edge indicates that all the points on this edge are unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The filled black circles, filled gray circles, and unfilled circles represent stable fixed points, saddle points, and unstable points, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' The parameters values are β = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='3, γ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='1, ϵ = −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 (left column), ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 (right column), b = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='5 (top row), and b = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2 (bottom row).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' matrix J1 is J1 = � � −1 + ϵ −1 + ϵ −b + β + ϵ 0 0 0 0 0 −1 + b − β � � (A2) and its corresponding eigenvalues are {λ1, λ2, λ3} = {0, −1 + b − β, −1 + ϵ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (A3) When b > β + 1, K1 is unstable because −1 + b − β is a positive eigenvalue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Otherwise, there is at least one zero eigenvalue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Thus, we use the center manifold theorem to analyze the stability of K1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Using b < β + 1 as an ex- ample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' First, there is an invertible matrix whose column elements are the eigenvectors of J1 P = � � −1 −1 1 1 0 0 0 1 0 � � (A4) and J1 can be diagonalized as P −1J1P = � � 0 0 0 0 −1 + b − β 0 0 0 −1 + ϵ � � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (A5) Then change of variable: � � x1 y1 z1 � � = P −1 � � x y z � � = � � y z x + y + z � � (A6) A B D E D D E D O AP NC AP NC D D c D D E D D E D C Q C AP NC AP NC D D13 and the system becomes ˙x1 =g(z1 − x1 − y1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' x1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' y1) =x1((1 − x1)(−ϵ − y1 + z1)− x1(−ϵ + bx1 + (b − β)(−x1 − y1 + z1))− y1(−ϵ + bx1 + (b − β)(−x1 − y1 + z1))) ˙y1 =h(z1 − x1 − y1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' x1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' y1) =y1(−x1(−ϵ − y1 + z1) − y1(−ϵ − y1 − x1y1 + z1)+ (1 − y1)(−ϵ + bx1 + (b − β)(−x1 − y1 + z1))) ˙z1 =f(z1 − x1 − y1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' x1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' y1) + g(z1 − x1 − y1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' x1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' y1) + h(z1 − x1 − y1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' x1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' y1) =x1(ϵ(−1 + 2x1 + y1) + (−1 + x1 + bx1 + by1)(y1 − z1)− β(x1 + y1)(x1 + y1 − z1))+ y1((−1 + y1)(ϵ + b(y1 − z1) − β(x1 + y1 − z1))+ x1(ϵ + y1 − z1) + y1(ϵ + y1 + x1y1 − z1))+ (x1 + y1 − z1)(ϵ + (1 − b + β + x1)y12− ϵz1 + (−1 + z1)z1 + y1(1 + x2 1 + x1(1 + β − z1)+ (−2 + b − β)z1)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (A7) Put the system into the form ˙X = AX + F(X, Y ) ˙Y = BY + G(X, Y ) , (A8) where X = [x1], Y = � y1 z1 � , and A = [0], B = � −1 + b − β 0 0 −1 + ϵ � , whose eigenvalues have zero and negative real parts, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' F and G are the func- tions of X and Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' They satisfy the condition F (0, 0) = 0, F ′(0, 0) = O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' According to the existence theorem of the center manifold, the system has the center manifold S = {(X, H(X))|H : R1 → R2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' We define a mapping (Mϕ)(X) =ϕ′(X)(AX + F (X, ϕ(X)) − Bϕ(X) − G(X, ϕ(X)) (A9) Set ϕ(Y ) = O(X2), we obtain ˙x1 = x1(−ϵ(1 − x1) − x1(−ϵ + bx1 − x1(b − β))) + O(x4 1) (A10) Then we define m(x1) = x1(−ϵ(1 − x1) − x1(−ϵ + bx1 + −x1(b−β))), and m(x1)′ = 2ϵx1−3x2 1β−ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Since m(0) < 0, then x1 = 0 is asymptotically stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Accordingly, we can conclude the point K1 is stable when b < β+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When b = β + 1, K1 is unstable in accordance with the center manifold theorem whose derivation process is similar to the above analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' For K2: (x, y, z, w) = (0, 1, 0, 0), the correspond- ing eigenvalues of J are {λ1, λ2, λ3} = {0, −1 + b, −1 + ϵ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (A11) K2 is unstable since −1 + b > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' For K3: (x, y, z, w) = (0, 0, 1, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Its correspond- ing eigenvalues of J are {λ1, λ2, λ3} = {0, ϵ, −γ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (A12) When ϵ < 0, K3 has an eigenvalue with zero real part and other eigenvalues with negative real part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' According to the center manifold theorem, K3 is stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When ϵ > 0, K3 is unstable because the eigenvalue ϵ has a positive real part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' For K4 : (x, y, z, w) = (0, 0, 0, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Its correspond- ing eigenvalues of J are {λ1, λ2, λ3} = {−ϵ, −ϵ, −ϵ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (A13) K4 is stable when ϵ > 0 because all eigenvalues have negative real parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' K4 is unstable when ϵ < 0 because all eigenvalues have positive real parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' For K5 : (x, y, z, w) = (ϵ, 0, 0, 1 − ϵ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Its corre- sponding eigenvalues of J are {λ1, λ2, λ3} = {0, ϵ(−1 + b − β), ϵ(1 − ϵ)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (A14) When 0 < ϵ < 1 or ϵ < 0 and b < 1 + β, K5 is unstable because one of its eigenvalues has a positive real part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When ϵ < 0 and b ≥ 1+β, K5 has at least one eigenvalue with a zero real part and the others have negative real parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' According to the center manifold theorem, K5 is unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' For K6 : (x, y, z, w) = (0, ϵ, 0, 1 − ϵ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Its corre- sponding eigenvalues of J are {λ1, λ2, λ3} = {0, ϵ(−1 + b), ϵ(1 − ϵ)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (A15) When ϵ > 0, K6 is unstable because eigenvalue ϵ(−1 + b) >.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When ϵ < 0, there is one eigenvalue with a zero real part and two eigenvalues with negative real parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' According to the center manifold theorem, K6 is unsta- ble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' For K7 : (x, y, z, w) = (x∗, 1 − x∗, 0, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Its corre- sponding eigenvalues of J are {λ1, λ2, λ3} = {0, −1 + ϵ, −1 + b − βx∗}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (A16) When x∗ > b−1 β , namely b < 1 + β, there is one eigen- value with a zero real part and others with negative real parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' According to the center manifold theorem, K7 is stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When x∗ < b−1 β , K7 is unstable because one of its eigenvalues has a positive real part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' For K8 : (x, y, z, w) = (x∗, ϵ − x∗, 0, 1 − ϵ + x∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Its corresponding eigenvalues of J are {λ1, λ2, λ3} = {0, ϵ − ϵ2, −ϵ + β − βx∗}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (A17) When ϵ > 0, K8 is unstable because ϵ − ϵ2 > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When ϵ < 0, K8 is unstable because −ϵ + β − βx∗ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' For K9 : (x, y, z, w) = ( −1+b β , 1−b+β β , 0, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Its corresponding eigenvalues of J are {λ1, λ2, λ3} = {0, 0, −1 + ϵ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (A18) 14 K9 exists only when b < 1 + β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' When K9 exists, there is one eigenvalue with a negative real part and two eigenval- ues with zero real parts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' According to the center manifold theorem, k9 is unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' For K10 : (x, y, z, w) = ( ϵ b−β , 0, ϵ−β−ϵβ (b−β)γ , 1 − ϵ(γ+1+β−b) (b−β)γ ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Its corresponding eigenvalues of J are {λ1, λ2, λ3} = {−ϵ(−1 + b − β) b − β ,−ϵ(−1 + b − β) b − β ,ϵ+ ϵ2(−1 + b − β + γ) (b − β)γ } .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (A19) K10 exists when 1 − ϵ(γ+1+β−b) (b−β)γ ) < 1, namely b > β + ϵ 1−γ γ+ϵ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Then its eigenvalue ϵ + ϵ2(−1+b−β+γ) (b−β)γ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Thus, K10 is unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' For K11 : (x, y, z, w) = ( (−1+b)ϵ β , ϵ−β+βϵ β , 0, 1−ϵ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Its corresponding eigenvalues of J are {λ1, λ2, λ3} = {0, 0, ϵ(1 − ϵ)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (A20) K11 exists when ϵ > 0, then eigenvalue ϵ(1 − ϵ) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Thus, K11 is unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' For K12 : (x, y, z, w) = ( γ 1−b+β+γ , 0, 1−b+β 1−b+β+γ , 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Its corresponding eigenvalues of J are {λ1, λ2, λ3} = { (1 − b + β)γ 1 − b + β + γ , (1 − b + β)γ 1 − b + β + γ , ϵ + (−b + β)γ 1 − b + β + γ }.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' (A21) K12 exists when b < 1+β, then eigenvalue (1−b+β)γ 1−b+β+γ > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Thus K12 is unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' [1] Clutton-Brock T H and Parker G A 1995 Nature 373 209–216 [2] West S A, Griffin A S and Gardner A 2007 Journal of evolutionary biology 20 415–432 [3] Henrich J, McElreath R, Barr A, Ensminger J, Barrett C, Bolyanatz A, Cardenas J C, Gurven M, Gwako E, Henrich N et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' 2006 Science 312 1767–1770 [4] Fehr E and G¨achter S 2002 Nature 415 137–140 [5] Egas M and Riedl A 2008 Proceedings of the Royal Society B: Biological Sciences 275 871–878 [6] Brandt H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Hauert C and Sigmund K 2006 Proceedings of the National Academy of Sciences 103 495–497 [7] Mathew S and Boyd R 2009 Proceedings of the Royal Society B: Biological Sciences 276 1167–1174 [8] Hauert C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Traulsen A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Brandt H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Nowak M A and Sig- mund K 2007 science 316 1905–1907 [9] Fowler J H 2005 Proceedings of the National Academy of Sciences 102 7047–7049 [10] Sasaki T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Br¨annstr¨om ˚A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Dieckmann U and Sigmund K 2012 Proceedings of the National Academy of Sciences 109 1165–1169 [11] Garcia J and Traulsen A 2012 Journal of theoretical bi- ology 307 168–173 [12] Santos M d,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Rankin D J and Wedekind C 2011 Pro- ceedings of the Royal Society B: Biological Sciences 278 371–377 [13] Rockenbach B and Milinski M 2006 Nature 444 718–723 [14] Brandt H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Hauert C and Sigmund K 2003 Proceedings of the royal society of London.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Series B: biological sciences 270 1099–1104 [15] Ohtsuki H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Iwasa Y and Nowak M A 2009 Nature 457 79–82 [16] Hilbe C and Traulsen A 2012 Scientific reports 2 1–4 [17] Boyd R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Gintis H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Bowles S and Richerson P J 2003 Pro- ceedings of the National Academy of Sciences 100 3531– 3535 [18] S¨a¨aksvuori L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Mappes T and Puurtinen M 2011 Pro- ceedings of the Royal Society B: Biological Sciences 278 3428–3436 [19] Gavrilets S and Fortunato L 2014 Nature communica- tions 5 1–11 [20] Helbing D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Szolnoki A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Perc M and Szab´o G 2010 PLoS computational biology 6 e1000758 [21] Szolnoki A and Perc M 2017 Physical Review X 7 041027 [22] Helbing D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Szolnoki A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Perc M and Szab´o G 2010 New Journal of Physics 12 083005 [23] Perc M and Szolnoki A 2012 New Journal of Physics 14 043013 [24] Molleman L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' K¨olle F,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Starmer C and G¨achter S 2019 Nature Human Behaviour 3 1145–1153 [25] Boyd R,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Gintis H and Bowles S 2010 Science 328 617– ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='620 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='[26] Przepiorka W and Diekmann A 2013 Proceedings of the ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='Royal Society B: Biological Sciences 280 20130247 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='[27] Han T A 2016 Emergence of social punishment and co- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='operation through prior commitments Proceedings of the ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='Thirtieth AAAI Conference on Artificial Intelligence pp ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='2494–2500 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='[28] Eldakar O T and Wilson D S 2008 Proceedings of the ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='National Academy of Sciences 105 6982–6986 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='[29] Orbell J M and Dawes R M 1993 American sociological ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='review 787–800 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content='[30] Hauert C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' De Monte S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Hofbauer J and Sigmund K 2002 Science 296 1129–1132 [31] Hauert C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' De Monte S,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Hofbauer J and Sigmund K 2002 Journal of Theoretical Biology 218 187–194 [32] Shen C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Jusup M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Shi L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Wang Z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Perc M and Holme P 2021 Journal of the Royal Society Interface 18 20200777 [33] Vukov J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Pinheiro F L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Santos F C and Pacheco J M 2013 PLoS computational biology 9 e1002868 [34] Fudenberg D and Imhof L A 2006 Journal of Economic Theory 131 251–262 [35] Imhof L A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Fudenberg D and Nowak M A 2005 Proceed- ings of the National Academy of Sciences 102 10797– 10800 [36] Santos F C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Pacheco J M and Skyrms B 2011 Journal of Theoretical Biology 274 30–35 [37] McAvoy A 2015 Journal of Economic Theory 159 66–69 15 [38] Nowak M A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Sasaki A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Taylor C and Fudenberg D 2004 Nature 428 646–650 [39] Traulsen A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Nowak M A and Pacheco J M 2006 Physical Review E 74 011909 [40] Dreber A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Rand D G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Fudenberg D and Nowak M A 2008 Nature 452 348–351 [41] Wu J J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Zhang B Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Zhou Z X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' He Q Q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Zheng X D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Cressman R and Tao Y 2009 Proceedings of the National Academy of Sciences 106 17448–17451 [42] Reichenbach T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Mobilia M and Frey E 2007 Nature 448 1046–1049 [43] Szolnoki A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Mobilia M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Jiang L L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Szczesny B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Ruck- lidge A M and Perc M 2014 Journal of the Royal Society Interface 11 20140735 [44] Szab´o G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Vukov J and Szolnoki A 2005 Physical Review E 72 047107 [45] Perc M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Jordan J J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Rand D G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Wang Z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Boccaletti S and Szolnoki A 2017 Physics Reports 687 1–51 [46] Szolnoki A and Perc M 2016 New Journal of Physics 18 083021 [47] Perc M 2017 European Journal of Physics 39 014001 [48] Herrmann B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Thoni C and Gachter S 2008 Science 319 1362–1367 [49] Denant-Boemont L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Masclet D and Noussair C N 2007 Economic theory 33 145–167 [50] G¨achter S and Herrmann B 2011 European economic re- view 55 193–210 [51] Rand D G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Ohtsuki H and Nowak M A 2009 Journal of theoretical biology 256 45–57 [52] Rand D G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Armao IV J J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Nakamaru M and Ohtsuki H 2010 Journal of theoretical biology 265 624–632 [53] Rand D G and Nowak M A 2011 Nature communications 2 1–7 [54] Gracia-L´azaro C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Ferrer A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Ruiz G,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Taranc´on A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Cuesta J A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' S´anchez A and Moreno Y 2012 Proceedings of the National Academy of Sciences 109 12922–12926 [55] Fehr E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Fischbacher U and G¨achter S 2002 Human nature 13 1–25 [56] Bowles S and Gintis H 2004 Theoretical population biol- ogy 65 17–28 [57] Yamagishi T,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Horita Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Mifune N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Hashimoto H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Li Y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Shinada M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Miura A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Inukai K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Takagishi H and Simunovic D 2012 Proceedings of the National Academy of Sciences 109 20364–20368 [58] Egloff B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Richter D and Schmukle S C 2013 Proceedings of the National Academy of Sciences 110 E786–E786 [59] Li X,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Jusup M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Wang Z,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Li H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Shi L,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Podobnik B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Stanley H E,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} +page_content=' Havlin S and Boccaletti S 2018 Proceedings of the National Academy of Sciences 115 30–35' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/49E4T4oBgHgl3EQfBAv2/content/2301.04849v1.pdf'} diff --git a/4dE4T4oBgHgl3EQfBAsA/content/tmp_files/2301.04847v1.pdf.txt b/4dE4T4oBgHgl3EQfBAsA/content/tmp_files/2301.04847v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..1bc21ab6a04835d645f144062d8ccf6f48856d0e --- /dev/null +++ b/4dE4T4oBgHgl3EQfBAsA/content/tmp_files/2301.04847v1.pdf.txt @@ -0,0 +1,630 @@ +Real-time FPGA implementation of the +Semi-Global Matching stereo vision algorithm +for a 4K/UHD video stream +Mariusz Grabowski +and Tomasz Kryjak +Embedded Vision Systems Group, Computer Vision Laboratory, +Department of Automatic Control and Robotics, +AGH University of Science and Technology, Krakow, Poland +grabowski@student.agh.edu.pl, tomasz.kryjak@agh.edu.pl +Abstract. In this paper, we propose a real-time FPGA implementation +of the Semi-Global Matching (SGM) stereo vision algorithm. The de- +signed module supports a 4K/Ultra HD (3840 × 2160 pixels @ 30 frames +per second) video stream in a 4 pixel per clock (ppc) format and a 64- +pixel disparity range. The baseline SGM implementation had to be mod- +ified to process pixels in the 4ppc format and meet the timing constrains, +however, our version provides results comparable to the original design. +The solution has been positively evaluated on the Xilinx VC707 devel- +opment board with a Virtex-7 FPGA device. +Keywords: SGM · FPGA · 4K · Ultra HD · real-time processing · stereo +vision. +1 +Introduction +Information on the 3D structure (depth) of a scene is very important in many +robotic systems, including self-driving cars and unmanned aerial vehicles (UAVs), +as it is used in object detection and navigation modules. The depth map can +be estimated using several different approaches, active: LiDAR (Light Detec- +tion and Ranging), Time of Flight (ToF) cameras, stereo vision with structured +lighting; and passive: stereo vision. Stereo vision uses two or more cameras that +acquire the same scene, but from slightly different points in space. A detailed +discussion of the advantages and disadvantages of different sensors can be found +in the work of Jamwal, Jindal, and Singh [1]. +Stereo vision, in its passive variant, is an often used solution in embedded +systems due to the low price of the equipment, its small size and weight (no +need for a laser light source, rotating elements or projectors). The accuracy +of the results obtained with this technology strictly depends on the algorithm +used to process the acquired images. The methods used can be divided into two +groups: local and global [2]. In both cases, the key element is to find the same +pixels in the image captured by the left (usually considered as the base) and +arXiv:2301.04847v1 [cs.CV] 12 Jan 2023 + +2 +M. Grabowski et al. +right camera (reference). Their offset expressed in pixels is referred to as the +disparity. This value can be easily converted to the distance from the sensors +using the vision system parameters. +Global methods introduce appropriate discontinuity penalties in order to +smooth the disparity map. Their aim is to optimise the energy function de- +fined over the whole image. By means of global algorithms, much more reliable +and accurate disparity maps are determined, but the smoothing task is NP-hard +and algorithms are very computationally demanding, and for this reason they +are not suitable for implementation in real-time systems. +It should be also noted that the current dominant trend is depth estimation +using deep neural networks [3]. However, due to the high computational com- +plexity, especially for high-resolution video streams, this topic remains outside +the focus of our present work. +The SGM (Semi-Global Matching) algorithm was introduced by Hirshm¨uller +in 2005 [4] and 2008 [5]. It is based on two components: (1) matching at a single +pixel level with the use of mutual information and (2) approximation of a global, +two-dimensional smoothness constraint (obtained by combining multiple 1D con- +straints). The SGM algorithm is an example of an intermediate method between +local and global approaches for determining disparity maps and is a compromise +between accuracy and computational complexity. However, using SGM for high- +resolution images is still challenging. For example, for a resolution of 1920×1080 +pixels at 30 frames per second, an execution of about 2 TOPS (Tera Operations +Per Second) with memory bandwidth of 39 Tb/s is required to process all pixels +(2 million) [6]. +In this paper we present an architecture of a stereo vision system with a mod- +ified SGM algorithm to process a 4K/Ultra HD (3840 × 2160 pixels @ 30 frames +per second) video stream in 4ppc (pixel per clock) format and its implemen- +tation in an FPGA (Field Programmable Gate Array) device. The proposed +modification solves the data dependency problem while not affecting the algo- +rithm’s accuracy. To the authors’ knowledge, this is the only verified hardware +implementation of the SGM method for 4K/Ultra HD resolution. +The reminder of this paper is organised as follows. In Section 2 we present +basic information about the SGM algorithm. In Section 3 we review the previous +work on SGM implementation on FPGAs. We describe the proposed method and +architecture, as well as the evaluation of the algorithm and the hardware im- +plementation in Section 4. The paper ends with conclusions and future research +directions. +2 +The SGM algorithm +As mentioned in the introduction, the SGM algorithm is an intermediate ap- +proach between local and global methods for determining disparity maps. Fur- +thermore, it is possible to implement it in an FPGA, in a pipelined vision system. +The input to the algorithm is a pair of rectified images. It consists of the +following steps: calculation of the matching cost, aggregation of the cost (cal- + +Real-time FPGA implementation of the SGM stereo vision in 4K +3 +Fig. 1: Matching cost calculation with the Census transform and the Hamming +distance metric, with example values. +culation of the smoothness constraint) and determination of the final disparity +map. +In this work, the cost of matching C(p, d) between a pixel p = [px, py]T +from the base image Ib, and the potentially corresponding pixel (shifted by the +disparity d in a horizontal line) in the reference image Im, is calculated using +the Census transform and the Hamming distance measure, as shown in Figure +1. +Determining the correspondence between pixels using only the matching cost +alone can lead to ambiguous and incorrect results. Therefore, an additional global +condition is proposed in the SGM algorithm, which adds a “penalty” for changing +the disparity value (i.e, supports the smoothness of the image), by aggregating +the costs along independent paths. +Let Lr denote the path in the direction r. The path cost Lr(p, d) is defined +recursively as: +Lr(p, d) = C(p, d) + min[Lr(p − r, d), +Lr(p − r, d − 1) + P1, +Lr(p − r, d + 1) + P1, +min +i +Lr(p − r, i) + P2] +− min +k Lr(p − r, k) +(1) +where: C(p, d) is the matching cost, and the second part of the equation is +the minimum path cost for the previous pixel p − r on the path, taking into +account the corresponding discontinuity penalty. Two penalties were applied in +the algorithm, P1 for a 1-level change in disparity and P2 for a larger change. +Finally, the matching cost is given as: +S(p, d) = +� +r +Lr(p, d) +(2) +The author of SGM recommend aggregation along at least 8 paths, i.e, ver- +tically, horizontally and diagonally in both directions (cf. Figure 3), although he +suggests that good results are achieved for the number 16. The disparity map +Db corresponding to the base image Ib is obtained by selecting for each value p +the disparity d that corresponds to the minimum cost i.e, mindS(p, d). Optional +element of the algorithm is the final post-processing: median filtering and map +consistency check (so called left-right consistency check). + +Ib (pxPy) +Cntx +Census +4 +Gen. +Transform +1314 +0010 +C(p,d) +Hamming +3 +Distance +(px+d,py) +11111 +6 +7 +6 +Cntx +Census +10 +3 +4 +3 +Gen. +Transform +1 +1100 +5 +24 +M. Grabowski et al. +Due to the reasonable trade-off between computational complexity and the +quality of the resulting disparity map, the SGM algorithm has become very +popular. It is a basic method in the popular OpenCV library and the Computer +Vision Toolbox of the Matlab software. It also provides an attractive solution +for hardware implementations in FPGAs. +3 +Previous work +The topic of implementing stereo correspondence using FPGAs is very extensive, +and hence this review is narrowed only to selected articles describing the SGM +algorithm. Interested readers are referred to the review [7]. +The paper written by Gehrig, Eberli, and Meye in 2009 [8] described an +SGM architecture for processing images with a resolution of 750 × 480 pixels +(effectively 340 × 200) @ 27 fps at 64 levels of disparity. It is worth noting that +this was the first implementation of the SGM method in an FPGA. +The paper of Hofmann, Korinth, and Koch from 2016 [9] also proposes a hard- +ware implementation of the SGM algorithm. The architecture features scalability +and combines coarse-grain and fine-grain parallelisation capabilities. The authors +performed tests for different configurations and resolutions. For 1920×1080 pix- +els @ 30 fps and 128 disparity levels, real-time processing was achieved at a clock +of 130 MHz (VC709 board with Virtex-7 FPGA device). +In the paper of Zhao et al. from 2020 [10], the authors presented the FP- +Stereo library, which uses the HLS language and allows the creation of SGM +disparity calculation modules. The module has been designed in the form of +an accelerator interfacing with a DMA controller, rather than directly with the +video stream. For a 300 MHz clock, a resolution of 1242 × 374 pixels and 128 +disparity range, 161 fps were achieved on the ZCU 102 board with the Xilinx +Zynq UltraScale+ MPSoC device. +In the latest publications by Shrivastava et al. in 2020 [11] and Lee with Kim +in 2021 [6], the support for parallel pixel processing has been added to increase +throughput. In this approach, the main challenge is the presence of an inherent +data dependency. In the paper from 2020 [11], it is addressed by dependency +relaxation, i.e, the aggregation is performed on the basis of the pixel k earlier, +where k is the number of pixels processed simultaneously. The author points out +that such a solution represents a trade-off between accuracy and throughput. +In the work from 2021 [6], on the other hand, a different approach is pre- +sented, in which operations involving the inherent data dependency are per- +formed not on a single pixel, but on a vector of pixels. This allows the genera- +tion of disparity maps with very close accuracy to the original SGM algorithm. +In both solutions, the matching costs are determined based on the Census trans- +form. In the first publication [11], for images at a resolution of 1280 × 960 pixels +and disparity range of 64, 322 fps, and in the second [6] for a resolution of +1920 × 1080 pixels and disparity range of 128, 103 fps were obtained. +We also propose a solution to the inherent data dependency problem. Our +architecture is based on estimating the previous pixel aggregation cost on a path + +Real-time FPGA implementation of the SGM stereo vision in 4K +5 +Fig. 2: A general scheme of the proposed SGM disparity estimation system. +with minimal additional logic needed. That allows us to process images with a 4K +resolution and also to obtain comparable results to the original SGM algorithm +without parallelism. +4 +The proposed hardware implementation +The aim of our work was to implement a hardware architecture capable of pro- +cessing a video stream with a resolution of 3840×2160 pixels in real-time (i.e pro- +cessing 30 frames per second with no pixel dropping). That stream transmitted +in a 1 pixel per clock format requires a pixel clock frequency of approximately +250 MHz. Adding to this value i.e, the vertical and horizontal blanking fields, +the required clock equals about 300 MHz, which is too high for the rather com- +plicated SGM algorithm. At the bottleneck, cost aggregation calculations take +more than 10 ns on our platform. So, in order to process the data in the de- +sired resolution, it is necessary to introduce parallelisation. In this work, a 4ppc +(pixel per clock) format is used, in which 4 pixels are processed in parallel. This +allows the pixel clock to be lowered to approximately 75 MHz. However, the use +of such format has significant implications on the implementation of the SGM +algorithm, due to the inherent data dependency. +A general scheme for the proposed vision system is shown in Figure 2. The +module accepts a synchronised video stream of rectified images, the base IB(p) +and the reference IM(p) one. Further processing consists of several steps: de- +termination of the matching cost C(p, d) using the Census transform based +matching method, calculation of the cost aggregation Lr(p, d), summation of +the aggregation costs from all directions S(p, d) and disparity determination +D(p). +4.1 +Determination of the matching cost +The 4ppc format does not introduce major complications into the hardware +architecture of the matching cost determination module, but only increases the +hardware resource requirements. First, 5×5 contexts are created for both images. +For the base image, in a given cycle, 4 contexts are created (as implied by the +4ppc format [12]), and for the reference image this number is increased by the +disparity range (4 + disp range − 1), so that it is possible to simultaneously +compare each of the 4 contexts of the base image with all the contexts in the +disparity range of the reference image. A Census transform is performed on the +generated contexts, and the contexts are then compared accordingly using the +Hamming distance metric. The output consists of matching cost vectors. + +Ib(p) +C(p, d) +Lr(p, d) +S(p,d) +Disparity +D(p) +Matching Costs +Costs +Im(p) +Sum +Selection +Determination +Aggregation6 +M. Grabowski et al. +Fig. 3: Cost aggregation paths in SGM. +4.2 +Cost aggregation +In the next step, a quasi-global optimisation is performed by aggregating the +costs for the whole image according to the SGM algorithm. In the current version +of the module, this is implemented on four paths in the directions 0°, 45°, 90°, +135°, as shown in Figure 3, which can be processed directly (without additional +video stream buffering). +Theoretically, it is also possible to realise the other four directions (180°, +225°, 270°, 315°), but this would require storing the entire image in external +RAM, using additional resources of the FPGA device, complex control logic and +introducing additional latency in image processing. +In order to calculate the aggregation cost for a given pixel, it is necessary to +know the value of the aggregation cost for the previous pixel on the path (cf. +Equations (1) and (2)). For the 45°, 90°, 135° paths, the aggregation costs for the +pixels in a given line are stored in Block RAM and read out accordingly during +the processing of the next image line to calculate the costs for the subsequent +pixels on these paths. The hardware architecture of this computation is shown in +Figure 4 and follows Equation (1). The grey part is replicated for the entire range +of disparities (disp range) and performs in parallel and one block of finding the +minimum value of aggregation costs of the previous pixel on the path minLr(p− +r) is exploited to calculate the aggregation cost for the current pixel for each +disparity value in the range. +For the 4ppc format, the difficulty arises for the 0° path. Using the aggrega- +tion cost of the previous pixel Lr(p − r, d), which for this path lies in the same +image line and potentially in the same 4ppc format data vector, results in the +need to process four pixels in the same clock cycle. In the worst case, for the +last pixel in the vector, in one clock cycle the data would have to propagate +through four serially connected aggregation cost calculation units, as in Figure +4. The critical path would contain 4 minimum modules of size disp range, four +minimum modules of size 4 and 12 adders/subtractors. For this reason, the cost +aggregation based on a baseline architecture (i.e, as proposed by the authors of +SGM) for the 0° path is not feasible for the considered 4K resolution, without +violating timing constraints. +It is therefore necessary to propose a new solution for the calculation of the +aggregation cost for the 0° path. Time constraints require that the new architec- +ture does not introduce significant additional propagation time and maintains + +video stream direction +45° +.06 +135° +。0 +dReal-time FPGA implementation of the SGM stereo vision in 4K +7 +Fig. 4: Hardware architecture of the aggregation cost calculation unit for path +r, pixel p and disparity d. +the approximation assumption of the global smoothness constraint of the SGM +algorithm. +In our work, we designed and implemented an architecture with a proposed +estimation of the aggregation cost value for consecutive pixels based on the +calculated aggregation cost for the last pixel of the previous 4ppc vector (the +pixel processed in the previous clock cycle) and the matching costs of the previous +pixels in the same 4ppc vector. +For the first pixel in the 4ppc vector, the aggregation cost of the previous +pixel is available during the calculation (it was calculated for the previous 4ppc +vector), i.e: +Lr(p1 − r, d) = Lr(plast, d) +(3) +where: Lr(p1 − r, d) is the aggregation cost of the previous pixel relative to the +first pixel in the 4ppc vector (p1 − r), and Lr(plast − r, d) is the aggregation cost +of the last pixel in the previous 4ppc vector. +For the consecutive pixels, we propose an estimation, which is performed +according to the following Equations: +L′ +r(p2 − r, d) = Lr(plast, d) + 1 +λ(C(p1, d) − Lr(plast, d)) +L′ +r(p3 − r, d) = Lr(plast, d) + 1 +λ(C(p1, d) + C(p2, d) +2 +− Lr(plast, d)) +L′ +r(p4 − r, d) = Lr(plast, d) + 1 +λ( +C(p1, d) + C(p2, d) +2 ++ C(p3, d) +2 +− Lr(plast, d)) +(4) +where: L′ +r(p−r, d) is the estimated aggregation cost for the previous pixel relative +to the pixel p, C(p, d) is the matching cost for a given pixel, and the coefficient + +Lr(p -r,d) +Lr(p - r,d - 1) +C(p, d) +P1 +Minimum +Lr(p,d) +Lr(p -r,min disp) +Lr(p -r,d + 1) +(size: 4) +Lr(p - r,min disp + 1) +P1 +Minimum +min Lr(p - r +(size: disp range) +P2 +Lr(p -r,max disp - 1 +Lr(p - r,max disp )8 +M. Grabowski et al. +Fig. 5: The architecture for estimating the aggregation cost of the previous pixel +for each pixel in the 4ppc vector. +λ may take a value which is a power of two (1, 2, 4, 8, 16, ...). The architecture of +this solution is shown in Figure 5. +The algorithm is based on the difference of the matching cost values of the +previous pixels in a given 4ppc vector with the aggregation cost for the last pixel +of the previous vector. The aggregation cost estimation architecture consists of +basic components and introduces an additional delay only by the propagation +time of the 3 adders/subtractors (critical path for Lr(p4−r, d). Note: multiplica- +tion/division by a number that is a power of two is only a bit shift and requires +no delay in the hardware implementation. +The solution takes into account the matching cost values of all previous pixels +with the possibility to adjust the impact of the matching cost of previous pixels +in a given vector by a factor of λ. +The estimated aggregation costs are then used to calculate the aggregation +costs according to the architecture in Figure 4. In the work of Shrivastava et al. +[11] the estimation has been omitted and in the work of Lee and Kim [6] it has +been solved by the cluster-wise cost aggregation. +The aggregation costs from all paths are then summed and the disparity is +calculated. This involves finding the minimum matching cost. +4.3 +Evaluation of the proposed method +The accuracy evaluation of the proposed algorithm was performed on a set of +stereo images from the Middlebury 2014 [13] dataset. We skipped the final post- +processing to better highlight the differences between the base SGM algorithm +and the modified version proposed in this paper (SGM 4ppc). The accuracy was + +Lr(p1 - r,d) +Lr(piast -r,d) +C(p1,d) +1 +Lr(p2 -r,d) +Lr(piast -r,d) +C(p1, d) +C(p2, d) +L'r(p3 -r,d) +Lr(plast -r,d) +C(p1, d) +4 +C(p2, d) +1 +C(p3, d) +1 +Lr(p4 -r,d) +X +-2 +Lr(piast -r, d)Real-time FPGA implementation of the SGM stereo vision in 4K +9 +(a) Input image – left +(b) Ground truth +(c) SGM 4ppc +(d) Local method based +on CT +(e) SGM – 3 paths +(f) SGM – 4 paths +Fig. 6: Comparison of output disparity maps for the Motorcycle image in Mid- +dlebury 2014 dataset: (a) the left input image, (b) the ground truth disparity +map, (c), (d), (e), (f) estimated disparity maps (on the top) and the error maps +(on the bottom). +measured by the ratio of pixels with incorrect disparity value to all pixels of the +image (all) and also to the non-occluded (noc) pixels (occluded pixels should be +filled with the Left/Right Check post-processing). +We compared the proposed method (SGM 4ppc) with the conventional local +block matching based on the Census transform and the SGM algorithm (also + +YAMRMA区X10 +M. Grabowski et al. +Table 1: Comparison of error rates for the Middlebury 2014 dataset, based on +all (all) and non-occluded (noc) pixels. +all +noc +Local based on CT +68.21% +63,36% +SGM 3 paths +38.01% +28.79% +SGM 4 paths +36.27% +26.88% +SGM 8 paths +33.31% +23.11% +SGM 4ppc +36.64% +27.32% +based on the Census transform) with 3 and 4 aggregation paths. Figure 6 shows +sample evaluation results on the Motorcycle images from the Middlebury 2014 +dataset. Table 1 shows the average evaluation results for the entire dataset. +The accuracy of the proposed method is comparable to the original SGM +algorithm with 4 paths. The difference between error rates is about 0.4%. +4.4 +Hardware implementation +We implemented the proposed stereo vision system on a VC707 evaluation board +with Xilinx’s Virtex-7 XC7VX485T-2FFG1761C device. We set up a test envi- +ronment to evaluate the system, with test images sent directly from a PC do the +board and later displayed on a 4K monitor. +We compared our solution with previous FPGA implementations of the SGM +algorithm in Table 2. We used the following metrics: Frames per Second (FPS), +Million Disparity Estimates per second (MDE/s) and MDE/s per Kilo LUTs +(Look-Up Tables) (MDE/s/KLUT). First of all, our solution is the only one ver- +ified in hardware for a 4K/ Ultra HD resolution. We also would like to point out +that the lower performance in FPS and MDE/s relative to previous work from +2020 [11] and 2021 [6] is due to the use of an FPGA chip with fewer resources. For +this work, it was necessary to select a suitable platform to enable image acquisi- +tion in 4K resolution (i.e, having two high-bandwidth FMCs (FPGA Mezzanine +Connectors) to which TB-FMCH-HDMI4K modules were attached). +It is also worth mentioning that the used FPGA technology differs not only +in the number of resources but also in the performance. To compare: the critical +path propagation time for the technology used in this paper after synthesis +is 12.967 ns, but for the Xilinx Virtex UltraScale+ XCVU9P-L2FLGA2104E +FPGA with the same parameters, it is 8.240 ns (36.45% faster). +5 +Conclusion +In this paper, we presented a hardware architecture for an SGM algorithm to +process a 4K/Ultra HD video stream in real-time. We proposed a solution to +the inherent data dependency problem. It allowed us to maintain high accuracy +of the depth map estimation, while making it possible to take advantage of the + +Real-time FPGA implementation of the SGM stereo vision in 4K +11 +Table 2: Comparison with previous FPGA implementations of the SGM algo- +rithm. +Image +Disparity +Platform +FPGA +Throughput +resolution +range +resources +LUT FF BRAM FPS MDE/s MDE/s/KLUT +[14] +1920x1080 +128 +Virtex-7 +195k 217k +368 +30 +7 963 +40.84 +[15] +1600x1200 +128 +Stratix-V +222k 149k +N/A +43 +10 472 +47.2 +[11] +1280x960 +64 +Virtex-7 690T 211k N/A +641 +322 25 056 +118.6 +[6] +1920x1080 +128 +Zynq US+ +222k 135k +252 +103 27 297 +123.0 +New 3840x2160 +64 +Virtex-7 485T 138k 65k +197 +30 +15 925 +116.2 +4ppc vector format. We implemented the module on a Virtex-7 FPGA platform +achieving 30 frames per second for a resolution of 3840 × 2160 pixels with 64 +disparity levels. +In future work, we plan to add more aggregation paths to the algorithm. With +that, it will be possible to get more accurate results, but at the cost of latency and +resource usage. We also plan to implement a video stream rectification module. +Acknowledgements The work presented in this paper was supported by: the +National Science Centre project no. 2016/23/D/ST6/01389 entitled ”The de- +velopment of computing resources organization in latest generation of hetero- +geneous reconfigurable devices enabling real-time processing of UHD/4K video +stream”, the AGH University of Science and Technology project no. 16.16.120.773 +and the program ”Excellence initiative — research university” for the AGH Uni- +versity of Science and Technology. +References +[1] +N. Jamwal, N. Jindal, and K. Singh. “A survey on depth map estima- +tion strategies”. In: International Conference on Signal Processing (ICSP +2016). 2016, pp. 1–5. doi: 10.1049/cp.2016.1453. +[2] +Daniel Scharstein and Richard Szeliski. “A Taxonomy and Evaluation of +Dense Two-Frame Stereo Correspondence Algorithms”. In: International +Journal of Computer Vision 47 (Apr. 2002), pp. 7–42. doi: 10.1023/A: +1014573219977. +[3] +Hamid Laga et al. “A Survey on Deep Learning Techniques for Stereo- +Based Depth Estimation”. In: IEEE Transactions on Pattern Analysis and +Machine Intelligence 44.4 (2022), pp. 1738–1764. doi: 10.1109/TPAMI. +2020.3032602. +[4] +H. Hirschmuller. “Accurate and efficient stereo processing by semi-global +matching and mutual information”. In: 2005 IEEE Computer Society Con- +ference on Computer Vision and Pattern Recognition (CVPR’05). Vol. 2. +2005, 807–814 vol. 2. doi: 10.1109/CVPR.2005.56. + +12 +M. Grabowski et al. +[5] +Hirschmuuller H. “Stereo processing by semiglobal matching and mutual +information.” In: IEEE Transactions on Pattern Analysis and Machine +Intelligence 30.2 (2008), pp. 328–341. issn: 0162-8828. +[6] +Yeongmin Lee and Hyeji Kim. “A High-Throughput Depth Estimation +Processor for Accurate Semiglobal Stereo Matching Using Pipelined Inter- +Pixel Aggregation”. In: IEEE Transactions on Circuits and Systems for +Video Technology (2021), pp. 1–1. doi: 10.1109/TCSVT.2021.3061200. +[7] +Zishen Wan et al. “A Survey of FPGA-Based Robotic Computing”. In: +IEEE Circuits and Systems Magazine 21.2 (2021), pp. 48–74. doi: 10. +1109/MCAS.2021.3071609. +[8] +Stefan K. Gehrig, Felix Eberli, and Thomas Meyer. “A real-time low-power +stereo vision engine using semi-global matching”. In: Lecture Notes in +Computer Science (including subseries Lecture Notes in Artificial Intel- +ligence and Lecture Notes in Bioinformatics) 5815 LNCS (2009), pp. 134– +143. issn: 03029743. doi: 10.1007/978-3-642-04667-4_14. +[9] +Jaco Hofmann, Jens Korinth, and Andreas Koch. “A Scalable High-Performance +Hardware Architecture for Real-Time Stereo Vision by Semi-Global Match- +ing”. In: 2016 IEEE Conference on Computer Vision and Pattern Recog- +nition Workshops (CVPRW). 2016, pp. 845–853. doi: 10.1109/CVPRW. +2016.110. +[10] +Jieru Zhao et al. “FP-Stereo: Hardware-Efficient Stereo Vision for Em- +bedded Applications”. In: 2020 30th International Conference on Field- +Programmable Logic and Applications (FPL). 2020, pp. 269–276. doi: 10. +1109/FPL50879.2020.00052. +[11] +Shashwat Shrivastava et al. “FPGA Accelerator for Stereo Vision using +Semi-Global Matching through Dependency Relaxation”. In: 2020 30th +International Conference on Field-Programmable Logic and Applications +(FPL). 2020, pp. 304–309. doi: 10.1109/FPL50879.2020.00057. +[12] +Marcin Kowalczyk, Dominika Przewlocka, and Tomasz Kryjak. “Real- +Time Implementation of Contextual Image Processing Operations for 4K +Video Stream in Zynq UltraScale+ MPSoC”. In: 2018 Conference on De- +sign and Architectures for Signal and Image Processing (DASIP). 2018, +pp. 37–42. doi: 10.1109/DASIP.2018.8597105. +[13] +Daniel Scharstein et al. “High-Resolution Stereo Datasets with Subpixel- +Accurate Ground Truth”. In: Pattern Recognition. Ed. by Xiaoyi Jiang, +Joachim Hornegger, and Reinhard Koch. Cham: Springer International +Publishing, 2014, pp. 31–42. isbn: 978-3-319-11752-2. +[14] +Jaco Hofmann, Jens Korinth, and Andreas Koch. “A Scalable High-Performance +Hardware Architecture for Real-Time Stereo Vision by Semi-Global Match- +ing”. In: 2016 IEEE Conference on Computer Vision and Pattern Recog- +nition Workshops (CVPRW). 2016, pp. 845–853. doi: 10.1109/CVPRW. +2016.110. +[15] +Wenqiang Wang et al. “Real-Time High-Quality Stereo Vision System in +FPGA”. In: IEEE Transactions on Circuits and Systems for Video Tech- +nology 25.10 (2015), pp. 1696–1708. doi: 10.1109/TCSVT.2015.2397196. + diff --git a/4dE4T4oBgHgl3EQfBAsA/content/tmp_files/load_file.txt b/4dE4T4oBgHgl3EQfBAsA/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..52371a6aaa4385fc8cd3319c22073b93209aa140 --- /dev/null +++ b/4dE4T4oBgHgl3EQfBAsA/content/tmp_files/load_file.txt @@ -0,0 +1,384 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf,len=383 +page_content='Real-time FPGA implementation of the Semi-Global Matching stereo vision algorithm for a 4K/UHD video stream Mariusz Grabowski and Tomasz Kryjak Embedded Vision Systems Group, Computer Vision Laboratory, Department of Automatic Control and Robotics, AGH University of Science and Technology, Krakow, Poland grabowski@student.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='agh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='pl, tomasz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='kryjak@agh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='pl Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In this paper, we propose a real-time FPGA implementation of the Semi-Global Matching (SGM) stereo vision algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The de- signed module supports a 4K/Ultra HD (3840 × 2160 pixels @ 30 frames per second) video stream in a 4 pixel per clock (ppc) format and a 64- pixel disparity range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The baseline SGM implementation had to be mod- ified to process pixels in the 4ppc format and meet the timing constrains, however, our version provides results comparable to the original design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The solution has been positively evaluated on the Xilinx VC707 devel- opment board with a Virtex-7 FPGA device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Keywords: SGM · FPGA · 4K · Ultra HD · real-time processing · stereo vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 1 Introduction Information on the 3D structure (depth) of a scene is very important in many robotic systems, including self-driving cars and unmanned aerial vehicles (UAVs), as it is used in object detection and navigation modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The depth map can be estimated using several different approaches, active: LiDAR (Light Detec- tion and Ranging), Time of Flight (ToF) cameras, stereo vision with structured lighting;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' and passive: stereo vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Stereo vision uses two or more cameras that acquire the same scene, but from slightly different points in space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' A detailed discussion of the advantages and disadvantages of different sensors can be found in the work of Jamwal, Jindal, and Singh [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Stereo vision, in its passive variant, is an often used solution in embedded systems due to the low price of the equipment, its small size and weight (no need for a laser light source, rotating elements or projectors).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The accuracy of the results obtained with this technology strictly depends on the algorithm used to process the acquired images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The methods used can be divided into two groups: local and global [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In both cases, the key element is to find the same pixels in the image captured by the left (usually considered as the base) and arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='04847v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='CV] 12 Jan 2023 2 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Grabowski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' right camera (reference).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Their offset expressed in pixels is referred to as the disparity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' This value can be easily converted to the distance from the sensors using the vision system parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Global methods introduce appropriate discontinuity penalties in order to smooth the disparity map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Their aim is to optimise the energy function de- fined over the whole image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' By means of global algorithms, much more reliable and accurate disparity maps are determined, but the smoothing task is NP-hard and algorithms are very computationally demanding, and for this reason they are not suitable for implementation in real-time systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' It should be also noted that the current dominant trend is depth estimation using deep neural networks [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' However, due to the high computational com- plexity, especially for high-resolution video streams, this topic remains outside the focus of our present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The SGM (Semi-Global Matching) algorithm was introduced by Hirshm¨uller in 2005 [4] and 2008 [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' It is based on two components: (1) matching at a single pixel level with the use of mutual information and (2) approximation of a global, two-dimensional smoothness constraint (obtained by combining multiple 1D con- straints).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The SGM algorithm is an example of an intermediate method between local and global approaches for determining disparity maps and is a compromise between accuracy and computational complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' However, using SGM for high- resolution images is still challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' For example, for a resolution of 1920×1080 pixels at 30 frames per second, an execution of about 2 TOPS (Tera Operations Per Second) with memory bandwidth of 39 Tb/s is required to process all pixels (2 million) [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In this paper we present an architecture of a stereo vision system with a mod- ified SGM algorithm to process a 4K/Ultra HD (3840 × 2160 pixels @ 30 frames per second) video stream in 4ppc (pixel per clock) format and its implemen- tation in an FPGA (Field Programmable Gate Array) device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The proposed modification solves the data dependency problem while not affecting the algo- rithm’s accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' To the authors’ knowledge, this is the only verified hardware implementation of the SGM method for 4K/Ultra HD resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The reminder of this paper is organised as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In Section 2 we present basic information about the SGM algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In Section 3 we review the previous work on SGM implementation on FPGAs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' We describe the proposed method and architecture, as well as the evaluation of the algorithm and the hardware im- plementation in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The paper ends with conclusions and future research directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 2 The SGM algorithm As mentioned in the introduction, the SGM algorithm is an intermediate ap- proach between local and global methods for determining disparity maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Fur- thermore, it is possible to implement it in an FPGA, in a pipelined vision system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The input to the algorithm is a pair of rectified images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' It consists of the following steps: calculation of the matching cost, aggregation of the cost (cal- Real-time FPGA implementation of the SGM stereo vision in 4K 3 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 1: Matching cost calculation with the Census transform and the Hamming distance metric, with example values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' culation of the smoothness constraint) and determination of the final disparity map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In this work, the cost of matching C(p, d) between a pixel p = [px, py]T from the base image Ib, and the potentially corresponding pixel (shifted by the disparity d in a horizontal line) in the reference image Im, is calculated using the Census transform and the Hamming distance measure, as shown in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Determining the correspondence between pixels using only the matching cost alone can lead to ambiguous and incorrect results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Therefore, an additional global condition is proposed in the SGM algorithm, which adds a “penalty” for changing the disparity value (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='e, supports the smoothness of the image), by aggregating the costs along independent paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Let Lr denote the path in the direction r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The path cost Lr(p, d) is defined recursively as: Lr(p, d) = C(p, d) + min[Lr(p − r, d), Lr(p − r, d − 1) + P1, Lr(p − r, d + 1) + P1, min i Lr(p − r, i) + P2] − min k Lr(p − r, k) (1) where: C(p, d) is the matching cost, and the second part of the equation is the minimum path cost for the previous pixel p − r on the path, taking into account the corresponding discontinuity penalty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Two penalties were applied in the algorithm, P1 for a 1-level change in disparity and P2 for a larger change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Finally, the matching cost is given as: S(p, d) = � r Lr(p, d) (2) The author of SGM recommend aggregation along at least 8 paths, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='e, ver- tically, horizontally and diagonally in both directions (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Figure 3), although he suggests that good results are achieved for the number 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The disparity map Db corresponding to the base image Ib is obtained by selecting for each value p the disparity d that corresponds to the minimum cost i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='e, mindS(p, d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Optional element of the algorithm is the final post-processing: median filtering and map consistency check (so called left-right consistency check).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Ib (pxPy) Cntx Census 4 Gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Transform 1314 0010 C(p,d) Hamming 3 Distance (px+d,py) 11111 6 7 6 Cntx Census 10 3 4 3 Gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Transform 1 1100 5 24 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Grabowski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Due to the reasonable trade-off between computational complexity and the quality of the resulting disparity map, the SGM algorithm has become very popular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' It is a basic method in the popular OpenCV library and the Computer Vision Toolbox of the Matlab software.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' It also provides an attractive solution for hardware implementations in FPGAs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 3 Previous work The topic of implementing stereo correspondence using FPGAs is very extensive, and hence this review is narrowed only to selected articles describing the SGM algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Interested readers are referred to the review [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The paper written by Gehrig, Eberli, and Meye in 2009 [8] described an SGM architecture for processing images with a resolution of 750 × 480 pixels (effectively 340 × 200) @ 27 fps at 64 levels of disparity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' It is worth noting that this was the first implementation of the SGM method in an FPGA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The paper of Hofmann, Korinth, and Koch from 2016 [9] also proposes a hard- ware implementation of the SGM algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The architecture features scalability and combines coarse-grain and fine-grain parallelisation capabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The authors performed tests for different configurations and resolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' For 1920×1080 pix- els @ 30 fps and 128 disparity levels, real-time processing was achieved at a clock of 130 MHz (VC709 board with Virtex-7 FPGA device).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In the paper of Zhao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' from 2020 [10], the authors presented the FP- Stereo library, which uses the HLS language and allows the creation of SGM disparity calculation modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The module has been designed in the form of an accelerator interfacing with a DMA controller, rather than directly with the video stream.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' For a 300 MHz clock, a resolution of 1242 × 374 pixels and 128 disparity range, 161 fps were achieved on the ZCU 102 board with the Xilinx Zynq UltraScale+ MPSoC device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In the latest publications by Shrivastava et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' in 2020 [11] and Lee with Kim in 2021 [6], the support for parallel pixel processing has been added to increase throughput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In this approach, the main challenge is the presence of an inherent data dependency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In the paper from 2020 [11], it is addressed by dependency relaxation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='e, the aggregation is performed on the basis of the pixel k earlier, where k is the number of pixels processed simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The author points out that such a solution represents a trade-off between accuracy and throughput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In the work from 2021 [6], on the other hand, a different approach is pre- sented, in which operations involving the inherent data dependency are per- formed not on a single pixel, but on a vector of pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' This allows the genera- tion of disparity maps with very close accuracy to the original SGM algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In both solutions, the matching costs are determined based on the Census trans- form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In the first publication [11], for images at a resolution of 1280 × 960 pixels and disparity range of 64, 322 fps, and in the second [6] for a resolution of 1920 × 1080 pixels and disparity range of 128, 103 fps were obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' We also propose a solution to the inherent data dependency problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Our architecture is based on estimating the previous pixel aggregation cost on a path Real-time FPGA implementation of the SGM stereo vision in 4K 5 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 2: A general scheme of the proposed SGM disparity estimation system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' with minimal additional logic needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' That allows us to process images with a 4K resolution and also to obtain comparable results to the original SGM algorithm without parallelism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 4 The proposed hardware implementation The aim of our work was to implement a hardware architecture capable of pro- cessing a video stream with a resolution of 3840×2160 pixels in real-time (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='e pro- cessing 30 frames per second with no pixel dropping).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' That stream transmitted in a 1 pixel per clock format requires a pixel clock frequency of approximately 250 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Adding to this value i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='e, the vertical and horizontal blanking fields, the required clock equals about 300 MHz, which is too high for the rather com- plicated SGM algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' At the bottleneck, cost aggregation calculations take more than 10 ns on our platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' So, in order to process the data in the de- sired resolution, it is necessary to introduce parallelisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In this work, a 4ppc (pixel per clock) format is used, in which 4 pixels are processed in parallel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' This allows the pixel clock to be lowered to approximately 75 MHz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' However, the use of such format has significant implications on the implementation of the SGM algorithm, due to the inherent data dependency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' A general scheme for the proposed vision system is shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The module accepts a synchronised video stream of rectified images, the base IB(p) and the reference IM(p) one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Further processing consists of several steps: de- termination of the matching cost C(p, d) using the Census transform based matching method, calculation of the cost aggregation Lr(p, d), summation of the aggregation costs from all directions S(p, d) and disparity determination D(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='1 Determination of the matching cost The 4ppc format does not introduce major complications into the hardware architecture of the matching cost determination module, but only increases the hardware resource requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' First, 5×5 contexts are created for both images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' For the base image, in a given cycle, 4 contexts are created (as implied by the 4ppc format [12]), and for the reference image this number is increased by the disparity range (4 + disp range − 1), so that it is possible to simultaneously compare each of the 4 contexts of the base image with all the contexts in the disparity range of the reference image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' A Census transform is performed on the generated contexts, and the contexts are then compared accordingly using the Hamming distance metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The output consists of matching cost vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Ib(p) C(p, d) Lr(p, d) S(p,d) Disparity D(p) Matching Costs Costs Im(p) Sum Selection Determination Aggregation6 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Grabowski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 3: Cost aggregation paths in SGM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='2 Cost aggregation In the next step, a quasi-global optimisation is performed by aggregating the costs for the whole image according to the SGM algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In the current version of the module, this is implemented on four paths in the directions 0°, 45°, 90°, 135°, as shown in Figure 3, which can be processed directly (without additional video stream buffering).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Theoretically, it is also possible to realise the other four directions (180°, 225°, 270°, 315°), but this would require storing the entire image in external RAM, using additional resources of the FPGA device, complex control logic and introducing additional latency in image processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In order to calculate the aggregation cost for a given pixel, it is necessary to know the value of the aggregation cost for the previous pixel on the path (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Equations (1) and (2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' For the 45°, 90°, 135° paths, the aggregation costs for the pixels in a given line are stored in Block RAM and read out accordingly during the processing of the next image line to calculate the costs for the subsequent pixels on these paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The hardware architecture of this computation is shown in Figure 4 and follows Equation (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The grey part is replicated for the entire range of disparities (disp range) and performs in parallel and one block of finding the minimum value of aggregation costs of the previous pixel on the path minLr(p− r) is exploited to calculate the aggregation cost for the current pixel for each disparity value in the range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' For the 4ppc format, the difficulty arises for the 0° path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Using the aggrega- tion cost of the previous pixel Lr(p − r, d), which for this path lies in the same image line and potentially in the same 4ppc format data vector, results in the need to process four pixels in the same clock cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In the worst case, for the last pixel in the vector, in one clock cycle the data would have to propagate through four serially connected aggregation cost calculation units, as in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The critical path would contain 4 minimum modules of size disp range, four minimum modules of size 4 and 12 adders/subtractors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' For this reason, the cost aggregation based on a baseline architecture (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='e, as proposed by the authors of SGM) for the 0° path is not feasible for the considered 4K resolution, without violating timing constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' It is therefore necessary to propose a new solution for the calculation of the aggregation cost for the 0° path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Time constraints require that the new architec- ture does not introduce significant additional propagation time and maintains video stream direction 45° .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='06 135° 。' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='0 dReal-time FPGA implementation of the SGM stereo vision in 4K 7 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 4: Hardware architecture of the aggregation cost calculation unit for path r, pixel p and disparity d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' the approximation assumption of the global smoothness constraint of the SGM algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In our work, we designed and implemented an architecture with a proposed estimation of the aggregation cost value for consecutive pixels based on the calculated aggregation cost for the last pixel of the previous 4ppc vector (the pixel processed in the previous clock cycle) and the matching costs of the previous pixels in the same 4ppc vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' For the first pixel in the 4ppc vector, the aggregation cost of the previous pixel is available during the calculation (it was calculated for the previous 4ppc vector), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='e: Lr(p1 − r, d) = Lr(plast, d) (3) where: Lr(p1 − r, d) is the aggregation cost of the previous pixel relative to the first pixel in the 4ppc vector (p1 − r), and Lr(plast − r, d) is the aggregation cost of the last pixel in the previous 4ppc vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' For the consecutive pixels,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' we propose an estimation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' which is performed according to the following Equations: L′ r(p2 − r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d) = Lr(plast,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d) + 1 λ(C(p1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d) − Lr(plast,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d)) L′ r(p3 − r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d) = Lr(plast,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d) + 1 λ(C(p1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d) + C(p2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d) 2 − Lr(plast,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d)) L′ r(p4 − r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d) = Lr(plast,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d) + 1 λ( C(p1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d) + C(p2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d) 2 + C(p3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d) 2 − Lr(plast,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d)) (4) where: L′ r(p−r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d) is the estimated aggregation cost for the previous pixel relative to the pixel p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' C(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d) is the matching cost for a given pixel,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' and the coefficient Lr(p -r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='d) Lr(p - r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='d - 1) C(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' d) P1 Minimum Lr(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='d) Lr(p -r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='min disp) Lr(p -r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='d + 1) (size: 4) Lr(p - r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='min disp + 1) P1 Minimum min Lr(p - r (size: disp range) P2 Lr(p -r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='max disp - 1 Lr(p - r,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='max disp )8 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Grabowski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 5: The architecture for estimating the aggregation cost of the previous pixel for each pixel in the 4ppc vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' λ may take a value which is a power of two (1, 2, 4, 8, 16, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The architecture of this solution is shown in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The algorithm is based on the difference of the matching cost values of the previous pixels in a given 4ppc vector with the aggregation cost for the last pixel of the previous vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The aggregation cost estimation architecture consists of basic components and introduces an additional delay only by the propagation time of the 3 adders/subtractors (critical path for Lr(p4−r, d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Note: multiplica- tion/division by a number that is a power of two is only a bit shift and requires no delay in the hardware implementation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The solution takes into account the matching cost values of all previous pixels with the possibility to adjust the impact of the matching cost of previous pixels in a given vector by a factor of λ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The estimated aggregation costs are then used to calculate the aggregation costs according to the architecture in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In the work of Shrivastava et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' [11] the estimation has been omitted and in the work of Lee and Kim [6] it has been solved by the cluster-wise cost aggregation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The aggregation costs from all paths are then summed and the disparity is calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' This involves finding the minimum matching cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='3 Evaluation of the proposed method The accuracy evaluation of the proposed algorithm was performed on a set of stereo images from the Middlebury 2014 [13] dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' We skipped the final post- processing to better highlight the differences between the base SGM algorithm and the modified version proposed in this paper (SGM 4ppc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=" The accuracy was Lr(p1 - r,d) Lr(piast -r,d) C(p1,d) 1 Lr(p2 -r,d) Lr(piast -r,d) C(p1, d) C(p2, d) L'r(p3 -r,d) Lr(plast -r,d) C(p1, d) 4 C(p2, d) 1 C(p3, d) 1 Lr(p4 -r,d) X 2 Lr(piast -r, d)Real-time FPGA implementation of the SGM stereo vision in 4K 9 (a) Input image – left (b) Ground truth (c) SGM 4ppc (d) Local method based on CT (e) SGM – 3 paths (f) SGM – 4 paths Fig." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 6: Comparison of output disparity maps for the Motorcycle image in Mid- dlebury 2014 dataset: (a) the left input image, (b) the ground truth disparity map, (c), (d), (e), (f) estimated disparity maps (on the top) and the error maps (on the bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' measured by the ratio of pixels with incorrect disparity value to all pixels of the image (all) and also to the non-occluded (noc) pixels (occluded pixels should be filled with the Left/Right Check post-processing).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' We compared the proposed method (SGM 4ppc) with the conventional local block matching based on the Census transform and the SGM algorithm (also YAMRMA区X10 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Grabowski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Table 1: Comparison of error rates for the Middlebury 2014 dataset, based on all (all) and non-occluded (noc) pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' all noc Local based on CT 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='21% 63,36% SGM 3 paths 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='01% 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='79% SGM 4 paths 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='27% 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='88% SGM 8 paths 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='31% 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='11% SGM 4ppc 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='64% 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='32% based on the Census transform) with 3 and 4 aggregation paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Figure 6 shows sample evaluation results on the Motorcycle images from the Middlebury 2014 dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Table 1 shows the average evaluation results for the entire dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The accuracy of the proposed method is comparable to the original SGM algorithm with 4 paths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' The difference between error rates is about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='4%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='4 Hardware implementation We implemented the proposed stereo vision system on a VC707 evaluation board with Xilinx’s Virtex-7 XC7VX485T-2FFG1761C device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' We set up a test envi- ronment to evaluate the system, with test images sent directly from a PC do the board and later displayed on a 4K monitor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' We compared our solution with previous FPGA implementations of the SGM algorithm in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' We used the following metrics: Frames per Second (FPS), Million Disparity Estimates per second (MDE/s) and MDE/s per Kilo LUTs (Look-Up Tables) (MDE/s/KLUT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' First of all, our solution is the only one ver- ified in hardware for a 4K/ Ultra HD resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' We also would like to point out that the lower performance in FPS and MDE/s relative to previous work from 2020 [11] and 2021 [6] is due to the use of an FPGA chip with fewer resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' For this work, it was necessary to select a suitable platform to enable image acquisi- tion in 4K resolution (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='e, having two high-bandwidth FMCs (FPGA Mezzanine Connectors) to which TB-FMCH-HDMI4K modules were attached).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' It is also worth mentioning that the used FPGA technology differs not only in the number of resources but also in the performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' To compare: the critical path propagation time for the technology used in this paper after synthesis is 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='967 ns, but for the Xilinx Virtex UltraScale+ XCVU9P-L2FLGA2104E FPGA with the same parameters, it is 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='240 ns (36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='45% faster).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 5 Conclusion In this paper, we presented a hardware architecture for an SGM algorithm to process a 4K/Ultra HD video stream in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' We proposed a solution to the inherent data dependency problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' It allowed us to maintain high accuracy of the depth map estimation, while making it possible to take advantage of the Real-time FPGA implementation of the SGM stereo vision in 4K 11 Table 2: Comparison with previous FPGA implementations of the SGM algo- rithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Image Disparity Platform FPGA Throughput resolution range resources LUT FF BRAM FPS MDE/s MDE/s/KLUT [14] 1920x1080 128 Virtex-7 195k 217k 368 30 7 963 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='84 [15] 1600x1200 128 Stratix-V 222k 149k N/A 43 10 472 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='2 [11] 1280x960 64 Virtex-7 690T 211k N/A 641 322 25 056 118.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='6 [6] 1920x1080 128 Zynq US+ 222k 135k 252 103 27 297 123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='0 New 3840x2160 64 Virtex-7 485T 138k 65k 197 30 15 925 116.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='2 4ppc vector format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' We implemented the module on a Virtex-7 FPGA platform achieving 30 frames per second for a resolution of 3840 × 2160 pixels with 64 disparity levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In future work, we plan to add more aggregation paths to the algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' With that, it will be possible to get more accurate results, but at the cost of latency and resource usage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' We also plan to implement a video stream rectification module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Acknowledgements The work presented in this paper was supported by: the National Science Centre project no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 2016/23/D/ST6/01389 entitled ”The de- velopment of computing resources organization in latest generation of hetero- geneous reconfigurable devices enabling real-time processing of UHD/4K video stream”, the AGH University of Science and Technology project no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='773 and the program ”Excellence initiative — research university” for the AGH Uni- versity of Science and Technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' References [1] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Jamwal, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Jindal, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Singh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' “A survey on depth map estima- tion strategies”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In: International Conference on Signal Processing (ICSP 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 1–5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='1049/cp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='1453.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' [2] Daniel Scharstein and Richard Szeliski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' “A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In: International Journal of Computer Vision 47 (Apr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 2002), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 7–42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='1023/A: 1014573219977.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' [3] Hamid Laga et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' “A Survey on Deep Learning Techniques for Stereo- Based Depth Estimation”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In: IEEE Transactions on Pattern Analysis and Machine Intelligence 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='4 (2022), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 1738–1764.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='1109/TPAMI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='3032602.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' [4] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Hirschmuller.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' “Accurate and efficient stereo processing by semi-global matching and mutual information”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In: 2005 IEEE Computer Society Con- ference on Computer Vision and Pattern Recognition (CVPR’05).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 2005, 807–814 vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='1109/CVPR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 12 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Grabowski et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' [5] Hirschmuuller H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' “Stereo processing by semiglobal matching and mutual information.” In: IEEE Transactions on Pattern Analysis and Machine Intelligence 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='2 (2008), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 328–341.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' issn: 0162-8828.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' [6] Yeongmin Lee and Hyeji Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' “A High-Throughput Depth Estimation Processor for Accurate Semiglobal Stereo Matching Using Pipelined Inter- Pixel Aggregation”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In: IEEE Transactions on Circuits and Systems for Video Technology (2021), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 1–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='1109/TCSVT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='3061200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' [7] Zishen Wan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' “A Survey of FPGA-Based Robotic Computing”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In: IEEE Circuits and Systems Magazine 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='2 (2021), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 48–74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 1109/MCAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='3071609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' [8] Stefan K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Gehrig, Felix Eberli, and Thomas Meyer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' “A real-time low-power stereo vision engine using semi-global matching”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intel- ligence and Lecture Notes in Bioinformatics) 5815 LNCS (2009), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 134– 143.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' issn: 03029743.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='1007/978-3-642-04667-4_14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' [9] Jaco Hofmann, Jens Korinth, and Andreas Koch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' “A Scalable High-Performance Hardware Architecture for Real-Time Stereo Vision by Semi-Global Match- ing”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In: 2016 IEEE Conference on Computer Vision and Pattern Recog- nition Workshops (CVPRW).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 845–853.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='1109/CVPRW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' [10] Jieru Zhao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' “FP-Stereo: Hardware-Efficient Stereo Vision for Em- bedded Applications”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In: 2020 30th International Conference on Field- Programmable Logic and Applications (FPL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 269–276.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 1109/FPL50879.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='00052.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' [11] Shashwat Shrivastava et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' “FPGA Accelerator for Stereo Vision using Semi-Global Matching through Dependency Relaxation”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In: 2020 30th International Conference on Field-Programmable Logic and Applications (FPL).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 304–309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='1109/FPL50879.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='00057.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' [12] Marcin Kowalczyk, Dominika Przewlocka, and Tomasz Kryjak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' “Real- Time Implementation of Contextual Image Processing Operations for 4K Video Stream in Zynq UltraScale+ MPSoC”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In: 2018 Conference on De- sign and Architectures for Signal and Image Processing (DASIP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 37–42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='1109/DASIP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='8597105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' [13] Daniel Scharstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' “High-Resolution Stereo Datasets with Subpixel- Accurate Ground Truth”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In: Pattern Recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' by Xiaoyi Jiang, Joachim Hornegger, and Reinhard Koch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' Cham: Springer International Publishing, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 31–42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' isbn: 978-3-319-11752-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' [14] Jaco Hofmann, Jens Korinth, and Andreas Koch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' “A Scalable High-Performance Hardware Architecture for Real-Time Stereo Vision by Semi-Global Match- ing”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In: 2016 IEEE Conference on Computer Vision and Pattern Recog- nition Workshops (CVPRW).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 845–853.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='1109/CVPRW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' [15] Wenqiang Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' “Real-Time High-Quality Stereo Vision System in FPGA”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' In: IEEE Transactions on Circuits and Systems for Video Tech- nology 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='10 (2015), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' 1696–1708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='1109/TCSVT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} +page_content='2397196.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/4dE4T4oBgHgl3EQfBAsA/content/2301.04847v1.pdf'} diff --git a/5dE1T4oBgHgl3EQfBAJm/content/tmp_files/2301.02846v1.pdf.txt b/5dE1T4oBgHgl3EQfBAJm/content/tmp_files/2301.02846v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..36b9deeae506bb544f4ada421fa2d4e4caf9c1d2 --- /dev/null +++ b/5dE1T4oBgHgl3EQfBAJm/content/tmp_files/2301.02846v1.pdf.txt @@ -0,0 +1,1687 @@ +Simulations of momentum correlation functions of light (anti)nuclei in relativistic +heavy-ion collisions at √sNN = 39 GeV +Ting-Ting Wang(王婷婷),1 Yu-Gang Ma(马余刚) +ID ,1, 2, ∗ and Song Zhang(张松) +ID 1, 2 +1Key Laboratory of Nuclear Physics and Ion-Beam Application (MOE), +Institute of Modern Physics, Fudan University, Shanghai 200433, China +2Shanghai Research Center for Theoretical Nuclear Physics，NSFC and Fudan University, Shanghai 200438, China +(Dated: January 10, 2023) +Momentum correlation functions of light (anti)nuclei formed by the coalescence mechanism of +(anti)nucleons are calculated for several central heavy-ion collision systems, namely 10 +5 B +10 +5 B, +16 +8 O +16 +8 O, 40 +20Ca +40 +20 Ca as well as 197 +79 Au +197 +79 Au in different centralities at center of mass energy +√sNN = 39 GeV within the framework of A Multi-Phase Transport (AMPT) model complemented +by the Lednick´y and Lyuboshitz analytical method. Momentum correlation functions for identical +or nonidentical light (anti)nuclei are constructed and analyzed for the above collision systems. The +Au + Au results demonstrate that emission of light (anti)nuclei occurs from a source with smaller +space extent in more peripheral collisions. The effect of system-size on the momentum correlation +functions of identical or nonidentical light (anti)nuclei is also explored by several collision system +in central collisions. The results indicate that the emission source-size of light (anti)nuclei pairs +deduced from their momentum correlation functions and system-size is self-consistent. Momentum +correlation functions of nonidentical light nuclei pairs gated on velocity are applied to infer the +average emission sequence of them. The results illustrate that protons are emitted in average on a +similar time scale with neutrons but earlier than deuterons or tritons in the small relative momentum +region. In addition, larger interval of the average emission order among them is exhibited for smaller +collision systems or at more peripheral collisions. +I. +INTRODUCTION +In heavy-ion collisions (HICs), two-particle momentum +correlation function is different from the original applica- +tion in astronomy [1, 2], and has been normally utilized +to extract space-time information of the emission source +and probe the dynamical evolution of nuclear collisions in +an extensive energy range [3–12]. Many different studies +on the two-particle momentum correlation functions in +intermediate energy HICs can be also found in literature, +eg. Refs. [12–27], which include the momentum correla- +tion functions of neutron, proton as well as light charged +particle (LCP) pairs. Multi-variable dependences of the +momentum correlation functions, such as impact param- +eters, total momentum of particle pairs, isospin of the +emission source, nuclear symmetry energy, nuclear equa- +tion of state (EOS) as well as in-medium nucleon-nucleon +cross section (NNCS) etc., contain a wealth of informa- +tion about the space-time characteristics of intermediate +energy HICs. In high energy HICs, two-hadron momen- +tum correlation function，also called as Hanbury Brown- +Twiss (HBT) interferometry, was also well extensively +measured and some interesting properties on emission +source were extracted [28, 29]. +Oscillations of the ex- +tracted HBT radii versus emission angle indicate that +emission source is elongated perpendicular to the reaction +plane. The results indicate that the initial shape is more +or less remained and could be identified even though the +collision system undergoes the pressure and expansion. +∗ Corresponding author: mayugang@fudan.edu.cn +Furthermore, interaction between antiprotons has been +also measured with the momentum correlation functions +and the equality of interactions between p-p and ¯p-¯p was +proved by the STAR Collaboration [30]. +The interac- +tion property of the particle pairs has been discussed for +other particles, for instance Λ pairs [31], proton-Ω and +proton-Ξ etc [32, 33], with the same momentum correla- +tion technique. Furthermore, the measurements of mo- +mentum correlation functions for nonidentical nucleons +and light clusters can be used to characterize the mean +emission sequence of them, which was firstly proposed in +Ref. [34]. Theoretical study has been extended to differ- +ent kinds of nonidentical particle pairs, for instance p-d, +n-p [35–38], π-p [39], K+-K− [40], d-t [12, 22] as well as +3He-α particles [41] in intermediate energy HICs. +In this work we extend the studies, for the first time, on +the momentum correlation functions of light (anti)nuclei +to ultra-relativistic heavy-ion collisions simulated by A +Multi-Phase Transport (AMPT) model [42, 43] coupled +with a dynamical coalescence model [44–46], specifically +at √sNN = 39 GeV. Different gating conditions such as +centrality gate, system-size gate as well as velocity gate +are applied to the momentum correlation functions of +light (anti)nuclei pairs. In particular, we report on the in- +dication of the emission chronology of protons, deuterons +and tritons which can be deduced from their correspond- +ing momentum correlation functions in ultra-relativistic +HICs at √sNN = 39 GeV. The emission sequence of +light clusters inferred from the correlation functions is +expected measurable in future experiments to verify our +deduction from the coalescence picture. +The rest of this article is organized as follows. In Sec- +tion II A and II B, we briefly describe A Multi-Phase +arXiv:2301.02846v1 [hep-ph] 7 Jan 2023 + +2 +Transport model [42, 43] and the coalescence model [44– +46], then introduce how to calculate the momentum cor- +relation functions of particle pairs by using the Lednick´y +and Lyuboshitz analytical formalism [3, 47–50] in Sec- +tion II C. In Section III, we summarize the simulated re- +sults of the light (anti)nuclei momentum correlation func- +tions gated on various parameters in relativistic heavy- +ion collisions. +Section III A compares the results of +proton-proton and proton-antiproton momentum corre- +lation functions with experimental data from the RHIC- +STAR collaboration. From Section III B to III D, iden- +tical and nonidentical light (anti)nuclei momentum cor- +relation functions gated on different conditions are sys- +tematically discussed. Finally, a summary and outlook +are given in Section IV. +II. +MODELS AND FORMALISM +A. +AMPT model +To obtain phase-space distributions of (anti)particles, +A Multi-Phase Transport model [42, 43] is used as the +event generator, which has been applied successfully for +studying heavy-ion collisions at relativistic energies, eg. +[45, 46, 51–59]. We briefly review the main components +of the AMPT model used in the present work. In the +version of AMPT, the initial phase-space information of +partons is generated by the heavy-ion jet interaction gen- +erator (HIJING) model [60, 61]. The interaction between +partons is then simulated by Zhang’s parton cascade +(ZPC) model [62]. +During the hadronization process, +a quark coalescence model is used to combine partons +into hadrons [63–65]. +Then, the hadronic rescattering +evolution is described by a relativistic transport (ART) +model [66]. +In this paper, the collisions of 10 +5 B +10 +5 B, 16 +8 O +16 +8 O, +40 +20Ca +40 +20 Ca at 0 − 10 % centrality and mid-rapidity +(|y| < 0.5) as well as 197 +79 Au+197 +79 Au at same mid-rapidity +for five centralities of 0−10 %, 10−20 %, 20−40 %, 40−60 +%, and 60 − 80 % at √sNN = 39 GeV are simulated. +Te phase-space distributions of (anti)particles are se- +lected at the final stage in the hadronic rescattering pro- +cess (ART model [66]) with considering baryon-baryon, +baryon-meson, and meson-meson elastic and inelastic +scatterings, as well as resonance decay or week decay. +The transverse momentum spectra of light (anti)nuclei +have been successfully reproduced by the AMPT model +with the maximum hadronic rescattering time (MRT) of +100 fm/c [46]. Therefore, the same maximum hadronic +rescattering time is used for the most calculations in this +work except for a quantitative comparison with the p-p +and p-¯p data from the STAR collaboration in Sec. III A. +B. +Coalescence model +The coalescence model has been used widely in de- +scribing the production of light clusters in the interme- +diate [67–71] and high [72, 73] energy heavy-ion colli- +sions. The detailed definitions of the probability for pro- +ducing a cluster of nucleons is in Ref. [44]. In our model +calculations, light (anti)clusters such as (anti)deuterons +and tritons are constructed by using the coalescence +model as follows [74, 75]. The probability for producing +M-nucleon cluster is determined by its Wigner phase- +space density and the nucleon phase-space distribution +at the freeze-out stage [44]. The multiplicity of an M- +nucleon cluster in transport model simulations for heavy- +ion collisions is given by, +NM = G +� +� +i1>i2>···>iM +d⃗ri1d⃗ki1 · · · d⃗riM−1d⃗kiM−1 +� +ρW +i +� +⃗ri1,⃗ki1, · · · ,⃗riM−1,⃗kiM−1 +�� +(1) +where ⃗ri1,⃗riM−1 and ⃗ki1,⃗kiM−1 are the relative coordi- +nates and momentum in the M-nucleon rest frame, and +spin-isospin statistical factor G is 3/8 for (anti)deuteron +and 1/3 for triton [44]. In addition, ρW is the Wigner +density function, which is different for all kinds of parti- +cles. Therefore, we will calculate separately the Wigner +phase-space density of (anti)deuteron and triton in de- +tail. The Wigner phase-space density of (anti)deuteron +is constructed by, +ρW +d (⃗r,⃗k) = 8 +15 +� +i=1 +c2 +i exp +� +−2ωir2 − k2 +2ωi +� ++ 16 +15 +� +i>j +cicj +� +4ωiωj +(ωi + ωj)2 +� 3 +4 +exp +� +− 4ωiωj +ωi + ωj +r2 +� +× exp +� +− +k2 +ωi + ωj +� +cos +� +2ωi − ωj +ωi + ωj +⃗r · ⃗k +� +(2) +where ⃗k = +� +⃗k1 − ⃗k2 +� +/2 is the relative momentum and +⃗r = (⃗r1 − ⃗r2) is the relative coordinate of (anti)proton +and (anti)neutron. The Wigner phase-space density of +triton is constructed by a spherical harmonic oscilla- +tor [44, 45, 76], +ρW +t +� +ρ, λ,⃗kρ,⃗kλ +� += +� +ψ +� +ρ + +⃗R1 +2 , λ + +⃗R2 +2 +� +ψ∗ +� +ρ − +⃗R1 +2 , λ − +⃗R2 +2 +� +× exp +� +−i⃗kρ · ⃗R1 +� +exp +� +−i⃗kλ · ⃗R2 +� +3 +3 +2 d⃗R1d⃗R2 += 82 exp +� +−ρ2 + λ2 +b2 +� +exp +� +− +� +⃗k2 +ρ + ⃗k2 +λ +� +b2� +(3) + +3 +where ρ and λ are relative coordinates, ⃗kρ and ⃗kλ are the +relative momenta in the Jacobi coordinate. +The above parameters of the Gaussian fit coefficient +ci and wi for (anti)deuteron as well as b for triton are +given in Ref. [44]. +Based on the phase-space informa- +tion of light (anti)cluster obtained by the above coa- +lescence model, the momentum correlation functions of +(non)identical light (anti)cluster pairs can be discussed +in the following. +C. +Lednik´ynd Lyuboshitz technique +Next, we briefly review the technique of the two- +particle momentum correlation function proposed by +Lednick´y and Lyuboshitz [47–49]. The method is based +on the principle as follows: when two particles are emit- +ted at small relative momentum, their momentum corre- +lation function is determined by the space-time charac- +teristics of the production processes owing to the effects +of quantum statistics (QS) and final-state interactions +(FSI) [3, 50]. The details on the formalism of the two- +particle momentum correlation function can be found in +Ref. [36]. +Here, comparing with our previous literature [36], more +particle pairs are considered in the article. Therefore, the +final-state interaction of different particle pairs can be +known well by introducing fc (k∗) particularly as follows: +fc (k∗) = +� +Kc (k∗) − 2 +ac +h (λ) − ik∗Ac (λ) +�−1 +(4) +fc (k∗) is the s-wave scattering amplitude renormalizied +by the long-range Coulomb interaction, with h (λ) = +λ2 �∞ +n=1 +� +n +� +n2 + λ2��−1−C −ln [λ] where C = 0.5772 is +the Euler constant. Kc (k∗) = +1 +f0 + 1 +2d0k∗2 +Pk∗4 +· · · is +the effective range function, where d0 is the effective ra- +dius of the strong interaction, f0 is the scattering length +and P is the shape parameter. The parameters of effec- +tive range function are important to characterize the es- +sential properties of the final-state interactions, and can +be extracted from the correlation function measured ex- +perimentally [30, 36, 77, 78]. Table I shows the param- +eters of the effective range function for different particle +pairs in the present work. +In the table I, for n-n (¯n-¯n) and n-p (¯n-¯p) momentum +correlation functions which include uncharged particle, +the Coulomb penetration factor (Ac (λ)) is not consid- +ered and only the short-range particle interaction works. +For the momentum correlation functions of charged parti- +cles such as p-¯p, p-p (¯p-¯p), d-d ( ¯d- ¯d), t-t, p-d (¯p- ¯d), p-t and +d-t, both the Coulomb interaction and the short-range in- +teraction dominated by the s-wave interaction are taken +into account. The momentum correlation function of p- +p (¯p-¯p) particle pairs is dominantly contributed by only +TABLE I. Experimental determination of the effective range +function parameters for n-n (¯n-¯n), p-p (¯p-¯p), t-t, n-p (¯n-¯p), +p-d (¯p- ¯d), p-t and d-t systems [30, 77, 78]. +System +Spin f0 (fm) d0 (fm) P +� +fm3� +n-n (¯n-¯n) +0 +17 +2.7 +0.0 +p-p (¯p-¯p) +0 +7.8 +2.77 +0.0 +t-t +0 +1 × 10−6 +0.0 +0.0 +n-p (¯n-¯p) +0 +23.7 +2.7 +0.0 +p-d (¯p- ¯d) +1/2 +-2.73 +2.27 +0.08 +3/2 +-11.88 +2.63 +-0.54 +p-t +0 +1 × 10−6 +0.0 +0.0 +d-t +0 +1 × 10−6 +0.0 +0.0 +the singlet (S = 0) s-wave final-state interactions while +both spins 1/2 and 3/2 contribute in the case of p-d (¯p- +¯d) system. Moreover, for (anti)deuteron-(anti)deuteron +momentum correlation function, a parametrization of the +s-wave phase shifts δ has been used from the solution of +Kc (k∗) = cot δ for each total pair spin S = 0, 1, 2. Note +that the effective range function for the total spin S = 1 +is irrelevant, since it does not contribute due to the quan- +tum statistics symmetrization. +III. +ANALYSIS AND DISCUSSION +A. +Comparison between our p-p and p-¯p correlation +functions with experimental data +Fig. 1 presents results of p-p and p-¯p correlation func- +tions for three different centrality classes of 0 − 10 %, +10−30 %, and 30−70 % calculated by the AMPT model +in Au + Au collisions at √sNN = 39 GeV. Within the +cut of transverse momentum pt and rapidity y, we con- +front the experimental data with the predictions of the +AMPT model combined with Lednick´y and Lyuboshitz +code. When the phase-space information of nucleons at +the maximum rescattering time among hadrons of 700 +fm/c is selected from the AMPT model, it is found that +the results can well describe the experimental data for +the momentum correlation functions of p-p and p-¯p from +the RHIC-STAR collaboration [79, 80], especially in more +central collisions. Considering that the preliminary ex- +perimental results were not corrected by feed-down effect +corrections [79, 80], the real correlation functions for pri- +mary p-p and p-¯p could be much more stronger. In this +case, using much longer MRT of 700 fm/c in the AMPT +model might be a reasonable choice for making quanti- +tative comparison with feed-down uncorrected data since +the system will become more expanded and weakly corre- +lated among particles after longer MRT in AMPT. How- +ever, the quantitative reproduction is not our main con- +cern in the present work. In the following calculations, we +fixed the MRT at 100 fm/c and presented systematic re- +sults among different light (anti)nuclei. However, as one +can notice that the results for p-p and p-¯p change substan- + +4 +tially when changing the MRT by comparing Fig. 1 and +2. To estimate this uncertainty, we also check some re- +sults for light nuclei correlations with different MRT. For +example, d-d or p-d correlations for MRT equal 700fm/c. +It is found that the correlation becomes slightly weaker +at smaller q (i.e. a little larger value of Cdd or Cpd close +to 1 at MRT = 700 fm/c), which has the similar trend as +p-p and p-¯p cases. But the uncertainty is less than 20% +at the lowest relative momentum and tends to vanish at +q > 50 MeV/c for light nuclei correlations (d-d or p-d) +when changing the MRT from 100fm/c to 700fm/c, which +can be essentially understood by weak feed-down effects +for light nuclei. In addition, we also check the p-d cor- +relation with different velocity selection. Only less than +10% uncertainty is found for lower q between the case +of MRT equal 700 fm/c to the one at 100fm/c. By this +comparison of results at MRT equal 700 and 100 fm/c, +we conclude that nucleon-(anti)nucleon correlations are +much influenced by the MRT but light nuclei correla- +tions only change slightly. Overall, the MRT = 100 fm/c +is basically safe choice for such light nuclei correlations. +0.7 +0.8 +0.9 +1.0 +1.1 +1.2 +1.3 +1.4 +1.5 +0 +20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 +0.6 +0.8 +1.0 +1.2 +1.4 + Cpp(q) + STAR data LL-model + 0-10% + 0-10% + 10-30% + 10-30% + 30-70% + 30-70% + + + + +Au+Au@√sNN=39GeV, |y|<0.5, 0.40 ∆v<0 + + 0-10% + + 10-20% + + 20-40% + + 40-60% + + 60-80% +(a) ∆v = vn-vp + Cnp(q) +3.0x10 +6 +6.0x10 +6 +(b) ∆v = vn-vp + counts (arb.unit) + 0-10% + 10-20% + 20-40% + 40-60% + 60-80% +0 +50 +100 +150 +200 +250 +300 +0.0 +0.5 +1.0 +(c) ∆v = vp-vp + Cpp(q) +q (MeV/c) +(d) ∆v = vp-vp + ∆v (c) +FIG. 6. +The velocity-gated momentum correlation functions +(left) and velocity difference (∆v) spectra (right) for n-p and +p-¯p as a function of five different centralities in mid-rapidity +(|y| < 0.5) for 39 GeV 197 +79 Au +197 +79 Au collision. The velocity +conditions are indicated in each panel: ∆v > 0 is remarked +by solid symbol and the ∆v < 0 by open symbol. +0 +1 +2 +3 +4 +5 +(a) ∆v = vn-vp + ∆v>0 ∆v<0 + + B+B + + + O+O + + Ca+Ca + + Au+Au + + + Cnp(q) +3.0x10 +6 +6.0x10 +6 + counts (arb.unit) +(b) ∆v = vn-vp +0 +50 +100 +150 +200 +250 +300 +0.0 +0.5 +1.0 +(c) ∆v = vp-vp + Cpp(q) +q (MeV/c) +-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 +3.0x10 +6 +6.0x10 +6 + +(d) ∆v = vp-vp + ∆v (c) + B+B + O+O + Ca+Ca + Au+Au +FIG. 7. +Same as Fig. 6 but for 0 − 10 % central collisions +of 10 +5 B +10 +5 B, 16 +8 O +16 +8 O, 40 +20Ca +40 +20 Ca as well as 197 +79 Au +197 +79 +Au systems at √sNN = 39 GeV. The velocity conditions are +indicated in each panel: ∆v > 0 is remarked by solid symbol +and the ∆v < 0 by open symbol. +is observed in smaller systems. In Fig. 5 (d) and (f), the +p-t and d-t momentum correlation functions appear more +sensitive to system-size only in the large system such as +Au and Ca. +0.90 +0.95 +1.00 +1.05 +0 +50 +100 150 200 250 300 +0.90 +0.95 +1.00 +1.05 +0 +50 +100 150 200 250 300 +(a) 39GeV AuAu ∆v = vn-vp +C∆v>0/C∆v<0 + 0-10% + 10-20% + 20-40% + 40-60% + 60-80% +(b) 39GeV 0-10% ∆v = vn-vp + B+B + O+O + Ca+Ca + Au+Au +(c) 39GeV AuAu ∆v = vp-vp +q (MeV/c) +(d) 39GeV 0-10% ∆v = vp-vp +q (MeV/c) +FIG. 8. +Ratios of the velocity-gated momentum correla- +tion functions (left) of n-p (a) and p-¯p (c) pairs for 39 GeV +197 +79 Au +197 +79 Au collision at mid-rapidity (|y| < 0.5) and five +different centralities. Ratios of the velocity-gated momentum +correlation functions (right) of n-p (b) and p-¯p (d) pairs for 0 +− 10 % central collisions of 10 +5 B+10 +5 B, 16 +8 O+16 +8 O, 40 +20Ca+40 +20 Ca +as well as 197 +79 Au +197 +79 Au systems at √sNN = 39 GeV. +D. +Velocity selected nonidentical light nuclei +momentum correlation functions +The momentum correlation functions of unlike par- +ticles can provide an independent constrain on their +mean emission order by simply making velocity selec- +tions [22, 34, 35, 81, 82]. The principle of comparing the +velocity-gated momentum correlation functions for the +nonidentical particle pair to infer their average emission +order is as follows. Here the two nonidentical particles +are named by “a”and “b”, respectively. If the ve- +locity of “a”particle is lower than “b”particle, the +(anti)correlation will be stronger when the “a”particle +is emitted averagely early than the “b”particle, be- +cause the space-size between them is reduced during the +flight and the final-state interaction (FSI) is enhanced, +and vice versa. In addition, the velocity difference (∆v) +spectrum between the two nonidentical particles is also +sensitive to the mean emission order. Fig. 6 presents the +velocity-gated momentum correlation functions as well as +velocity difference (∆v) spectra of unlike particles pairs +n-p and p-¯p for 39 GeV 197 +79 Au +197 +79 Au collisions at dif- +ferent centralities of 0 − 10 %, 10 − 20 %, 20 − 40 %, +40 − 60 %, and 60 − 80 %. In Fig. 6 (a) and (c), the +centrality dependence on the velocity-gated momentum +correlation functions of n-p and p-¯p is similar to Fig. 4. +In Fig. 6 (a), the momentum correlation function for n-p +pair with vn > vp is similar to one with the reverse situ- +ation. The symmetry of velocity difference (∆v) spectra +for n-p pairs is shown in Fig. 6 (b). The results demon- +strate that the average emission sequence of neutrons and +protons is almost the same and is insensitive to the cen- +trality. In Fig. 6 (c), the momentum correlation function +for p-¯p pair with vp > v¯p is slightly higher than one with + +8 +0.0 +0.5 +1.0 +(a) ∆v = vp-vd + Cpd(q) + ∆v>0 ∆v<0 + + 0-10% + + 10-20% + + 20-40% + + 40-60% + + 60-80% +3.0x10 +6 +6.0x10 +6 + counts (arb.unit) +(b) ∆v = vp-vd + + 0-10% + 10-20% + 20-40% + 40-60% + 60-80% +0.0 +0.5 +1.0 +(c) ∆v = vp-vt + Cpt(q) +3.0x10 +6 +6.0x10 +6 +(d) ∆v = vp-vt + 60-80%*10 +0 +50 +100 +150 +200 +250 +300 +0.0 +0.5 +1.0 +(e) ∆v = vd-vt + Cdt(q) +q (MeV/c) +-0.8 -0.6 -0.4-0.2 0.0 0.2 0.4 0.6 0.8 +3.0x10 +6 +6.0x10 +6 + 60-80%*10 +(f) ∆v = vd-vt + + ∆v (c) +FIG. 9. +Same as Fig. 6 but for p-d (a) and (b), p-t (c) and (d), and d-t (e) and (f) pairs. +the reverse situation. The slight asymmetry of velocity +difference (∆v) spectra for p-¯p pairs is shown in Fig. 6 (d), +which indicates that the mean order of emission sequence +between proton and antiproton may be a little different +but is not sensitive to the centrality. In Fig. 7 (a), the +momentum correlation functions for n-p pairs with vn > +vp are always similar to one with the reverse situation +with increasing system-size. The symmetry of velocity +difference (∆v) spectra for n-p pairs in different systems +is shown in Fig. 7 (b). The comparison of velocity-gated +momentum correlation functions illustrates that the av- +erage emission sequence between neutrons and protons is +always identical for different centrality and system-size, +which is also learned from their ratios in Fig. 8 (a) and +(b). In Fig. 7 (c) and (d), the comparison of velocity- +gated momentum correlation functions for p-¯p indicates +that the mean order of emission sequence between pro- +tons and antiprotons may be a little different but has no +dependence of system-size, which is also learned by their +ratios in Fig. 8 (c) and (d). +Fig. 9 and Fig. 10 show centrality and system-size de- +pendences of velocity-gated momentum correlation func- +tions and velocity difference (∆v) spectra of p-d, p-t and +d-t pairs, respectively. +For p-d and p-t pairs, the mo- +mentum correlation functions with vp < vd (vp < vt) +are stronger than the ones with the reverse situation +vp > vd (vp > vt) in Fig. 9. +The comparison of two +velocity-gated correlation strengths gives that the mean +order of emission of protons are emitted averagely ear- +lier than deuterons and tritons according to the above +criteria. The similar trend for d-t pairs is not so obvi- +ous overall, except for in peripheral collision the momen- +tum correlation function with vd < vt is stronger and +deuterons are emitted averagely earlier than tritons. In +contrast with the emission order as shown in many pre- +vious results of the intermediate energy heavy-ion colli- +sions [12, 36, 37, 81], the average emission sequence of +protons, deuterons, and tritons is opposite for 39 GeV + +9 +0.0 +0.5 +1.0 +(a) ∆v = vp-vd + Cpd(q) + ∆v>0 ∆v<0 + + + B+B + + + O+O + + + Ca+Ca + + + Au+Au +3.0x10 +6 +6.0x10 +6 + counts (arb.unit) +(b) ∆v = vp-vd + + B+B + O+O + Ca+Ca + Au+Au +0.0 +0.5 +1.0 +(c) ∆v = vp-vt + Cpt(q) +3.0x10 +6 +6.0x10 +6 +(d) ∆v = vp-vt + B+B*10 + O+O*10 + +0 +50 +100 +150 +200 +250 +300 +0.0 +0.5 +1.0 +(e) ∆v = vd-vt + Cdt(q) +q (MeV/c) +-0.8 -0.6 -0.4-0.2 0.0 0.2 0.4 0.6 0.8 +0.0 +3.0x10 +6 +6.0x10 +6 +(f) ∆v = vd-vt + B+B*10 + O+O*10 + ∆v (c) +FIG. 10. +Same as Fig. 7 but for p-d (a) (b), p-t (c) (d) and d-t (e) (f) pairs. +heavy-ion collisions. Meanwile, Fig. 9 presents velocity +difference spectra for p-d, p-t and d-t pairs, respectively. +The velocity difference spectra are all asymmetric due to +the mean emission order. In addition, an enhanced dif- +ference between the momentum correlation functions for +p-d (p-t or d-t) pairs with vp > vd (vp > vt or vd > vt) and +ones on the reverse situation at larger centrality, which +manifests the larger interval of the mean emission or- +der for unlike light nuclei in peripheral collisions. Their +ratios in Fig. 11 (a), (c) and (e) can also illustrate the +above phenomenon. The system-size dependence for p- +d, p-t and d-t pairs can be found by the fact that mo- +mentum correlation functions with vp < vd (vp < vt or +vd < vt) are stronger than the ones with the reverse sit- +uation vp > vd (vp > vt or vd > vt) in Fig. 10. Cor- +respondingly, the velocity difference spectra for p-d, p-t +and d-t pairs are all asymmetric about ∆v = 0 caused by +the average emission order in Fig. 10. Therefore, protons +are emitted averagely earliest and deuterons are emitted +averagely earlier than tritons in smaller system-size col- +lision. The system-size dependence of the velocity-gated +momentum correlation functions is also clearly seen by +their ratios in Fig. 11. With decreasing system-size, we +can also observe an enhanced difference between the mo- +mentum correlation functions for p-d (p-t or d-t) pair with +vp > vd (vp > vt or vd > vt) and the ones with the reverse +situation in Fig. 11 (b), (d) and (f). +IV. +SUMMARY +In summary, with the AMPT model complemented +by the Lednick´y and Lyuboshitz analytical method, we +have constructed and analyzed the momentum correla- +tion functions of light (anti)nuclei formed by the coa- +lescence mechanism of (anti)nucleons for heavy-ion colli- +sions with different system sizes and centralities at √sNN += 39 GeV. We present a comparison of proton−proton + +10 +0.7 +0.8 +0.9 +1.0 +1.1 +1.2 +0.7 +0.8 +0.9 +1.0 +1.1 +1.2 +1.3 +1.4 +0 +50 +100 +150 +200 +250 +300 +0.7 +0.8 +0.9 +1.0 +1.1 +1.2 +1.3 +1.4 +1.5 +1.6 +1.7 +1.8 +0 +50 +100 +150 +200 +250 +300 +(a) 39GeV AuAu ∆v = vp-vd + 0-10% + 10-20% + 20-40% + 40-60% + 60-80% +(b) 39GeV 0-10% ∆v = vp-vd + B + O + Ca + Au + C∆v>0/C∆v<0 +(c) 39GeV AuAu ∆v = vp-vt +(d) 39GeV 0-10% ∆v = vp-vt +(e) 39GeV AuAu ∆v = vd-vt +q (MeV/c) +(f) 39GeV 0-10% ∆v = vd-vt +q (MeV/c) +FIG. 11. +Same as Fig. 8 but for p-d (a) and (b), p-t (c) and (d) and d-t (e) and (f) pairs. +and proton−antiproton momentum correlation functions +with the experimental data from the RHIC-STAR col- +laboration [79, 80]. +Taking the same transverse mo- +mentum and rapidity phase space coverage correspond- +ing to the experimental situation as well as the maxi- +mum hadronic rescattering time of 700 fm/c in AMPT, +it is found that the p-p and p-¯p momentum correla- +tion functions simulated by the present model can match +the experimental data. We further study centrality and +system-size dependence of momentum correlation func- +tions for identical and nonidentical light (anti)nuclei +pairs, respectively, which is in the condition of the +maximum hadronic rescattering time of 100 fm/c in +AMPT. The shape of momentum correlation functions +for light (anti)nuclei pairs is consistent with previous +works [13, 30, 36, 37, 79, 80], which is caused by both +QS and FSI. The similar structure between light nuclei +momentum correlation functions and anti-ones indicates +that the interaction between them are the same, which +has been confirmed in Ref. [30] only about proton and +antiproton. +The centrality dependence of momentum +correlation functions for light (anti)nuclei is investigated +by 197 +79 Au +197 +79 Au collisions at different five centralities +of 0 − 10 %, 10 − 20 %, 20 − 40 %, 40 − 60 %, and +60 − 80 % at √sNN = 39 GeV. It is found that with +increasing centralities from center to periphery, the mo- +mentum correlation functions for light (anti)nuclei be- +come stronger, which are probably emitted from smaller +source. +The momentum correlation functions of light +(anti)nuclei are sensitive to system-size through studying +10 +5 B +10 +5 B, 16 +8 O +16 +8 O, 40 +20Ca +40 +20 Ca and 197 +79 Au +197 +79 Au in +central collisions, and used to obtain the emission source- +size of light (anti)nuclei which is self-consistent with their +system-size. +Momentum correlation functions between + +11 +nonidentical light nuclei can provide important informa- +tion about the average emission sequence of them. The +average emission time scale between neutrons and pro- +tons is almost identical. However, heavier light clusters +(deuterons or tritons) are emitted later than protons in +the small relative momentum region. In the future we +can explore further the energy dependence of the aver- +age emission sequence of light nuclei and understand the +physical interpretation. +ACKNOWLEDGMENTS +T. T. Wang thanks for discussion with Ms. +Yi- +Ling Cheng for the AMPT data. +This work was +supported in part by the National Natural Science +Foundation of China under contract Nos. +11890710, +11890714, 11875066, 11925502, 11961141003, 11935001, +12147101 and 12047514, the Strategic Priority Research +Program of CAS under Grant No. +XDB34000000, +National Key R&D Program of China under Grant +No. +2018YFE0104600 and 2016YFE0100900, Guang- +dong Major Project of Basic and Applied Basic Research +No. 2020B0301030008, and the China PostDoctoral Sci- +ence Foundation under Grant No. 2020M681140. +[1] R. Hanbury Brown, R. Q. Twiss, Nature 177, 27 (1956). +[2] R. Hanbury Brown, R. Q. Twiss, Nature 178, 1046 +(1956). +[3] S. E. Koonin, Phys. Lett. B 70, 43 (1977). +[4] M. A. Lisa, S. Pratt, R. Soltz, U. Wiedemann, Ann. Rev. +Nucl. Part. Sci. 55, 357 (2005). +[5] U. A. Wiedemann, U. Heinz, Phys. Rep. 319, 145 (1999). +[6] G.Goldhaber, S. Goldhaber, W. Lee, and A. Pais, Phys. +Rev. 120, 300 (1960). +[7] A. Bialas et al., Phys. Rev. 62, 114007 (2000). +[8] R. Ghetti et al., Nucl. Phys. A 674, 277 (2000). +[9] D. H. Boal, C. K. Gelbke, B. K. Jennings, Rev. Mod. +Phys. 62, 553 (1990). +[10] D. Ardouin, Int. J. Mod. Phys. E 6, 391 (1997). +[11] J. J. He, S. Zhang, Y. G. Ma, J. H. Chen, C. Zhong, Eur. +Phys. J. A 56, 52 (2020). +[12] R. Ghetti, J. Helgesson, V. Avdeichikov, P. Golubev, B. +Jakobsson, N.Colonna, G. Tagliente et al., Phys. Rev. +Lett. 91, 092701 (2003). +[13] T. T. Wang, Y. G. Ma, C. J. Zhang, and Z. Q. Zhang, +Phys. Rev. C 97, 034617 (2018). +[14] R. Kotte et al., Eur. Phys. J. A, 23, 271-278 (2005). +[15] J. Pochodzalla, C. K. Gelbke, W. G. Lynch, M. Maier, +D. Ardouin, H. Delagrange et al., Phys. Rev. C 35, 1695 +(1987). +[16] W. G. Gong, W. Bauer, C. K. Gelbke, and S. Pratt, Phys. +Rev. C 43, 781 (1991). +[17] Y. G. Ma, Y. B. Wei, W. Q. Shen et al., Phys. Rev. C +73, 014604 (2006). +[18] R. Ghetti, V. Avdeichikov, B. Jakobsson et al., Phys. +Rev. C. 69, 031605(R) (2004). +[19] L. W. Chen, V. Greco, C. M. Ko, and B. A. Li, Phys. +Rev. Lett. 90, 162701 (2003). +[20] D. Q. Fang, Y. G. Ma, X. Y. Sun et al., Phys. Rev. C +94, 044621 (2016). +[21] B. S. Huang, Y. G. Ma, Phys. Rev. C 101, 034615 (2020). +[22] D. Gourio et al., Eur. Phys. J. A 7, 245 (2000). +[23] L. Shen, B. S. Huang, and Y. G. Ma, Phys. Rev. C 105, +014603 (2022). +[24] T. T. Wang, Y. G.Ma, D. Q. Fang, H. L. Liu, Phys. Rev. +C 105, 024620 (2022). +[25] L. M. Fang, Y. G. Ma, S. Zhang, Euro. Phys. J. A 58, +81 (2022). +[26] P. Li, J. Steinheimer, T. Reichert, A. Kittiratpattana, M. +Bleicher, and Q. Li, Science China - Physics, Mechanics, +and Astrophysics in press, (2023). +[27] P. Li, Y. Wang, Q. Li, and H. Zhang, Science China - +Physics, Mechanics, and Astrophysics in press, (2023). +[28] J. Adams et al. (STAR Collaboration), Phys. Rev. Lett. +93, 012301 (2004) . +[29] C. Adler et al. (STAR Collaboration), Phys. Rev. Lett. +87, 082301 (2001). +[30] L. Adamczyk et al. (STAR Collaboration), Nature 527, +345 (2015). +[31] L. Adamczyk et al. (STAR Collaboration), Phys. Rev. +Lett. 114, 022301 (2015). +[32] J. Adam et al. (STAR Collaboration), Phys. Lett. B 790, +490 (2019). +[33] S. Acharya et al. (ALICE Collaboration), Nature 588, +232 (2020). +[34] C. J. Gelderloos and J. M. Alexander, Nucl. Instrum. +Methods. A. 349, 618 (1994). +[35] R. Lednick´y, V.L. Lyuboshitz, B. Erazmus, and D. +Nouais, Phys. Lett. B 373, 30 (1996). +[36] Ting-Ting Wang, +Yu-Gang Ma, +Zheng-Qiao Zhang, +Phys. Rev. C 99, 054626 (2019). +[37] Yijie Wang, Fenhai Guan, Qianghua Wu et al., Phys. +Lett. B 825, 136856 (2022). +[38] B. S. Xi, Z. Q. Zhang, S. Zhang and Y. G. Ma, Phys. +Rev. C 102, 064901 (2020). +[39] S. Voloshin, R. Lednick´y, S. Panitkin, and Nu Xu, Phys. +Rev. L 79, 4766 (1997). +[40] D. Ardouin et al., Phys. Lett. B 446, 191 (1999). +[41] R. Kotte et al., Eur. Phys. J. A, 6, 185 (1999). +[42] Z.-W. Lin, C. M. Ko, B.-A. Li, B. Zhang, and S. Pal, +Phys. Rev. C 72, 064901 (2005). +[43] Z. W. Lin and L. Zheng, Nucl. Sci. Tech. 32, 113 (2021). +[44] L. W. Chen, C. M. Ko, and B. A. Li, Nucl. Phys. A 729, +809 (2003). +[45] S. Zhang, J. H. Chen, H. Crawford, D. Keane, Y. G. Ma, +and Z. Xu, Phys. Lett. B 684, 224 (2010). +[46] Yi-Lin Cheng, Song Zhang and Yu-Gang Ma, Eur. Phys. +J. A, 57, 330 (2021). +[47] R. Lednick´y, Nucl. Phys. A 774, 189 (2006). +[48] R. Lednick´y, Phys. Part. Nucl. 40, 307 (2009). +[49] R. Lednick´y, Phys. Ato. Nucl. 71, 1572 (2008). +[50] R. Lednick´y, Braz. J. Phys. 37, 939 (2007). + +12 +[51] B. Alver, G. Roland, Phys. Rev. C 81, 054905 (2010). +[52] G. L. Ma, X. N. Wang, Phys. Rev. Lett. 106, 162301 +(2011). +[53] L. X. Han, G. L. Ma, Y. G. Ma, X. Z. Cai, J. H. Chen, +S. Zhang, C. Zhong, Phys. Rev. C 84, 064907 (2011). +[54] A. Bzdak, G. L. Ma, Phys. Rev. Lett. 113, 252301 (2014). +[55] S. Zhang, Y. G. Ma, J. H. Chen, W. B. He, C. Zhong, +Phys. Rev. C 95, 064904 (2017). +[56] Zheng-Qiao Zhang, Song Zhang and Yu-Gang Ma, Chi- +nese Phys. C 38, 014102 (2014). +[57] H. Zhang, J. F. Liao, E. K. Wang, Q. Wang, H. X. Xing, +Phys. Rev. Lett. 126, 012301 (2021). +[58] H. Wang, J. H. Chen, Nucl. Sci. Tech. 32, 2 (2021). +[59] H. Wang, J. H. Chen, Nucl. Sci. Tech. 33, 15 (2022). +[60] X.-N. Wang and M. Gyulassy, Phys. Rev. D 44, 3501 +(1991). +[61] M. Gyulassy and X.-N. Wang, Computer Physics Com- +munications 83, 307 (1994). +[62] B. Zhang, Computer Physics Communications 109, 193 +(1998). +[63] Zi-wei Lin, Subrata Pal, C. M. Ko, Bao-An Li, and Bin +Zhang, Phys. Rev. C 64, 011902(R) (2001). +[64] S. Pal, C. M. Ko, Zi-Wei Lin, Nucl. Phys. A 730, 143 +(2004). +[65] S. Pal, C. M. Ko, Zi-Wei Lin, Nucl. Phys. A 707, 525 +(2002). +[66] B. A. Li and C. M. Ko, Phys. Rev. C 52, 2037 (1995). +[67] Lie-Wen Chen, C. M. Ko, and Bao-An Li, Phys. Rev. C +68, 017601 (2003). +[68] M. Gyulassy et al., Nucl. Phys. A 402, 596 (1983). +[69] J. Aichelin, +A. Rosenhauer, +G.Peilert, +H. Stoecker, +W.Greiner, Phys. Rev. Lett. 58, 1926 (1987). +[70] V. Koch et al., Phys. Lett. B 241, 174 (1990). +[71] P. Pawlowski et al., Eur. Phys. J. A 9, 371 (2000). +[72] R. Mattiello, H. Sorge, H. Stocker, W. Greiner, Phys. +Rev. C 55, 1443 (1997). +[73] J.L. Nagle, B. S. Kumar, D. Kusnezov, H. Sorge, R. Mat- +tiello, Phys. Rev. C 53, 367 (1996). +[74] L. Csernai and J. I. Kapusta, Physics Reports 131, 223 +(1986). +[75] Jinhui Chen, Declan Keane, Yu-Gang Ma, Aihong Tang, +Zhangbu Xu, Physics Reports 760, 1 (2018). +[76] K. J. Sun and L.-W. Chen, Phys. Lett. B 751, 272 (2015). +[77] B. Erazmus, L. Martin, R. Lednicky, N. Carjan, Phys. +Rev. C 49, 349 (1994). +[78] J. Arvieux, Nucl. Phys. A 221, 253 (1974). +[79] H.P. Zbroszczyk, Acta Phys. Pol. B Proc. Suppl. 12, 205 +(2019). +[80] Sebastian Siejka (STAR Collaboration), Nucl. Phys. A +982, 359 (2019). +[81] C. J. Gelderloos, R. Sun, N. N. Ajitanand, J. M. Alexan- +der, E. Bauge, A. Elmaani et al., Phys. Rev. C 52, R2834 +(1995). +[82] Bo-Song Huang, Yu-Gang Ma, Chin. Phys. C 44, 094105 +(2020). + diff --git a/5dE1T4oBgHgl3EQfBAJm/content/tmp_files/load_file.txt b/5dE1T4oBgHgl3EQfBAJm/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..20b3710e8ae991e1534fe24adc48145691be9b10 --- /dev/null +++ b/5dE1T4oBgHgl3EQfBAJm/content/tmp_files/load_file.txt @@ -0,0 +1,1061 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf,len=1060 +page_content='Simulations of momentum correlation functions of light (anti)nuclei in relativistic heavy-ion collisions at √sNN = 39 GeV Ting-Ting Wang(王婷婷),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='1 Yu-Gang Ma(马余刚) ID ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' ∗ and Song Zhang(张松) ID 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' 2 1Key Laboratory of Nuclear Physics and Ion-Beam Application (MOE),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Institute of Modern Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Fudan University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Shanghai 200433,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' China 2Shanghai Research Center for Theoretical Nuclear Physics，' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='NSFC and Fudan University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Shanghai 200438,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' China (Dated: January 10,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' 2023) Momentum correlation functions of light (anti)nuclei formed by the coalescence mechanism of (anti)nucleons are calculated for several central heavy-ion collision systems,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' namely 10 5 B +10 5 B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' 16 8 O +16 8 O,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' 40 20Ca +40 20 Ca as well as 197 79 Au +197 79 Au in different centralities at center of mass energy √sNN = 39 GeV within the framework of A Multi-Phase Transport (AMPT) model complemented by the Lednick´y and Lyuboshitz analytical method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Momentum correlation functions for identical or nonidentical light (anti)nuclei are constructed and analyzed for the above collision systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The Au + Au results demonstrate that emission of light (anti)nuclei occurs from a source with smaller space extent in more peripheral collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The effect of system-size on the momentum correlation functions of identical or nonidentical light (anti)nuclei is also explored by several collision system in central collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The results indicate that the emission source-size of light (anti)nuclei pairs deduced from their momentum correlation functions and system-size is self-consistent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Momentum correlation functions of nonidentical light nuclei pairs gated on velocity are applied to infer the average emission sequence of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The results illustrate that protons are emitted in average on a similar time scale with neutrons but earlier than deuterons or tritons in the small relative momentum region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' In addition, larger interval of the average emission order among them is exhibited for smaller collision systems or at more peripheral collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' INTRODUCTION In heavy-ion collisions (HICs), two-particle momentum correlation function is different from the original applica- tion in astronomy [1, 2], and has been normally utilized to extract space-time information of the emission source and probe the dynamical evolution of nuclear collisions in an extensive energy range [3–12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Many different studies on the two-particle momentum correlation functions in intermediate energy HICs can be also found in literature, eg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Refs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' [12–27], which include the momentum correla- tion functions of neutron, proton as well as light charged particle (LCP) pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Multi-variable dependences of the momentum correlation functions, such as impact param- eters, total momentum of particle pairs, isospin of the emission source, nuclear symmetry energy, nuclear equa- tion of state (EOS) as well as in-medium nucleon-nucleon cross section (NNCS) etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=', contain a wealth of informa- tion about the space-time characteristics of intermediate energy HICs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' In high energy HICs, two-hadron momen- tum correlation function，also called as Hanbury Brown- Twiss (HBT) interferometry, was also well extensively measured and some interesting properties on emission source were extracted [28, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Oscillations of the ex- tracted HBT radii versus emission angle indicate that emission source is elongated perpendicular to the reaction plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The results indicate that the initial shape is more or less remained and could be identified even though the collision system undergoes the pressure and expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' ∗ Corresponding author: mayugang@fudan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='cn Furthermore, interaction between antiprotons has been also measured with the momentum correlation functions and the equality of interactions between p-p and ¯p-¯p was proved by the STAR Collaboration [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The interac- tion property of the particle pairs has been discussed for other particles, for instance Λ pairs [31], proton-Ω and proton-Ξ etc [32, 33], with the same momentum correla- tion technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Furthermore, the measurements of mo- mentum correlation functions for nonidentical nucleons and light clusters can be used to characterize the mean emission sequence of them, which was firstly proposed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Theoretical study has been extended to differ- ent kinds of nonidentical particle pairs, for instance p-d, n-p [35–38], π-p [39], K+-K− [40], d-t [12, 22] as well as 3He-α particles [41] in intermediate energy HICs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' In this work we extend the studies, for the first time, on the momentum correlation functions of light (anti)nuclei to ultra-relativistic heavy-ion collisions simulated by A Multi-Phase Transport (AMPT) model [42, 43] coupled with a dynamical coalescence model [44–46], specifically at √sNN = 39 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Different gating conditions such as centrality gate, system-size gate as well as velocity gate are applied to the momentum correlation functions of light (anti)nuclei pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' In particular, we report on the in- dication of the emission chronology of protons, deuterons and tritons which can be deduced from their correspond- ing momentum correlation functions in ultra-relativistic HICs at √sNN = 39 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The emission sequence of light clusters inferred from the correlation functions is expected measurable in future experiments to verify our deduction from the coalescence picture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The rest of this article is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' In Sec- tion II A and II B, we briefly describe A Multi-Phase arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='02846v1 [hep-ph] 7 Jan 2023 2 Transport model [42, 43] and the coalescence model [44– 46], then introduce how to calculate the momentum cor- relation functions of particle pairs by using the Lednick´y and Lyuboshitz analytical formalism [3, 47–50] in Sec- tion II C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' In Section III, we summarize the simulated re- sults of the light (anti)nuclei momentum correlation func- tions gated on various parameters in relativistic heavy- ion collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Section III A compares the results of proton-proton and proton-antiproton momentum corre- lation functions with experimental data from the RHIC- STAR collaboration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' From Section III B to III D, iden- tical and nonidentical light (anti)nuclei momentum cor- relation functions gated on different conditions are sys- tematically discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Finally, a summary and outlook are given in Section IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' MODELS AND FORMALISM A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' AMPT model To obtain phase-space distributions of (anti)particles, A Multi-Phase Transport model [42, 43] is used as the event generator, which has been applied successfully for studying heavy-ion collisions at relativistic energies, eg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' [45, 46, 51–59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' We briefly review the main components of the AMPT model used in the present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' In the version of AMPT, the initial phase-space information of partons is generated by the heavy-ion jet interaction gen- erator (HIJING) model [60, 61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The interaction between partons is then simulated by Zhang’s parton cascade (ZPC) model [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' During the hadronization process, a quark coalescence model is used to combine partons into hadrons [63–65].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Then, the hadronic rescattering evolution is described by a relativistic transport (ART) model [66].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' In this paper, the collisions of 10 5 B +10 5 B, 16 8 O +16 8 O, 40 20Ca +40 20 Ca at 0 − 10 % centrality and mid-rapidity (|y| < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='5) as well as 197 79 Au+197 79 Au at same mid-rapidity for five centralities of 0−10 %, 10−20 %, 20−40 %, 40−60 %, and 60 − 80 % at √sNN = 39 GeV are simulated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Te phase-space distributions of (anti)particles are se- lected at the final stage in the hadronic rescattering pro- cess (ART model [66]) with considering baryon-baryon, baryon-meson, and meson-meson elastic and inelastic scatterings, as well as resonance decay or week decay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The transverse momentum spectra of light (anti)nuclei have been successfully reproduced by the AMPT model with the maximum hadronic rescattering time (MRT) of 100 fm/c [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Therefore, the same maximum hadronic rescattering time is used for the most calculations in this work except for a quantitative comparison with the p-p and p-¯p data from the STAR collaboration in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' III A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Coalescence model The coalescence model has been used widely in de- scribing the production of light clusters in the interme- diate [67–71] and high [72, 73] energy heavy-ion colli- sions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The detailed definitions of the probability for pro- ducing a cluster of nucleons is in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' In our model calculations, light (anti)clusters such as (anti)deuterons and tritons are constructed by using the coalescence model as follows [74, 75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The probability for producing M-nucleon cluster is determined by its Wigner phase- space density and the nucleon phase-space distribution at the freeze-out stage [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The multiplicity of an M- nucleon cluster in transport model simulations for heavy- ion collisions is given by, NM = G � � i1>i2>···>iM d⃗ri1d⃗ki1 · · · d⃗riM−1d⃗kiM−1 � ρW i � ⃗ri1,⃗ki1, · · · ,⃗riM−1,⃗kiM−1 �� (1) where ⃗ri1,⃗riM−1 and ⃗ki1,⃗kiM−1 are the relative coordi- nates and momentum in the M-nucleon rest frame, and spin-isospin statistical factor G is 3/8 for (anti)deuteron and 1/3 for triton [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' In addition, ρW is the Wigner density function, which is different for all kinds of parti- cles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Therefore, we will calculate separately the Wigner phase-space density of (anti)deuteron and triton in de- tail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The Wigner phase-space density of (anti)deuteron is constructed by, ρW d (⃗r,⃗k) = 8 15 � i=1 c2 i exp � −2ωir2 − k2 2ωi � + 16 15 � i>j cicj � 4ωiωj (ωi + ωj)2 � 3 4 exp � − 4ωiωj ωi + ωj r2 � × exp � − k2 ωi + ωj � cos � 2ωi − ωj ωi + ωj ⃗r · ⃗k � (2) where ⃗k = � ⃗k1 − ⃗k2 � /2 is the relative momentum and ⃗r = (⃗r1 − ⃗r2) is the relative coordinate of (anti)proton and (anti)neutron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The Wigner phase-space density of triton is constructed by a spherical harmonic oscilla- tor [44, 45, 76], ρW t � ρ, λ,⃗kρ,⃗kλ � = � ψ � ρ + ⃗R1 2 , λ + ⃗R2 2 � ψ∗ � ρ − ⃗R1 2 , λ − ⃗R2 2 � × exp � −i⃗kρ · ⃗R1 � exp � −i⃗kλ · ⃗R2 � 3 3 2 d⃗R1d⃗R2 = 82 exp � −ρ2 + λ2 b2 � exp � − � ⃗k2 ρ + ⃗k2 λ � b2� (3) 3 where ρ and λ are relative coordinates, ⃗kρ and ⃗kλ are the relative momenta in the Jacobi coordinate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The above parameters of the Gaussian fit coefficient ci and wi for (anti)deuteron as well as b for triton are given in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' [44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Based on the phase-space informa- tion of light (anti)cluster obtained by the above coa- lescence model, the momentum correlation functions of (non)identical light (anti)cluster pairs can be discussed in the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Lednik´ynd Lyuboshitz technique Next, we briefly review the technique of the two- particle momentum correlation function proposed by Lednick´y and Lyuboshitz [47–49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The method is based on the principle as follows: when two particles are emit- ted at small relative momentum, their momentum corre- lation function is determined by the space-time charac- teristics of the production processes owing to the effects of quantum statistics (QS) and final-state interactions (FSI) [3, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The details on the formalism of the two- particle momentum correlation function can be found in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Here, comparing with our previous literature [36], more particle pairs are considered in the article.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Therefore, the final-state interaction of different particle pairs can be known well by introducing fc (k∗) particularly as follows: fc (k∗) = � Kc (k∗) − 2 ac h (λ) − ik∗Ac (λ) �−1 (4) fc (k∗) is the s-wave scattering amplitude renormalizied by the long-range Coulomb interaction, with h (λ) = λ2 �∞ n=1 � n � n2 + λ2��−1−C −ln [λ] where C = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='5772 is the Euler constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Kc (k∗) = 1 f0 + 1 2d0k∗2 +Pk∗4 +· · · is the effective range function, where d0 is the effective ra- dius of the strong interaction, f0 is the scattering length and P is the shape parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The parameters of effec- tive range function are important to characterize the es- sential properties of the final-state interactions, and can be extracted from the correlation function measured ex- perimentally [30, 36, 77, 78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Table I shows the param- eters of the effective range function for different particle pairs in the present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' In the table I, for n-n (¯n-¯n) and n-p (¯n-¯p) momentum correlation functions which include uncharged particle, the Coulomb penetration factor (Ac (λ)) is not consid- ered and only the short-range particle interaction works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' For the momentum correlation functions of charged parti- cles such as p-¯p, p-p (¯p-¯p), d-d ( ¯d- ¯d), t-t, p-d (¯p- ¯d), p-t and d-t, both the Coulomb interaction and the short-range in- teraction dominated by the s-wave interaction are taken into account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' The momentum correlation function of p- p (¯p-¯p) particle pairs is dominantly contributed by only TABLE I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Experimental determination of the effective range function parameters for n-n (¯n-¯n), p-p (¯p-¯p), t-t, n-p (¯n-¯p), p-d (¯p- ¯d), p-t and d-t systems [30, 77, 78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' System Spin f0 (fm) d0 (fm) P � fm3� n-n (¯n-¯n) 0 17 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='0 p-p (¯p-¯p) 0 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='77 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='0 t-t 0 1 × 10−6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='0 n-p (¯n-¯p) 0 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='7 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='0 p-d (¯p- ¯d) 1/2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='73 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='27 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='08 3/2 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='88 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='63 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='54 p-t 0 1 × 10−6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='0 d-t 0 1 × 10−6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='0 the singlet (S = 0) s-wave final-state interactions while both spins 1/2 and 3/2 contribute in the case of p-d (¯p- ¯d) system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Moreover, for (anti)deuteron-(anti)deuteron momentum correlation function, a parametrization of the s-wave phase shifts δ has been used from the solution of Kc (k∗) = cot δ for each total pair spin S = 0, 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Note that the effective range function for the total spin S = 1 is irrelevant, since it does not contribute due to the quan- tum statistics symmetrization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' ANALYSIS AND DISCUSSION A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Comparison between our p-p and p-¯p correlation functions with experimental data Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' 1 presents results of p-p and p-¯p correlation func- tions for three different centrality classes of 0 − 10 %, 10−30 %, and 30−70 % calculated by the AMPT model in Au + Au collisions at √sNN = 39 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Within the cut of transverse momentum pt and rapidity y, we con- front the experimental data with the predictions of the AMPT model combined with Lednick´y and Lyuboshitz code.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' When the phase-space information of nucleons at the maximum rescattering time among hadrons of 700 fm/c is selected from the AMPT model, it is found that the results can well describe the experimental data for the momentum correlation functions of p-p and p-¯p from the RHIC-STAR collaboration [79, 80], especially in more central collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Considering that the preliminary ex- perimental results were not corrected by feed-down effect corrections [79, 80], the real correlation functions for pri- mary p-p and p-¯p could be much more stronger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' In this case, using much longer MRT of 700 fm/c in the AMPT model might be a reasonable choice for making quanti- tative comparison with feed-down uncorrected data since the system will become more expanded and weakly corre- lated among particles after longer MRT in AMPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' How- ever, the quantitative reproduction is not our main con- cern in the present work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' In the following calculations, we fixed the MRT at 100 fm/c and presented systematic re- sults among different light (anti)nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' However, as one can notice that the results for p-p and p-¯p change substan- 4 tially when changing the MRT by comparing Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' To estimate this uncertainty, we also check some re- sults for light nuclei correlations with different MRT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' For example, d-d or p-d correlations for MRT equal 700fm/c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' It is found that the correlation becomes slightly weaker at smaller q (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' a little larger value of Cdd or Cpd close to 1 at MRT = 700 fm/c), which has the similar trend as p-p and p-¯p cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' But the uncertainty is less than 20% at the lowest relative momentum and tends to vanish at q > 50 MeV/c for light nuclei correlations (d-d or p-d) when changing the MRT from 100fm/c to 700fm/c, which can be essentially understood by weak feed-down effects for light nuclei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' In addition, we also check the p-d cor- relation with different velocity selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Only less than 10% uncertainty is found for lower q between the case of MRT equal 700 fm/c to the one at 100fm/c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' By this comparison of results at MRT equal 700 and 100 fm/c, we conclude that nucleon-(anti)nucleon correlations are much influenced by the MRT but light nuclei correla- tions only change slightly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' Overall, the MRT = 100 fm/c is basically safe choice for such light nuclei correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='5 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='4 Cpp(q) STAR data LL-model 0-10% 0-10% 10-30% 10-30% 30-70% 30-70% Au+Au@√sNN=39GeV, |y|<0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/5dE1T4oBgHgl3EQfBAJm/content/2301.02846v1.pdf'} +page_content='4 0, +the cyclotron motion in classical picture, and all M > 0 are degenerate up to M ∼ eBR2, +when the cyclotron orbit reaches the boundary. While the energy of a Landau level depends +only on q and n. The nonzero angular velocity ω weight different M differently through the +Boltzmann factor eMω/T in the ensemble of a macroscopic angular momentum. On the other +hand, the requirement of subluminal linear speed on the boundary limits the radius of the +2 + +cylinder R < 1/ω and the thermodynamic limit R → ∞ is unrealistic and the degeneracy of +the Landau levels becomes finite. We shall take the thermodynamic approximation by retaining +the leading term in power in 1/R in the thermodynamic potential, keeping in mind ωR = O(1)1, +and a sharp cutoff in the summation over angular momentum states within a Landau level is +introduced to tak care of the finite size effect of the spectrum. Consequently, the implication +of the rotation in the dHvA oscillation dependes on the size of the size of the system and the +angular velocity. As we shall see, the dHvA is completely suppressed for typical parameters +appropriate in a neutron star but may lead to observaservable effect for a cold and dense QGP +fire ball created in future RHIC project. For a strongly degenerate non-relativistic electron gas, +the reduction of the dHvA may be detectable in a rotating metallic sample. +This paper is organized as follows. +In section II, the dHvA term of an rotating ultra- +relativistic quark gas is calculated and its implications is discussed. +The same effect for a +non-relativistic electron is examined in section III. Section IV concludes the paper. +II. +ULTRA RELATIVISTIC FERMI GAS +A. +Solution of Dirac Equation in Cylindrical Cooredinate +For a massless fermion of electric charge e in a constant magnetic field ⃗B = Bˆz reads, the +Hamiltonian in chiral representation reads +H = −i⃗α · (⃗∇ − ieA) = +� +� −i⃗σ · (⃗∇ − ieA) +0 +0 +i⃗σ · (⃗∇ − ieA) +� +� +(1) +where the vector potential +⃗A = 1 +2 +⃗B × ⃗r +(2) +We adapt the circular gauge instead of Landau gauge for the convenience of investigating a +rotating Fermi gas. As the fermions of opposite chiralities have identical spectrum, we shall +focus one of them in what follows with the Hamiltonian +H = −i⃗σ · (⃗∇ − ieA) +(3) +1 In this case the kinetic energy of rotation grows with the volume, like other extensive thermodynamic +quantities. +3 + +and the eigenvalue equation Hχ = Eχ. For the ansatz of the two-component wave function χ +in cylindrical coordinates, i.e. +χ(⃗r) = +� +� f(ρ)ei(M− 1 +2)φ +g(ρ)ei(M+ 1 +2)φ +� +� eiqz +(4) +we have the equations for the radial functions f(ρ) and g(ρ) +� +� +� +� +� +qf(ρ) − i +� +d +dρ + +M+ 1 +2 +ρ +− 1 +2eBρ +� +g(ρ) = Ef(ρ) +−i +� +d +dρ − +M− 1 +2 +ρ ++ 1 +2eBρ +� +f(ρ) − qg(ρ) = Eg(ρ) +(5) +where, q and M are the eigenvalue of the momentum and total angular momentum in the +direction of the magnetic field with M = ±1/2, ±3/2, .... The equation (5) can be solved in +terms of the generaliized Laguerre polynomial Lµ +n(z) and we end up with the normalized wave +function [28], +χnMqs(⃗r) = 1 +2π +� +n! +(n + m)!e− ζ +2 +� +� +� +eB(E+q) +2E +ζ +m +2 Lm +n (ζ)eimφ +iseB +√ +E(E−q)ζm+1Lm+1 +n−1 (ζ)ei(m+1)φ +� +� eiqz +(6) +for M > 0, and +χnMqs(⃗r) = 1 +2π +� +n! +(n + |m|)!e− ζ +2 +� +� +� +eB(E+q) +2E +ζ +|m| +2 L|m| +n (ζ)eimφ +− iseB(n+|m|) +√ +E(E−q) ζ +(|m|−1) +2 +L|m|−1 +n +(ζ)ei(m+1)φ +� +� eiqz +(7) +for M < 0, where ζ ≡ 1 +2eBρ2, m ≡ M − 1/2, n = 0, 1, 2, ... and s = ±. The corresponding +eigenvalue of energy is E = sEnMq with +EnMq = +� +� +� +� +� +� +2neB + q2 +for M > 0 +� +2(n + |m|)eB + q2 +for M < 0 +(8) +Care must be exercised for the case n = 0 of the solution (6) because of the nonexistence of +Lm+1 +−1 +and the sigularity at E = −q. For E = ±q, eq.(5) becomes +� +� +� +� +� +� +d +dρ + m+1 +ρ +− 1 +2eBρ +� +g(ρ) = i(±q − q)f(ρ) +� +d +dρ − m +ρ + 1 +2eBρ +� +f(ρ) = i(±q + q)g(ρ) +(9) +A normalizable solution exists only if E = q and reads +χ0Mqs(⃗r) = 2m+1 +√π (eB) +m+1 +2 ρme− 1 +4 eBρ2+imφ+iqz +� +� 1 +0 +� +� +(10) +4 + +with s = sign(q), which implies up(down) mover for positive(negative) energy solution. The +wave function (7) corresponds to the classical motion along the cyclotron orbit and the spectrum +(8) constitues the entire set of Landau levels and is responsible to magnetic properties including +de Haas - van Alphen effect to be discussed below in thermodynamic approximation. The wave +function (7) and the spectrum (8) is specific to the cylindrical coordinates and is subleading in +the thermodynamic approximation as we shall see below. +B. +Thermodynamic Pressure +The Hamiltonian of massless fermion field in a magnetic filed is given by +H = +� +d3⃗rψ†Hψ +(11) +where H the single particle Hamiltonian (3) and the field operator +ψ(⃗r) = +� +nMq +ηnM(q)(anMqχnMq+(⃗r) + b† +nM−qχnMq−(⃗r)) +(12) +where +ηnM(q) = +� +� +� +� +� +θ(q) +for M > 0 and n = 0 +1 +otherwise +(13) +We have +H = +� +n,M,q +ηnM(q)EnMq(a† +nMqanMq + b† +nMqbnMq) +(14) +Correspondingly, the fermion number operator +Q = +� +d3⃗rψ†ψ += +� +n,M,q +ηnM(q)(a† +nMqanMq − b† +nMqbnMq) +(15) +and the angular momemtum projection operator +Jz = +� +d3⃗rψ† +� +−i ∂ +∂φ + 1 +2σz +� +ψ += +� +n,M,q +ηnM(q)M(a† +nMqanMq − b† +nMqbnMq) +(16) +5 + +Consequently, the thermodynamic pressure at temperature T and chemical potential µ of a +system rotating about z-axis with an angular velocity ω is +P =T +Ω +� +n=0,M>0,q>0 +[ln +� +1 + e−β(|q|−Mω−µ)� ++ ln +� +1 + e−β(|q|+Mω+µ)� +] ++ T +Ω +� +n=0,M>0,q +[ln +� +1 + e−β(√ +q2+2neB−Mω−µ)� ++ ln +� +1 + e−β(√ +q2+2neB+Mω+µ)� +] ++ T +Ω +� +n̸=0,M>0,q +[ln +� +1 + e−β(√ +q2+2(n+M+ 1 +2 )eB+Mω−µ)� ++ ln +� +1 + e−β(√ +q2+2(n+M+ 1 +2 )eB−Mω+µ)� +] +where we have switched the sign of M of the lower branch of the spectrum (8) for clarity. For +a cylinder of radius R and length L, Ω = πR2L, +� +n,M,q +(...) = +1 +πR2 +� ∞ +−∞ +dq +2π +� +n,M +(...) +(17) +To avoid superluminal linear speed on the boundary, we require v ≡ ωR < 1. So the true +thermodynamic limit R → ∞ is not attainable but we may still take the thermodynamic +approximation for sufficiently large R by sorting the terms according to its power keeping in +mind that ωR = O(1). For a finite R summation over M is limited. If follows from eqs. (6) and +(7) that the square of the wave function for large M and finite n is peaked at the maximum +of ρ2|m| exp +� +− 1 +2eBρ2� +, which gives rise to ρ2 = 2|m|/(eB). When this ρ becomes comparable +with R the finite size effect will distore the spectrum (8). Therefore, we introduce a cutoff for +the summation over M, i.e. +M ≤ Mc = [1 +2eBR2] >> 1 +(18) +with [...] tuncate the argument inside to its integer part. As will be shown below, this cutoff +produces the dHvA effect obtained from the Landau gauge in the absence of rotation. Without +solving the boundary value problem of the edge states, we assume the uncertainty δMc = O(1) +of the cutoff. +Assuming strong degeneracy, µ >> T, the antiparticle contributions may be ignored 2 and +2 To be cautious, let us examine whether the combination E ≡ +� +q2 + 2(n + M + 1 +2)eB − Mω in the last +term of (17) can become negative and compete with µ for large M. +For the maximum M(= Mc), E > +√2MceB − Mcω ≃ eBR(1 − v/2) > 0. The approximation of dropping the antiparticle contribution appears +safe. +6 + +we end up with +P = T +πR2 +� ∞ +0 +dq +4π +� +M>0 +ln +� +1 + e−β(|q|−Mω−µ)� ++ +T +πR2 +� ∞ +−∞ +dq +2π +� +n>0,M>0 +ln +� +1 + e−β(√ +q2+2neB−Mω−µ)� ++ +T +πR2 +� ∞ +−∞ +dq +2π +� +n,M>0 +ln +� +1 + e−β(√ +q2+2(n+M+ 1 +2 )eB+Mω−µ)� +(19) +where the contribution of the lowest Landau level has been isolated from higher Landau levels +because different integration domain of q. The summation over M in the third term of (19) +converges in the limit Mc → ∞ and thereby does not contribute to the thermadynamic limit +and we are left with the Landau level terms only, i.e. +P = T +πR2 +� ∞ +0 +dq +4π +� +M>0 +ln +� +1 + e−β(|q|−Mω−µ)� ++ +T +πR2 +� ∞ +−∞ +dq +2π +� +n>0,M>0 +ln +� +1 + e−β(√ +q2+2neB−Mω−µ)� +≡ 1 +πR2PM +(20) +where +PM = T +� ∞ +0 +dq +4π ln +� +1 + e−β(|q|−µM)� ++ T +� ∞ +−∞ +dq +2π +� +n>0 +ln +� +1 + e−β(√ +q2+2neB−µM)� +(21) +with µM = µ + Mω. +C. +de Haas - van Alphen Oscillation +As the standard derivation of the de Haas - van Alphen (dHvA) effect, the summation over +the Landau level index n can be carried out with the aid of the Poisson formula +∞ +� +n=0 +f(n) = +� ∞ +0 +f(n)dn + 2Re +∞ +� +l=1 +� ∞ +0 +f(n)e2iπlndx +(22) +We have +FM = F0M + 2Re +∞ +� +l=1 +FlM +(23) +where +FlM = T +� ∞ +−∞ +dq +2π +� ∞ +0 +dnei2πln ln +� +1 + e−β(√ +q2+2neB−µM)� +(24) +The dHvA oscillation resides in the second term of (23) and we shall focus on it. +Transforming the integration variables from q, n to q, ϵ with ϵ = +� +q2 + 2neB, we find, via +twice integration by part with respect to ϵ, that +FlM = IlM + IIlM + IIIlM +(25) +7 + +for l > 0, where +IlM = ieBT +4π2l +� ∞ +−∞ +dq ln +� +1 + e−β(q−µM� +), +(26) +IIlM = +eB +4iπ2l +� +eB +πl +� ∞ +−∞ +dqe−i lπ +eB q2 φ +�� +lπ +eB|q| +� +eβ(q−µM) + 1 +(27) +and +IIIlM = − eB +4iπ2l +� +eB +lπ +� ∞ +0 +dϵφ +�� +lπ +eB ϵ +� +βeβ(ϵ−µM) +[eβ(ϵ−µM) + 1]2 +� ϵ +−ϵ +dqe−i lπ +eB q2 +(28) +with +φ(z) ≡ +� ∞ +z +dxeix2 +(29) +IlM is imaginary thereby does not contribute to (23). Assuming the condition +T ≪ +√ +eB ≪ µ +(30) +the leading terms of IIlM and IIIlM can be worked out and we ontain that +IIlM = +eB +4π3l2 +� +ln +�� +4lπ +eB µM +� ++ 1 +2γE − iπ +4 +� +(31) +with γE = 0.5772... the Euler constant (See Appendix A for the derivation), and +IIIlM = −(eB) +1 +2T +4π +e +i +� +lπ2 +eB µ2 +M− π +4 +� +l3/2 sinh 2lπ2T(µ+Mω) +eB +. +(32) +where the integration formula +� ∞ +−∞ +dx +ex+iα +(ex + 1)2 = +πα +sinh πα +(33) +and the asymptotic form +φ(z) = i +2zeiz2 + ... for z → ∞ +(34) +have been employed to reduce IIIM. The dHvA osillation stems from IIIM. Summing over M, +we end up with the dHvA term of the thermodynamic pressure under rotation, i.e. +PdHvA ≡ +1 +πR2 +� +M>0 +� +2Re +∞ +� +l=1 +IIIlM +� += −(eB) +1 +2 +2π2R2 +∞ +� +l=1 +1 +l3/2 +� +M>0 +cos +� lπ +eB(µ + Mω)2 − π +4 +� +sinh 2lπ2T(µ+Mω) +eB +(35) +In the absence of rotation, ω = 0, eq.(35) becomes +PdHvA = −T(eB) +3 +2 +4π2 +∞ +� +l=1 +1 +l3/2 +cos +� lπ +eBµ2 − π +4 +� +sinh 2lπ2Tµ +eB +→ (eB) +5 +2 +8π4µ +∞ +� +l=1 +1 +l5/2 cos +� lπ +eB µ2 − π +4 +� +(36) +8 + +in agreement with the expression derived from the Landau gauge. +Eq.(35) can be further simplified at zero temperature, i.e. +PdHvA = −(eB) +3 +2 +4π4R2 +� +M>0 +1 +µ + Mω +∞ +� +l=1 +1 +l5/2 cos +� lπ +eB (µ + Mω)2 − π +4 +� +(37) +The angular velocity and magnetic field considered throught this work satisfy the condition +ω << +√ +eB and the summation over M can be approximated by an integral. Consequently +PdHvA ≃ − (eB) +3 +2 +4π4R2ω +� µ+Mcω +µ +dx1 +x +∞ +� +l=1 +1 +l5/2 cos +� lπ +eB x2 − π +4 +� += − +(eB) +3 +2 +8 +√ +2π4R2ω +∞ +� +l=1 +1 +l5/2 +� +Ci +� lπ +eB (µ + Mcω)2 +� +− Ci +� lπ +eB µ2 +� ++Si +� lπ +eB (µ + Mcω)2 +� +− Si +� lπ +eB µ2 +�� +≃ (eB) +5 +2 +8π5R2ω +∞ +� +l=1 +1 +l7/2 +� +sin +� lπ +eBµ2 − π +4 +� +µ2 +− sin +� lπ +eB(µ + Mcω)2 − π +4 +� +(µ + Mcω)2 +� +(38) +where Ci(z) and Si(z) are cosine and sine integrals and the last step follows from their +asymptotic forms for z ≫ 1, i.e. +� +� +� +� +� +Si(z) ≈ π +2 − cos z +z +Ci(z) ≈ sin z +z +(39) +are employed in the last step. If the maximum rotation energy Mcω dominates, i.e. Mcω >> µ, +the second term of (38) can be dropped and we have +PdHvA ≃ +(eB) +5 +2 +8π5µ2R2ω +∞ +� +l=1 +1 +l7/2 sin +� lπ +eB µ2 − π +4 +� +(40) +and the uncertainty of Mc does not contribute. +D. +Numerical Estimates +As pointed out in the introduction, the rotation will lift the degeneracy of states within +each Landau level and thereby reduce the de Haas - van Alphen oscillation. In this section, +we shall estimate the amount of reduction using the parameters appropriate for two realistic +rotating ultra-relativistic fermion system in a magnetic field, the quark matter core and a QGP +droplet at high baryon density. Since the Fermi gas approximation of these two system tends +to be poor and the condition of the latter syetem is highly transient, we are not attempting +to model the two system. The signifinace of our result below is only in the sense of order of +9 + +magnitude. For the ultra-relativistic system, we shall use mπ = 130MeV as the scale of the +chemical potential and temperature and m2 +π = 1014G as the scale of the magnetic field. The +estimate of the impact of the de Haas - van Alphen effect in a non-relativistic fermion system +is deferred to the next section. +The quark matter core of a neutron star +μ2=10mπ +2 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +-1.5×10-12 +-1. ×10-12 +-5. ×10-13 +0 +5. ×10-13 +1. ×10-12 +1.5×10-12 +eB/mπ +2 +PdHvA +Neutron Star +ωR = 0.06 +ωR = 0.045 +ωR = 0.03 +ωR = 0.015 +FIG. 1. The oscillatory term of pressure P1 as a function of magnetic field eB +m2π . Here, mπ = 140MeV, +R = 1km. +The radius of a neutron star is of the order of 10km and we assume a quark matter core +made of light flavors of smaller radius R with a chemical potential of several hundreds of MeV, +i.e. few times of pion’s rest energy, mπ. The magnetic field inside a neutron star can reach as +high as 1015G, i.e. 1.4×10−3m2 +π. For the fastest spinning neutron star, PSR J1748-2446ad, the +frequency is 716Hz and the linear speed at the boundary of the core is v ≃ 0.015 (in the unit +of the speed of light). Consequently +µ +Mcω = µ +mπ +· m2 +π +eB · +10−16 +R(km)v << 1 +(41) +PdHvA +PdHvA∥ω=0 +∼ +2 +µRv ≃ +3.86 × 10−16 +µ(MeV)R(km)v +(42) +for a typical neutron star. The approximation (40) is valid and we estimate +PdHvA +PdHvA∥ω=0 +∼ +2 +µRv ≃ +3.86 × 10−16 +µ(MeV)R(km)v +(43) +leading to huge suppression of dHvA oscillation. +The thermodynamic pressure at µ2 = 10m2 +π and zero temperature versus magnetic field +0 < eB < 0.01m2 +π is plotted in Fig. 1 for several linear speeds at the boundary of the rotating +quark matter core. As a benchmark, the thermodynamic pressure in the absence of rotation is +10 + +ω=0 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +-150000 +-100000 +-50000 +0 +50000 +100000 +150000 +eB/mπ +2 +PdHvA +μ2 = 20 mπ2 +μ2 = 15 mπ2 +μ2 = 10 mπ2 +μ2 = 5 mπ2 +FIG. 2. The oscillatory term of pressure P1 as a function of magnetic field eB +m2π . Here, ω = 0 and T = 0. +displayed in Fig. 2. The parameters underlying both figures satisfy the approximation condition +(30) for the analytic expressions. The effect is suppressed by 17 order of magnitude. +A cold and dense QGP droplet +μ2=10mπ +2 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +-150000 +-100000 +-50000 +0 +50000 +100000 +150000 +eB/mπ +2 +PdHvA +R = 10 fm +ωR = 0.03 +ωR = 0.02 +ωR = 0.01 +ωR = 0 +FIG. 3. The oscillatory term of pressure P1 as a function of magnetic field +eB +m2π . Here, we fix the +chemical potential µ2 = 10m2 +π and the radius is R = 10fm. +The suppression of dHvA in a neutron star may be attributed to its large size. +Let us +switch to a cold and dense QGP droplet where the suppression of dHvA oscillation with the +angular velocity becomes modest. The dHvA term of the thermodynamic pressure of eq.(38) for +R = 10fm versus the magnetic field at fixed chemical potential and temperature and is plotted +for several angular velocity including ω = 0 in Fig. 3. The same equation at fixed chemical +potential and a nonzero angular velocity is plotted for several temperatures in Fig. 4. The dHvA +without rotation, eq.(36) at the same chemical potential and the same set of tempertatures is +plotted in Fig. 5 for reference. Notice that the suppression of dHvA with temperature becomes +milder with ω ̸= 0. The selection of the size, chemical potential and the magnetic field is +11 + +μ2=20mπ +2 +0.30 0.32 0.34 0.36 0.38 0.40 +-1.5×10-11 +-1. ×10-11 +-5. ×10-120 +5. ×10-12 +1. ×10-11 +1.5× 10-11 +2. ×10-11 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +-0.10 +-0.05 +0.00 +0.05 +0.10 +0.15 +eB/mπ +2 +PdHvA +R = 10 fm +T = 56 MeV +T = 54 MeV +T = 52 MeV +T = 50 MeV +FIG. 4. The oscillatory term of pressure +P1 +(eB/m2π)30 as a function of magnetic field eB +m2π . Here, we fix the +chemical potential µ2 = 10m2 +π, v = 0.01 and the radius is R = 10fm. +μ2=20 mπ +2 +0.80 +0.85 +0.90 +0.95 +1.00 +-2. ×10-9 +-1. ×10-9 +0 +1. ×10-9 +2. ×10-9 +eB/mπ +2 +PdHvA +ω = 0 +T = 56 MeV +T = 54 MeV +T = 52 MeV +T = 50 MeV +FIG. 5. The oscillatory term of pressure +P1 +(eB/m2π)30 as a function of magnetic field eB +m2π . Here, we fix the +chemical potential µ2 = 10m2 +π, and ω = 0. +motivated by the conditions of the current heavy ion collisions in RHIC and LHC. +While the RHIC STAR fixed target experiment is expected to generate QGP of lower energy +and higher bayon density, i.e., closer to the density axis of the QCD phase diagram, there may +still be a gap to meet the condition of the cold and dense QGP described above. Even it did, +the rapid expansion would hinder the observability of the effect because of non-equilibrium. So +our discussions here are highly speculative. +III. +NON RELATIVISTIC FERMI GAS +The Hamiltonin of a non-relativistic electron reads +H = − 1 +2me +(⃗∇ − ie ⃗A)2 + 1 +2σzωB +(44) +12 + +with the vector potential +⃗A = 1 +2Bˆz × ⃗r, +(45) +where ωB = eB/me is the cyclotron frequency and σz = diag.(1, −1). +The spectrum in +cylindrical coordinates can be found in many textbook of quantum mechnics and are given +by +Enmqσ = +q2 +2me ++ +� +n + m − |m| +2 ++ 1 +2 +� +ωB + 1 +2σωB +(46) +where q is the momentum along z-direction, n = 0, 1, 2, ... are radial quantum number and +m=0,±1, ±2, ...,±Mc are the z-component of the orbital angular momentum and σ = ± +labels spin projections. The Landau levels correspond to m ≥ 0 and are labeled by n. The +corresponding wave function reads +ψnmqσ(⃗r) = +� +n!eB +2π(n + |m|)!Lζ +|m| +2 e− ζ +2L|m| +n (ζ)ei(mφ+qz) +(47) +In a cylinder of finite radius, the thermodynamic approximation limits the azimuthal quantum +number as (18), i.e. +|m| < mc = [1 +2eBR2] >> 1. +(48) +with an uncertainty δmc = O(1) as in the ultra-relativistic case. +A. +Thermodynamic Pressure and dHvA +For a free non-relativistic electron gas, the dHvA can be extracted using the same Poisson +formula (22) as in most of the textbooks in solid state physics. Here we adapt a more elegant +approach via Mellin transformation [29]. +The thermodynamic pressure of the electron gas in a rotating cylindrical volume of radius +R and length Lz reads +P = +1 +πR2 +� +m +Pm(ζm) +(49) +where +Pm(ζm) = T +Lz +� +n,q,σ +ln +� +1 + 1 +ζm +e−βEqnmσ +� +(50) +with ω the angular velocity and +ζm = e−β(µ+mω) +(51) +13 + +The case of strong degeneracy corresponds to ζm << 1. The Mellin transformation of the +function Pm(ζ) with respect to ζ is given by +Q(s) = +� ∞ +0 +dζζs−1Pm(ζ) += +πT +Lzs sin πs +� +n,q,σ +e−sβ(Enmqσ− 1 +2 σω) +(52) +for 0 < Res < 1. The last equality follows from an integration by part and the formula +� ∞ +0 +dx xs−1 +x + 1 = +π +sin πs +(53) +For the same reason as in the relativistic case, the contribution from m < 0 is subleading in +the thermodynamic approximation and we focus only on the branch m ≥ 0 of the spectrum. +We have for m ≥ 0 +FIG. 6. Contour integration [29]. +Q(s) = +πT +Lzs sin πs +� +q +e− sβq2 +2me +� +n,σ +e−(n+ 1 +2)sβωB− 1 +2 σsβ(ωB−ω) += +πT +λs3/2 sin πs +cosh 1 +2sβ(ωB − ω) +sinh 1 +2sβωB +(54) +where λ = +� +2π/(mT) is the thermal wavelength. It follows from the Mellin inversion formula +that +Pm(ζ) = +� c+i∞ +c−i∞ +ds +2πiζ−sQ(s) +(55) +with 0 < c < 1. The integrand on the complex s-plane consists of a branch cut running along +the negative real axis, poles along both real and imaginary axes, i.e. +s = l +s = 2lπT +ωB +i +(56) +14 + +Im s +21元T +wB +Re swith l = 0, ±1, ±2, .... Closing the contour from the left as shown in Fig.6 for ζ < 1, we find +Pm(ζ) = Im(ζ) + IIm(ζ) +(57) +where Im is the integral around the branch cut and IIm stems from the poles along the imaginary +axis. The former contributes to the Landau diamagnetism and Pauli paramagnetism along with +the Barnett effect and the latter gives rise to dHvA oscillation. Summing up the residues of +the poles within the contour, we end up with +IIm(ζm) = 2T +λ +� ωB +2πT +∞ +� +l=1 +1 +l3/2csch2lπ2T +ωB +cos lπω +ωB +cos +�2lπ(µ + mω) +ωB +− π +4 +� +(58) +Summing up the orbital angular momentum, we obtain that +PdHvA = +1 +πR2 +mc +� +m=0 +IIm += −T(meωB)1/2 +π2R2 +∞ +� +l=1 +cos lπω +ωB +sin +� +2lπµ +ωB − lπω +ωB − π +4 +� +− sin +� +2lπµ +ωB + lπω +ωB − π +4 + 2lπmcω +ωB +� +l3/2 sinh 2lπ2T +ωB sin lπω +ωB +(59) +Without rotation, ω = 0, the well-known dHvA formula +PdHvA|ω=0 = −T(meωB)3/2 +2π2 +∞ +� +l=1 +1 +l3/2csch2lπ2T +ωB +cos +�2lπµ +ωB +− π +4 +� +(60) +emerges. At zero temperature, eq. (59) becomes +PdHvA|T=0 = −(meωB)3/2 +4π4meR2 +∞ +� +l=1 +cos lπω +ωB +sin +� +2lπµ +ωB + lπω +ωB − π +4 + lπmeωR2� +− sin +� +2lπµ +ωB − lπω +ωB − π +4 +� +l5/2 sin lπω +ωB +≃ − (meωB)5/2 +4π5m2 +eωR2 +∞ +� +l=1 +1 +l7/2 +� +sin +�2lπµ +ωB +− π +4 + 2lπmcω +ωB +� +− sin +�2lπµ +ωB +− π +4 +�� +(61) +where the approximation ω << ωB is made for the typical parameters in condensed matter +physics. This expression is to be compared with the zero temperature limit of (62), i.e. +PdHvA|ω=0 = −(meωB)5/2 +4π4 +∞ +� +l=1 +1 +l5/2 cos +�2lπµ +ωB +− π +4 +� +. +(62) +At this point, it is interesting to compare the non-relativistic dHvA and the ultra-relativistic +dHvA. As shown in eq.(46), given q and σ, the non-relativistic Landau levels (m>0) are +equally spaced while the spacing between successive ultra-relativistic Landau levels in the upper +equation of (8) decreases with the label n. Since the dHvA is sensitive to the energy levels +around the chemical potential µ, the amplitude of the oscillation is expected to be independent +15 + +of µ in the non-relativistic case but decreases with µ in the ultra-relativistic case as reflected +in the large µ suppression by sinh 2lπ2Tµ +eB +of (36) in the latter case. When rotation is turned +on, the effective chemical potential increases with the angular momentum quantum number. +Consequently, the non-relativistic dHvA appears less vulnerable than the ultra-relativistic one. +B. +Numerical Estimates +The electron gas in a good metal at room temperature, T ∼ 1/40eV can be well approximated +by a free Fermi in the strong degeneracy limit. The chemical potential is of 1 ∼ 10eV, which +makes µ/T ∼ 40 ∼ 400 >> 1 and the zero temperature approximation works well. For a +magnetic field up to few Tesla’s and an angular velocity is Hz, we have +ω/ωB ≃ 5.57 × 10−12 ω(Hz) +B(Tesla) +(63) +justifying the approximation made in the (61) for mechanical rotation achievable in laboratory. +The same condition also makes the contribution of the uncertainty in the angular momentum +cutoff mc to the phase of the oscillation in (59) and (61) negligible. The dHvA oscillation is +expected to be significantly reduced when the largest rotation energy mcω within a Landau +level exceeds the spacing between successive levels, ωB. With R in cm, the linear velocity of +the corcumference v = ωR in terms of cm/s, it follows from (48) that +mcω +ωB +≃ 0.43Rv, +(64) +independent of the magnetic field. +ω = 0 +1.00000 +1.00002 +1.00004 +1.00006 +1.00008 +1.00010 +-0.0004 +-0.0003 +-0.0002 +-0.0001 +0.0000 +0.0001 +0.0002 +B(T) +PdHvA +μ = 7 eV +μ = 5 eV +μ = 3 eV +μ = 1 eV +FIG. 7. The oscillatory term of non-relativistic pressure P1 as a function of magnetic field B when +T = 0 and ω = 0. +16 + +ωR = 2 cm/s +1.00000 +1.00002 +1.00004 +1.00006 +1.00008 +1.00010 +-0.00010 +-0.00005 +0.00000 +0.00005 +B(T) +PdHvA +R = 1 cm +μ = 7 eV +μ = 5 eV +μ = 3 eV +μ = 1 eV +FIG. 8. The oscillatory term of non-relativistic pressure P1 as a function of magnetic field B when +T = 0. Here, we fix ωR = 2cm/s and R = 1 cm . +μ = 5 eV +1.00000 +1.00002 +1.00004 +1.00006 +1.00008 +1.00010 +-0.0003 +-0.0002 +-0.0001 +0.0000 +0.0001 +0.0002 +B(T) +PdHvA +R = 1 cm +ωR = 6 cm/s +ωR= 4 cm/s +ωR = 2 cm/s +ωR = 0 +FIG. 9. The oscillatory term of non-relativistic pressure P1 as a function of magnetic field B when +T = 0. Here, we fix the chemical potential µ = 5eV and the radius is R = 1cm. +The dHvA term of the thermodynamic pressure of a strongly degenerate electron gas versus +magnetic field for a long cylinder of radius R = 1cm at T = 0 is plotted in Fig. 7, Fig. 8 and +Fig. 9. The magnetic field varies in a small neighborhood of 1T and the angular velocity is taken +such that RHS of (64) is of order one. The dHvA effect without rotation, eq.(62), for different +chemical potentials is shown in Fig. 7 sas benchmark. The parallel setup for ωR = 2cm/s, +eq.(61), is shown in Fig. 8 with similar profiles. More important is Fig. 9 where dHvA at +different ωR is displayed and the suppression of the oscillation by rotation is evident. +IV. +CONCLUDING REMARKS +Let us recaptulate what we presented in preceding sections. We examined the robustness +of the de Haas-van Alphen effect in a strongly degenerate Fermi gas under rotation. +We +17 + +derived the formula for dHvA oscillation in an long cylinder rotating about its axis in the +ultra-relativistic limit and non-relativistic limit. As the macroscopic degeneracy of Landau +levels is offset by rotation energy of states of different angular momentum within each Landau +level. The amplitude of the scillation is reduced. The amount of reduction depends on the +angular velocity ω and the radius of the cylinder R and the oscillation is expected to become +insignificant for sufficiently large ω and R. The ultra-relativistic dHvA appear more vulnerable +than the non-relativistic one because of decreasing Landau level spacing with energy. +Applying the ultra-relativistic formula to estimate dHvA with typical parameters of a +neutron star, and with typical parameters of a cold and dense QGP droplet, we noted that +the dHvA oscillation is completely suppressed in the former case and remains in the latter. +The non-relativistic formula, on the other hand showed that for a typical electron gas in a +good metal, the variation of dHvA oscillation with angular velocity appears detectable, via +magnetization and/or magnetic susceptibility. +As self-criticism, our approximation of the finite size effect by introducing the maximum +angular momentum within a Landau level in (18) and (48) may be crude. Limited by the +analytical tractability, the cylindrical shape of the system is not suitable to model a neutron +star or a QGP droplet. Though the effect is expected to remain for a Fermi liquid, the strong +correlation in quark matter may modify significantly the quantitative prediction. In this sense, +our result is very preliminary. +ACKNOWLEDGMENTS +We thank Ren-Hong Fang for fruitful discussions. This work is supported by the National +Key Research and Development Program of China (No. 2022YFA1604900). This work also +is supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. +11735007, 11890711, 11890710, 12275104. +Appendix A: Appendix +For µ >> T, eq.(55) can be approximated as +IIlM ≃ +1 +2iπ2l +� +eB +lπ +� µM +0 +dqe−i lπ +eB q2φ +�� +lπ +eB q +� += +eB +2iπ3l2J +(A1) +18 + +where +J = +� K +0 +dxe−ix2φ(x) = +� K +0 +dxe−ix2 � ∞ +x +dξeiξ2 +(A2) +with K = +� +lπ +eBµM. Introducing ξ = xt, we find +J = +� K +0 +dxe−ix2x +� ∞ +1 +dteit2x2 = 1 +2i +� ∞ +1 +dteiK2(t2−1) − 1 +t2 − 1 += −1 +2K2 +� ∞ +1 +dteiK2(t2−1)t ln t − 1 +t + 1 +(A3) +where the last equality follows from an integration by part. Introducing z = t2 − 1, we have +J = −1 +4K2 +� ∞ +0 +dzeiK2z ln +√z + 1 − 1 +√z + 1 + 1 +(A4) +If follows from the Jordan lemma that integration path can be rotated to the imaginary axis +on the z− plane and we end up with +J = − i +4K2 +� ∞ +0 +dye−K2y ln +√1 + iy − 1 +√1 + iy + 1 +(A5) +For K >> 1, we have +J ≃ − i +4K2 +� ∞ +0 +dye−K2y ln iy +4 = i +2 +� +ln(2K) + 1 +2γE +� ++ π +8 +(A6) +This gives rise to RHS of (A1). +[1] L. Adamczyk et al. Global Λ hyperon polarization in nuclear collisions: evidence for the most +vortical fluid. Nature, 548:62–65, 2017. +[2] B. I. Abelev et al. Global polarization measurement in Au+Au collisions. Phys. Rev. C, 76:024915, +2007. [Erratum: Phys.Rev.C 95, 039906 (2017)]. +[3] Jaroslav Adam et al. Global polarization of Λ hyperons in Au+Au collisions at √sNN = 200 GeV. +Phys. Rev. C, 98:014910, 2018. +[4] Jaroslav Adam et al. Polarization of Λ (¯Λ) hyperons along the beam direction in Au+Au collisions +at √sNN = 200 GeV. Phys. Rev. Lett., 123(13):132301, 2019. +[5] Jaroslav Adam et al. Measurement of inclusive J/ψ polarization in p + p collisions at √s =200 +GeV by the STAR experiment. Phys. Rev. D, 102(9):092009, 2020. +[6] J. Adam et al. Global Polarization of Ξ and Ω Hyperons in Au+Au Collisions at √sNN = 200 +GeV. Phys. Rev. Lett., 126(16):162301, 2021. +19 + +[7] M. S. Abdallah et al. Global Λ-hyperon polarization in Au+Au collisions at √sNN=3 GeV. Phys. +Rev. C, 104(6):L061901, 2021. +[8] M. S. Abdallah et al. Search for the Chiral Magnetic Effect via Charge-Dependent Azimuthal +Correlations Relative to Spectator and Participant Planes in Au+Au Collisions at √sNN = +200 GeV. Phys. Rev. Lett., 128(9):092301, 2022. +[9] M. S. Abdallah et al. +Pair invariant mass to isolate background in the search for the chiral +magnetic effect in Au + Au collisions at √sNN=200 GeV. Phys. Rev. C, 106(3):034908, 2022. +[10] Mohamed Abdallah et al. Search for the chiral magnetic effect with isobar collisions at √sNN=200 +GeV by the STAR Collaboration at the BNL Relativistic Heavy Ion Collider. +Phys. Rev. C, +105(1):014901, 2022. +[11] Francesco Becattini, Jinfeng Liao, and Michael Lisa. Strongly Interacting Matter Under Rotation: +An Introduction. Lect. Notes Phys., 987:1–14, 2021. +[12] Hao-Lei Chen, Kenji Fukushima, Xu-Guang Huang, and Kazuya Mameda. +Analogy between +rotation and density for Dirac fermions in a magnetic field. Phys. Rev. D, 93(10):104052, 2016. +[13] Kenji Fukushima, Takuya Shimazaki, and Lingxiao Wang. Mode decomposed chiral magnetic +effect and rotating fermions. Phys. Rev. D, 102(1):014045, 2020. +[14] Koichi Hattori and Yi Yin. Charge redistribution from anomalous magnetovorticity coupling. +Phys. Rev. Lett., 117:152002, Oct 2016. +[15] Yizhuang Liu and Ismail Zahed. Rotating Dirac fermions in a magnetic field in 1+2 and 1+3 +dimensions. Phys. Rev. D, 98(1):014017, 2018. +[16] Emil Mottola and Andrey V. Sadofyev. +Chiral Waves on the Fermi-Dirac Sea: +Quantum +Superfluidity and the Axial Anomaly. Nucl. Phys. B, 966:115385, 2021. +[17] R. Gonzalez Felipe, A. Perez Martinez, H. Perez Rojas, and M. Orsaria. Magnetized strange +quark matter and magnetized strange quark stars. Phys. Rev. C, 77:015807, 2008. +[18] Chinatsu Watanabe, Naotaka Yoshinaga, and Shuichiro Ebata. Equations of State for Hadronic +Matter and Mass-Radius Relations of Neutron Stars with Strong Magnetic Fields. +Universe, +8(1):48, 2022. +[19] Pétri Jérôme. Particle acceleration and radiation reaction in a strongly magnetised rotating dipole. +Astron. Astrophys., 666:A5, 2022. +[20] Debarati Chatterjee, Jérôme Novak, and Micaela Oertel. Structure of ultra-magnetised neutron +stars. Eur. Phys. J. A, 57(8):249, 2021. +[21] A Einstein and W de Haas. Verh. d. deutsch. Phys. Ges, 17:152, 1915. +20 + +[22] Samuel J Barnett. Gyromagnetic and electron-inertia effects. Reviews of Modern Physics, 7(2):129, +1935. +[23] Samapan Bhadury, Wojciech Florkowski, Amaresh Jaiswal, Avdhesh Kumar, and Radoslaw +Ryblewski. Relativistic Spin Magnetohydrodynamics. Phys. Rev. Lett., 129(19):192301, 2022. +[24] Y. ¯Onuki. +Magnetic systems: De haas–van alphen studies of fermi surface. +In K.H. Jürgen +Buschow, Robert W. Cahn, Merton C. Flemings, Bernhard Ilschner, Edward J. Kramer, Subhash +Mahajan, and Patrick Veyssière, editors, Encyclopedia of Materials: Science and Technology, +pages 4964–4968. Elsevier, Oxford, 2001. +[25] W. Z. Jiang and N. Van Giai. Magnetic susceptibility oscillation in neutron stars with the hadron- +quark transition. AIP Conf. Proc., 865(1):256–261, 2006. +[26] Daniel Cangemi and Gerald V. Dunne. Temperature expansions for magnetic systems. Annals +Phys., 249:582–602, 1996. +[27] Cheng Zhang, Ren-Hong Fang, Jian-Hua Gao, and De-Fu Hou. Thermodynamics of chiral fermion +system in a uniform magnetic field. Phys. Rev. D, 102(5):056004, 2020. +[28] Ren-Hong Fang. Thermodynamics for a Rotating Chiral Fermion System in the Uniform Magnetic +Field. Symmetry, 14(6):1106, 2022. +[29] Huanwu Peng and Xishen Xu. Fundamentals of Theoretical Physics. Peking University Press, +1998. +21 + diff --git a/8NE1T4oBgHgl3EQfBwLj/content/tmp_files/load_file.txt b/8NE1T4oBgHgl3EQfBwLj/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..c1dcbc38d3fb87cf21f67b07edac448d89f50ab1 --- /dev/null +++ b/8NE1T4oBgHgl3EQfBwLj/content/tmp_files/load_file.txt @@ -0,0 +1,647 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf,len=646 +page_content='De Haas - van Alphen Effect under Rotation Shu-Yun Yang,1, ∗ Ren-Da Dong,1 De-Fu Hou,1, † and Hai-Cang Ren2, 1, ‡ 1Institute of Particle Physics and Key Laboratory of Quark and Lepton Physics (MOS), Central China Normal University, Wuhan 430079, China 2Physics Department, The Rockefeller University, 1230 York Avenue, New York, NY 10021-6399 Abstract We explored the interplay between magnetic field and rotation in the de Hass - van Alphen oscillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The effect is found to be reduced because of the re-weighting of different states within the same Landau level by rotation energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The implications of our results on high energy physics and condensed matter physics are speculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ∗ yangsy@mails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='ccnu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='cn † Co-corresponding author: houdf@mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='ccnu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='cn ‡ Co-corresponding author: renhc@mail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='ccnu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='cn 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='02857v1 [hep-ph] 7 Jan 2023 I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' INTRODUCTION The experimental activities for recent years regarding the polarization [1–7] and chiral magnetic effects [8–10] in off-central relativistic heavy ion collisions promoted theoretical research interests in a rotating thermodynamic system in a magnetic field [11–16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The same physical conditions are also present in a neutron star [17–20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' One of the inteplay between the magnetism and rotation, the Barnett effect (or Einstein-de Haas effect) [21–23] has been considered in hydrodynamic modeling of the collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' In this work, we examine another interplay between magnetism and rotation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' the de Haas - van Alphen effect [24, 25] in a strongly degenerate rotating Fermi gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Though purely theoretical at present stage, the implications are expected to shed light on the magnetic properties of the quark matter core, if exists, in a neutron star and/or the QGP droplet of generated in the RHIC STAR fixed target experiment, where the quark density is towards the strong degeneracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The conclusion may also be tested directly in condensaed matter physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' De Haas-van Alphen effect is the consequence of charged fermions filling discrete but highly degenerate Landau levels [26, 27] in a magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' In the absence of rotation, all degenerate Landau levels are equally populated at thermal equilibrium and the disceteness of different Laudau level is refelected in the thermodynamic limit as the oscillatory terms with respect to the chemical potential and the magnetic field in the thermodynamic potential, magnetization and magnetic susceptibility as well as some transport coefficients.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' When the system is in rotation, the thermodynamic equilibrium is established under a nonzero macroscopc angular momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The equal distribution of different angular momentum states within a Laudau level is offset by the nonzero angular velocity with higher angular momenta more favored than lower ones, which amounts to lifts the degeneracy of the Landau level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The dHvA oscillation is thereby expected to be reduced by the rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Consider a cylindrical volume of radius R with a constant magnetic field parallel to its axis, the states of each fermion is characterized by the z-component of the momentum q, the z-component of the angular momentum M, and the radial quantum number of the wave function, n(≥ 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' A Laudau levels corresponds M > 0, the cyclotron motion in classical picture, and all M > 0 are degenerate up to M ∼ eBR2, when the cyclotron orbit reaches the boundary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' While the energy of a Landau level depends only on q and n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The nonzero angular velocity ω weight different M differently through the Boltzmann factor eMω/T in the ensemble of a macroscopic angular momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' On the other hand, the requirement of subluminal linear speed on the boundary limits the radius of the 2 cylinder R < 1/ω and the thermodynamic limit R → ∞ is unrealistic and the degeneracy of the Landau levels becomes finite.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' We shall take the thermodynamic approximation by retaining the leading term in power in 1/R in the thermodynamic potential, keeping in mind ωR = O(1)1, and a sharp cutoff in the summation over angular momentum states within a Landau level is introduced to tak care of the finite size effect of the spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Consequently, the implication of the rotation in the dHvA oscillation dependes on the size of the size of the system and the angular velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' As we shall see, the dHvA is completely suppressed for typical parameters appropriate in a neutron star but may lead to observaservable effect for a cold and dense QGP fire ball created in future RHIC project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' For a strongly degenerate non-relativistic electron gas, the reduction of the dHvA may be detectable in a rotating metallic sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' This paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' In section II, the dHvA term of an rotating ultra- relativistic quark gas is calculated and its implications is discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The same effect for a non-relativistic electron is examined in section III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Section IV concludes the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ULTRA RELATIVISTIC FERMI GAS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Solution of Dirac Equation in Cylindrical Cooredinate For a massless fermion of electric charge e in a constant magnetic field ⃗B = Bˆz reads, the Hamiltonian in chiral representation reads H = −i⃗α · (⃗∇ − ieA) = � � −i⃗σ · (⃗∇ − ieA) 0 0 i⃗σ · (⃗∇ − ieA) � � (1) where the vector potential ⃗A = 1 2 ⃗B × ⃗r (2) We adapt the circular gauge instead of Landau gauge for the convenience of investigating a rotating Fermi gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' As the fermions of opposite chiralities have identical spectrum, we shall focus one of them in what follows with the Hamiltonian H = −i⃗σ · (⃗∇ − ieA) (3) 1 In this case the kinetic energy of rotation grows with the volume, like other extensive thermodynamic quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 3 and the eigenvalue equation Hχ = Eχ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' For the ansatz of the two-component wave function χ in cylindrical coordinates, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' χ(⃗r) = � � f(ρ)ei(M− 1 2)φ g(ρ)ei(M+ 1 2)φ � � eiqz (4) we have the equations for the radial functions f(ρ) and g(ρ) � � � � � qf(ρ) − i � d dρ + M+ 1 2 ρ − 1 2eBρ � g(ρ) = Ef(ρ) −i � d dρ − M− 1 2 ρ + 1 2eBρ � f(ρ) − qg(ρ) = Eg(ρ) (5) where, q and M are the eigenvalue of the momentum and total angular momentum in the direction of the magnetic field with M = ±1/2, ±3/2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='. The equation (5) can be solved in terms of the generaliized Laguerre polynomial Lµ n(z) and we end up with the normalized wave function [28], χnMqs(⃗r) = 1 2π � n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (n + m)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='e− ζ 2 � � � eB(E+q) 2E ζ m 2 Lm n (ζ)eimφ iseB √ E(E−q)ζm+1Lm+1 n−1 (ζ)ei(m+1)φ � � eiqz (6) for M > 0, and χnMqs(⃗r) = 1 2π � n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (n + |m|)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='e− ζ 2 � � � eB(E+q) 2E ζ |m| 2 L|m| n (ζ)eimφ − iseB(n+|m|) √ E(E−q) ζ (|m|−1) 2 L|m|−1 n (ζ)ei(m+1)φ � � eiqz (7) for M < 0, where ζ ≡ 1 2eBρ2, m ≡ M − 1/2, n = 0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' and s = ±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The corresponding eigenvalue of energy is E = sEnMq with EnMq = � � � � � � 2neB + q2 for M > 0 � 2(n + |m|)eB + q2 for M < 0 (8) Care must be exercised for the case n = 0 of the solution (6) because of the nonexistence of Lm+1 −1 and the sigularity at E = −q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' For E = ±q, eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (5) becomes � � � � � � d dρ + m+1 ρ − 1 2eBρ � g(ρ) = i(±q − q)f(ρ) � d dρ − m ρ + 1 2eBρ � f(ρ) = i(±q + q)g(ρ) (9) A normalizable solution exists only if E = q and reads χ0Mqs(⃗r) = 2m+1 √π (eB) m+1 2 ρme− 1 4 eBρ2+imφ+iqz � � 1 0 � � (10) 4 with s = sign(q), which implies up(down) mover for positive(negative) energy solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The wave function (7) corresponds to the classical motion along the cyclotron orbit and the spectrum (8) constitues the entire set of Landau levels and is responsible to magnetic properties including de Haas - van Alphen effect to be discussed below in thermodynamic approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The wave function (7) and the spectrum (8) is specific to the cylindrical coordinates and is subleading in the thermodynamic approximation as we shall see below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Thermodynamic Pressure The Hamiltonian of massless fermion field in a magnetic filed is given by H = � d3⃗rψ†Hψ (11) where H the single particle Hamiltonian (3) and the field operator ψ(⃗r) = � nMq ηnM(q)(anMqχnMq+(⃗r) + b† nM−qχnMq−(⃗r)) (12) where ηnM(q) = � � � � � θ(q) for M > 0 and n = 0 1 otherwise (13) We have H = � n,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='q ηnM(q)EnMq(a† nMqanMq + b† nMqbnMq) (14) Correspondingly,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' the fermion number operator Q = � d3⃗rψ†ψ = � n,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='q ηnM(q)(a† nMqanMq − b† nMqbnMq) (15) and the angular momemtum projection operator Jz = � d3⃗rψ† � −i ∂ ∂φ + 1 2σz � ψ = � n,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='q ηnM(q)M(a† nMqanMq − b† nMqbnMq) (16) 5 Consequently,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' the thermodynamic pressure at temperature T and chemical potential µ of a system rotating about z-axis with an angular velocity ω is P =T Ω � n=0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='M>0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='q>0 [ln � 1 + e−β(|q|−Mω−µ)� + ln � 1 + e−β(|q|+Mω+µ)� ] + T Ω � n=0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='M>0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='q [ln � 1 + e−β(√ q2+2neB−Mω−µ)� + ln � 1 + e−β(√ q2+2neB+Mω+µ)� ] + T Ω � n̸=0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='M>0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='q [ln � 1 + e−β(√ q2+2(n+M+ 1 2 )eB+Mω−µ)� + ln � 1 + e−β(√ q2+2(n+M+ 1 2 )eB−Mω+µ)� ] where we have switched the sign of M of the lower branch of the spectrum (8) for clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' For a cylinder of radius R and length L, Ω = πR2L, � n,M,q (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=') = 1 πR2 � ∞ −∞ dq 2π � n,M (.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=') (17) To avoid superluminal linear speed on the boundary, we require v ≡ ωR < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' So the true thermodynamic limit R → ∞ is not attainable but we may still take the thermodynamic approximation for sufficiently large R by sorting the terms according to its power keeping in mind that ωR = O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' For a finite R summation over M is limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' If follows from eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (6) and (7) that the square of the wave function for large M and finite n is peaked at the maximum of ρ2|m| exp � − 1 2eBρ2� , which gives rise to ρ2 = 2|m|/(eB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' When this ρ becomes comparable with R the finite size effect will distore the spectrum (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Therefore, we introduce a cutoff for the summation over M, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' M ≤ Mc = [1 2eBR2] >> 1 (18) with [.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='] tuncate the argument inside to its integer part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' As will be shown below, this cutoff produces the dHvA effect obtained from the Landau gauge in the absence of rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Without solving the boundary value problem of the edge states, we assume the uncertainty δMc = O(1) of the cutoff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Assuming strong degeneracy, µ >> T, the antiparticle contributions may be ignored 2 and 2 To be cautious, let us examine whether the combination E ≡ � q2 + 2(n + M + 1 2)eB − Mω in the last term of (17) can become negative and compete with µ for large M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' For the maximum M(= Mc), E > √2MceB − Mcω ≃ eBR(1 − v/2) > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The approximation of dropping the antiparticle contribution appears safe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 6 we end up with P = T πR2 � ∞ 0 dq 4π � M>0 ln � 1 + e−β(|q|−Mω−µ)� + T πR2 � ∞ −∞ dq 2π � n>0,M>0 ln � 1 + e−β(√ q2+2neB−Mω−µ)� + T πR2 � ∞ −∞ dq 2π � n,M>0 ln � 1 + e−β(√ q2+2(n+M+ 1 2 )eB+Mω−µ)� (19) where the contribution of the lowest Landau level has been isolated from higher Landau levels because different integration domain of q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The summation over M in the third term of (19) converges in the limit Mc → ∞ and thereby does not contribute to the thermadynamic limit and we are left with the Landau level terms only, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' P = T πR2 � ∞ 0 dq 4π � M>0 ln � 1 + e−β(|q|−Mω−µ)� + T πR2 � ∞ −∞ dq 2π � n>0,M>0 ln � 1 + e−β(√ q2+2neB−Mω−µ)� ≡ 1 πR2PM (20) where PM = T � ∞ 0 dq 4π ln � 1 + e−β(|q|−µM)� + T � ∞ −∞ dq 2π � n>0 ln � 1 + e−β(√ q2+2neB−µM)� (21) with µM = µ + Mω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' de Haas - van Alphen Oscillation As the standard derivation of the de Haas - van Alphen (dHvA) effect,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' the summation over the Landau level index n can be carried out with the aid of the Poisson formula ∞ � n=0 f(n) = � ∞ 0 f(n)dn + 2Re ∞ � l=1 � ∞ 0 f(n)e2iπlndx (22) We have FM = F0M + 2Re ∞ � l=1 FlM (23) where FlM = T � ∞ −∞ dq 2π � ∞ 0 dnei2πln ln � 1 + e−β(√ q2+2neB−µM)� (24) The dHvA oscillation resides in the second term of (23) and we shall focus on it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Transforming the integration variables from q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' n to q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ϵ with ϵ = � q2 + 2neB,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' we find,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' via twice integration by part with respect to ϵ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' that FlM = IlM + IIlM + IIIlM (25) 7 for l > 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' where IlM = ieBT 4π2l � ∞ −∞ dq ln � 1 + e−β(q−µM� ),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (26) IIlM = eB 4iπ2l � eB πl � ∞ −∞ dqe−i lπ eB q2 φ �� lπ eB|q| � eβ(q−µM) + 1 (27) and IIIlM = − eB 4iπ2l � eB lπ � ∞ 0 dϵφ �� lπ eB ϵ � βeβ(ϵ−µM) [eβ(ϵ−µM) + 1]2 � ϵ −ϵ dqe−i lπ eB q2 (28) with φ(z) ≡ � ∞ z dxeix2 (29) IlM is imaginary thereby does not contribute to (23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Assuming the condition T ≪ √ eB ≪ µ (30) the leading terms of IIlM and IIIlM can be worked out and we ontain that IIlM = eB 4π3l2 � ln �� 4lπ eB µM � + 1 2γE − iπ 4 � (31) with γE = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='5772.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' the Euler constant (See Appendix A for the derivation), and IIIlM = −(eB) 1 2T 4π e i � lπ2 eB µ2 M− π 4 � l3/2 sinh 2lπ2T(µ+Mω) eB .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (32) where the integration formula � ∞ −∞ dx ex+iα (ex + 1)2 = πα sinh πα (33) and the asymptotic form φ(z) = i 2zeiz2 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' for z → ∞ (34) have been employed to reduce IIIM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The dHvA osillation stems from IIIM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Summing over M, we end up with the dHvA term of the thermodynamic pressure under rotation, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' PdHvA ≡ 1 πR2 � M>0 � 2Re ∞ � l=1 IIIlM � = −(eB) 1 2 2π2R2 ∞ � l=1 1 l3/2 � M>0 cos � lπ eB(µ + Mω)2 − π 4 � sinh 2lπ2T(µ+Mω) eB (35) In the absence of rotation, ω = 0, eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (35) becomes PdHvA = −T(eB) 3 2 4π2 ∞ � l=1 1 l3/2 cos � lπ eBµ2 − π 4 � sinh 2lπ2Tµ eB → (eB) 5 2 8π4µ ∞ � l=1 1 l5/2 cos � lπ eB µ2 − π 4 � (36) 8 in agreement with the expression derived from the Landau gauge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (35) can be further simplified at zero temperature, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' PdHvA = −(eB) 3 2 4π4R2 � M>0 1 µ + Mω ∞ � l=1 1 l5/2 cos � lπ eB (µ + Mω)2 − π 4 � (37) The angular velocity and magnetic field considered throught this work satisfy the condition ω << √ eB and the summation over M can be approximated by an integral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Consequently ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='PdHvA ≃ − (eB) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='4π4R2ω ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� µ+Mcω ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='µ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='dx1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='x ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='∞ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='l=1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='l5/2 cos ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� lπ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='eB x2 − π ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='= − ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='(eB) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='√ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='2π4R2ω ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='∞ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='l=1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='l5/2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='Ci ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� lπ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='eB (µ + Mcω)2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='− Ci ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� lπ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='eB µ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='+Si ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� lπ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='eB (µ + Mcω)2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='− Si ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� lπ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='eB µ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='�� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='≃ (eB) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='8π5R2ω ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='∞ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='l=1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='l7/2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='sin ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� lπ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='eBµ2 − π ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='µ2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='− sin ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� lπ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='eB(µ + Mcω)2 − π ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='(µ + Mcω)2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='(38) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='where Ci(z) and Si(z) are cosine and sine integrals and the last step follows from their ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='asymptotic forms for z ≫ 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' � � � � � Si(z) ≈ π 2 − cos z z Ci(z) ≈ sin z z (39) are employed in the last step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' If the maximum rotation energy Mcω dominates, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Mcω >> µ, the second term of (38) can be dropped and we have PdHvA ≃ (eB) 5 2 8π5µ2R2ω ∞ � l=1 1 l7/2 sin � lπ eB µ2 − π 4 � (40) and the uncertainty of Mc does not contribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Numerical Estimates As pointed out in the introduction, the rotation will lift the degeneracy of states within each Landau level and thereby reduce the de Haas - van Alphen oscillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' In this section, we shall estimate the amount of reduction using the parameters appropriate for two realistic rotating ultra-relativistic fermion system in a magnetic field, the quark matter core and a QGP droplet at high baryon density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Since the Fermi gas approximation of these two system tends to be poor and the condition of the latter syetem is highly transient, we are not attempting to model the two system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The signifinace of our result below is only in the sense of order of 9 magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' For the ultra-relativistic system, we shall use mπ = 130MeV as the scale of the chemical potential and temperature and m2 π = 1014G as the scale of the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The estimate of the impact of the de Haas - van Alphen effect in a non-relativistic fermion system is deferred to the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The quark matter core of a neutron star μ2=10mπ 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='5×10-12 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ×10-12 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ×10-13 0 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ×10-13 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ×10-12 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='5×10-12 eB/mπ 2 PdHvA Neutron Star ωR = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='06 ωR = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='045 ωR = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='03 ωR = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='015 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The oscillatory term of pressure P1 as a function of magnetic field eB m2π .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Here, mπ = 140MeV, R = 1km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The radius of a neutron star is of the order of 10km and we assume a quark matter core made of light flavors of smaller radius R with a chemical potential of several hundreds of MeV, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' few times of pion’s rest energy, mπ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The magnetic field inside a neutron star can reach as high as 1015G, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='4×10−3m2 π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' For the fastest spinning neutron star, PSR J1748-2446ad, the frequency is 716Hz and the linear speed at the boundary of the core is v ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='015 (in the unit of the speed of light).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Consequently µ Mcω = µ mπ m2 π eB · 10−16 R(km)v << 1 (41) PdHvA PdHvA∥ω=0 ∼ 2 µRv ≃ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='86 × 10−16 µ(MeV)R(km)v (42) for a typical neutron star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The approximation (40) is valid and we estimate PdHvA PdHvA∥ω=0 ∼ 2 µRv ≃ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='86 × 10−16 µ(MeV)R(km)v (43) leading to huge suppression of dHvA oscillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The thermodynamic pressure at µ2 = 10m2 π and zero temperature versus magnetic field 0 < eB < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='01m2 π is plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 1 for several linear speeds at the boundary of the rotating quark matter core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' As a benchmark, the thermodynamic pressure in the absence of rotation is 10 ω=0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0 150000 100000 50000 0 50000 100000 150000 eB/mπ 2 PdHvA μ2 = 20 mπ2 μ2 = 15 mπ2 μ2 = 10 mπ2 μ2 = 5 mπ2 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The oscillatory term of pressure P1 as a function of magnetic field eB m2π .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Here, ω = 0 and T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The parameters underlying both figures satisfy the approximation condition (30) for the analytic expressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The effect is suppressed by 17 order of magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' A cold and dense QGP droplet μ2=10mπ 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0 150000 100000 50000 0 50000 100000 150000 eB/mπ 2 PdHvA R = 10 fm ωR = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='03 ωR = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='02 ωR = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='01 ωR = 0 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The oscillatory term of pressure P1 as a function of magnetic field eB m2π .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Here, we fix the chemical potential µ2 = 10m2 π and the radius is R = 10fm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The suppression of dHvA in a neutron star may be attributed to its large size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Let us switch to a cold and dense QGP droplet where the suppression of dHvA oscillation with the angular velocity becomes modest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The dHvA term of the thermodynamic pressure of eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (38) for R = 10fm versus the magnetic field at fixed chemical potential and temperature and is plotted for several angular velocity including ω = 0 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The same equation at fixed chemical potential and a nonzero angular velocity is plotted for several temperatures in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The dHvA without rotation, eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (36) at the same chemical potential and the same set of tempertatures is plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 5 for reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Notice that the suppression of dHvA with temperature becomes milder with ω ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The selection of the size, chemical potential and the magnetic field is 11 μ2=20mπ 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='32 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='34 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='38 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='40 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='5×10-11 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ×10-11 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ×10-120 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ×10-12 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ×10-11 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='5× 10-11 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ×10-11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='15 eB/mπ 2 PdHvA R = 10 fm T = 56 MeV T = 54 MeV T = 52 MeV T = 50 MeV FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The oscillatory term of pressure P1 (eB/m2π)30 as a function of magnetic field eB m2π .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Here, we fix the chemical potential µ2 = 10m2 π, v = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='01 and the radius is R = 10fm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' μ2=20 mπ 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='85 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='90 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='95 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ×10-9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ×10-9 0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ×10-9 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ×10-9 eB/mπ 2 PdHvA ω = 0 T = 56 MeV T = 54 MeV T = 52 MeV T = 50 MeV FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The oscillatory term of pressure P1 (eB/m2π)30 as a function of magnetic field eB m2π .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Here, we fix the chemical potential µ2 = 10m2 π, and ω = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' motivated by the conditions of the current heavy ion collisions in RHIC and LHC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' While the RHIC STAR fixed target experiment is expected to generate QGP of lower energy and higher bayon density, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=', closer to the density axis of the QCD phase diagram, there may still be a gap to meet the condition of the cold and dense QGP described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Even it did, the rapid expansion would hinder the observability of the effect because of non-equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' So our discussions here are highly speculative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' NON RELATIVISTIC FERMI GAS The Hamiltonin of a non-relativistic electron reads H = − 1 2me (⃗∇ − ie ⃗A)2 + 1 2σzωB (44) 12 with the vector potential ⃗A = 1 2Bˆz × ⃗r, (45) where ωB = eB/me is the cyclotron frequency and σz = diag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (1, −1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The spectrum in cylindrical coordinates can be found in many textbook of quantum mechnics and are given by Enmqσ = q2 2me + � n + m − |m| 2 + 1 2 � ωB + 1 2σωB (46) where q is the momentum along z-direction, n = 0, 1, 2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' are radial quantum number and m=0,±1, ±2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=',±Mc are the z-component of the orbital angular momentum and σ = ± labels spin projections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The Landau levels correspond to m ≥ 0 and are labeled by n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The corresponding wave function reads ψnmqσ(⃗r) = � n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='eB 2π(n + |m|)!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='Lζ |m| 2 e− ζ 2L|m| n (ζ)ei(mφ+qz) (47) In a cylinder of finite radius, the thermodynamic approximation limits the azimuthal quantum number as (18), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' |m| < mc = [1 2eBR2] >> 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (48) with an uncertainty δmc = O(1) as in the ultra-relativistic case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Thermodynamic Pressure and dHvA For a free non-relativistic electron gas, the dHvA can be extracted using the same Poisson formula (22) as in most of the textbooks in solid state physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Here we adapt a more elegant approach via Mellin transformation [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The thermodynamic pressure of the electron gas in a rotating cylindrical volume of radius R and length Lz reads P = 1 πR2 � m Pm(ζm) (49) where Pm(ζm) = T Lz � n,q,σ ln � 1 + 1 ζm e−βEqnmσ � (50) with ω the angular velocity and ζm = e−β(µ+mω) (51) 13 The case of strong degeneracy corresponds to ζm << 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The Mellin transformation of the function Pm(ζ) with respect to ζ is given by Q(s) = � ∞ 0 dζζs−1Pm(ζ) = πT Lzs sin πs � n,q,σ e−sβ(Enmqσ− 1 2 σω) (52) for 0 < Res < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The last equality follows from an integration by part and the formula � ∞ 0 dx xs−1 x + 1 = π sin πs (53) For the same reason as in the relativistic case, the contribution from m < 0 is subleading in the thermodynamic approximation and we focus only on the branch m ≥ 0 of the spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' We have for m ≥ 0 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Contour integration [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Q(s) = πT Lzs sin πs � q e− sβq2 2me � n,σ e−(n+ 1 2)sβωB− 1 2 σsβ(ωB−ω) = πT λs3/2 sin πs cosh 1 2sβ(ωB − ω) sinh 1 2sβωB (54) where λ = � 2π/(mT) is the thermal wavelength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' It follows from the Mellin inversion formula that Pm(ζ) = � c+i∞ c−i∞ ds 2πiζ−sQ(s) (55) with 0 < c < 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The integrand on the complex s-plane consists of a branch cut running along the negative real axis, poles along both real and imaginary axes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' s = l s = 2lπT ωB i (56) 14 Im s 21元T wB Re swith l = 0, ±1, ±2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='. Closing the contour from the left as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='6 for ζ < 1, we find Pm(ζ) = Im(ζ) + IIm(ζ) (57) where Im is the integral around the branch cut and IIm stems from the poles along the imaginary axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The former contributes to the Landau diamagnetism and Pauli paramagnetism along with the Barnett effect and the latter gives rise to dHvA oscillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Summing up the residues of the poles within the contour,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' we end up with IIm(ζm) = 2T λ � ωB 2πT ∞ � l=1 1 l3/2csch2lπ2T ωB cos lπω ωB cos �2lπ(µ + mω) ωB − π 4 � (58) Summing up the orbital angular momentum,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' we obtain that PdHvA = 1 πR2 mc � m=0 IIm = −T(meωB)1/2 π2R2 ∞ � l=1 cos lπω ωB sin � 2lπµ ωB − lπω ωB − π 4 � − sin � 2lπµ ωB + lπω ωB − π 4 + 2lπmcω ωB � l3/2 sinh 2lπ2T ωB sin lπω ωB (59) Without rotation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ω = 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' the well-known dHvA formula PdHvA|ω=0 = −T(meωB)3/2 2π2 ∞ � l=1 1 l3/2csch2lπ2T ωB cos �2lπµ ωB − π 4 � (60) emerges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' At zero temperature, eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (59) becomes PdHvA|T=0 = −(meωB)3/2 4π4meR2 ∞ � l=1 cos lπω ωB sin � 2lπµ ωB + lπω ωB − π 4 + lπmeωR2� − sin � 2lπµ ωB − lπω ωB − π 4 � l5/2 sin lπω ωB ≃ − (meωB)5/2 4π5m2 eωR2 ∞ � l=1 1 l7/2 � sin �2lπµ ωB − π 4 + 2lπmcω ωB � − sin �2lπµ ωB − π 4 �� (61) where the approximation ω << ωB is made for the typical parameters in condensed matter physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' This expression is to be compared with the zero temperature limit of (62), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' PdHvA|ω=0 = −(meωB)5/2 4π4 ∞ � l=1 1 l5/2 cos �2lπµ ωB − π 4 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (62) At this point, it is interesting to compare the non-relativistic dHvA and the ultra-relativistic dHvA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' As shown in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (46), given q and σ, the non-relativistic Landau levels (m>0) are equally spaced while the spacing between successive ultra-relativistic Landau levels in the upper equation of (8) decreases with the label n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Since the dHvA is sensitive to the energy levels around the chemical potential µ, the amplitude of the oscillation is expected to be independent 15 of µ in the non-relativistic case but decreases with µ in the ultra-relativistic case as reflected in the large µ suppression by sinh 2lπ2Tµ eB of (36) in the latter case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' When rotation is turned on, the effective chemical potential increases with the angular momentum quantum number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Consequently, the non-relativistic dHvA appears less vulnerable than the ultra-relativistic one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Numerical Estimates The electron gas in a good metal at room temperature, T ∼ 1/40eV can be well approximated by a free Fermi in the strong degeneracy limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The chemical potential is of 1 ∼ 10eV, which makes µ/T ∼ 40 ∼ 400 >> 1 and the zero temperature approximation works well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' For a magnetic field up to few Tesla’s and an angular velocity is Hz, we have ω/ωB ≃ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='57 × 10−12 ω(Hz) B(Tesla) (63) justifying the approximation made in the (61) for mechanical rotation achievable in laboratory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The same condition also makes the contribution of the uncertainty in the angular momentum cutoff mc to the phase of the oscillation in (59) and (61) negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The dHvA oscillation is expected to be significantly reduced when the largest rotation energy mcω within a Landau level exceeds the spacing between successive levels, ωB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' With R in cm, the linear velocity of the corcumference v = ωR in terms of cm/s, it follows from (48) that mcω ωB ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='43Rv, (64) independent of the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ω = 0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00000 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00002 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00004 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00006 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00008 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0004 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0003 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0002 B(T) PdHvA μ = 7 eV μ = 5 eV μ = 3 eV μ = 1 eV FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The oscillatory term of non-relativistic pressure P1 as a function of magnetic field B when T = 0 and ω = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 16 ωR = 2 cm/s 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00000 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00002 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00004 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00006 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00008 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00005 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00005 B(T) PdHvA R = 1 cm μ = 7 eV μ = 5 eV μ = 3 eV μ = 1 eV FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The oscillatory term of non-relativistic pressure P1 as a function of magnetic field B when T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Here, we fix ωR = 2cm/s and R = 1 cm .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' μ = 5 eV 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00000 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00002 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00004 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00006 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00008 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='00010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0003 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='0002 B(T) PdHvA R = 1 cm ωR = 6 cm/s ωR= 4 cm/s ωR = 2 cm/s ωR = 0 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The oscillatory term of non-relativistic pressure P1 as a function of magnetic field B when T = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Here, we fix the chemical potential µ = 5eV and the radius is R = 1cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The dHvA term of the thermodynamic pressure of a strongly degenerate electron gas versus magnetic field for a long cylinder of radius R = 1cm at T = 0 is plotted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 7, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 8 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The magnetic field varies in a small neighborhood of 1T and the angular velocity is taken such that RHS of (64) is of order one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The dHvA effect without rotation, eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (62), for different chemical potentials is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 7 sas benchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The parallel setup for ωR = 2cm/s, eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (61), is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 8 with similar profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' More important is Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 9 where dHvA at different ωR is displayed and the suppression of the oscillation by rotation is evident.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' CONCLUDING REMARKS Let us recaptulate what we presented in preceding sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' We examined the robustness of the de Haas-van Alphen effect in a strongly degenerate Fermi gas under rotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' We 17 derived the formula for dHvA oscillation in an long cylinder rotating about its axis in the ultra-relativistic limit and non-relativistic limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' As the macroscopic degeneracy of Landau levels is offset by rotation energy of states of different angular momentum within each Landau level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The amplitude of the scillation is reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The amount of reduction depends on the angular velocity ω and the radius of the cylinder R and the oscillation is expected to become insignificant for sufficiently large ω and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The ultra-relativistic dHvA appear more vulnerable than the non-relativistic one because of decreasing Landau level spacing with energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Applying the ultra-relativistic formula to estimate dHvA with typical parameters of a neutron star, and with typical parameters of a cold and dense QGP droplet, we noted that the dHvA oscillation is completely suppressed in the former case and remains in the latter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' The non-relativistic formula, on the other hand showed that for a typical electron gas in a good metal, the variation of dHvA oscillation with angular velocity appears detectable, via magnetization and/or magnetic susceptibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' As self-criticism, our approximation of the finite size effect by introducing the maximum angular momentum within a Landau level in (18) and (48) may be crude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Limited by the analytical tractability, the cylindrical shape of the system is not suitable to model a neutron star or a QGP droplet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Though the effect is expected to remain for a Fermi liquid, the strong correlation in quark matter may modify significantly the quantitative prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' In this sense, our result is very preliminary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ACKNOWLEDGMENTS We thank Ren-Hong Fang for fruitful discussions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' This work is supported by the National Key Research and Development Program of China (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 2022YFA1604900).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' This work also is supported by the National Natural Science Foundation of China (NSFC) under Grant Nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 11735007, 11890711, 11890710, 12275104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Appendix A: Appendix For µ >> T, eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' (55) can be approximated as IIlM ≃ 1 2iπ2l � eB lπ � µM 0 dqe−i lπ eB q2φ �� lπ eB q � = eB 2iπ3l2J (A1) 18 where J = � K 0 dxe−ix2φ(x) = � K 0 dxe−ix2 � ∞ x dξeiξ2 (A2) with K = � lπ eBµM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Introducing ξ = xt, we find J = � K 0 dxe−ix2x � ∞ 1 dteit2x2 = 1 2i � ∞ 1 dteiK2(t2−1) − 1 t2 − 1 = −1 2K2 � ∞ 1 dteiK2(t2−1)t ln t − 1 t + 1 (A3) where the last equality follows from an integration by part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Introducing z = t2 − 1, we have J = −1 4K2 � ∞ 0 dzeiK2z ln √z + 1 − 1 √z + 1 + 1 (A4) If follows from the Jordan lemma that integration path can be rotated to the imaginary axis on the z− plane and we end up with J = − i 4K2 � ∞ 0 dye−K2y ln √1 + iy − 1 √1 + iy + 1 (A5) For K >> 1, we have J ≃ − i 4K2 � ∞ 0 dye−K2y ln iy 4 = i 2 � ln(2K) + 1 2γE � + π 8 (A6) This gives rise to RHS of (A1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [1] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Adamczyk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Global Λ hyperon polarization in nuclear collisions: evidence for the most vortical fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Nature, 548:62–65, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [2] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Abelev et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Global polarization measurement in Au+Au collisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' C, 76:024915, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [Erratum: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='C 95, 039906 (2017)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [3] Jaroslav Adam et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Global polarization of Λ hyperons in Au+Au collisions at √sNN = 200 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' C, 98:014910, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [4] Jaroslav Adam et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Polarization of Λ (¯Λ) hyperons along the beam direction in Au+Au collisions at √sNN = 200 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=', 123(13):132301, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [5] Jaroslav Adam et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Measurement of inclusive J/ψ polarization in p + p collisions at √s =200 GeV by the STAR experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' D, 102(9):092009, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [6] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Adam et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Global Polarization of Ξ and Ω Hyperons in Au+Au Collisions at √sNN = 200 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=', 126(16):162301, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 19 [7] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Abdallah et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Global Λ-hyperon polarization in Au+Au collisions at √sNN=3 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' C, 104(6):L061901, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [8] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Abdallah et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Search for the Chiral Magnetic Effect via Charge-Dependent Azimuthal Correlations Relative to Spectator and Participant Planes in Au+Au Collisions at √sNN = 200 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=', 128(9):092301, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [9] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Abdallah et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Pair invariant mass to isolate background in the search for the chiral magnetic effect in Au + Au collisions at √sNN=200 GeV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' C, 106(3):034908, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [10] Mohamed Abdallah et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Search for the chiral magnetic effect with isobar collisions at √sNN=200 GeV by the STAR Collaboration at the BNL Relativistic Heavy Ion Collider.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' C, 105(1):014901, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [11] Francesco Becattini, Jinfeng Liao, and Michael Lisa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Strongly Interacting Matter Under Rotation: An Introduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Lect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Notes Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=', 987:1–14, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [12] Hao-Lei Chen, Kenji Fukushima, Xu-Guang Huang, and Kazuya Mameda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Analogy between rotation and density for Dirac fermions in a magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' D, 93(10):104052, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [13] Kenji Fukushima, Takuya Shimazaki, and Lingxiao Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Mode decomposed chiral magnetic effect and rotating fermions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' D, 102(1):014045, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [14] Koichi Hattori and Yi Yin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Charge redistribution from anomalous magnetovorticity coupling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=', 117:152002, Oct 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [15] Yizhuang Liu and Ismail Zahed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rotating Dirac fermions in a magnetic field in 1+2 and 1+3 dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' D, 98(1):014017, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [16] Emil Mottola and Andrey V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Sadofyev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Chiral Waves on the Fermi-Dirac Sea: Quantum Superfluidity and the Axial Anomaly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' B, 966:115385, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [17] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Gonzalez Felipe, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Perez Martinez, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Perez Rojas, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Orsaria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Magnetized strange quark matter and magnetized strange quark stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' C, 77:015807, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [18] Chinatsu Watanabe, Naotaka Yoshinaga, and Shuichiro Ebata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Equations of State for Hadronic Matter and Mass-Radius Relations of Neutron Stars with Strong Magnetic Fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Universe, 8(1):48, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [19] Pétri Jérôme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Particle acceleration and radiation reaction in a strongly magnetised rotating dipole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=', 666:A5, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [20] Debarati Chatterjee, Jérôme Novak, and Micaela Oertel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Structure of ultra-magnetised neutron stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' A, 57(8):249, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [21] A Einstein and W de Haas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Verh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' deutsch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Ges, 17:152, 1915.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 20 [22] Samuel J Barnett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Gyromagnetic and electron-inertia effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Reviews of Modern Physics, 7(2):129, 1935.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [23] Samapan Bhadury, Wojciech Florkowski, Amaresh Jaiswal, Avdhesh Kumar, and Radoslaw Ryblewski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Relativistic Spin Magnetohydrodynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=', 129(19):192301, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [24] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' ¯Onuki.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Magnetic systems: De haas–van alphen studies of fermi surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' In K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Jürgen Buschow, Robert W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Cahn, Merton C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Flemings, Bernhard Ilschner, Edward J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Kramer, Subhash Mahajan, and Patrick Veyssière, editors, Encyclopedia of Materials: Science and Technology, pages 4964–4968.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Elsevier, Oxford, 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [25] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Jiang and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Van Giai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Magnetic susceptibility oscillation in neutron stars with the hadron- quark transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' AIP Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=', 865(1):256–261, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [26] Daniel Cangemi and Gerald V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Dunne.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Temperature expansions for magnetic systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Annals Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=', 249:582–602, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [27] Cheng Zhang, Ren-Hong Fang, Jian-Hua Gao, and De-Fu Hou.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Thermodynamics of chiral fermion system in a uniform magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' D, 102(5):056004, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [28] Ren-Hong Fang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Thermodynamics for a Rotating Chiral Fermion System in the Uniform Magnetic Field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Symmetry, 14(6):1106, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' [29] Huanwu Peng and Xishen Xu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Fundamentals of Theoretical Physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' Peking University Press, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} +page_content=' 21' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8NE1T4oBgHgl3EQfBwLj/content/2301.02857v1.pdf'} diff --git a/8NE2T4oBgHgl3EQflQeg/vector_store/index.faiss b/8NE2T4oBgHgl3EQflQeg/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..882a75b64b6be3b445f8f65e89d6e070ce937a50 --- /dev/null +++ b/8NE2T4oBgHgl3EQflQeg/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:74ab3b2bb647124d9dbfd84bb1a22984925e19554d4be7ba57029b99f7c33e6a +size 5177389 diff --git a/8dE4T4oBgHgl3EQf2w3D/content/tmp_files/2301.05301v1.pdf.txt b/8dE4T4oBgHgl3EQf2w3D/content/tmp_files/2301.05301v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..663f514754afa18a88d9ad3215edb348e13a69cd --- /dev/null +++ b/8dE4T4oBgHgl3EQf2w3D/content/tmp_files/2301.05301v1.pdf.txt @@ -0,0 +1,9125 @@ +A Minimal Formulation of Session Types +Alen Arslanagić1, Jorge A. Pérez1, and Dan Frumin1 +1University of Groningen, The Netherlands +January 16, 2023 +Abstract +Session types are a type-based approach to the verification of message-passing programs. +They specify communication structures essential for program correctness; a session type says +what and when should be exchanged through a channel. Central to session-typed languages are +sequencing constructs in types and processes that explicitly specify the order of actions in a +protocol. +In this paper we study session types without sequencing. The resulting framework of minimal +session types is arguably the simplest form of session types one could conceive. In the context +of a core process calculus with sessions and higher-order concurrency (abstraction-passing), we +establish two main technical results. First, we prove that every process P typable with standard +session types can be compiled down into a process D(P) typable with minimal session types. +Second, we prove that P and D(P) are behaviorally equivalent. These results indicate that +having sequencing constructs in processes and session types is convenient but redundant: only +sequentiality in processes is truly indispensable, as it can correctly codify sequentiality in types. +Our developments draw inspiration from work by Parrow on behavior-preserving decompo- +sitions of untyped processes. By casting Parrow’s results in the realm of typed processes, our +developments reveal a conceptually simple formulation of session types and a principled avenue +to the integration of session types into programming languages without sequencing in types. +1 +Introduction +Session types are a type-based approach to the verification of message-passing programs. A session +type specifies what and when should be exchanged through a channel. This makes session types a +useful tool to enforce safety and liveness properties related to communication correctness. Originated +in the realm of concurrency theory, session types have had a significant impact on the foundations of +programming languages [14], but also on their practice [1]. Our goal in this work is to understand to +what extent session types can admit simpler, more fundamental formulations. This foundational +question has concrete practical ramifications, as we discuss next. +In session-typed languages, sequencing constructs in types and processes specify the intended +structure of message-passing protocols. For example, in the session type S =?(int);?(int);!⟨bool⟩;end, +sequencing (denoted ‘;’) allows us to specify a protocol for a channel that first receives (?) two integers, +then sends (!) a boolean, and finally ends. As such, S could type a service that checks for integer +equality. Sequencing in types goes hand-in-hand with sequencing in processes, which is specified +using prefix constructs (denoted ‘.’). The π-calculus process P = s?(x1).s?(x2).s!⟨x1 = x2⟩.0 is an +implementation of the equality service: it first expects two values on name s, then outputs a boolean +on s, and finally stops. Thus, name s in P conforms to the session type S. Session types can also +specify sequencing within labeled choices and recursion; these typed constructs are also in close +match with their respective process expressions. +Session types have been originally developed as a typing discipline for π-calculus for the analysis +of message-passing protocols between exactly two parties [12]. Since then session types have been +extended in many directions. We find, for instance, multiparty session types [13], and extensions +1 +arXiv:2301.05301v1 [cs.PL] 12 Jan 2023 + +P = s?(x1).s?(x2).s!⟨x1 = x2⟩.0 +s : ?(int); ?(int); !⟨bool⟩; end +D(P) +c2?().s1?(x1).c3!⟨x1⟩ +∥ +c3?(y1).s2?(x2).c4!⟨y1, x2⟩ +∥ c4?(x1, x2).s3!⟨x1 = x2⟩.c5!⟨⟩ +s1 : ?(int); end +c2 : ?(); end +s2 : ?(int); end +c3 : ?(int); end +s3 : !⟨bool⟩; end +c4 : ?(int, int); end +Figure 1: The process decomposition, illustrated. Arrows in magenta indicate synchronizations +orchestrated by the decomposition D(P). +with dependent types, assertions, exceptions, and time (cf. [8, 14] for surveys). All these extensions +seek to address natural research questions on the expressivity and applicability of session types +theories. +Here we address a different, if opposite, question: is there a minimal formulation of session +types? This is an appealing question from a theoretical perspective, but seems particularly relevant +to the practice of session types: identifying the “core” of session types could enable their integration +in languages whose type systems do not have certain advanced constructs present in session types, +such as sequencing. For instance, the Go programming language offers primitive support for message- +passing concurrency; it comes with a static verification mechanism which can only enforce that +messages exchanged along channels correspond with their declared payload types—it cannot ensure +essential correctness properties associated with the ordering of messages and the structure of the +protocols. This observation has motivated the development of advanced static verification tools +based on session types for Go programs; see, e.g., [20, 19]. +This paper identifies and studies the properties of an elementary formulation of session types, +which we call minimal session types. Minimal session types are session types without sequencing. +That is, in session types such as ‘!⟨U⟩;S’ and ‘?(U);S’, we stipulate that S can only correspond to +end, the type of the terminated protocol. +Adopting minimal session types entails dispensing with sequencing, which is arguably the most +distinctive feature of session types. While this may appear as a far too drastic restriction, it turns out +that it is not: we show that for every process P typable under standard (non minimal) session types, +there is a decomposition of P, denoted D(P), a process that codifies the sequencing information +given by the session types (protocols) of P using additional synchronizations, extracted from its +protocols. Figure 1 illustrates the key idea of the decomposition using the process P and session +type S motivated above. Because P contains three actions in sequence (as stipulated by S), its +decomposition D(P) consists of three processes in parallel—each of them implementing one action +of P—as well as of mechanisms for orchestrating these parallel processes: the synchronizations on +names c2, . . . , c5 ensure that the sequencing in P is preserved and that received names are properly +propagated. These three parallel processes are typable with minimal session types (in the figure, +they are given below each process), which are obtained by suitably “slicing” S. +Our main finding is that D(P) satisfies two important properties: first, it is well-typed using +minimal session types (static correctness); second, it is behaviorally equivalent to P (dynamic +correctness). +These properties ensure that having sequencing in both types and processes is +convenient but redundant: only sequencing at the level of processes is truly indispensable. +2 + +The definition of D(P) is interesting on its own, as it draws inspiration from a known result by +Parrow [21], who showed that any untyped π-calculus process can be decomposed as a collection of +trio processes, i.e., processes with at most three nested prefixes [21]. +The question of how to relate session types with other type systems has attracted interest in the +past. Session types have been encoded into, for instance, generic types [9] and linear types [7, 5, 6]. As +such, these prior studies concern the relative expressiveness of session types, where the expressivity of +session types stands with respect to that of some other type system. In sharp contrast, we study the +absolute expressiveness of session types: how session types can be explained in terms of themselves. +To our knowledge, this is the first study of its kind. +Session types have been developed on top of different process languages (mainly, dialects of +the π-calculus), and so choosing the target language for minimal session types is an important +decision in our developments. In this paper, our target language is HO, the core process calculus for +session-based concurrency studied by Kouzapas et al. [17, 18]. HO is a very small language, which +only supports passing of abstractions (i.e., functions from names to processes) and lacks name-passing +and recursion. Nonetheless, HO is very expressive, because both features can be encoded in HO +in a fully abstract way. Moreover, HO has a well-developed theory of behavioral equivalences [18]. +The combination of minimal number of features and expressivity makes HO an excellent candidate +for studying a minimal formulation of session types. Indeed, as we will see, several aspects of our +decomposition take advantage of the higher-order nature of HO. Being a higher-order language, HO +is very different from the (untyped, first-order) π-calculus considered by Parrow [21]. Therefore, our +technical results arise in a context very different from Parrow’s. +Contributions & Outline. +In summary, in this paper we present the following contributions: +1. We identify the class of minimal session types (MST) as a simple fragment of standard session +types for HO without sequencing that retains its absolute expressiveness (Definition 3.1). +2. We show how to decompose standard session types into minimal session types, and how to +decompose processes typable with standard session types into processes typable with minimal +session types. This is a result of static correctness (Theorem 3.1). +3. We show that the decomposition of a process is behaviorally equivalent to the original process. +This is a result of dynamic correctness, formalized in terms of MST bisimulations, a typed +behavioral equivalence that we introduce here (Theorem 4.1). +4. We develop optimizations and extensions of our decomposition that bear witness to its +robustness. +The rest of the paper is organized as follows. In Section 2 we recall the preliminaries on the session +type system for HO, which is the core process calculus for session-based concurrency on which we +base our developments. In Section 3 we present minimal session types, and the decomposition +of well-typed HO processes into minimal session types processes, accompanied by explanations +and examples. In Section 4 we show the correctness of the decomposition, by establishing an +MST bisimulation between an HO process and its decomposition. In Section 5 we examine two +optimizations of the decomposition that are enabled by the higher-order nature of our setting. In +Section 6 we discuss extensions of our approach to consider constructs for branching and selection. +Finally, in Section 7 we elaborate further on related work and in Section 8 we present some closing +remarks. The appendix contains omitted definitions and proofs. +Differences with the conference version. +An earlier version of this paper was presented at +ECOOP 2019 [3]. The current paper revises the conference version, includes further examples, and +incorporates a major addition: Section 4 on dynamic correctness, including the notion of an MST +bisimulation and the constructed bisimulation relation, is completely new to this presentation. +3 + +Colors. +Throughout the paper we use different colors (such as pink and green) to improve +readability. However, the usage of colors is not indispensable, and the paper can be followed in +black-and-white. +2 +The Source Language +We start by recalling the syntax, semantics, and type system for HO, the higher-order process +calculus for session-based concurrency studied by Kouzapas et al. [17, 18]. Our presentation of HO +follows the aforementioned papers, which concern definitions and results for HOπ, the super-calculus +of HO with name-passing, abstraction-passing, and recursion. +HO is arguably the simplest language for session types: it supports passing of abstractions +(functions from names to processes) but does not support name-passing nor process recursion. Still, +HO is very expressive: it can encode name-passing, recursion, and polyadic communication via +type-preserving encodings that are fully-abstract with respect to contextual equivalence [17]. +2.1 +Syntax and Semantics +Definition 2.1 (HO processes). The syntax of names, variables, values, and HO processes is defined +as follows: +n, m ::= a, b | s, s +u, w ::= n | x, y, z +V, W ::= x, y, z | λx. P +P, Q ::= u!⟨V ⟩.P | u?(x).P | V u | P | Q | (ν n) P | 0 +We use a, b, c, . . . to range over shared names, and s, s, . . . to range over session names. Shared +names are used for unrestricted, non-deterministic interactions; session names are used for linear, +deterministic interactions. We write n, m to denote session or shared names, and assume that the +sets of session and shared names are disjoint. The dual of a name n is denoted n; we define s = s +and a = a, i.e., duality is only relevant for session names. Variables are denoted with x, y, z, . . . . +An abstraction λx. P is a process P with parameter x. Values V, W, . . . include variables and +abstractions, but not names. +Process V u is the application which substitutes name u on abstraction V . Constructs for inaction +0, parallel composition P1 | P2, and name restriction (ν n) P are standard. HO lacks name-passing +and recursion, but they are expressible in the language (see Example 2.1 below). +To enhance readability, we often omit trailing 0’s, so we write, e.g., u!⟨V ⟩ instead of u!⟨V ⟩.0. +Also, we write u!⟨⟩.P and u?().P whenever the exchanged value is not relevant (cf. Remark 3.2). +Restriction for shared names (ν a) P is as usual; session name restriction (ν s) P simultaneously +binds session names s and s in P. Functions fv(P), fn(P), and fs(P) denote, respectively, the +sets of free variables, names, and session names in P, and are defined as expected. If fv(P) = ∅, +we call P closed. We write P{u/y} (resp., P{V/y}) for the capture-avoiding substitution of name +u (resp., value V ) for y in process P. We identify processes up to consistent renaming of bound +names, writing ≡α for this congruence. We shall rely on Barendregt’s variable convention, under +which free and bound names are different in every mathematical context. +The operational semantics of HO is defined in terms of a reduction relation, denoted −→. +Reduction is closed under structural congruence, denoted ≡, which is defined as the smallest +congruence on processes such that: +P | 0 ≡ P +P1 | P2 ≡ P2 | P1 +P1 | (P2 | P3) ≡ (P1 | P2) | P3 +(ν n) 0 ≡ 0 +P | (ν n) Q ≡ (ν n) (P | Q) (n /∈ fn(P)) +P ≡ Q if P ≡α Q +We assume the expected extension of ≡ to values V . The reduction relation expresses the behavior +4 + +t!⟨⌜˜u⌝⟩.P ≜ t!⟨λz.z?(x).(x ˜u)⟩.P +t?(⌜˜x⌝).Q ≜ t?(y). +� +(ν z) (y z | z!⟨λ˜x.Q⟩) +� +⌜�S⌝ ≜ (?(��S�⊸⋄);end)⊸⋄ +⌜⟨�S⟩⌝ ≜ (?(⟨��S�⟩⊸⋄);end)⊸⋄ +⌜ �C ⊸⋄⌝ ≜ � �C�⊸⋄ +⌜ �C →⋄⌝ ≜ � �C�→⋄ +�!⟨U⟩;S� ≜ !⟨⌜U⌝⟩;�S� +�?(U);S� ≜ ?(⌜U⌝);�S� +�C1, . . . , Cn� ≜ �C1�, . . . , �Cn� +Figure 2: Encoding name passing in HO +of processes; it is defined as follows: +(λx. P) u −→ P{u/x} +[App] +n!⟨V ⟩.P | n?(x).Q −→ P | Q{V/x} +[Pass] +P −→ P ′ ⇒ (ν n) P −→ (ν n) P ′ +[Res] +P −→ P ′ ⇒ P | Q −→ P ′ | Q +[Par] +P ≡ Q −→ Q′ ≡ P ′ ⇒ P −→ P ′ +[Cong] +Rule [App] defines name application (β-reduction). Rule [Pass] defines a shared or session interaction, +depending on the nature of n. Other rules are standard π-calculus rules. We write −→k for a k-step +reduction, and −→∗ for the reflexive, transitive closure of −→. +We illustrate HO processes and their semantics by means of an example. +Example 2.1 (Encoding Name-Passing). The HO calculus lacks the name-passing primitives of +HOπ. Hence, it cannot express reductions of the form +n!⟨m⟩.P | n?(x).Q −→ P | Q{m/x} +(1) +Fortunately, name-passing can be encoded in HO in a fully-abstract way: as shown in [17], one can +use abstraction passing to “pack” a name. To this end, Figure 2 defines the required syntactic sugar, +at the level of processes and types. Then, the reduction (1) can be mimicked as +n!⟨⌜m⌝⟩.P | n?(⌜x⌝).Q = n! +� +λz. z?(x).(x m) +� +.P | n?(y).(ν s)(y s | s!⟨λx. Q⟩) +−→ P | (ν s)(λz. z?(x).(x m) s | s!⟨λx. Q⟩) +−→ P | (ν s)(s?(x).(x m) | s!⟨λx. Q⟩) +−→ P | (λx. Q) m +−→ P | Q{m/x} +◁ +Remark 2.1 (Polyadic Communication). HO as presented above allows only for monadic commu- +nication, i.e., the exchange of tuples of values with length 1. We will find it convenient to use HO +with polyadic communication, i.e., the exchange of tuples of values �V = (V1, . . . , Vk), with length +|�V | = k. We will use similar notation for tuples of names and variables, and we will use ϵ to denote +the empty tuple. +5 + +In HO, polyadicity appears in session synchronizations and applications, but not in synchroniza- +tions on shared names. This entails having the following reduction rules: +(λ�x. P) �u −→ P{�u/�x} +s!⟨�V ⟩.P | s?(�x).Q −→ P | Q{�V/�x} +where the simultaneous substitutions P{�u/�x} and P{�V/�x} are as expected. This polyadic HO can +be readily encoded into (monadic) HO [18]; for this reason, by a slight abuse of notation we will +often write HO when we actually mean “polyadic HO”. +We discuss two simple examples that illustrate how HO can implement mechanisms resembling +servers and forms of partial instantiation; these mechanisms shall come in handy later, when defining +the process decomposition in Section 3. +Example 2.2 (A Server of a Kind). Let Sa denote the process a?(x).(x r), which receives an +abstraction on the shared name a and then applies it to r. Consider the following process composition: +P = (ν r) (ν a) +� +a!⟨V ⟩.0 | a!⟨W⟩.0 | Sa | r?(x1).r?(x2).Q +� +V = λy. (y!⟨V ′⟩.Sa{y/r}) +W = λz. (z!⟨W ′⟩.Sa{z/r}) +where V ′ and W ′ are some unspecified shared values. In P, process Sa operates as a server that +provides r upon an invocation on a. Dually, the outputs on a are requests to this server. One +possible reduction sequence for P is the following: +P −→ (ν r) (ν a) +� +a!⟨W⟩.0 | V r | r?(x1).r?(x2).Q +� +−→ (ν r) (ν a) +� +a!⟨W⟩.0 | r!⟨V ′⟩.Sa | r?(x1).r?(x2).Q +� +−→ (ν r) (ν a) +� +a!⟨W⟩.0 | Sa | r?(x2).Q{V ′/x1} +� += P ′ +In this reduction sequence, the value V in the first request is instantiated with the name r by +consuming a copy of Sa available in P. However, a copy of the server Sa is restored through the +value V , after an communication on r. This way, in P ′ the exchange of W ′ on r can take place: +P ′ −→∗ (ν r) (ν a) +� +Sa | Q{V ′/x1}{W ′/x2} +� +Example 2.3 (Partial Instantiation). Let Sa and Sb be servers as defined in the previous example: +Sa = a?(x).(x r) +Sb = b?(x).(x v) +Further, let R be a process in which requests to Sa and Sb are nested within abstractions: +R = a! +� +λy. b!⟨λz. V (y, z)⟩ +� +Notice how the polyadic application ‘V (y, z)’ is enclosed in the innermost abstraction. Now consider +the following composition: +P = (ν a, b) R | Sa | Sb +The structure of R induces a form of partial instantiation for y, z, implemented by combining +synchronizations and β-reductions. To see this, let us inspect one possible reduction chain for P: +P −→ (ν b) (λy. b!⟨λz. V (y, z)⟩ r) | Sb +−→ (ν b) b!⟨λz. V (r, z)⟩ | Sb = P ′ +The first request of R, aimed to obtain name r, is realized by the first reduction, i.e., the communica- +tion with Sa on name a: the result is the application of the top-level abstraction to r. Subsequently, +the application step substitutes y with r. Hence, in P ′, names in the nested application are only +partially instantiated: at this point, we have ‘V (r, z)’. +Process P ′ can then execute the same steps to instantiate z with name v by interacting with Sb. +After two reductions, we obtain the fully instantiated application V (r, v): +P ′ −→ λz. V (r, z) v −→ V (r, v) +6 + +2.2 +Session Types for HO +We give essential definitions and properties for the session type system for HO, following [18]. +Definition 2.2 (Session Types for HO). Let us write ⋄ to denote the process type. The syntax of +value types U, channel types C, and session types S for HO is defined as follows: +U ::= C →⋄ | C ⊸⋄ +C ::= S | ⟨U⟩ +S ::= !⟨U⟩;S | ?(U);S | µt.S | t | end +As we have seen, HO only admits the exchange of abstractions; accordingly, value types include +C →⋄ and C ⊸⋄, which denote shared and linear higher-order types, respectively. Channel types +include session types and the shared types ⟨U⟩. +Session types follow the standard binary session type syntax [12], in which sequencing specifies +communication structures. This way, the output type !⟨U⟩;S describes a session in which first a value +of type U is sent, and then the session proceeds as S. Dually, the input type ?(U);S describes a +session in which first a value of type U is received, and then the session proceeds as S. In examples, +we often assume basic types (such as int, bool, str) are exchanged in communications. Session types +also include recursive types µt.S, in which the variable t is assumed to occur guarded in S, i.e., types +such as µt.t are not allowed. In most cases, recursive types will be tail-recursive, although instances +of non-tail-recursive session types will also be relevant (cf. Example 3.3). Finally, type end is the +type of the terminated protocol. +Notation 2.1. As mentioned in the introduction, we shall study session types in which the continu- +ation S in !⟨U⟩;S and ?(U);S is always end. Given this, we may sometimes omit trailing end’s and +write !⟨U⟩ and ?(U) rather than !⟨U⟩;end and ?(U);end, respectively. +In theories of session types duality is a key notion: implementations derived from dual session +types will respect their protocols at run-time, avoiding communication errors. Intuitively, duality is +obtained by exchanging ! by ? (and vice versa), including the fixed point construction. We write +S dual T if session types S and T are dual according to this intuition; the formal definition is +coinductive, and given in [18] (see also [10]). +We consider shared, linear, and session environments, denoted Γ, Λ, and ∆, resp.: +Γ ::= ∅ | Γ, x : C →⋄ | Γ, u : ⟨U⟩ +Λ ::= ∅ | Λ, x:C ⊸⋄ +∆ ::= ∅ | ∆, u:S +Γ maps variables and shared names to value types; Λ maps variables to linear higher-order types. +∆ maps session names to session types. While Γ admits weakening, contraction, and exchange +principles, both Λ and ∆ are only subject to exchange. The domains of Γ, Λ, and ∆ are assumed +pairwise distinct. We write ∆1 · ∆2 to denote the disjoint union of ∆1 and ∆2. +We write Γ\x to denote the environment obtained from Γ by removing the assignment x : C →⋄, +for some C. Notations ∆\u and Γ\�x are defined similarly and have the expected readings. With a +slight abuse of notation, given a tuple of variables �x, we sometimes write (Γ, ∆)(�x) to denote the +tuple of types assigned to the variables in �x by the environments Γ and ∆. +The typing judgements for values V and processes P are denoted +Γ; Λ; ∆ ⊢ V ▷ U +and +Γ; Λ; ∆ ⊢ P ▷ ⋄ +Figure 3 shows the typing rules; we briefly describe them and refer the reader to [18] for a full +account. The shared type C →⋄ is derived using Rule (Prom) only if the value has a linear type +with an empty linear environment. Rule (EProm) allows us to freely use a shared type variable as +linear. Abstraction values are typed with Rule (Abs). Application typing is governed by Rule (App): +the type C of an application name u must match the type of the application variable x (C ⊸⋄ or +7 + +(Sess) +Γ; ∅; {u : S} ⊢ u ▷ S +(Sh) +Γ, u : U; ∅; ∅ ⊢ u ▷ U +(LVar) +Γ; {x : C ⊸⋄}; ∅ ⊢ x ▷ C ⊸⋄ +(RVar) +Γ, X : ∆; ∅; ∆ ⊢ X ▷ ⋄ +(Abs) +Γ; Λ; ∆1 ⊢ P ▷ ⋄ +Γ; ∅; ∆2 ⊢ x ▷ C +Γ\x; Λ; ∆1\∆2 ⊢ λx. P ▷ C ⊸⋄ +(App) +Γ; Λ; ∆1 ⊢ V ▷ C ⇝⋄ +⇝ ∈ {⊸, →} +Γ; ∅; ∆2 ⊢ u ▷ C +Γ; Λ; ∆1, ∆2 ⊢ V u ▷ ⋄ +(Prom) +Γ; ∅; ∅ ⊢ V ▷ C ⊸⋄ +Γ; ∅; ∅ ⊢ V ▷ C →⋄ +(EProm) +Γ; Λ, x : C ⊸⋄; ∆ ⊢ P ▷ ⋄ +Γ, x : C →⋄; Λ; ∆ ⊢ P ▷ ⋄ +(End) +Γ; Λ; ∆ ⊢ P ▷ T +u ̸∈ dom(Γ, Λ, ∆) +Γ; Λ; ∆, u : end ⊢ P ▷ ⋄ +(Rec) +Γ, X : ∆; ∅; ∆ ⊢ P ▷ ⋄ +Γ; ∅; ∆ ⊢ µX.P ▷ ⋄ +(Par) +Γ; Λi; ∆i ⊢ Pi ▷ ⋄ +i = 1, 2 +Γ; Λ1, Λ2; ∆1, ∆2 ⊢ P1 | P2 ▷ ⋄ +(Nil) +Γ; ∅; ∅ ⊢ 0 ▷ ⋄ +(Req) +Γ; Λ; ∆1 ⊢ P ▷ ⋄ +Γ; ∅; ∅ ⊢ u ▷ ⟨U⟩ +Γ; ∅; ∆2 ⊢ V ▷ U +Γ; Λ; ∆1, ∆2 ⊢ u!⟨V ⟩.P ▷ ⋄ +(Acc) +Γ; Λ1; ∆1 ⊢ P ▷ ⋄ +Γ; ∅; ∅ ⊢ u ▷ ⟨U⟩ +Γ; Λ2; ∆2 ⊢ x ▷ U +Γ\x; Λ1\Λ2; ∆1\∆2 ⊢ u?(x).P ▷ ⋄ +(Send) +u : S ∈ ∆1, ∆2 +Γ; Λ1; ∆1 ⊢ P ▷ ⋄ +Γ; Λ2; ∆2 ⊢ V ▷ U +Γ; Λ1, Λ2; ((∆1, ∆2) \ u : S), u :!⟨U⟩;S ⊢ u!⟨V ⟩.P ▷ ⋄ +(Rcv) +Γ; Λ1; ∆1, u : S ⊢ P ▷ ⋄ +Γ; Λ2; ∆2 ⊢ x ▷ U +Γ\x; Λ1\Λ2; ∆1\∆2, u :?(U);S ⊢ u?(x).P ▷ ⋄ +(ResS) +Γ; Λ; ∆, s : S1, s : S2 ⊢ P ▷ ⋄ +S1 dual S2 +Γ; Λ; ∆ ⊢ (ν s) P ▷ ⋄ +(Res) +Γ, a : ⟨S⟩; Λ; ∆ ⊢ P ▷ ⋄ +Γ; Λ; ∆ ⊢ (ν a) P ▷ ⋄ +Figure 3: Typing Rules for HO. +C →⋄). Rules (Req) and (Acc) type interaction along shared names; the type of the sent/received +object V (i.e., U) should match the type of the subject s (⟨U⟩). In Rule (Send), the type U of the +value V should appear as a prefix in the session type !⟨U⟩;S of u. Rule (Rcv) is its dual. +To state type soundness, we require two auxiliary definitions on session environments. First, +a session environment ∆ is balanced (written balanced(∆)) if whenever s : S1, s : S2 ∈ ∆ then +S1 dual S2. Second, we define the reduction relation −→ on session environments as: +∆, s :!⟨U⟩;S1, s :?(U);S2 +−→ +∆, s : S1, s : S2 +∆, s : ⊕{li : Si}i∈I, s : &{li : S′ +i}i∈I +−→ +∆, s : Sk, s : S′ +k (k ∈ I) +Theorem 2.1 (Type Soundness [18]). Suppose Γ; ∅; ∆ ⊢ P ▷ ⋄ with balanced(∆). Then P −→ P ′ +implies Γ; ∅; ∆′ ⊢ P ′ ▷ ⋄ and ∆ = ∆′ or ∆ −→ ∆′ with balanced(∆′). +8 + +Remark 2.2 (Typed Polyadic Communication). When using processes with polyadic communication +(cf. Remark 2.1), we shall assume the extension of the type system defined in [18]. +Example 2.4 (Typing name-passing constructs). In Example 2.1 we recalled how to encode name- +passing constructs in HO; now we show that this translation is typed. Following the name-passing +encoding from [17] we define a syntactic sugar for types. The following typing rules for name-passing +are derivable: +(SendN) +Γ; Λ1; ∆1 ⊢ P ▷ ⋄ +Γ; Λ2; ∆2 ⊢ �b ▷ �C +Γ; Λ1, Λ2; ∆1, ∆2, t :!⟨⌜ �C⌝⟩;end ⊢ t!⟨⌜�b⌝⟩.P ▷ ⋄ +(RcvN) +Γ; Λ1; ∆1 ⊢ P ▷ ⋄ +Γ; Λ2; ∆2 ⊢ �x ▷ �C +Γ\x; Λ1\Λ2; ∆1\∆2, t :?(⌜ �C⌝);end ⊢ t?(⌜�x⌝).P ▷ ⋄ +Example 2.5 (Typing Recursive Servers). Here we show how to type the processes from Example 2.2. +Let us define: +T = µt.!⟨U⟩;t +C = ⟨T ⊸⋄⟩ +where U is some value type. We recall process P from Example 2.2 with the additional typing +information on bound names r and a: +P = (ν r : T) (ν a : C) +� +a!⟨V ⟩.0 | a!⟨W⟩.0 | Sa | r?(x1).r?(x2).Q +� +V = λy. (y!⟨V ′⟩.Sa{y/r}) +W = λz. (z!⟨W ′⟩.Sa{z/r}) +where Sa stands for a?(x).(x r). Let us assume there is a shared environment Γ under which V ′ and +W ′ implement type U: +Γ; ∅; ∅ ⊢ V ′ ▷ U +(2) +Γ; ∅; ∅ ⊢ W ′ ▷ U +(3) +Also, we assume that process r?(x1).r?(x2).Q is well-typed under the following environments: +Γ, a : C; ∅; r : T ⊢ r?(x1).r?(x2).Q ▷ ⋄ +(4) +Under these assumptions, it holds that the body of process P correctly implements name a with +type C, i.e., +Γ; ∅; r : T ⊢ (ν a : C) +� +a!⟨V ⟩.0 | a!⟨W⟩.0 | Sa +� +▷ ⋄ +We detail the corresponding typing derivations: +(LVar) Γ, a : C; x : T ⊸⋄; ∅ ⊢ x ▷ T ⊸⋄ +(Sess) Γ, a : C; ∅; y : T ⊢ y ▷ T +(App) +Γ, a : C; x : T ⊸⋄; y : T ⊢ x y ▷ ⋄ +(5) +(5) +(Sh) +Γ, a : C; ∅; ∅ ⊢ a ▷ ⟨T ⊸⋄⟩ +(LVar) Γ, a : C; x : T ⊸⋄; ∅ ⊢ x ▷ T ⊸⋄ +(Acc) +Γ, a : C; ∅; y : T ⊢ a?(x).(x y) ▷ ⋄ +(6) +(6) +(2) +(Send) +Γ, a : C; ∅; y : T ⊢ y!⟨V ′⟩.Sa{y/r} ▷ ⋄ +(Sess) +Γ, a : C; ∅; y : T ⊢ y ▷ T +(Abs) +Γ, a : C; ∅; ∅ ⊢ V ▷ T ⊸⋄ +(7) +(Nil) +Γ, a : C; ∅; ∅ ⊢ 0 ▷ ⋄ +(Sh) +Γ, a : C; ∅; ∅ ⊢ a ▷ ⟨T ⊸⋄⟩ +(7) +(Req) +Γ, a : C; ∅; ∅ ⊢ a!⟨V ⟩.0 ▷ ⋄ +(8) +9 + +In the following derivation tree the right-hand side is shown similarly to (8) using assumption (3) +instead of (2): +(8) +Γ, a : C; ∅; ∅ ⊢ a!⟨W⟩.0 ▷ ⋄ +(Par) +Γ, a : C; ∅; ∅ ⊢ a!⟨V ⟩.0 | a!⟨W⟩.0 ▷ ⋄ +(9) +Finally we have: +(9) +Γ, a : C; ∅; r : T ⊢ Sa ▷ ⋄ +(Par) +Γ, a : C; ∅; r : T ⊢ a!⟨V ⟩.0 | a!⟨W⟩.0 | Sa | r?(x1).r?(x2).Q ▷ ⋄ +(4) +(Par) +Γ, a : C; ∅; r : T, r : T ⊢ a!⟨V ⟩.0 | a!⟨W⟩.0 | Sa | r?(x1).r?(x2).Q ▷ ⋄ +(Res) +Γ; ∅; r : T, r : T ⊢ (ν a : C) +� +a!⟨V ⟩.0 | a!⟨W⟩.0 | Sa | r?(x1).r?(x2).Q +� +▷ ⋄ +(ResS) +Γ; ∅; ∅ ⊢ (ν r : T) (ν a : C) +� +a!⟨V ⟩.0 | a!⟨W⟩.0 | Sa | r?(x1).r?(x2).Q +� +▷ ⋄ +Above, we have omitted details of the right-hand side derivation; it the same as (6) with name y +substituted with r. +Example 2.6 (Typing Nested Abstractions). Here we show how to type process P from Example 2.3. +Let types C1 and C2 be defined as Ci = ⟨Si ⊸⋄⟩ where i ∈ {1, 2} and Si stands for a tail-recursive +type. For simplicity, we assume that value V has the following typing: +a : C1, b : C2; ∅; ∅ ⊢ V ▷ (S1, S2)⊸⋄ +(10) +The following holds: +∅; ∅; ∅ ⊢ (ν a : C1) (ν b : C2) R | Sa | Sb ▷ ⋄ +(11) +In the following typing derivations, we rely on the following two typing rules for polyadic elements; +they can be derived from monadic typing rules from Figure 3 (see Remark A.1 for details): +(PolySess) +Γ; ∅; �u : �S ⊢ �u ▷ �S +⇝∈ {⊸, →} +Γ; Λ; ∆1 ⊢ V ▷ �C ⇝ ⋄ +Γ; ∅; ∆2 ⊢ �u ▷ �C +(PolyApp) +Γ; Λ; ∆1, ∆2 ⊢ V �u +Now, we detail the typing derivations that show (11): +(10) +(PolySess) +a : C1, b : C2; ∅; y : S1, z : S2 ⊢ y, z ▷ S1, S2 +(PolyApp) +a : C1, b : C2; ∅; y : S1, z : S2 ⊢ V (y, z) ▷ ⋄ +(12) +(12) +(Sess) +a : C1, b : C2; ∅; z : S2 ⊢ z ▷ S2 +(Abs) +a : C1, b : C2; ∅; y : S1 ⊢ λz. V (y, z) ▷ S2 ⊸⋄ +(13) +(Nil) a : C1, b : C2; ∅; ∅ ⊢ 0 ▷ ⋄ +(Sh) a : C1, b : C2; ∅; ∅ ⊢ b ▷ ⟨S2 ⊸⋄⟩ +(13) +(Req) +a : C1, b : C2; ∅; y : S1 ⊢ b!⟨λz. V (y, z)⟩ ▷ ⋄ +(14) +(14) +(Sess) +a : C1, b : C2; ∅; y : S1 ⊢ y ▷ S1 +(Abs) +a : C1, b : C2; ∅; ∅ ⊢ λy. b!⟨λz. V (y, z)⟩ ▷ S1 ⊸⋄ +(15) +10 + +a : C1, b : C2; ∅; ∅ ⊢ 0 ▷ ⋄ +(Sh) a : C1, b : C2; ∅; ∅ ⊢ a ▷ ⟨S1 ⊸⋄⟩ +(15) +(Req) +a : C1, b : C2; ∅; ∅ ⊢ a! +� +λy. b!⟨λz. V (y, z)⟩ +� +▷ ⋄ +(16) +Finally we have: +(16) +a : C1, b : C2; ∅; ∅ ⊢ Sa ▷ ⋄ +(Par) +a : C1, b : C2; ∅; ∅ ⊢ R | Sa ▷ ⋄ +a : C1, b : C2; ∅; ∅ ⊢ Sb ▷ ⋄ +(Par) +a : C1, b : C2; ∅; ∅ ⊢ R | Sa | Sb ▷ ⋄ +(Res) +a : C1; ∅; ∅ ⊢ (ν b : C2) R | Sa | Sb ▷ ⋄ +(Res) +∅; ∅; ∅ ⊢ (ν a : C1) (ν b : C2) R | Sa | Sb ▷ ⋄ +In the above typing derivation, we remark that the judgments +a : C1, b : C2; ∅; ∅ ⊢ Sa ▷ ⋄ +(17) +a : C1, b : C2; ∅; ∅ ⊢ Sb ▷ ⋄ +(18) +are shown similarly as in (6) from Example 2.5. Indeed, to derive (17) reusing the derivation tree +from (6) we need to substitute y with r and then weaken the shared environment (6) with b : C2 +(see Lemma A.2). Similarly, by substituting a with b and y with r in the derivation tree (6) and +then by weakening the shared environment with a : C1 in its conclusion we can obtain (18). +Notation 2.2 (Type Annotations). We shall often annotate bound names and variables with their +respective type. We will write, e.g., (ν s : S) P to denote that the type of s in P is S. Similarly +for values: we shall write λu : C. P. Also, letting ⇝∈ {⊸, →}, we may write λu : C⇝. P to +denote that the value is linear (if ⇝=⊸) or shared (if ⇝=→). That is, we write λu : C⇝. P if +Γ; Λ; ∆ ⊢ λu. P ▷ C ⇝ ⋄, for some Γ, Λ, and ∆. +Having introduced the core session process language HO, we now move to detail its type-preserving +decomposition into minimal session types. +3 +Decomposing Session-Typed Processes +In this section we define minimal session types and present a decomposition of well-typed processes: +given a process P typable with (standard) session types, our decomposition returns a process denoted +D(P), typable with minimal session types. +The definition of D(P) follows Parrow’s trio processes for the π-calculus [21]. A trio process is a +process with at most three sequential prefixes. Roughly speaking, if P is a process with k sequential +actions, then D(P) will contain k trios running in parallel: each of them will enact exactly one +action from P. The decomposition is carefully designed to ensure that trios trigger each other by +preserving the sequencing in P. +This section is organized as follows. First, in Section 3.1, we use examples to discuss some key +ideas of the decomposition. Then, in Section 3.2, we give the full definitions of minimal session types +and the decomposition functions. We define decomposition functions for types G(−) and for processes +D(−). The former “slices” a session type S and returns a list of minimal session types, corresponding +to individual actions in S; the latter breaks down an HO process into a parallel composition of +processes. We demonstrate these notions on a number of examples in Section 3.3. Finally, in +Section 3.4 we establish the static correctness result (Theorem 3.1): if P is well-typed under session +types S1, . . . , Sn, then D(P) is typable using the minimal session types G(S1), . . . , G(Sn). The +issue of dynamic correctness, i.e., the operational correspondence between P and D(P), is treated +separately in Section 4. +Remark 3.1 (Color Convention). We use colors to differentiate the operations on processes (in pink) +and on types (in green). The usage of the colors is for visual aid only, and is not important for the +mathematical content of the presented material. +11 + +Source process P1: +P1 +P2 +P3 +0 +u :?(str) +u :?(int) +u :!⟨bool⟩ +Decomposed process D(P1): +Q1 +Q′ +1 +u1 :?(str) +∥ +Q2 +Q′ +2 +u2 :?(int) +∥ +Q3 +Q′ +3 +u3 :!⟨bool⟩ +∥ +Q4 +x : str +x : str, y : int +Figure 4: Our decomposition function D(−), illustrated. Nodes represent process states, ‘∥’ represents parallel +composition of processes, black arrows stand for actions, and red arrows indicate synchronizations that +preserve the sequentiality of the source process by activating trios and propagating (bound) values. +3.1 +Key Ideas +Consider a process P1 that implements the (standard) session type S =?(str);?(int);!⟨bool⟩;end along +name u. In process P1, name u is not a single-use resource; rather, it is used several times to +implement the communication actions in S; Figure 4 (top) graphically depicts the actions and the +corresponding states. +The decomposition D(P1) is illustrated in the bottom part of Figure 4: it is defined as the +parallel composition of four processes Qi (for i ∈ {1, . . . , 4}). Each process Q1, Q2, and Q3 mimic +one action of P1 on an indexed name ui, while Q4 simulates the termination of the session. This +way, a single name u in P1 is decomposed into a sequence of names u1, u2, u3 in D(P1). +The processes Q1, Q2, Q3, and Q4 are composed in parallel, but we would like to retain the same +sequentiality of actions on the channels ui as we have on the channel u. To that end, each process +Qi, with the exception of Q1, does not perform its designated action on ui until it gets activated by +the previous process. In turn, after Qi performs an action on ui it evolves to a state Q′ +i, which is +responsible for activating the next process Qi+1. In Figure 4, the activations are indicated by red +arrows. In general, the decomposition orchestrates the activation of sub-processes, following the +sequencing prescribed by the session types of the given process. Therefore, assuming a well-typed +source process, our decomposition codifies the sequentiality in session types into the process level. +The activation mechanism includes the propagation of values across sub-processes (cf. the labels +on red arrows). This establishes a flow of values from sub-processes binding them to those that +use them (i.e., it makes variable bindings explicit). For example, in P1, the Boolean value being +sent over as part of the session S might depend on the previously received string and integer values. +Therefore, both of those values have to be propagated to the process Q3, which is responsible for +sending out the Boolean. +In this example a single name u : S is decomposed into a sequence �u = (u1, . . . , un): each ui ∈ �u +is a single-use resource, as prescribed by its minimal session type. Such is the case for non-recursive +types S. When S is recursive, the situation is more interesting: each action of S can be repeated +many times, and therefore the names �u should be propagated across trios to enable potentially many +uses. As an example, consider the recursive session type S = µt.?(int);!⟨int⟩;t, in which an input and +an output actions are repeated indefinitely. Consider the following process +R1 = r?(z). +� �� � +T1 +r!⟨−z⟩. +� �� � +T2 +r?(z). +� �� � +T3 +r!⟨z⟩. +� �� � +T4 +V r +���� +T5 +which makes use of the channel r : S and where V has type S →⋄. Figure 5 (top) gives the first four +12 + +actions of R1 and the corresponding sates: the body of type S prescribes two actions on name r, +performed sequentially in R1 and R2; subsequent actions (enabled in R3 and R4) correspond to a +“new instance” of the body of S. +The decomposition D(R1), depicted in Figure 5 (bottom), generates a trio process for each prefix +in R1; we denote prefixes with their corresponding trios T1, . . . , T5. The type decomposition function +on types, G(−), slices S into two minimal tail-recursive types: M1 = µt.?(int);t and M2 = µt.!⟨int⟩;t. +In the recursive case, a key idea is that trios that mimic actions prescribed by a recursive session +types should reuse names, which should be propagated across trios. This way, for instance, trios +T1 and T3 mimic the same (input) action, and so they both should use the same name (r1). To +achieve this, we devise a mechanism that propagates names with tail-recursive types (such as (r1, r2)) +through the trios. These propagation actions are represented by blue arrows in Figure 5 (bottom). +In our example, T3 gathers the complete decomposition of names from preceding trios (r1, r2); it +mimics an input action on r1 and makes (r1, r2) available to future trios (i.e., T4 and T5). +Since the same tail-recursive names can be (re)used infinitely often, we propagate tail-recursive +names through the following process. All the names �r corresponding to the decomposition of a +tail-recursive name r are bound in the process +cr?(x).x �r, +which is similar to the servers discussed in Example 2.2. We call these processes recursive propagators, +and each tail-recursive name in the original process P has a dedicated propagator in D(P) on the +channel cr. Whenever a trio has to perform an action α(ri) on one of the decomposed tail-recursive +names (i.e., a decomposition of an input action ‘r?(y).’ or an output action ‘r!⟨V ⟩.’ on the name +r), it first has to request the name from the corresponding recursive propagator by performing an +output action cr! +� +N +� +, where value N is the abstraction +N = λ�z. α(zi). +� +ck+1!⟨ �w⟩ | cr?(x).x �z +� +. +A synchronization on cr will result in the reduction: +cr?(x).x �r | cr! +� +N +� +−→ α(ri). +� +ck+1!⟨ �w⟩ | cr?(x).x �r +� +. +The resulting process first simulates α(r) and subsequently reinstates the recursive propagator on cr, +for the benefit of the other trios requiring access to the names �r. See Examples 3.9 and 3.10 below +(Page 24) for further illustration of this method. +This decomposition strategy handles HO processes with recursive types which are simple and +contractive. That is, recursive types of the form µt.S, where the body S ̸= t does not itself contain +recursive types. Unless stated otherwise, we consider tail-recursive session types such as, e.g., +S = µt.?(int);?(bool);!⟨bool⟩;t. Non-tail-recursive session types such as µt.?(( �T, t)→⋄);end, used in +the fully-abstract encoding of HOπ into HO [17], can also be accommodated; see Example 3.3 below. +3.2 +The Decomposition +Here we formally present the decomposition of HO processes. We start introducing some preliminary +definitions, including the definition of an auxiliary function, called the breakdown function. +Following Parrow [21] we adopt some useful terminology and notation on trios. The context +of a trio is a tuple of variables �x, possibly empty, which makes variable bindings explicit. We use +a reserved set of propagator names (or simply propagators), denoted with ck, ck+1, . . ., to carry +contexts and trigger the subsequent trio. A process with less than three sequential prefixes is called +a degenerate trio. Also, a leading trio is the one that receives a context, performs an action, and +triggers the next trio; a control trio only activates other trios. +The breakdown function works on both processes and values. The breakdown of process P is +denoted by Bk +˜x +� +P +� +, where k is the index for the propagators ck, and �x is the context to be received +by the previous trio. Similarly, the breakdown of a value V is denoted by V˜x +� +V +� +. +13 + +Source process R1: +R1 +R2 +R3 +R4 +R5 +r :?(int) +r :!⟨int⟩ +r :?(int) +r :!⟨int⟩ +Decomposed process D(R1): +T1 +T ′ +1 +r1 : ?(int) +∥ +T2 +T ′ +2 +r2 : !⟨int⟩ +∥ +T3 +T ′ +3 +r1 :?(int) +∥ +T4 +T ′ +4 +r2 :!⟨int⟩ +∥ +T5 +r1,r2 +r1,r2 +r1,r2 +r1,r2 +Figure 5: Decomposition of processes with recursive session types, illustrated. Dashed blue arrows represent +the propagation of tail-recursive names (r1,r2) across trios. +3.2.1 +Minimal Session Types and Decomposing Types +We start by introducing minimal session types as a fragment of Definition 2.2: +Definition 3.1 (Minimal Session Types). The syntax of minimal session types for HO is defined as +follows: +U ::= �C →⋄ | �C ⊸⋄ +C ::= M | ⟨U⟩ +M ::= γ | !⟨�U⟩;γ | ?(�U);γ | µt.M +γ ::= end | t +The above definition is minimal in its use of sequencing, which is only present in recursive session +types such as µt.!⟨U⟩;t and µt.?(U);t—these are tail-recursive session types with exactly one session +prefix. Clearly, this minimal type structure induces a reduced set of typable HO processes. A type +system for HO based on minimal session types can be straightforwardly obtained by specializing the +definitions, typing rules, and results summarized in Section 2.2. We refer to HO processes and terms +typeable with minimal session types as MST processes and terms, respectively. +We now define how to “slice” a standard session type into a list of minimal session types. We +need the following auxiliary definition. +Definition 3.2 (Predicates on Types and Names). Let C be a channel type. +• We write tr(C) to indicate that C is a tail-recursive session type. +• Given u : C, we write lin(u) if a session type (i.e. C = S for some S) that is not tail recursive. +With a slight abuse of notation, we write tr(u) to mean u : C and tr(C) (and similarly for ¬tr(u)). +Definition 3.3 (Decomposing Session Types). Given the session, higher-order, and shared types of +Definition 2.2, the type decomposition function G(−) is defined using the auxiliary function R(−) as +in Figure 6. We write |G(S)| to denote the length of G(S) (and similarly for R(−)). +The decomposition is self-explanatory; intuitively, if a session type S contains k input/output actions, +the list G(S) will contain k minimal session types. For a tail recursive µt.S, G(µt.S) is a list of +minimal recursive session types, obtained using the auxiliary function R(−) on S: if S has k prefixes +then the list G(µt.S) will contain k minimal recursive session types. +We illustrate Definition 3.3 with three examples. +14 + +G(!⟨U⟩;S) = +� +!⟨G(U)⟩ +if S = end +!⟨G(U)⟩ , G(S) +otherwise +G(?(U);S) = +� +?(G(U)) +if S = end +?(G(U)) , G(S) +otherwise +G(µt.S) = +� +R(S) +if tr(µt.S) +µt.G(S) +if ¬tr(µt.S) and G(S) is a singleton +G(end) = end +G(t) = t +G(C ⊸⋄) = G(C)⊸⋄ +G(C →⋄) = G(C)→⋄ +G(⟨U⟩) = ⟨G(U)⟩ +R(t) = ϵ +R(!⟨U⟩;S) = µt.!⟨G(U)⟩;t, R(S) +R(?(U);S) = µt.?(G(U));t, R(S) +Figure 6: Decomposing session types into minimal session types (Definition 3.3) +Example 3.1 (Decomposition a Non-recursive Type). Let S =?(int);?(int);!⟨bool⟩;end be the session +type given in Section 1. Then G(S) denotes the list ?(int) , ?(int) , !⟨bool⟩. +◁ +Example 3.2 (Decomposing a Recursive Type). Let S = µt.S′ be a recursive session type, with +S′ =?(int);?(bool);!⟨bool⟩;t. By Definition 3.3, since S is tail-recursive, G(S) = R(S′). Further, +R(S′) = µt.?(G(int));t, R(?(bool);!⟨bool⟩;t). By definition of R(−), we obtain +G(S) = µt.?(int);t, µt.?(bool);t, µt.!⟨bool⟩;t, R(t) +(using G(int) = int and G(bool) = bool). Since R(t) = ϵ, we obtain +G(S) = µt.?(int);t, µt.?(bool);t, µt.!⟨bool⟩;t +◁ +In addition to tail-recursive types that are handled by R(−), we need to support non-tail-recursive +types of form µt.?(( �T, t)→⋄);end that are essential for the encoding of recursion in HOπ into HO. +The following example illustrates such a decomposition. +Example 3.3 (Decomposing a Non-tail-recursive Type). Let S = µt.?((?(str);!⟨str⟩;end, t)→⋄);end +be a non-tail-recursive type. We obtain the following decomposition: +G(S) = µt.G(?((?(str);!⟨str⟩;end, t)→⋄);end) += µt.?(G((?(str);!⟨str⟩;end, t)→⋄)) += µt.?((?(str), !⟨str⟩, t)→⋄) = M +We can see that we have generated minimal non-tail-recursive type M. +◁ +Now, we illustrate the encoding of HOπ recursive processes into HO from [17] using the non-tail- +recursive type S given in the above example. +Example 3.4 (Encoding Recursion). Consider the process P = µX.a?(m).a!⟨m⟩.X, which contains +recursion and so it is not an HO process. Still, P can be encoded into HO as follows [17]: +�P� = a?(m).a!⟨m⟩.(ν s) (V (a, s) | s!⟨V ⟩) +15 + +where the value V is an abstraction that potentially reduces to �P�: +V = λ(xa, y1). y1?(zx).xa?(m).xa!⟨m⟩.(ν s) (zx (xa, s) | s!⟨zx⟩.0) +As detailed in [17], this encoding relies on non-tail-recursive types. In particular, the bound +name s in �P� is typed with the following type, discussed above in Example 3.3: +S = µt.?((?(str);!⟨str⟩;end, t)→⋄);end +We compose �P� with an appropriate client process to illustrate the encoding of recursion. Below +R stands for some unspecified process such that a ∈ rn(R): +�P� | a!⟨W⟩.a?(b).R −→2 (ν s) (V (a, s) | s!⟨V ⟩) | R +−→ (ν s) (s?(zx).a?(m).a!⟨m⟩.(ν s′) (zx (a, s′) | s′!⟨zx⟩) | s!⟨V ⟩) | R +−→ a?(m).a!⟨m⟩.(ν s′) (V (a, s′) | s′!⟨V ⟩) | R += �P� | R +3.2.2 +Decomposing Processes +As we have seen, each session type S is decomposed into G(S), a list of minimal session types. +Accordingly, given an assignment s : S, we decompose s into a series of names, one for each action in +S. We use indexed names to formalize the names used by minimally typed processes. Formally, an +indexed name is a pair (n, i) with i ∈ N, which we denote as ni. We refer to processes with indexed +names as indexed processes. +The decomposition of processes is defined in Definition 3.9, and it relies on a breakdown function, +denoted Bk +˜x +� +− +� +, which operates on indexed processes. Before we dive into those functions we present +some auxiliary definitions. +Preliminaries. +To handle the unfolding of recursive types, we shall use the following auxiliary +function, which decomposes guarded recursive types, by first ignoring all the actions until the +recursion. +Definition 3.4 (Decomposing an Unfolded Recursive Type). Let S be a session type. The function +R⋆(−): is defined as follows +R⋆(µt.S) = R(S) +R⋆(?(U);S) = R⋆(S) +R⋆(!⟨U⟩;S) = R⋆(S) +Example 3.5. Let T =?(bool);!⟨bool⟩;S be a derived unfolding of S from Example 3.2. Then, by +Definition 3.3, R⋆(T) is the list of minimal recursive types obtained as follows: first, R⋆(T) = +R⋆(!⟨bool⟩;µt.S′) and after one more step, R⋆(!⟨bool⟩;µt.S′) = R⋆(µt.S′). Finally, we have R⋆(µt.S′) = +R(S′). We get the same list of minimal types as in Example 3.2: R⋆(T) = µt.?(int);t, µt.?(bool);t, µt.!⟨bool⟩;t. +◁ +Given an unfolded recursive session type S, the auxiliary function [S⟩ returns the position of the +top-most prefix of S within its body. +Definition 3.5 (Index function). Let S be an (unfolded) recursive session type. The function [S⟩ is +defined as follows: +[S⟩ = +� +[S′{S/t}⟩⋆ +0 +if S = µt.S′ +[S⟩⋆ +0 +otherwise +16 + +where [S⟩⋆ +l : +[µt.S⟩⋆ +l = |R(S)| − l + 1 +[!⟨U⟩;S⟩⋆ +l = [S⟩⋆ +l+1 +[?(U);S⟩⋆ +l = [S⟩⋆ +l+1 +Example 3.6. Let S′ =?(bool);!⟨bool⟩;S where S is as in Example 3.2. Then [S′⟩ = 2 since the +top-most prefix of S′ (‘?(bool);’) is the second prefix in the body of S. +◁ +In order to determine the required number of propagators (ck, ck+1, . . .) required in the breakdown +of processes and values, we define the degree of a process: +Definition 3.6 (Degree of a Process). Let P be an HO process. The degree of P, denoted �P�, is +defined as follows: +�P� = +� +� +� +� +� +� +� +� +� +� +� +�Q� + 1 +if P = ui!⟨V ⟩.Q or P = ui?(y).Q +�P ′� +if P = (ν s : S) P ′ +�Q� + �R� + 1 +if P = Q | R +1 +if P = V ui or P = 0 +We define an auxiliary function that “initializes” the indices of a tuple of names, for turning a regular +process into an indexed process. +Definition 3.7 (Initializing an indexed process). Let �u = (a, b, s, s′, r, r′, . . .) be a finite tuple of +names. We shall write init(�u) to denote the tuple of indexed names (a1, b1, s1, s′ +1, r1, r′ +1, . . .). +Definition 3.8 (Subsequent index substitution). Let ni be an indexed name. We define next(ni) = +(lin(ni)) ? {ni+1/ni}: {}. +Remark 3.2. Recall that we write ‘ck?()’ and ‘ck!⟨⟩’ to denote input and output prefixes in which +the value communicated along ck is not relevant. While ‘ck?()’ stands for ‘ck?(x)’, ‘ck!⟨⟩’ stands for +‘ck!⟨λx. 0⟩’. Their corresponding minimal types are ?(end→⋄) and !⟨end→⋄⟩, which are denoted by +?(−) and !⟨−⟩, respectively. +Given a typed process P, we write rn(P) to denote the set of free names of P whose types are +recursive. As mentioned above, for each r ∈ rn(P) with r : S we shall rely on a control trio of the +form cr?(x).x �r, where �r = r1, . . . , r|G(S)|. +Definition 3.9 (Decomposition of a Process). Let P be a closed HO process with �u = fn(P) and +�v = rn(P). The decomposition of P, denoted D(P), is defined as: +D(P) = (ν �c) (ν �cr) +� +ck!⟨⟩.0 | Bk +ϵ +� +Pσ +� +| +� +r∈˜v +cr?(x).x �r +� +where: k > 0; �c = (ck, . . . , ck+�P�−1); �cr = � +r∈˜v cr; σ = {init(�u)/�u}. +Notice that when rn(P) = ∅, then D(P) = (ν �c) (ck!⟨⟩.0 | Bk +ϵ +� +Pσ +� +). We now discuss the breakdown +of process P, denoted Bk +˜x +� +P +� +. +The Breakdown Function. +Given a context �x and a k > 0, the breakdown of an indexed process +P, denoted Bk +˜x +� +P +� +, is defined recursively on the structure of processes. The definition of Bk +˜x +� +− +� +relies +on an auxiliary breakdown function on values, denoted V˜x +� +− +� +. When V = y, then the breakdown +function is simply the identity: V˜x +� +y +� += y. +The breakdown function relies on type information, in two ways. First, names are decomposed +based on their session types. Second, for most constructs the shape of decomposed process depends +on whether the associated session type is tail-recursive or not. The definition of the breakdown +function is given in Table 1. Next, we describe each of the cases of the definition. In Section 3.3 +(Page 21) we develop several examples. +17 + +P +Bk +˜x +� +P +� +ui!⟨V ⟩.Q +• ¬tr(S): +ck?(�x).ui! +� +V˜y +� +V σ +�� +.ck+1!⟨ �w⟩ | Bk+1 +˜w +� +Qσ +� +• tr(S): +ck?(�x).cu! +� +NV +� +| Bk+1 +˜w +� +Q +� +where: +NV = λ�z. z[S⟩! +� +V˜y +� +V +�� +. +� +ck+1!⟨ �w⟩ | cu?(x).x �z +� +ui : S +�y = fv(V ) +�w = fv(Q) +σ = next(ui) +�z = (z1, . . . , z|R⋆(S)|) +ui?(y).Q +• tr(S): +ck?(�x).ui?(y).ck+1!⟨ �w⟩ | Bk+1 +˜w +� +Qσ +� +• ¬tr(S): +ck?(�x).cu! +� +Ny +� +| Bk+1 +˜w +� +Q +� +where: +Ny = λ�z. z[S⟩?(y). +� +ck+1!⟨ �w⟩ | cu?(x).x �z +� +ui : S +�w = fv(Q) +σ = next(ui) +�z = (z1, . . . , z|R⋆(S)|) +V (�r, ui) +ck?(�x). +n=|˜r| +cr1! +� +λ�z1.cr2!⟨λ�z2. · · · .crn!⟨λ�zn. Q⟩ ⟩ +� +where: +Q = V˜x +� +V +� +(�z1, . . . , �zn, �m) +ui : C +∀ri ∈ �r.(ri : Si ∧ tr(Si)∧ +�zi = (zi +1, . . . , zi +|R⋆(Si)|)) +�m = (ui, . . . , ui+|G(C)|−1) +(ν s : C) P ′ +•¬tr(C) : +(ν �s : G(C)) Bk +˜x +� +P ′σ +� +• tr(C) : +(ν �s : G(C)) (ν cs) cs?(x).x �s | +(ν c¯s) c¯s?(x).x�s | Bk +˜x +� +P ′σ +� +�x = fv(P ′) +�s = (s1, . . . , s|G(C)|) +�s = (s1, . . . , s|G(C)|) +σ = {s1s1/ss} +Q | R +ck?(�x).ck+1!⟨�y⟩.ck+l+1!⟨ �w⟩ | Bk+1 +˜y +� +Q +� +| Bk+l+1 +˜w +� +R +� +�y = fv(Q) +�w = fv(R) +l = �Q� +0 +ck?().0 +V +V˜x +� +V +� +y +y +λ(�yz). P +λ( �y1, . . . , � +yn, �z) : (� +M) +⇝. N +where: +� +M = (G(S1), . . . , G(Sn), G(C)) +N = (ν �c) (ν �cr) � +i∈|�y|(cyi?(x).x �yi) | c1!⟨�x⟩ | +B1 +˜x +� +P{z1/z} +� +�yz : �SC +∀yi ∈ �y.(yi : Si ∧ tr(Si)∧ +�yi = (yi +1, . . . , yi +|G(Si)|)) +�z = (z1, . . . , z|G(C)|) +�c = (c1, . . . , c�P�) +�cr = � +r∈˜y cr +Table 1: The breakdown function for processes and values. +Output: +The decomposition of ui!⟨V ⟩.Q is arguably the most interesting case, as both the sent +value V and the continuation Q have to be decomposed. We distinguish two cases: +• If ¬tr(ui) then ui is linear or shared, and then we have: +Bk +˜x +� +ui!⟨V ⟩.Q +� += ck?(�x).ui! +� +V˜y +� +V σ +�� +.ck+1!⟨ �w⟩ | Bk+1 +˜w +� +Qσ +� +This decomposition consists of a leading trio that mimics an output action in parallel with the +breakdown of Q. The context �x must include the free variables of V and Q, which are denoted +18 + +�y and �w, respectively. These tuples are not necessarily disjoint: variables with shared types +can appear free in both V and Q. The value V is then broken down with parameters �y and +k + 1; the latter serves to consistently generate propagators for the trios in the breakdown of V , +denoted V˜y +� +V σ +� +(see below). The substitution σ increments the index of session names; it is +applied to both V and Q before they are broken down. By taking σ = next(ui) we distinguish +two cases (see Definition 3.8): +– If name ui is linear (i.e., it has a session type) then its future occurrences are renamed +into ui+1, and σ = {ui+1/ui}; +– Otherwise, if ui is shared, then σ = {}. +Note that if ui is linear then it appears either in V or Q and σ affects only one of them. The +last prefix activates the breakdown of Q with its corresponding context �w. +In case V = y, the same strategy applies; because V˜y +� +yσ +� += y, we have: +Bk +˜x +� +ui!⟨y⟩.Q +� += ck?(�x).ui!⟨y⟩.ck+1!⟨ �w⟩ | Bk+1 +˜w +� +Qσ +� +Notice that variable y is not propagated further if it does not appear free in Q. +• If tr(ui) then ui is tail-recursive and then we have: +Bk +˜x +� +ui!⟨V ⟩.Q +� += ck?(�x).cu! +� +NV +� +| Bk+1 +˜w +� +Q +� +where: NV = λ�z. z[S⟩! +� +V˜y +� +V +�� +. +� +ck+1!⟨ �w⟩ | cu?(x).x �z +� +The decomposition consists of a leading trio that mimics the output action running in parallel +with the breakdown of Q. After receiving the context �x, the leading trio sends an abstraction +NV along cu, which performs several tasks. First, NV collects the sequence of names ˜u; then, +it mimics the output action of P along one of such names (u[S⟩) and triggers the next trio, +with context �w; finally, it reinstates the server on cu for the next trio that uses u. Notice that +indexing is not relevant in this case. +In case V = y, we have V˜y +� +yσ +� += y and �y� = 0, hence: +Bk +˜x +� +ui!⟨y⟩.Q +� += ck?(�x).cu! +� +λ�z. z[S⟩!⟨y⟩. +� +ck+1!⟨ �w⟩ | cu?(x).x �z +�� +| Bk+1 +˜w +� +Q +� +Input: +To decompose a process ui?(y).Q we distinguish two cases, as before: (i) name ui is linear +or shared or (ii) tail-recursive. In case (i), the breakdown is defined as follows: +Bk +˜x +� +ui?(y).Q +� += ck?(�x).ui?(y).ck+1!⟨ �w⟩ | Bk+1 +˜w +� +Qσ +� +where �w = fv(Q). A leading trio mimics the input action and possibly extends the context with the +received variable y. The substitution σ is defined as in the output case. +In case (ii), when ui has tail-recursive session type S, the decomposition is as in the output case: +Bk +˜x +� +ui?(y).Q +� += ck?(�x).cu! +� +λ�z. z[S⟩?(y). +� +ck+1!⟨ �w⟩ | cu?(x).x �z +�� +| Bk+1 +˜w +� +Q +� +Application: +For simplicity we consider the breakdown of applications of the form V (�r, ui), where +every ri ∈ �r is such that tr(ri) and only ui is such that ¬tr(ui). The general case (involving different +orders in names and multiple names with non-recursive types) is similar. We have: +Bk +˜x +� +V (�r, ui) +� +=ck?(�x). +n=|˜r| +cr1! +� +λ�z1.cr2!⟨λ�z2. · · · .crn!⟨λ�zn. V˜x +� +V +� +(�z1, . . . , �zn, �m)⟩ ⟩ +� +19 + +Let us first discuss how names in (�r, ui) are decomposed using types. Letting |˜r| = n and +i ∈ {1, . . . , n}, for each ri ∈ �r (with ri : Si) we generate a sequence �zi = (zi +1, . . . , zi +|R⋆(Si)|) as in the +output case. We decompose name ui (with ui : C) as �m = (ui, . . . , ui+|G(C)|−1). +The decomposition first receives a context �x for value V : we break down V with �x as a context +since these variables need to be propagated to the abstracted process. Subsequently, an output on +cr1 sends a value containing n abstractions that occur nested within output prefixes—this is similar +to the mechanism for partial instantiation shown in Example 2.3. For each j ∈ {1, . . . , n − 1}, each +abstraction binds �zj and sends the next abstraction along crj+1. The innermost abstraction abstracts +over �zn and encloses the process V˜x +� +V +� +(�z1, . . . , �zn, �m), which effectively mimics the application. +This abstraction nesting binds all variables �zi, the decompositions of all tail-recursive names (�r). +The breakdown of a value application of the form y (�r, ui) results into the following specific case: +Bk +˜x +� +y (�r, ui) +� += ck?(�x). +n=|˜r| +cr1! +� +λ�z1.cr2!⟨λ�z2. · · · .crn!⟨λ�zn. y (�z1, . . . , �zn, �m)⟩ ⟩ +� +Restriction: +The decomposition of (ν s : C) P ′ depends on C: +• If ¬tr(C) then +Bk +˜x +� +(ν s : C) P ′� += (ν �s : G(C)) Bk +˜x +� +P ′σ +� +By construction, �x = fv(P ′). Similarly as in the decomposition of ui into �m discussed above, +we use the type C of s to obtain the tuple �s of length |G(C)|. We initialize the index of s in +P ′ by applying the substitution σ. This substitution depends on C: if it is a shared type then +σ = {s1/s}; otherwise, if C is a session type, then σ = {s1s1/ss}. +• Otherwise, if tr(C) then we have: +Bk +˜x +� +(ν s : C) P ′� += (ν �s : R(S)) (ν cs) cs?(x).x �s | (ν c¯s) c¯s?(x).x�s | Bk +˜x +� +P ′� +We decompose s into �s = (s1, . . . , s|G(S)|) and s into �s = (s1, . . . , s|G(S)|). Notice that as tr(C) +we have C ≡ µt.S, therefore G(C) = R(S). The breakdown introduces two servers in parallel +with the breakdown of P ′; they provide names for s and s along cs and cs, respectively. The +server on cs (resp. cs) receives a value and applies it to the sequence �s (resp. �s). We restrict +over �s and propagators cs and cs. +Composition: +The breakdown of a process Q | R is as follows: +Bk +˜x +� +Q | R +� += ck?(�x).ck+1!⟨�y⟩.ck+l+1!⟨ �w⟩ | Bk+1 +˜y +� +Q +� +| Bk+l+1 +˜w +� +R +� +A control trio triggers the breakdowns of Q and R; it does not mimic any action of the source +process. The tuple �y ⊆ �x (resp. �w ⊆ �x) collects the free variables in Q (resp. R). To avoid name +conflicts, the trigger for the breakdown of R is ck+l+1, with l = �Q�. +Inaction: +To breakdown 0, we define a degenerate trio with only one input prefix that receives a +context that by construction will always be empty (i.e., �x = ϵ, cf. Remark 3.2): +Bk +˜x +� +0 +� += ck?().0 +Value: +For simplicity, let us consider values of the form V = λ(�y, z) : (�S, C) +⇝. P, where tr(yi) +holds for every yi ∈ �y and ¬tr(z), and ⇝∈ {⊸, →}. The general case is defined similarly. We have: +V˜x +� +λ(�y, z) : (�S, C) +⇝. P +� += λ( �y1, . . . , � +yn, �z) : (� +M) +⇝. N +where: +� +M = G(S1), . . . , G(Sn), G(C) +N = (ν �c) (ν �cr) +� +i∈|�y| +cyi?(x).x �yi | c1!⟨�x⟩ | B1 +˜x +� +P{z1/z} +� +20 + +Every yi (with yi : Si) is decomposed into �yi = (y1, . . . , y|G(Si)|). We use C to decompose z into +�z. We abstract over �y1, . . . , �yn, �z; the body of the abstraction (i.e. N) is the composition of recursive +names propagators, the control trio, and the breakdown of P, with name index initialized with the +substitution {z1/z}. For every yi ∈ �y there is a server cyi?(x).x �yi as a subprocess in the abstracted +composition—the rationale for these servers is as in previous cases. We restrict the propagators +�c = (c1, . . . , c�P�): this enables us to type the value in a shared environment when ⇝=→. Also, we +restrict special propagator names �cr = � +r∈˜v cr. +3.3 +The Decomposition by Example +We illustrate the decompositions by means of several examples. +3.3.1 +Decomposing Processes with Non-Recursive Names +Example 3.7. Consider process P = (ν u) (Q | R) whose body implements end-points of channel u +with session type S =?(U);?(bool);end, with U = (?(bool);end)⊸⋄, where: +Q = u?(x). +Q′ +� +�� +� +u?(y).(ν s) +� +x s | s!⟨y⟩ +� +R = u!⟨V ⟩.u!⟨true⟩.0 +V = λz. z?(b).0 +The process P reduces as follows: +P −→ (ν u) +� +u?(y).(ν s) +� +V s | s!⟨y⟩ +� +| u!⟨true⟩.0 +� +−→ (ν s) +� +V s | s!⟨true⟩ +� +−→ (ν s) +� +s?(b).0 | s!⟨true⟩ +� += P ′ +By Definition 3.9 we have that the decomposition of P is as follows: +D(P) = (ν c1, . . . , c10) (c1!⟨⟩ | B1 +ϵ +� +Pσ +� +) +where σ = {u1u1/uu}. We have: +B1 +ϵ +� +Pσ +� += (ν u1, u2) c1?().c2!⟨⟩.c3!⟨⟩ | B2 +ϵ +� +Qσ +� +| B8 +ϵ +� +Rσ +� +The breakdowns of sub-processes Q and R are as follows: +B2 +ϵ +� +Qσ +� += c2?().u1?(x).c3!⟨x⟩ | B3 +ϵ +� +Q′σ′� +B3 +x +� +Q′σ′� += c3?(x).u2?(y).c4!⟨x, y⟩ | B4� +(ν s) +� +x s | s!⟨y⟩ +�� +B4 +x,y +� +(ν s) +� +x s | s!⟨y⟩ +�� += (ν s1) +� +c4?(x, y).c5!⟨x⟩.c6!⟨y⟩ | c5?(x).x s1 | c6?(y).s1!⟨y⟩.c7!⟨⟩ | c7?().0 +� +B8 +ϵ +� +Rσ +� += c8?().u1!⟨Vϵ +� +V +� +⟩.c9!⟨⟩ | B9 +ϵ +� +u2!⟨true⟩.0 +� +B9 +ϵ +� +u2!⟨true⟩.0 +� += c9?().u2!⟨true⟩.c10!⟨⟩ | c10?().0 +Vϵ +� +V +� += λz1. ((ν cV +1 , cV +2 ) cV +1 !⟨⟩ | cV +1 ?().z1?(b).cV +2 !⟨⟩ | cV +2 ?().0) +where σ′ = {u2u2/uu}. By G(−) from Definition 3.3 we decompose S into M1 and M2 given as +follows: +M1 =?(G(U));end =?(U);end +M2 =?(bool);end +Above we may notice that G(U) = U. We remark that D(P) accordingly implements indexed names +u1, u2 typed with M1, M2, respectively. +21 + +Let us inspect the reductions of D(P). First, there are three synchronizations on c1, c2, and c8: +D(P) −→ (ν c2, . . . , c10) (ν u1, u2) c2!⟨⟩.c8!⟨⟩ | B2 +ϵ +� +Qσ +� +| B8 +ϵ +� +Rσ +� +−→2 (ν c3, . . . , c7, c9, c10) u1?(x). c3!⟨x⟩ | B3 +ϵ +� +Q′σ′� +| u1!⟨Vϵ +� +V +� +⟩. c9!⟨⟩ +| B9 +ϵ +� +u2!⟨true⟩.0 +� += D1 +After reductions on propagators, D1 is able to mimic the original synchronization on channel u +(highlighted above). It is followed by two administrative reductions on c3 and c9: +D1 −→ (ν c3, . . . , c7, c9, c10) c3!⟨Vϵ +� +V +� +⟩ | c3?(x).u2?(y).c4!⟨x, y⟩ | B4� +(ν s) +� +x s | s!⟨y⟩ +�� +| +c9!⟨⟩ | c9?().u2!⟨true⟩.c10!⟨⟩ | c10?().0 +−→2 (ν c4, . . . , c7, c10) u2?(y). c4!⟨Vϵ +� +V +� +, y⟩ | +(ν s1) +� +c4?(x, y).c5!⟨x⟩.c6!⟨y⟩ | c5?(x).x s1 | c6?(y).s1!⟨y⟩.c7!⟨⟩ | c7?().0 +� +| +u2!⟨true⟩. c10!⟨⟩ | c10?().0 = D2 +Similarly, D2 can mimic the next synchronization of the original process on name u2. Following up +on that, syncronization on c10 takes place: +D2 −→2 (ν c4, . . . , c7) c4!⟨Vϵ +� +V +� +, true⟩ | +(ν s1) +� +c4?(x, y).c5!⟨x⟩.c6!⟨y⟩ | c5?(x).x s1 | c6?(y).s1!⟨y⟩.c7!⟨⟩ | c7?().0 +� += D3 +Now, we can see that the next three reductions on c4, c5, and c6 appropriately propagate values +Vϵ +� +V +� +and true to the breakdown of sub-processes. Subsequently, value Vϵ +� +V +� +is applied to name s1: +D3 −→ (ν c5, . . . , c7) (ν s1) +� +c5!⟨Vϵ +� +V +� +⟩.c6!⟨true⟩ | c5?(x).x s1 | c6?(y).s1!⟨y⟩.c7!⟨⟩ | c7?().0 +� +−→2 (ν c7) (ν s1) +� +Vϵ +� +V +� +s1 | s1!⟨true⟩.c7!⟨⟩ | c7?().0 +� +−→ (ν c7) (ν s1) ((ν cV +1 , cV +2 ) cV +1 !⟨⟩ | cV +1 ?().s1?(b).cV +2 !⟨⟩ | cV +2 ?().0) | s1!⟨true⟩.c7!⟨⟩ | c7?().0 = D4 +Finally, after syncronization on cV +1 we reach the process D5 that is clearly able to simulate P ′, and +its internal communication on the channel s: +D4 −→ (ν c7) (ν s1) ((ν cV +2 ) s1?(b).cV +2 !⟨⟩ | cV +2 ?().0) | s1!⟨true⟩.c7!⟨⟩ | c7?().0 = D5 +◁ +Example 3.8 (Breaking Down Name-Passing). Consider the following process P, in which a channel +m is passed, through which a boolean value is sent back: +P = (ν u) (u!⟨⌜m⌝⟩.m?(b) | u?(⌜x⌝).x!⟨true⟩) +After expanding the syntactic sugar of name-passing, we get a process P = (ν u) (Q | R), where +Q = u!⟨V ⟩.m?(y).(ν s) (y s | s!⟨λb. 0⟩) +V = λz. z?(x).(x m) +R = u?(y).(ν s) (y s | s!⟨W⟩) +W = λx. x!⟨W ′⟩ with W ′ = λz. z?(x).(x true) +Note that to mimic the name-passing synchronization, we require exactly four reduction steps: +P −→4 �m?(b) | m!⟨true⟩� −→4 0 +(19) +We will now investigate the decomposition of P and its reduction chain. First, we use Definition 3.6 +to compute �Q� = 6, and similarly, �R� = 5. Therefore, �P� = 12. Following Definition 3.9, we +see that σ = {m1m1/mm}, which we silently apply. Taking k = 1, the breakdown of P and its +subprocesses is shown in Table 2. +22 + +D(P) = (ν c1, . . . , c12) +� +c1!⟨⟩ | (ν u1) +� +c1?().c2!⟨⟩.c8!⟨⟩ | B2 +ϵ +� +Q +� +| B8 +ϵ +� +R +��� +B2 +ϵ +� +Q +� += c2?().u1!⟨Vϵ +� +V +� +⟩.c3!⟨⟩ | c3?().m1?(y).c4!⟨y⟩ | +(ν s1) (c4?(y).c5!⟨y⟩.c6!⟨⟩ | c5?(y).(y s1) | c6?().s1!⟨Vϵ +� +λb. 0 +� +⟩.c7!⟨⟩ | c7?()) +B8 +ϵ +� +R +� += c8?().u1?(y).c9!⟨y⟩ | +(ν s1) +� +c9?(y).c10!⟨y⟩.c11!⟨⟩ | c10?(y).(y s1) | c11?().s1!⟨Vϵ +� +W +� +⟩.c12!⟨⟩ | c12?() +� +Vϵ +� +V +� += λz1. (ν cV +1 , cV +2 ) (cV +1 !⟨⟩ | cV +1 ?().z1?(x).cV +2 !⟨x⟩ | cV +2 ?(x).(x m1)) +Vϵ +� +λb. 0 +� += λb1. (ν cb +1) (cb +1!⟨⟩ | cb +1?()) +Vϵ +� +W +� += λx1. (ν cW +1 , cW +2 ) (cW +1 !⟨⟩ | cW +1 ?().x1!⟨Vϵ +� +W ′� +⟩.cW +2 !⟨⟩ | cW +2 ?()) +Vϵ +� +W ′� += λz1. (ν cW ′ +1 , cW ′ +2 ) (cW ′ +1 !⟨⟩ | cW ′ +1 ?().z1?(x).cW ′ +2 !⟨x⟩ | cW ′ +2 ?(x).(x true)) +Table 2: The decomposition on processes discussed in Example 3.8. +In Table 2 we have omitted substitutions that have no effect and trailing 0s. The first interesting +action appears after synchronizations on c1, c2, and c8. At that point, the process will be ready to +mimic the first action that is performed by P, i.e., u1 will send Vϵ +� +V +� +, the breakdown of V , from +the breakdown of Q to the breakdown of R. Next, c9 and c10 will synchronize, and Vϵ +� +V +� +is passed +further along, until s1 is ready to be applied to it in the breakdown of R. At this point, we know +that P −→7 (ν �c) P ′, where �c = (c3, . . . , c12), and +P ′ = c3!⟨⟩ | c3?().m1?(y).c4!⟨y⟩ +| (ν s1) (c4?(y).c5!⟨y⟩.c6!⟨⟩ | c5?(y).y s1 | c6?().s1!⟨Vϵ +� +λb. 0 +� +⟩.c7!⟨⟩ | c7?()) +| (ν s1) +� +Vϵ +� +V +� +s1 | s1!⟨Vϵ +� +W +� +⟩.c12!⟨⟩ | c12?() +� +After s1 is applied, the trio guarded by c3 will be activated, where z1 has been substituted by +s1. Then s1 and s1 will synchronize, and the breakdown of W is passed along. Then c4 and +c19 synchronize, and now m1 is ready to be applied to Vϵ +� +W +� +, which was the input for c4 in the +breakdown of V . After this application, c3 and cW +1 +can synchronize with their duals, and we know +that (ν �c) P ′ −→8 (ν �c′) P ′′, where �c′ = (c4, . . . , c7, cW ′ +2 ), and +P ′′ = m1?(y).c4!⟨y⟩ | m1!⟨Vϵ +� +W ′� +⟩.cW ′ +2 !⟨⟩ | cW ′ +2 ?() +| (ν s1) (c4?(y).c5!⟨y⟩.c6!⟨⟩ | c5?(y).y s1 | c6?().s1!⟨Vϵ +� +λb. 0 +� +⟩.c7!⟨⟩ | c7?()) +Remarkably, P ′′ is standing by to mimic the encoded exchange of value true. Indeed, the decomposi- +tion of the four-step reduced process in (19) will reduce in three steps to a process that is equal (up +to ≡α) to the process we obtained here. This strongly suggests a tight operational correspondence +between a process and its decomposition, which we will explore in Section 4. +◁ +3.3.2 +Decomposing Processes with Recursive Names +Next, we illustrate the decomposition of processes involving names with tail-recursive types. Recall +process R1, which we used in Section 3.1 to motivate the need for recursive propagators: +R1 = r?(z).r!⟨−z⟩.r?(z).r!⟨z⟩.V r +Two following examples illustrate the low-level workings of the propagation mechanism of the +decomposition in Figure 5. The first example illustrates how the propagation of recursive names +works in the case of input and output actions on names with recursive types (the “first part” of R1). +The second example shows how an application where a value is applied to a tuple of names with +recursive names is broken down (the “second part” of R1). +23 + +Example 3.9 (Decomposing Processes with Recursive Names (I)). Let P = r?(x).r!⟨x⟩.P ′ be a +process where r has type S = µt.?(int);!⟨int⟩;t and r ∈ fn(P ′). By Definition 3.9 we have: +D(P) = (ν �c) (ν cr) +� +c1!⟨⟩ | B1 +ϵ +� +P +� +| cr?(x).x (r1, r2) +� +where �c = (c1, . . . , c|P|). The control trio in the parallel composition provides a decomposition of r +on name cr, which is shared. The decomposition B1 +ϵ +� +P +� +is defined as follows: +B1 +ϵ +� +P +� += c1!⟨⟩ | c1?().cr!⟨N1⟩ | c2?(y).cr!⟨N2⟩ | B3 +ϵ +� +P ′�� +N1 = λ(z1, z2). z1?(x).cr?(x).x (z1, z2) +N2 = λ(z1, z2). z2!⟨x⟩.c3!⟨⟩.cr?(x).x (z1, z2) +Each trio in B1 +ϵ +� +P +� +that mimics some action on r requests the sequence ˜r from the server on cr. We +can see that this request is realized by a higher-order communication: trios send abstractions (N1 +and N2) to the server; these abstractions contain further actions of trios and it will be applied to +the sequence ˜r. Hence, the formal arguments for these values are meant to correspond to ˜r. +After two reductions (the trio activation on c1 and the communication on cr), we have: +D(P) −→2 (ν c2, . . . , c�P�) r1?(x).c2!⟨x⟩.cr?(x).x (r1, r2) | c2?(y).cr!⟨N2⟩ | B3 +ϵ +� +P ′� += P1 +By synchronizing with the top-level server on cr, the bound names in N1 are instantiated with r1, r2. +Now, the first trio in P1 is able to mimic the action on r1 that is followed by the activation of the +next trio on c2. Then, the server on cr gets reinstantiated making names r1, r2 available for future +trios. The break down of the output action follows the same pattern. +◁ +Example 3.10 (Decomposing Processes with Recursive Names (II)). Let S = µt.?(int);!⟨int⟩;t and +T = µt.?(bool);!⟨bool⟩;t, and define Q = V (u, v) as a process where u : S and v : T, where V is some +value of type (S, T)→⋄. By Definition 3.9, the decomposition of Q is as in the previous example, +except that now there are two servers, one for u and one for v: +D(Q) = (ν c1˜c) (ν cucv) +� +cu?(x).x (u1, u2) | cv?(x).x (v1, v2) | c1!⟨⟩ | B1 +ϵ +� +Q +�� +B1 +ϵ +� +Q +� += c1?().cu! +� +λ(x1, x2). cv!⟨λ(y1, y2). Vϵ +� +V +� +(x1, x2, y1, y2)⟩ +� +with ˜c = (c2, . . . , c�Q�). Process Q is broken down in such a way that it communicates with both +servers to collect ˜u and ˜v. To this end, B1 +ϵ +� +Q +� +is a process in which abstractions are nested using +output prefixes and whose innermost process is an application. After successive communications +with multiple servers this innermost application will have collected all names in ˜u and ˜v. +Observe that we use two nested outputs, one for each name with recursive types in Q. We now +look at the reductions of D(Q) to analyze how the communication of nested abstractions allows us +to collect all name sequences needed. After the first reduction along c1 we have: +D(Q) −→(ν ˜c) (ν cucv) +� +cu?(x).x (u1, u2) | cv?(x).x (v1, v2) | +cu! +� +λ(x1, x2). cv!⟨λ(y1, y2). Vϵ +� +V +� +(x1, x2, y1, y2)⟩ +�� += R1 +From R1 we have a synchronization along name cu: +R1 −→(ν ˜c) (ν cucv) +� +(λ(x1, x2). cv!⟨λ(y1, y2). Vϵ +� +V +� +(x1, x2, y1, y2)⟩) (u1, u2) | cv?(x).x (v1, v2) +� += R2 +Upon receiving the value, the server applies it to (u1, u2), thus obtaining the following process: +R2 −→(ν ˜c) (ν cucv) +� +cv!⟨λ(y1, y2). Vϵ +� +V +� +(u1, u2, y1, y2)⟩ | cv?(x).x (v1, v2) +� += R3 +Up to here, we have partially instantiated name variables of a value with the sequence ˜u. Next, the +first trio in R3 can communicate with the server on name cv: +R3 −→(ν ˜c) (ν cucv) +� +λ(y1, y2). Vϵ +� +V +� +(u1, u2, y1, y2) (v1, v2) +� +−→(ν ˜c) (ν cucv) +� +Vϵ +� +V +� +(u1, u2, v1, v2) +� +This completes the instantiation of name variables with appropriate sequences of names with recursive +types. At this point, D(Q) can proceed to mimic the application in Q. +◁ +24 + +Example 3.11 (Breakdown of Recursion Encoding). We recall process �P� from Example 3.4: +�P� = a?(m).a!⟨m⟩.(ν s) (V (a, s) | s!⟨V ⟩) +V = λ(xa, y1). y1?(zx).xa?(m).xa!⟨m⟩.(ν s) (zx (xa, s) | s!⟨zx⟩.0) +Here, bound name s is typed with S, from Example 3.3, defined as: +S = µt.?((?(str);!⟨str⟩;end, t)→⋄);end +We now analyze D(�P�) and its reduction chain. By Definition 3.6, we have ��P�� = 7. Then, we +choose k = 1 and observe that σ = {a1a1/aa}. Following Definition 3.9, we get: +D(�P�) = (ν c1, . . . , c7) (ν ca) (ca?(x).x (a1, a2) | c1!⟨⟩ | B1 +ϵ +� +�P�σ +� +) +B1 +ϵ +� +�P� +� += c1?().ca!⟨λ(z1, z2). z1?(m).c2!⟨m⟩.ca?(x).x (z1, z2)⟩ +| c2?(m).ca!⟨λ(z1, z2). z2!⟨m⟩.c3!⟨⟩.ca?(x).x (z1, z2)⟩ +| (ν s1) +� +c3?().c4!⟨⟩.c5!⟨⟩ | c4?().ca!⟨λ(z1, z2). Vϵ +� +V +� +(z1, z2, s1)⟩ +| c5?().s1!⟨Vϵ +� +V +� +⟩.c7!⟨⟩ | c7?() +� +In accordance with Example 3.3, the type of s1 in the decomposed process is +M = µt.?((?(str), !⟨str⟩, t)→⋄). +The decomposition relies twice on Vϵ +� +V +� +, the breakdown of value V , which we give below. For +this, we observe that V is an abstraction of a process Q with |Q| = 7. We also α-convert the process +abstracted in Vϵ +� +V +� +renaming bound propagators c1, . . . , c7 to cV +1 , . . . , cV +7 to avoid name clashes. +Vϵ +� +V +� += λ(xa1, xa2, y1). (ν cV +1 , . . . , cV +7 ) +� +cV +1 !⟨⟩ | B1 +ϵ +� +Q +� +{cV +1 , . . . , cV +7/c1, . . . , c7} | cxa?(x).x (xa1, xa2) +� +B1 +ϵ +� +Q +� += c1?().y1?(zx).c2!⟨zx⟩ +| c2?(zx).ca!⟨λ(z1, z2). z1?(m).c3!⟨zx, m⟩.ca?(x).x (z1, z2)⟩ +| c3?(zx).ca!⟨λ(z1, z2). z2!⟨m⟩.c4!⟨zx⟩.ca?(x).x (z1, z2)⟩ +| (ν s1) +� +c4?(xz).c5!⟨zx⟩.c6!⟨zx⟩ | +c5?(zx).ca!⟨λ(z1, z2). zx (z1, z2, s1)⟩ | c6?(zx).s1!⟨zx⟩.c7!⟨⟩ | c7?() +� +We follow the reduction chain on D(�P�) until it is ready to mimic the first action with channel +a, which is an input. First, c1 will synchronize, after which ca sends the abstraction to which then +(a1, a2) is applied. We obtain D(�P�) −→3 (ν c2, . . . , c7, ca) P ′, where +P ′ = a1?(m).c2!⟨m⟩.ca?(x).x (a1, a2) +| c2?(m).ca!⟨λ(z1, z2). z2!⟨m⟩.c3!⟨⟩.ca?(x).x (z1, z2)⟩ +| (ν s1) +� +c3?().c4!⟨⟩.c5!⟨⟩. | c4?().ca!⟨λ(z1, z2). Vϵ +� +V +� +(z1, z2, s1)⟩ | +c5?().s1!⟨Vϵ +� +V +� +⟩.c7!⟨⟩ | c7?() +� +Note that this process is awaiting an input on channel a1, after which c2 can synchronize with its +dual. At that point, ca is ready to receive another abstraction that mimics an input on a1. This +strongly suggests a tight operational correspondence between a process P and its decomposition in +the case where P performs higher-order recursion. +◁ +3.4 +Static Correctness +Having presented and illustrated our decomposition, we may now state its technical results. Given +an environment ∆ = ∆1, ∆2, below we write ∆1 ◦ ∆2 to indicate the split of ∆ into a ∆1 containing +non-recursive names and a ∆2 containing recursive names. +We extend the decomposition function G(−) to typing environments in the obvious way. We +rely on the following notation. Given a tuple of names �s = s1, . . . , sn and a tuple of (session) +types �S = S1, . . . , Sn of the same length, we write �s : �S to denote a list of typing assignments +s1 : S1, . . . , sn : Sn. +25 + +Definition 3.10 (Decomposition of Environments). Let Γ, Λ, and ∆ be typing environments. We +define G(Γ), G(Λ), and G(∆) inductively as follows: +G(∆, ui : S) = G(∆), (ui, . . . , ui+|G(S)|−1) : G(S) +G(Γ, ui : ⟨U⟩) = G(Γ), ui : G(⟨U⟩) +G(Γ, x : U) = G(Γ), x : G(U) +G(Λ, x : U) = G(Λ), x : G(U) +G(∅) = ∅ +Lemma 3.1. Let P be an indexed HO process and V be a value. +1. If Γ; Λ; ∆ ◦ ∆µ ⊢ P ▷ ⋄ then G(Γ1), Φ; ∅; G(∆), Θ ⊢ Bk +˜x +� +P +� +▷ ⋄, where: +• k > 0 +• �r = dom(∆µ) +• Φ = � +r∈˜r cr : ⟨R⋆(∆µ(r))⊸⋄⟩ +• �x = fv(P) +• Γ1 = Γ \ �x +• dom(Θ) = {ck, . . . , ck+�P�−1} ∪ {ck+1, . . . , ck+�P�−1} +• Θ(ck) =?(U1, . . . , Un), where (G(Γ), G(Λ))(�x) = (x1 : U1, . . . , xn : Un) +• balanced(Θ) +2. If Γ; Λ; ∆ ◦ ∆µ ⊢ V ▷ �T ⊸⋄ then G(Γ), Φ; G(Λ); G(∆) ⊢ V˜x +� +V +� +▷ G( �T)⊸⋄, where: +• �x = fv(V ) +• Φ = � +r∈˜r cr : ⟨R⋆(∆µ(r))⊸⋄⟩ +Proof. By mutual induction on the structure of P and V . See Appendix B.1 for details. +Using the above lemma we can prove our static correctness result, which explains how our +decomposition induces minimal session types. +Theorem 3.1 (Static Correctness). Let P be a closed HO process (i.e. fv(P) = ∅) with �u = fn(P). +If Γ; ∅; ∆ ◦ ∆µ ⊢ P ▷ ⋄, then G(Γσ); ∅; G(∆σ), G(∆µσ) ⊢ D(P) ▷ ⋄, where σ = {init(�u)/�u}. +Proof. Directly from the definitions, using Lemma 3.1. See Appendix B.2 for details. +4 +Dynamic Correctness +In this section, we establish the dynamic correctness of our decomposition, stated in terms of a +typed behavioral equivalence. More specifically, we would like to show that any typed process +P is equivalent to its decomposition D(P). But how do we even state it formally? Both P and +D(P) are typed HO processes (as any minimally typed process is also an HO process), so we can +consider compare them as HO terms inside the HO type system. The conventional notion of typed +equivalence for HO processes is contextual equivalence, which is given a local characterization in +terms of higher-order bisimulations [18]. In our case, however, contextual equivalence is not the +right choice: contextual equivalence applies to processes of the same type, whereas the process P +and its decomposition D(P) have different types and typing contexts. Instead of using contextual +equivalence, we generalize the notion of higher-order bisimilarity to a notion that we call MST +bisimilarity, which relates processes of (potentially) different types. +This section is organized as follows. In Section 4.1 we recall the notion of higher-order bisimulation, +used for characterizing behavioral equivalence in HO, and discuss its limitations for our purposes. +26 + +We use higher-order bisimulation as a basis to give a formal definition of MST bisimulation in +Section 4.2, which we will use as a notion of behavioral equivalence for comparing P and D(P). In +order to show that our decomposition is correct, in Section 4.3 we exhibit a bisimulation relation S +which relates a process and its decomposition, containing a number of intermediate pairs, working +from a motivating example in Section 4.3.1. Finally, in Section 4.4 we show that S is indeed an +MST bisimulation. +4.1 +Behavioral Equivalence in HO and its Limitations +Let us begin by recalling the notion of HO bisimulation, defined in [18] to characterize contextual +equivalence of HO processes. +Definition 4.1 (Definition 17 in [18]). A typed relation ℜ is an HO bisimulation if for all Γ1; Λ1; ∆1 ⊢ +P1 ℜ Γ2; Λ2; ∆2 ⊢ Q1, +1) Whenever Γ1; Λ1; ∆1 ⊢ P1 +(ν � +m1) n!⟨V1⟩ +�−−−−−−−−→ Λ′ +1; ∆′ +1 ⊢ P2 then there exist Q2, ∆′ +2, and Λ′ +2 such that +Γ2; Λ2; ∆2 ⊢ Q1 +(ν � +m2) n!⟨V2⟩ +�========⇒ Λ′ +2; ∆′ +2 ⊢ Q2 where, for a fresh t, +Γ1; Λ1; ∆′′ +1 ⊢ (ν � +m1)(P2 | t ←�H V1) ℜ Γ2; Λ2; ∆′′ +2 ⊢ (ν � +m2)(Q2 | t ←�H V2) +2) Whenever Γ1; Λ1; ∆1 ⊢ P1 +ℓ�−→ Λ′ +1; ∆′ +1 ⊢ P2, with ℓ not an output, then there exist Q2, Λ′ +2, and ∆′ +2 +such that Γ2; Λ2; ∆2 ⊢ Q1 +ˆℓ�=⇒ Λ′ +2; ∆′ +2 ⊢ Q2 and Γ1; Λ′ +1; ∆′ +1 ⊢ P2 ℜ Γ2; Λ′ +2; ∆′ +2 ⊢ Q2. +3) The symmetric cases of 1, 2. +The largest such bisimulation is called HO bisimilarity, denoted by ≈H. +There are two points worth highlighting in this definition. Firstly, the labeled transition system +ℓ�−→ used in the definition of ≈H is what is called the refined transition system, different from the +standard labeled transition system for the higher-order π-calculus. The idea behind the refined +transition system is that we want to disallow arbitrary inputs P +x(V ) +�−−−→ P ′; having to consider such +transitions in the definition of bisimilarity is undesirable, because it involves input of an arbitrary +(higher-order) value V , making the definition very much non-local and ensuring that the bisimulations +are very large. As it turns out, due to the typed nature of the system, it suffices to consider inputs +of the processes of a very particular kind—characteristic values, defined based on the type. +Secondly, because the inputs are restricted in the refined LTS, there is some price to pay in the +handling of the outputs. If an output action P1 +(ν � +m1) n!⟨V1⟩ +�−−−−−−−−→ P2 is matched by an output action +Q1 +(ν � +m2) n!⟨V2⟩ +�========⇒ Q2, then we need to ensure that that the output processes V1 and V2 are somehow +related. We have to ensure this in the output clause, because on the receiving end transitions +inputing values V1 or V2 might not even be considered. To that extent, we package the values V1 or +V2 in trigger processes (denoted t ←�H V1 and t ←�H V2), which are defined based on the typing. We +then make them part of the processes that are considered at the “next step” of the bisimulation. +This notion of HO bisimilarity works for processes of the same type. For our case, we need to +compare processes of different, but related types. To that extent we make several changes to the +definition above. Firstly, during the decomposition a single name x in a source process is decomposed +into a sequence of names x1, . . . , xk in the target process. So in the definition of MST bisimilarity +we match an action on a name x with an action on an indexed name xi. Secondly, such discrepancy +between names might arise in input and output values. This also needs to be considered as part of +the definition. For this, we need to accommodate the difference between characteristic values and +trigger processes for MST and HO. In the next subsection we work out the details sketched above. +27 + +4.2 +MST Bisimilarity +In this section we define a generalized version of HO bisimilarity allowing for comparing MST and HO +process terms. Our goal is to define MST bisimilarity (denoted ≈M), a typed behavioral equivalence, +which we give in Definition 4.9. To define ≈M, we require some auxiliary definitions, in particular: +• A refined LTS on typed processes (Definition 4.5); +• A relation ▷◁ on values (Definition 4.6) and on names (Definition 4.14); +• A revised notion of trigger processes (Definition 4.8). +Refined LTS and characteristic values. +The idea behind defining the refined LTS is to restrict +the input of arbitrary processes (values) and make the transition system image-finite (modulo names). +The refined LTS for HO is defined in [18] in three layers. First comes the untyped LTS P +ℓ−→ P ′, +which describes reductions of untyped processes in the usual style of the LTS semantics for π-calculus. +Secondly, there is a notion of the environmental LTS (Γ1; Λ1; ∆1) ℓ−→ (Γ2; Λ2; ∆2), which describes +reductions of typing environments. This LTS describes the way a typing context can evolve in +accordance with its session types. On top of these layers there are notions of refined environmental +LTS and refined LTS for processes. The former restricts the environmental LTS to inputs on +characteristic values, as we discussed in Section 4.1. Finally, the refined LTS for processes restricts +the untyped LTS to those actions which are supported by the refined environmental LTS. +We follow this approach for defining the refined LTS for MST processes. Both the untyped LTS +for processes and the environmental LTS for MST processes coincides with the same LTSs for HO +(or, to be more precise, with its restriction to minimal session types). It remains, then, to define the +refined environmental LTS for MST processes, with the idea that the refined LTS restricts inputs to +the inputs on minimal characteristic values and minimal trigger values. +Definition 4.2 (Minimal trigger value). Given a value type C ⇝ ⋄ and fresh (indexed) name t1, +the minimal trigger value on t1 of type G(C) ⇝ ⋄ is defined as the abstraction +λ�x. t1?(y).y �x +where �x = (x1, . . . , x|G(C)|). +Definition 4.3 (Minimal characteristic values). Let u be a name and i > 0. We define ⟨−⟩u +i and +⟨−⟩ on types as follows. +⟨?(L);S⟩u +i +def += +ui?(x).(t1!⟨⌜ui+1, . . . , ui+|G(S)|⌝⟩.0 | ⟨L⟩x +i ) +⟨S⟩ +def += +�s (|�s| = |G(S)|, �s fresh) +⟨!⟨L⟩;S⟩u +i +def += +ui!⟨⟨L⟩⟩.t1!⟨⌜ui+1, . . . , ui+|G(S)|⌝⟩.0 +⟨⟨L⟩⟩ +def += +a1 (a1 fresh) +⟨end⟩u +i +def += +0 +⟨C →⋄⟩ +def += +λ(x1, . . . , x|G(C)|). ⟨C⟩x +1 +⟨µt.S⟩u +i +def += +⟨S{end/t}⟩u +i +⟨C ⊸⋄⟩ +def += +λ(x1, . . . , x|G(C)|). ⟨C⟩x +1 +⟨⟨L⟩⟩u +i +def += +u1!⟨⟨L⟩⟩.t1!⟨⌜u1⌝⟩.0 +⟨C →⋄⟩x +i +def += +x ⟨C⟩ +⟨C ⊸⋄⟩x +i +def += +x ⟨C⟩ +where t1 is a fresh (indexed) name. In this definition we use name-passing constructs, as outlined in +Example 2.1. +Definition 4.4 (Refined environmental LTS). The refined LTS, denoted +ℓ +�−−→m, is defined on top of +the environmental LTS using the following rules: +[MTr] +(Γ1; Λ1; ∆1) ℓ−→ (Γ2; Λ2; ∆2) +ℓ ̸= n?⟨V ⟩ +(Γ1; Λ1; ∆1) +ℓ +�−−→m (Γ2; Λ2; ∆2) +28 + +[MRcv] +(Γ1; Λ1; ∆1) +n?⟨V ⟩ +−−−−→ (Γ2; Λ2; ∆2) +(V ≡ ⟨L⟩) ∨ (V ≡ λ�x. t1?(y).(y �x)) +with t1 fresh +(Γ1; Λ1; ∆1) +n?⟨V ⟩ +�−−−−→m (Γ2; Λ2; ∆2) +where λ�x. t1?(y).(y �x) is a minimal trigger value of type G(C) (Definition 4.2). +Finally, the refined LTS for MST processes is just a combination of the untyped LTS with the +refined environmental LTS: +Definition 4.5 (Refined LTS). The environmental refined LTS extends to the typed refined LTS +on processes. We write Γ1; Λ1; ∆1 ⊢ P1 +ℓ +�−−→m Λ′ +1; ∆′ +1 ⊢ P2 when +• P1 +ℓ−→ P2, and +• (Γ1; Λ1; ∆1) +ℓ +�−−→m (Γ2; Λ2; ∆2). +We write +ℓ�=⇒m for the weak version of the transition +ℓ�−→m. Notice that while the untyped LTS and +the non-refined environmental LTS coincide with that of HO, the refinement that we impose on the +environmental LTS is different from its HO counterpart. Specifically in Rule [MRcv] we take special +care to use minimal characteristic processes ⟨−⟩, instead of general HO characteristic process [(−)]c +as defined in [18]. +Relating trigger and characteristic values. +As we mentioned earlier, the notion of bisimulation +that we consider requires matching transitions of the source HO term with the transitions of the +target MST term. However, the two transitions might differ on the inputs of characteristic values. +We accommodate for that difference by establishing a relation between the trigger and characteristic +values of HO and MST. +Definition 4.6. We define the relation ▷◁ between HO processes and indexed processes inductively +as: +|˜x| = |G(C)| +λx : C. t?(y).y x ▷◁ λ˜x : G(C). t1?(y).y ˜x +[(C ⇝ ⋄)]c ▷◁ ⟨C ⇝ ⋄⟩ +where λ�x : G(C). t1?(y).(y �x) is a minimal trigger value of type G(C) ⇝ ⋄ (Definition 4.2) and [(−)]c +denotes the characteristic values defined in [18]. We write λx : C. t1?(y).y x to mean that value +λx. t1?(y).y x is of type C ⇝ ⋄. +Trigger processes and MST bisimilarity. +Before we give the definition of MST bisimilarity, +we establish the following notations: +Definition 4.7 (Indexed name). Given a name n, we write ˘n to either denote n or any indexed +name ni, with i > 0. +Definition 4.8 (Trigger process). Given a value V , a trigger process for a fresh (indexed) name t1 +is defined as: +t1 ←�H V def += t1?(�x).(V �x) +where |�x| = | �C| for V : �C ⇝ ⋄. +Lemma 4.1. If Γ; Λ; ∆ ⊢ V ▷ �C ⇝ ⋄, then Γ; Λ; ∆, t1 :?( �C) ⊢ t1 ←�H V ▷ ⋄. +Finally, we are ready to formally define MST bisimilarity. +Definition 4.9 (MST Bisimilarity). A typed relation ℜ is an MST bisimulation if for all Γ1; Λ1; ∆1 ⊢ +P1 ℜ Γ2; Λ2; ∆2 ⊢ Q1, +29 + +1) Whenever Γ1; Λ1; ∆1 ⊢ P1 +(ν � +m1) n!⟨V1⟩ +�−−−−−−−−→ Λ′ +1; ∆′ +1 ⊢ P2 then there exist Q2, ∆′ +2, and Λ′ +2 such that +Γ2; Λ2; ∆2 ⊢ Q1 +(ν � +m2) ˘n!⟨V2⟩ +�========⇒m Λ′ +2; ∆′ +2 ⊢ Q2 where, for a fresh t, +Γ1; Λ1; ∆′′ +1 ⊢ (ν � +m1)(P2 | t ←�H V1) ℜ Γ2; Λ2; ∆′′ +2 ⊢ (ν � +m2)(Q2 | ˘t ←�H V2) +2) Whenever Γ1; Λ1; ∆1 ⊢ P1 +n?(V1) +�−−−−→ Λ′ +1; ∆′ +1 ⊢ P2 then there exist Q2, Λ′ +2, and ∆′ +2 such that +Γ2; Λ2; ∆2 ⊢ Q1 +˘n?(V2) +�====⇒m Λ′ +2, ∆′ +2 ⊢ Q2 where V1 ▷◁ V2 and Γ1; Λ′ +1; ∆′ +1 ⊢ P2 ℜ Γ2; Λ′ +2; ∆′ +2 ⊢ Q2, +3) The symmetric cases of 1 and 2. +The largest such bisimulation is called MST bisimilarity, denoted by ≈M. +In all clauses, we use the refined LTS (Definition 4.5) and rely on notation ˘n (Definition 4.7). In +the output clause, we use the triggers (Definition 4.8). In the input clause, we use the relation ▷◁ on +values (Definition 4.6). +We discuss differences between MST bisimilarity and higher-order bisimilarity as defined in [18]. +First, an action in P1 must be matched by an action on an indexed name in Q1, and refined LTS +actions in P1 are matched by minimal refined LTS actions in Q1 (Definition 4.6). As a consequence +of the latter, in the input case the observed values are not identical but related by ▷◁ (Definition 4.6). +In other words, whenever P1 receives a trigger or a characteristic value, then Q1 should receive their +minimal counterparts (Definition 4.2 and Definition 4.3). Further, as names could be indexed on the +right-hand side, the typing environments could differ for open processes, so the MST bisimilarity +assumes different typing environments on both sides. +4.3 +The Bisimulation Relation +Our goal is to complement our static correctness result (Theorem 3.1) by proving the following +statement about the decomposition of processes (Definition 3.9): +Theorem 4.1. Let P be an HO process such that Γ; ∆; Λ ⊢ P ▷ ⋄. We have +Γ; Λ; ∆ ⊢ P ≈M G(Γ); G(Λ); G(∆) ⊢ D(P) +To show that P and D(P) are MST-bisimilar, we provide a concrete bisimulation relation S +that contains (P, D(P)). Defining S to be just the set of such pairs is, however, not going to work; +instead, the relation S should also contain pairs corresponding to “intermediate” states in which the +process and its decomposition may get “desynchronized”. Before we give the concrete definition of +S we look at an example, illustrating the need for such intermediate pairs. +4.3.1 +A Motivating Example +Consider the following process: +P1 = u?(t).v?(x).(ν s : S) (u!⟨x⟩.0 | t s | s!⟨x⟩.0) | v!⟨V ⟩.0 +where u :?(⟨Ut⟩);!⟨UV ⟩;end and v : S with S = ?(UV ), Ut = S →⋄, and UV is some shared value type, +i.e. UV = SV →⋄, for some session type SV . Further, V is some value, such that V = λy : SV . R. +Thus, P1 is typed using the typing of its constituents: +∅; ∅; v : S ⊢ v!⟨V ⟩.0 ▷ ⋄ +∅; ∅; u :?(⟨Ut⟩);!⟨UV ⟩;end, v : S ⊢ u?(t).v?(x).(ν s : S) (u!⟨x⟩.0 | t s | s!⟨x⟩.0) ▷ ⋄ +∅; ∅; u :?(⟨Ut⟩);!⟨UV ⟩;end, v : S, v : S ⊢ P1 ▷ ⋄ +30 + +P1 +P2 +P3 +P4 +P5 +P6 +P7 +P8 +u?(Vc) +τ +u!⟨V ⟩ +τ +τ +τ +u!⟨V ⟩ +u!⟨V ⟩ +τ +Q1 +Q′ +1 +Q′′ +1 +Q2 +Q′ +2 +Q′′ +2 +Q3 +Q′ +3 +Q′′ +3 +Q4 +Q′ +4 +Q′′ +4 +Q5 +Q′ +5 +Q′′ +5 +Q6 +Q′ +6 +Q′′ +6 +Q7 +Q′ +7 +Q′′ +7 +Q8 +u1?(V m +c ) +τ +τ +τ +τ +τ +u2!⟨V +� +V +� +⟩ +τ +τ +τ +τ +τ +τ +τ +τ +τ +u2!⟨V +� +V +� +⟩ +u2!⟨V +� +V +� +⟩ +τ +τ +τ +τ +τ +Figure 7: Transitions of P1 and Q1 = D(P1) in Section 4.3.1. The blue nodes represent processes that contain +characteristic values and trigger processes induced by the bisimilarites defined in [18]. +The decomposition of P1 is as follows: +D(P1) = (ν �c) +� +c1!⟨⟩ | B1 +ϵ +� +P1 +�� += (ν �c) +� +c1!⟨⟩ | c1?().c2!⟨⟩.c11!⟨⟩ +| c2?().u1?(t).c3!⟨t⟩ | c3?(t).v1?(x).c4!⟨t, x⟩ +| (ν s1) (c4?(t, x).c5!⟨x⟩.c6!⟨t, x⟩ | c5?(x).u2!⟨x⟩.c6!⟨⟩ | c6?() | +| c7?(t, x).c8!⟨t⟩.c9!⟨x⟩ | c8?(t).t s1 | c9?(x).s1!⟨x⟩.c10!⟨⟩ | c10?()) +| c11?().v1!⟨Vϵ +� +V +� +⟩.c12!⟨⟩ | c12?() +� +, +where �c = c1, . . . , c12. Let us write Q1 for the decomposition D(P1). +We wish to show P1 ≈M Q1. For this, we must exhibit a relation S included in ≈M such that +(P1, D(P1)) ∈ S . To illustrate the notions required to define the additional pairs, we consider +31 + +possible transitions of P1 and Q1, denoted schematically in Figure 7. First, let us consider a possible +(refined) transition of P1, an input on u of a characteristic value: +P1 +u?⟨VC⟩ +−−−−→ v?(x).(ν s : S) (u!⟨x⟩.0 | VC s | s!⟨x⟩.0) | v!⟨V ⟩.0 = P2 +where VC = [(Ut)]c = λy : S. y?(x′).(!⟨⟩.0 | x′ s′) is the characteristic value of Ut.1 Process Q1 can +weakly match this input action on the indexed name u1. This input does not involve VC but the +minimal characteristic value of type Ut (Definition 4.3). We have: +Q1 +τ−→ Q′ +1 +τ−→ Q′′ +1 +u1?⟨V m +C ⟩ +−−−−−→ (ν �c•) c3!⟨V m +C ⟩ | c3?(t).v1?(x).c4!⟨t, x⟩ | c11!⟨⟩ +| (ν s1) (c4?(t, x).c5!⟨x⟩.c7!⟨t, x⟩ | c5?(x).u2!⟨x⟩.c6!⟨⟩ | c6?() | +| c7?(t, x).c8!⟨t⟩.c9!⟨x⟩ | c8?(t).t s1 | c9?(x).s1!⟨x⟩.c10!⟨⟩ | c10?()) +| c11?().v1!⟨Vϵ +� +V +� +⟩.c12!⟨⟩ | c12?() = Q2 +where V m +C = ⟨Ut⟩ = λ(y1). y1?(x′).(t1!⟨⟩.0 | x′ �s′), with y1 :?(S), |�s′| = |G(SV )|, and �c• = c3, . . . , c12. +Hence, we should have P2 S Q2. Observe that Q2 is not exactly the decomposition of P2. First, +V m +C is not the breakdown of VC. Second, V m +C is not at the same position in Q2 as VC; the later being +in the application position and the former being pushed through several propagators. Therefore, the +relation S needs to (1) relate VC and V m +C and (2) account for the fact that a value related to VC +and thus it needs to be propagated (as in Q2). To address the first point, we establish a relation ⊠ +between characteristic values and their minimal counterparts. For the second point, we record this +fact by “decomposing” the process as P2 = P ′ +2{VC/t}, and propagating the information about this +substitution when computing the set of processes that are related to P2. +The same considerations we mentioned also apply to the value V , which is transmitted internally, +via a synchronization: +P2 +τ−→ (ν s) (u!⟨V ⟩.0 | VC s | s!⟨V ⟩.0) = P3 +Value V transmitted in P2 should be related to its corresponding breakdown Vϵ +� +V +� +, which should +be propagated through the decomposition: +Q2 +τ−→ Q′ +2 +τ−→ Q′′ +2 +τ=⇒ (ν �c••) c4!⟨V m +C , Vϵ +� +V +� +⟩ +| (ν s1) (c4?(t, x).c5!⟨x⟩.c7!⟨t, x⟩ | c5?(x).u2!⟨x⟩.c6!⟨⟩ | c6?() | +| c7?(t, x).c8!⟨t⟩.c9!⟨x⟩ | c8?(t).t s1 | c9?(x).s1!⟨x⟩.c10!⟨⟩ | c10?()) | +| c12!⟨⟩ | c12?() = Q3 +where �c•• = c4, . . . , c10, c12. +Now, in P3 we can observe the output of V along u: +P3 +u!⟨V ⟩ +−−−→ (ν s) (0 | VC s | s!⟨x⟩.0) = P4 +Process Q3 mimics this action by sending the process Vϵ +� +V +� +along name u2: +Q3 +u2!⟨Vϵ +� +V +� +⟩ +=======⇒ (ν �c∗) c7!⟨V m +C , Vϵ +� +V +� +⟩ | c6!⟨⟩ | c6?() | +| c7?(t, x).c8!⟨t⟩.c9!⟨x⟩ | c8?(t).t s1 | c9?(x).s1!⟨x⟩.c10!⟨⟩ | c10?()) = Q4 +where �c∗ = c6, . . . , c10. Following the definition of higher-order bisimilarity, we should have: +P4 ∥ t′ ←�H V S Q4 ∥ t′ +1 ←�H Vϵ +� +V +� +1We use blue to denote characteristic values and trigger processes that do no occur in the original process, but +which are induced by the bisimilarities defined in [18]. +32 + +for a fresh t′, where we have used ‘∥’ (rather than ‘|’) to denote process composition: we find it +convenient to highlight those sub-processes in parallel that originate from trigger and characteristic +processes. +We can see that the trigger process for V on the left-hand side should be matched with a trigger +process for the breakdown of V on the right-hand side. Moreover, the definition of trigger processes +should be generalized to polyadic values, as Vϵ +� +V +� +could be polyadic (see Definition 4.8). +Let us briefly consider how P4 ∥ t′ ←�H V evolves after due to the synchronization in sub-process +Vc s within P4: +P4 ∥ t′ ←�H V +τ−→ (ν s) (s?(x′).(t!⟨⟩ | x′ s′) ∥ s!⟨V ⟩.0) ∥ t′ ←�H V = P6 ∥ t′ ←�H V +We can see that Q4 can mimic this synchronization after a few administrative reductions on +propagators: +Q4 +τ=⇒ (ν c9c10) c9!⟨Vϵ +� +V +� +⟩ | s1?(x′).(t1!⟨⟩ | x′ �s′) | c9?(x).s1!⟨x⟩.c10!⟨⟩ | c10?()) ∥ t′ +1 ←�H Vϵ +� +V +� += Q6 ∥ t′ +1 ←�H Vϵ +� +V +� +Therefore, we need to have: +P6 ∥ t′ ←�H V S Q6 ∥ t′ +1 ←�H Vϵ +� +V +� +To ensure that this pair is in S , we introduce an auxiliary relation, denoted ⋄ (Definition 4.15), which +allows us to account for the sub-processes that originate from characteristic values or trigger processes +(in blue). We need to account for them separately, because one of them is not the decomposition of +the other. We thus decree: +s?(x′).(t!⟨⟩ | x′ s′) ⋄ s1?(x′).(t1!⟨⟩ | x′ �s′) +t′ ←�H V ⋄ t′ +1 ←�H Vϵ +� +V +� +Next, the synchronization on s in P6 is mimicked by Q6 with a synchronization on s1: +P6 ∥ t ←�H V +τ−→ (t!⟨⟩.0 | V s′) ∥ t′ ←�H V = P8 ∥ t′ ←�H V +Q6 ∥ t′ +1 ←�H Vϵ +� +V +� τ=⇒ (ν c10) (t1!⟨⟩ | Vϵ +� +V +� +�s′) | c10!⟨⟩ | c10?()) = Q8 ∥ t′ +1 ←�H Vϵ +� +V +� +Finally, we can see that after the output on the trigger name t there is an application that activates +R, the body of V : +P8 +t!⟨⟩ +−−→ V s′ τ−→ R{s′/y} +Q8 +t!⟨⟩ +−−→ Vϵ +� +V +� +�s′ τ−→ (ν �c∗∗) c12!⟨⟩ | B12 +ϵ +� +R +� +{�s′/�y} ≡ D(R{s′/y}) +We reached the point where we relate process R{s′/y} with its decomposition D(R{s′/y}). Hence, +the remaining pairs in S are obtained in the same way. +Key insights. +We summarize some key insights from the example: +• A received value can either be a pure value or a characteristic value. In the former case, the +pure value has to be related to its decomposition, but in the later case the value should be +related to an MST characteristic value of the same type. We define the relation ⊠ on values to +account for this (Definition 4.13). +• Trigger processes mentioned in the output case of MST bisimilarity should be matched with +their minimal counterparts, and the same applies to processes originating from such trigger +processes. The relation ⋄ accounts for this (see Definition 4.15). +• Any value in process P could have been previously received. The definition of S takes this +into account by explicitly relating processes with substitutions (see Definition 4.17). That +is, for P, it relates P ′{ ˜W/˜x} such that P ′{ ˜W/˜x} = P. Here, the substitution { ˜W/˜x} records +values that should be propagated. +33 + +4.3.2 +The relation S +In this section we give the definition of the relation S (Definition 4.17), following the insights +gathered from the example. More specifically, we define +• a relation ⊠ on values, which includes the relation ▷◁ from Definition 4.6, (Definition 4.13); +• a relation ⋄ on processes, for relating characteristic and trigger processes with their MST +counterparts, (Definition 4.15); +• a set C ˜ +W +˜x +� +P +� +of processes correlated to a process P{ ˜W/˜x}, (Table 3). +Because we will be working extensively with indexed processes, we will use the following function, +which returns a set of all valid indexing substitutions for a list of names. +Definition 4.10 (Indexed names substitutions). Let �u = (a, b, r, r, r′, r′, s, s, s′, s′, . . .) be a finite +tuple of names, where a, b, . . . denote shared names, r, r, r′, r′, . . . denote tail-recursive names , and +s, s, s′, s′, . . . denote linear (non tail-recursive names). We write index(�u) to denote +index(�u) = {a1, b1, r1, r1, r′ +1, r′ +1, si, si, s′ +j, s′ +j, . . ./a, b, r, r, r′, r′, s, s, s′, s′, . . . : i, j, . . . > 0} +Any substitution σ ∈ index(fn(P)) turns an HO process P into an indexed process Pσ. +Correlated values. +The main ingredient in defining the relation S is the the set C ˜ +W +˜x +� +P +� +, which +contains processes correlated to process P with a substitution { ˜W/˜x}. The substitution, as discussed +above, denotes previously received values, and we assume that fv(P) = �x. Essentially, C− +− +� +− +� +computes a breakdown of P{ ˜W/˜x} in parallel with an activating trio, that mimics the original actions +of P up to transitions on propagators. The activating trio propagates not the original values ˜W, +but the values related to ˜W. To do that we introduce the set C− +− +� +V +� +of correlated values and the +relation ⊠ on values, which are defined mutually recursively in the three following definitions. +Definition 4.11 (Broken down values). Given a value V , the set C +� +V +� +is defined as follows: +C +� +V +� += +� � +C +˜ +W +˜x +� +V ′� +: V = V ′{ ˜W/˜x} and V ′ is not a variable +� +We extend C +� +− +� +to work on a list of values �V component-wise, that is: +C +� +V1, . . . , Vn +� += {B1, . . . , Bn : Bi ∈ C +� +Vi +� +for i ∈ 1 . . . n}. +This way, the elements in C +� +V +� +differ in the propagated values � +W. Consider the following example: +Example 4.1. Let V = λy. y!⟨V1⟩.y!⟨V2⟩.0. There are four possibilities of V ′, � +W, and �x such that +V = V ′{ ˜W/˜x}. That is, +• V = V 1{V1V2/x1x2} where V1 = λy. y!⟨x1⟩.y!⟨x2⟩.0 +• V = V 2{V1/x1} where V 2 = λy. y!⟨x1⟩.y!⟨V2⟩.0 +• V = V 3{V2/x2} where V 3 = λy. y!⟨V1⟩.y!⟨x2⟩.0 +• Finally, we can take the identity substitution � +W = ϵ and �x = ϵ. +Thus, we have C +� +V +� += +� +CV1V2 +x1x2 +� +V 1� +, CV1 +x1 +� +V 2� +, CV2 +x2 +� +V 3� +, Cϵ +ϵ +� +V +�� +. +Definition 4.12. Given a value V , the set C ˜ +W +˜x +� +V +� +, where fn(V ) = �x is defined as follows: +C +˜ +W +˜x +� +V +� += +� +V˜x +� +V +� +{ ˜B/˜x} | � +W ⊠ �B +� +. +34 + +Definition 4.13 (Relating values). The relation ⊠ on values (with indexed names) is defined as +follows: +V1⊠V2 ⇐⇒ +� +∃V ′ +1, σ ∈ index(fn(V ′ +1)). V1 = V ′ +1σ ∧ V ′ +1 ▷◁ V2 +if V1 is a characteristic or a trigger value +V2 ∈ C +� +V1 +� +otherwise. +where ▷◁ is the relation from Definition 4.6. +Thus, in the definition of C ˜ +W +˜x +� +V +� +, the value V is related to the triggered break down values with +�B substituted for �x such that � +W ⊠ �B. +Additionally, to define C ˜ +W +˜x +� +− +� +for processes, we have to observe the behaviour of processes +enclosed in the received trigger and characteristic values. Further, we have to observe the behaviour +of trigger processes of shape t ←�H V . For this we need to define a relation ⋄ on processes that +contains pairs +([(C)]x, ⟨C⟩x +1), (t?(y).y x, t1?(y).y �x), (t ←�H V, t1 ←�H W) +where x : C and |�x| = |G(C)| and V ⊠ W. +Before we define ⋄ we need the following auxiliary definition: +Definition 4.14 (Relating names). We define ⋄ as the relation on names defined as +ϵ ⋄ ϵ +Γ; Λ; ∆ ⊢ ni ▷ C +ni ⋄ (ni, . . . , ni+|G(C)|−1) +˜n ⋄ ˜m1 +ni ⋄ ˜m2 +˜n, ni ⋄ ˜m1, ˜m2 +where ϵ denotes the empty list. +Now, we are ready to relate processes, modulo indexed names (cf. Definition 4.7), using the relation +⋄ defined as follows: +Definition 4.15 (⋄ Indexed process relation). We define the relation ⋄ as +[IPApp] +V ⊠ W +xi ⋄ ˜x +V xi ⋄ W ˜x +[IPPar] +P ⋄ P ′ +Q ⋄ Q′ +P | Q ⋄ P ′ | Q′ +[IPInact] +0 ⋄ 0 +[IPSnd] +Pσ ⋄ P ′ +V σ ⊠ W +σ = next(ni) +ni!⟨V ⟩.P ⋄ ni!⟨W⟩.P ′ +[IPRcv] +Pσ ⋄ P ′ +σ = next(ni) +ni?(y).P ⋄ ni?(y).P ′ +[IPNews] +P ⋄ P ′ +˜m1 ⋄ ˜m2 +(ν ˜m1) P ⋄ (ν ˜m2) P ′ +We can now show the property that we wanted, namely that: the bodies of trigger values and +minimal trigger values (Definition 4.2) are related; the bodies of characteristic values and minimal +characteristic values (Definition 4.3) are related; and that the trigger processes and minimal trigger +processes (Definition 4.8) are related, with appropriate name substitutions. +Lemma 4.2. We have: +� +([(C)]x{xi, t1/x, t}, ⟨C⟩x +i ), (t1?(y).y x{xi/x}, t1?(y).y �x), (t ←�H V σ, t1 ←�H W) +� +⊂ ⋄ +where i, j > 0, x : C, �x = (xi, . . . , xi+|G(C)|−1), σ ∈ index(�u), �u = fn(V ), and V σ ⊠ W. +Proof (Sketch). We may notice that ⋄ relates process up to incremented indexed names and values +related by V σ ⊠ W for some σ. More precisely, free names as subject of actions are indexed and +incremented accordingly in a related process, and names as objects of output actions are broken +down in a related process, by V σ ▷◁ W when V σ = mi, that is mi ▷◁ ˜m where mi : C and +˜m = (mi, . . . , mi+|G(C)|−1). +For the first pair ([(C)]x{xi, t1/x, t}, ⟨C⟩x +i ) by inspection of Definition 4.7 we can observe that +⟨C⟩x +i is essentially [(C)]x with its subject names indexed and incremented (starting with index i) and +objects names broken down. Thus, it is contained in ⋄. Similarly, (t?(y).y x{xi/x}, t1?(y).y �x) is +contained by observing that xi ⋄ �x. Finally, for (t ←�H V σ, t1 ←�H W), by Definition 4.8, V σ ⊠W. +35 + +Correlated processes. +Finally, we can use the introduced notions to define the set C− +− +� +− +� +of +correlated processes. As mentioned, the set C ˜ +W +˜x +� +P +� +contains processes correlated to process P with +a substitution { ˜W/˜x}. The definition of C− +− +� +− +� +is given in Table 3. Before looking into the details, +we first describe how the C− +− +� +− +� +is used. +We introduce auxiliary notions for treating free (tail-recursive) names in processes. +Definition 4.16 (Auxiliary Notions). Let P be an HO process. +• We write fpn(P) to denote the set of free propagator names in P. +• We define rfv(P) to denote free tail-recursive names in values in P. +• We define cr(P) to denote free names of form cr in P. +• We define rfni(P) such that r ∈ rfni(P) if and only if (ri, . . . , rj) ⊆ rn(P) for some i, j > 0. +• Given r : S and �r = (r1, . . . , r|G(S)|), we write R˜v to denote the process +R˜v = +� +r∈˜v +cr?(x).x �r +Definition 4.17 (Relation S ). Let P{ ˜W/˜x} be a well-typed process such that fn(P) ∩ fn(� +W) = ∅, +and let the C-set be as in Table 3. We define the relation S as follows: +S = +�� +P{ ˜W/˜x}, (ν �cr) (ν �c) R +� +: R ∈ C +˜ +Wσ +˜x +� +Pσ +� +with �u = fn(P{ ˜W/˜x}), σ ∈ index(�u), �cr = cr(R), �c = fpn(R) +� +Now we describe the definition of C− +− +� +− +� +in Table 3. Essentially, C− +− +� +− +� +computes a breakdown +of P{ ˜W/˜x} in parallel with an activating trio, that mimics the original actions of P up to transitions +on propagators. This is done with the help of J − +− +� +− +� +(also given in Table 3), which computes a +closure of a process with respect to τ-transitions on propagators. +To define the C-set we distinguish processes that do not appear in the given process, but that +are composed in parallel by the clauses of MST bisimilarity (Definition 4.9). For this we use the +following notions: +Definition 4.18 (Trigger Collections). We let H, H′ to range over trigger collections: processes of +the form P1 | · · · | Pn (with n ≥ 1), where each Pi is a trigger process or a process that originates +from a trigger or from a characteristic value. +Example 4.2. Let H1 = t1 ←�H V | [(C)]u1 | t2!⟨u2⟩.0 where t1, t2, u1, u2 are channel names, V is a +value, and C a channel type. Then, we could see that t2!⟨u2⟩.0 originates from a characteristic value. +Thus, H1 is a trigger collection. +Notice that we write P to denote a “pure” process that is not composed with a trigger collection. +For processes with trigger collections, the following notation is relevant: +Definition 4.19 (Process in parallel with a trigger or a characteristic process). We write P ∥ Q to +stand for P | Q where either P or Q is a trigger collection. +Now we can describe all the cases in the definitions of the J -set and the C-set in Table 3 (Page 37). +Observe that the second and third columns in Table 3 are closely related: the third column lists +side conditions for the definitions in the second column. Note that in each case we assume the +substitution ρ = { ˜W/˜x}. We start with the cases for C ˜ +W +˜x +� +P +� +: +36 + +P +C ˜ +W +˜x +� +P +� +Q1 ∥ Q2 +� +R1 ∥ R2 : R1 ∈ C +˜ +W1 +˜y +� +Q1 +� +, R2 ∈ C +˜ +W2 +˜w +� +Q2 +�� +�y = fv(Q1), �w = fv(Q2) +{ ˜W/˜x} = { ˜W1/˜y} · { ˜W2/ ˜w} +(ν m : C) Q +� +(ν �m : G(C)) (ν ˜cm) R : R ∈ C ˜ +W +˜x +� +Qσ +�� +�m = (m1, . . . , m|G(C)|) +σ = {m1m1/mm} +˜cm = (tr(C)) ? cm · cm: ϵ +Q +� +R˜v | ck!⟨ �B⟩ | Bk +˜x +� +P +� +} +∪ +� +R˜v\˜r | R : R ∈ J ˜ +W +˜x +� +P +� +, �r = rfni(R) +� +� +W ⊠ �B +�v = rn(P{ ˜W/˜x}) +H +� +R˜v ∥ H′ : H{ ˜W/˜x} ⋄ H′� +˜v = rn(H{ ˜W/˜x}) +P +J ˜ +W +˜x +� +P +� +ui!⟨V1⟩.Q +• ¬tr(C): +� +ui!⟨V2⟩.ck!⟨ �B2⟩ | Bk +˜z +� +Qσ +�� +• tr(C): +� +cu! +� +M +˜B2 +V2 +� +| Bk +˜w +� +Q +� +, M +˜B2 +V2 �u | Bk +˜w +� +Q +� +, +u[S⟩! +� +V2 +� +.(ck!⟨ �B2⟩ | cu?(x).x �u) | Bk +˜w +� +Q +�� +where: +M ˜B +V = λ�z. z[S⟩! +� +V +� +. (ck!⟨ �B⟩ | cu?(x).x �z) +�y = fv(V1), �w = fv(Q) +{ ˜W/˜x} = { ˜W1/˜y} · { ˜W2/ ˜w} +σ = next(ui) +V1σ{ ˜W1/˜y} ⊠ V2, � +W2 ⊠ �B2 +�z = (z1, . . . , z|R⋆(S)|) +�u = (u1, . . . , u|R⋆(S)|) +ui?(y).Q +• ¬tr(C): +� +ui?(y).ck!⟨ �By⟩ | Bk +˜xy +� +Qσ +�� +• tr(C): +� +cu! +� +M ˜B +y +� +| Bk +˜xy +� +Q +� +, M ˜B +y �u | Bk +˜xy +� +Q +� +, +u[S⟩?(y).(ck!⟨ �By⟩ | cu?(x).x �u) | Bk +˜xy +� +Q +�� +where: +M ˜B +y = λ�z. z[S⟩?(y).(ck!⟨ �By⟩ | cu?(x).x �z) +� +W ⊠ �B +σ = next(ui) +�z = (z1, . . . , z|R⋆(S)|) +�u = (u1, . . . , u|R⋆(S)|) +V1 (�r, ui) +� +|˜r|−l+1 +crl! +� +λ�zl.crl+1!⟨λ�zl+1. · · · .crn!⟨λ�zn. Ql⟩ ⟩ +� +, +λ�zl. +|˜r|−l +crl+1!⟨λ�zl+1. · · · .crn!⟨λ�zn. Ql⟩ +� +�rl, +: 1 ≤ l ≤ n, V1{ ˜W/˜x} ⊠ V2 +� +∪ {V2 �r1, . . . , �rn, �m : V1{ ˜W/˜x} ⊠ V2} +where: +Ql = V2 (�r1, . . . , �rl−1, �zl, . . . , �zn, �m) +∀ri ∈ �r.(ri : Si ∧ tr(Si)∧ +�zi = (zi +1, . . . , zi +|R⋆(Si)|), +�ri = (ri +1, . . . , ri +|R⋆(Si)|)) +ui : C +�m = (ui, . . . , ui+|G(C)|−1) +Q1 | Q2 +� +ck!⟨ �B1⟩.ck+l!⟨ �B2⟩ | Bk +˜y +� +Q1 +� +| Bk+l +˜z +� +Q2 +�� +∪� +(R1 | R2) : R1 ∈ C +˜ +W1 +˜y +� +Q1 +� +, R2 ∈ C +˜ +W2 +˜z +� +Q2 +�� +l = �Q1�, � +W1 ⊠ �B1, � +W2 ⊠ �B2 +�y = fv(Q1), �z = fv(Q2) +{ ˜W/˜x} = { ˜W1/˜y} · { ˜W2/˜z} +0 +0 +Table 3: The sets C ˜ +W +˜x +� +P +� +and J ˜ +W +˜x +� +P +� +. +Parallel with a trigger collection: The C-set of Q1 ∥ Q2 is defined as: +{R1 ∥ R2 : R1 ∈ C +˜ +W1 +˜y +� +Q1 +� +, R2 ∈ C +˜ +W2 +˜w +� +Q2 +� +} +By Definition 4.19, either Q1 or Q2 is a trigger collection. Notice that a composition Q1 | Q2 +37 + +(where both Q1 and Q2 are “pure”) is handled by J +� +− +� +, see below. We treat Q1 ∥ Q2 +compositionally: we split the substitution into parts concerning Q1 and Q2, i.e., { ˜W/˜x} = +{ ˜W1/˜y} · { ˜W2/ ˜w} such that �y = fv(Q1) and �w = fv(Q2), and relate it to a parallel composition +whose components come from a corresponding C-set. +Restriction: The C-set of (ν m : C) Q is inductively defined as: +� +(ν �m : G(C)) R : (ν ˜cm) R ∈ C +˜ +W +˜x +� +Qσ +�� +where σ = {m1m1/mm} and �m = (m1, . . . , m|G(C)|) is the decomposition of m under C. The +elements are processes from the C-set of Q with names �m restricted. In the case when restricted +name m is a tail-recursive then we also restrict the special propagator names cm and cm which +appear in R. Notice that the processes of the form (ν m) (Q1 ∥ Q2), which are induced by the +output clause of MST bisimilarity, are treated in this case in the definition of C +� +− +� +. +Pure process: The C-set of a pure process Q is defined as follows: +� +R˜v | ck!⟨ �B⟩ | Bk +˜x +� +Q +� +: � +W ⊠ �B +� +∪ +� +R˜v\˜r | R : R ∈ J ˜ +W +˜x +� +Q +� +, �r = rfni(R) +� +where �v = rn(Q{ ˜W/˜x}). The elements in the first set are essentially the decomposition of +Q (without restrictions of recursive propagators, which are handled in S ) up to different +possibilities of values �B that are ⊠-related to � +W (see Definition 4.13). Here, we remark that +R˜v is recursive name providers for all tail-recursive names of Q and � +W (by �v = rn(Q{ ˜W/˜x})). +The second set contains elements of the J -set of Q in parallel with R˜v\˜r where �r = rfni(R). +By Definition 4.16 we can see that rfni(R) denotes tail-recursive names already gathered in R +by communications that consumed R˜r : thus, we have R˜v\˜r as providers at top level. +In this sense, the processes from the second set can be seen as reducts of the processes from the +first set. For example, if we examine the C-set corresponding to the process P2 from Figure 7, +we note that the process Q2 belongs to the first set, and the processes Q′ +2 and Q′′ +3 belong to +the second set. +Trigger collection: The C-set of a trigger collection H contains its minimal counterparts, defined +using the relation ⋄ (Definition 4.15): +� +R˜v ∥ H′ : H{ ˜W/˜x} ⋄ H′� +. +where �v = rn(H{ ˜W/˜x}). In this case we do not use the information on the substitution +{ ˜W/˜x}, because the substitution information is needed for values that are, or were, propagated. +However, because H is a trigger collection, it will only contain propagators as part of values. +The substitutions related the propagators in values are already handled by the relation ⊠, +invoked by ⋄. As in the case with pure processes, the process R˜r is the recursive names provider +for the tail-recursive names of H. +We now discuss the cases for J ˜ +W +˜x +� +P +� +: +Output: The J -set of ui!⟨V1⟩.Q depends on whether (i) ui is linear or shared name (i.e., ¬tr(ui)) +or (ii) ui is a tail-recursive name (i.e., tr(ui)). In sub-case (i) J -set is defined as follows: +� +ui!⟨V2⟩.ck!⟨ �B2⟩ | Bk +˜z +� +Qσ +� +: V1σ{ ˜W1/˜y} ⊠ V2, � +W2 ⊠ �B2 +� +where σ = next(ui). By the definition, the substitution σ depends on whether ui is linear or +shared: in the former case, we use a substitution that increments ui; in the latter case we use +38 + +an identity substitution. We split � +W into � +W1 and � +W2, associated to the emitted value V1 and +the continuation Q, respectively. +Instead of the emitted value V1 we consider values V2 that are ⊠-related to V1σ{ ˜W1/˜y}. This +way, we uniformly handle cases when (i) V1 is a pure value, (ii) variable, and (iii) a characteristic +value. In particular, if V1 is a pure value, the set C +˜ +W1 +˜y +� +V1σ +� +is included in all the values ⊠-related +to V1σ{ ˜W1/˜y}. +Further, the propagator ck actives the next trio with the values �B2 such that � +W2 ⊠ �B2: as +� +W2 denotes previously received values, we take a context of ⊠-related values. Again, received +values could be either trigger and characteristic values (required to be observed by MST +bisimilarity, cf. Definition 4.9) or pure values originated from internal actions. Again, by ⊠ +(Definition 4.13) we account for both cases. +In sub-case (ii), when ui is a tail-recursive name, the elements are as follows: +� +cu! +� +M +˜B2 +V2 +� +| Bk +˜w +� +Q +� +, M +˜B2 +V2 �u | Bk +˜w +� +Q +� +, u[S⟩! +� +V2 +� +.(ck!⟨ �B2⟩ | cu?(x).x �u) | Bk +˜w +� +Q +� +: V1{ ˜W1/˜y} ⊠ V2, � +W2 ⊠ �B2 +� +where M +˜B +V = λ�z. z[S⟩! +� +V +� +.(ck!⟨ �B⟩ | cu?(x).x �z) +The first element is a process obtained by the activation from the preceding trio. +The +second element is a result of a communication of the first element with top-level provider Rui +(Definition 4.16) on channel cu. By this synchronization, the decomposition of recursive name +u, that is �u, is gathered in application M +˜B2 +V2 �u. Finally, the third element represents the result +of the application: it is a process ready to mimic the original output action on u[S⟩. Differently +from sub-case (i), here we do not have to increment index of ui in Q and V1 as indices of +recursive names are obtained based on the type S, that is [S⟩. +Input: The J -set of ui?(y).Q depends on whether (i) ui is linear or shared name (i.e., ¬tr(ui)) or +(ii) ui is a tail-recursive name (i.e., tr(ui)). In both sub-cases J -set is defined similarly to the +output case, with only one caveat: we need to expand the context for the continuation with a +newly received value y. The J -set in sub-case (i) is defined as follows: +� +ui?(y).ck!⟨ �By⟩ | Bk +˜xy +� +Qσ +� +: � +W ⊠ �B +� +where σ = next(ui). The J -set in sub-case (ii) is defined as follows: +� +cu! +� +M ˜B +y +� +| Bk +˜xy +� +Q +� +, M ˜B +y �u | Bk +˜xy +� +Q +� +, u[S⟩?(y).(ck!⟨ �By⟩ | cu?(x).x �z) | Bk +˜xy +� +Q +� +: � +W ⊠ �B +� +where: +M ˜B +y = λ�z. z[S⟩?(y).(ck!⟨ �By⟩ | cu?(x).x �z). +The elements of the set represent steps of obtaining name u[S⟩, along which the original action +is mimicked, by synchronizing with the top-level provider Rui, obtained in the corresponding +C-set. +Application: The J -set of V1 (�r, ui) where �r are tail-recursive names, is a union of two sets as +follows: +� +|˜r|−l+1 +crl! +� +λ�zl.crl+1!⟨λ�zl+1. · · · .crn!⟨λ�zn. Ql⟩ ⟩ +� +, +(λ�zl. +|˜r|−l +crl+1!⟨λ�zl+1. · · · .crn!⟨λ�zn. Ql⟩ +� +) �rl : 1 ≤ l ≤ n, +V1{ ˜W/˜x} ⊠ V2 +� +∪ +� +V2 �r1, . . . , �rn, �m : V1{ ˜W/˜x} ⊠ V2 +� +where: +Ql = V2 (�r1, . . . , �rl−1, �zl, . . . , �zn, �m) +39 + +The first set contains intermediate processes emerging while collecting recursive names using +synchronizations with recursive name providers. We can see that the body of the inner-most +abstraction, Ql, is an application of V2 (such that V1{ ˜W/˜y} ⊠ V2) to partially instantiated +recursive names: l denotes that decompositions of first l − 1 recursive names are retrieved. The +final tuple in arguments of Ql, �m = (ui, . . . , ui+|G(C)|−1), is a full decomposition of non-recursive +(linear or shared) name ui. Just like in the previous cases, by taking V2 as a ⊠-related value +to V1{ ˜W/˜y}, we uniformly handle all the three possibilities for V1 (pure value, variable, and +characteristic value). +In the first set, the first element is a process is ready to send an abstraction to an appropriate +name provider, in order to retrieve the decomposition of l-th recursive name. The second +element is a process that results from a communication of the first element with a provider: an +application which will instantiate l-th recursive name in Ql. Finally, the second set contains +application processes in which the decompositions of all n recursive names are gathered, and it +is ready to mimic the silent action (application reduction) of the original process. +Parallel composition: The J -set of Q1 | Q2 is defined using two sets: +� +ck!⟨ �B1⟩.ck+l!⟨ �B2⟩ | Bk +˜y +� +Q1 +� +| Bk+l +˜z +� +Q2 +� +: � +W1 ⊠ �B1, � +W2 ⊠ �B2 +� +∪� +(R1 | R2) : R1 ∈ C +˜ +W1 +˜y +� +Q1 +� +, R2 ∈ C +˜ +W2 +˜z +� +Q2 +�� +The first set contains a control trio that is ready to activate the decomposition of the two +components in parallel. Just like in the other cases, the control trio propagates values that are +⊠-related to ˜W1 and ˜W2. In order to close the set with respect to the τ-actions on propagators, +the second set contains the composition of processes drawn from the C-sets of Q1 and Q2, with +appropriate substitutions. +4.4 +Proving Operational Correspondence +Recall that we aim to establish Theorem 4.1. To that end, we prove that S (Definition 4.17) is an +MST bisimulation, by establishing two results: +• Lemma 4.6 covers the case in which the given process performs an action, which is matched by +an action of the decomposed process. In terms of operational correspondence (see, e.g., [11]), +this establishes completeness of the decomposition. +• Lemma 4.7 covers the converse direction, in which the decomposed process performs an action, +which is matched by the initial process. This established the soundness of the decomposition. +For proving both operational completeness and soundness, we will need the following result. +Following Parrow [21], we refer to prefixes that do not correspond to prefixes of the original process, +i.e. prefixes on propagators ci, as non-essential prefixes. Then the relation S is closed under +reductions that involve non-essential prefixes. +Lemma 4.3. Given an indexed process P1{ ˜W/˜x}, the set C ˜ +W +˜x +� +P1 +� +is closed under τ-transitions +on non-essential prefixes. That is, if R1 ∈ C ˜ +W +˜x +� +P1 +� +and R1 +τ−→ R2 is inferred from the actions on +non-essential prefixes, then R2 ∈ C ˜ +W +˜x +� +P1 +� +. +Proof. By the induction on the structure of P1. See Appendix C.1 for more details. +Operational completeness. +We first consider transitions using the unrestricted and untyped +LTS; in Lemma 4.6 we will consider transitions with the refined LTS. +40 + +Lemma 4.4. Assume P1{ ˜W/˜x} is a process such that Γ1; Λ1; ∆1 ⊢ P1{ ˜W/˜x} ▷ ⋄ with balanced(∆1) +and P1{ ˜W/˜x} S Q1. +1. Whenever P1{ ˜W/˜x} +(ν �m1) n!⟨V1⟩ +−−−−−−−−→P2 , such that n ̸∈ fn(P1{ ˜W/˜x}), then there exist Q2 and V2 +such that Q1 +(ν �m2) ˘n!⟨V2⟩ +========⇒Q2 and, for a fresh t, +(ν �m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν �m2)(Q2 ∥ t1 ←�H V2) +2. Whenever P1{ ˜W/˜x} +n?(V1) +−−−−→P2 , such that n ̸∈ fn(P1{ ˜W/˜x}), then there exist Q2, V2, and σ +such that Q1 +˘n?(V2) +====⇒Q2 where V1σ ⊠ V2 and P2 S Q2, +3. Whenever P1 +τ−→P2 then there exists Q2 such that Q1 +τ=⇒Q2 and P2 S Q2. +Proof. By transition induction. See Appendix C.2 for more details. +The following statement builds upon the previous one to address the case of the typed LTS +(Definition 4.5): +Lemma 4.5. Assume P1{ ˜W/˜x} is a process and P1{ ˜W/˜x} S Q1. +1. Whenever Γ1; Λ1; ∆1 ⊢ P1{ ˜W/˜x} +(ν � +m1) n!⟨V1⟩ +−−−−−−−−→ Λ′ +1; ∆′ +1 ⊢ P2 then there exist Q2, V2, ∆′ +2, and Λ′ +2 +such that Γ2; Λ2; ∆2 ⊢ Q1 +(ν � +m2) ˘n!⟨V2⟩ +========⇒ Λ′ +2; ∆′ +2 ⊢ Q2 and, for a fresh t, +(ν � +m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν � +m2)(Q2 ∥ t1 ←�H V2) +2. Whenever Γ1; Λ1; ∆1 ⊢ P1{ ˜W/˜x} +n?(V1) +−−−−→ Λ′ +1; ∆′ +1 ⊢ P2 then there exist Q2, V2, σ, Λ′ +2, and ∆′ +2 +such that Γ2; Λ2; ∆2 ⊢ Q1 +˘n?(V2) +====⇒ Λ′ +2, ∆′ +2 ⊢ Q2 where V1σ ⊠ V2 and P2 S Q2, +3. Whenever Γ1; Λ1; ∆1 ⊢ P1{ ˜W/˜x} τ−→ Λ′ +1; ∆′ +1 ⊢ P2 then there exist Q2, Λ′ +2, and ∆′ +2 such that +Γ2; Λ2; ∆2 ⊢ Q1 +τ=⇒ Λ′ +2; ∆′ +2 ⊢ Q2 and P2 S Q2. +Proof. The proof uses results of Lemma 4.4. We consider the first case, the other two being similar. +By the definition of the typed LTS we have: +Γ1; Λ1; ∆1 ⊢ P1{ ˜W/˜x} +(20) +(Γ1; ∅; ∆1) +(ν �m) n!⟨V ⟩ +−−−−−−−→ (Γ1; ∅; ∆2) +(21) +By (21) we further have +Γ, Γ′; Λ′; ∆′ ⊢ V ▷ U +∆′\(∪j∆j) ⊆ (∆, n : S) +Γ′; ∅; ∆j ⊢ mj ▷ Uj +Γ′; ∅; ∆′ +j ⊢ mj ▷ U ′ +j +n /∈ dom(∆) +Λ′ ⊆ Λ +[SSnd] +(Γ; Λ; ∆, s :!⟨U⟩;S) +(ν �m) n!⟨V ⟩ +−−−−−−−→ (Γ, Γ′; Λ\Λ′; (∆, n : S, ∪j∆′ +j)\∆′) +By (20) and the condition n /∈ dom(∆) we have n ̸∈ fn(P1{ ˜W/˜x}). Therefore, we can apply Item 1 +of Lemma 4.4. +Finally, we are in a position to address the case of the refined typed LTS (Definition 4.5): +Lemma 4.6. Assume P1{ ˜W/˜x} is a process and P1{ ˜W/˜x} S Q1. +41 + +1. Whenever Γ1; Λ1; ∆1 ⊢ P1{ ˜W/˜x} +(ν � +m1) n!⟨V1⟩ +�−−−−−−−−→ Λ′ +1; ∆′ +1 ⊢ P2 then there exist Q2, V2, ∆′ +2, and Λ′ +2 +such that Γ2; Λ2; ∆2 ⊢ Q1 +(ν � +m2) ˘n!⟨V2⟩ +�========⇒m Λ′ +2; ∆′ +2 ⊢ Q2 and, for a fresh t, +(ν � +m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν � +m2)(Q2 ∥ t1 ←�H V2) +2. Whenever Γ1; Λ1; ∆1 ⊢ P1{ ˜W/˜x} +n?(V1) +�−−−−→ Λ′ +1; ∆′ +1 ⊢ P2 then there exist Q2, V2, Λ′ +2, and ∆′ +2 such +that Γ2; Λ2; ∆2 ⊢ Q1 +˘n?(V2) +�====⇒m Λ′ +2, ∆′ +2 ⊢ Q2 where V1 ▷◁ V2 and P2 S Q2, +3. Whenever Γ1; Λ1; ∆1 ⊢ P1{ ˜W/˜x} τ�−→ Λ′ +1; ∆′ +1 ⊢ P2 then there exist Q2, Λ′ +2, and ∆′ +2 such that +Γ2; Λ2; ∆2 ⊢ Q1 +τ�=⇒m Λ′ +2; ∆′ +2 ⊢ Q2 and P2 S Q2. +Proof. By case analysis of the transition label ℓ. It uses results of Lemma 4.5. We consider two +cases: (i) ℓ ≡ n?(V1) and (ii) ℓ ̸≡ n?(V1). +(i) Case ℓ ≡ n?(V1). This case concerns Part (2) of the lemma. In this case we know P1 = n?(y).Q. +We have the following transition inference tree: +⟨Rv⟩ +(n?(y).P2){ ˜W/˜x} +n?(V1) +−−−−→ P2 +(22) +(22) +V1 ≡ [(U)]c ∨ V1 ≡ λx. t?(y).(y x) t fresh +⟨RRcv⟩ +(n?(y).P2){ ˜W/˜x} +n?(V1) +�−−−−→ P2 +(23) +From (22) and Lemma 4.5 we know that there exist Q2, and V2 such that Q1 +˘n?(V2) +====⇒ Q2 +and P2 S Q2 where V1σ ⊠ V2. Since V1 is a characteristic or a trigger value, we have V1 ▷◁ V2 +and that V2 is a minimal characteristic or a trigger value. Hence, Q1 +˘n?(V2) +�====⇒m Q2 using the +Rule MTr (Definition 4.5). +• Case ℓ ̸≡ n?(V ). This case concerns Parts (1) and (3) of the lemma. We only consider the +first part, when ℓ ≡ (ν �m1) n!⟨V1⟩, since the other part is similar. +We apply Lemma 4.4 to obtain Q2 such that Q1 +(ν � +m2) ˘n!⟨V2⟩ +�========⇒Q2, and, for a fresh t, +(ν � +m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν � +m2)(Q2 ∥ t1 ←�H V2). +Since we are dealing with an output action, we can immediately conclude that Q1 +(ν � +m2) ˘n!⟨V2⟩ +�========⇒mQ2. +Operational soundness. +For the proof of operational soundness we follow the same strategy of +stratifying it into three lemmas. +Lemma 4.7. Assume P1{ ˜W/˜x} is a process and P1{ ˜W/˜x} S Q1. +1. Whenever Q1 +(ν � +m2) ni!⟨V2⟩ +−−−−−−−−→Q2 , such that ni ̸∈ fn(Q1), then there exist P2 and V2 such that +P1{ ˜W/˜x} +(ν � +m2) n!⟨V2⟩ +−−−−−−−−→P2 and, for a fresh t, +(ν � +m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν � +m2)(Q2 ∥ t1 ←�H V2). +2. Whenever Q1 +ni?(V2) +−−−−→Q2 , such that ni ̸∈ fn(Q1), there exist P2, V2, and σ such that P1{ ˜W/˜x} +n?(V1) +−−−−→P2 +where V1σ ⊠ V2 and P2 S Q2. +42 + +3. Whenever Q1 +τ−→ Q2 either (i) P1{ ˜W/˜x} S Q2 or (ii) there exists P2 such that P1 +τ−→P2 and +P2 S Q2. +Proof (Sketch). By transition induction. See Appendix C.3 for more details. +Lemma 4.8. Assume P1{ ˜W/˜x} is a process and P1{ ˜W/˜x} S Q1. +1. Whenever Γ2; Λ2; ∆2 ⊢ Q1 +(ν � +m2) ˘n!⟨V2⟩ +−−−−−−−−→ Λ′ +2; ∆′ +2 ⊢ Q2 then there exist P2, V1, ∆′ +1, and Λ′ +1 such +that Γ1; Λ1; ∆1 ⊢ P1{ ˜W/˜x} +(ν � +m1) n!⟨V1⟩ +========⇒ Λ′ +1; ∆′ +1 ⊢ P2 and, for a fresh t, +(ν � +m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν � +m2)(Q2 ∥ t1 ←�H V2) +2. Whenever Γ2; Λ2; ∆2 ⊢ Q1 +˘n?(V2) +−−−−→ Λ′ +2; ∆′ +2 ⊢ Q2 then there exist P2, V1, σ, Λ′ +1, and ∆′ +1 such +that Γ1; Λ1; ∆1 ⊢ P1{ ˜W/˜x} +n?(V1) +====⇒ Λ′ +1, ∆′ +1 ⊢ P2 where V1σ ⊠ V2 and P2 S Q2, +3. Whenever Γ2; Λ2; ∆2 ⊢ Q1 +τ−→ Λ′ +2; ∆′ +2 ⊢ Q2 then there exist P2, Λ′ +1, and ∆′ +1 such that +Γ1; Λ1; ∆1 ⊢ P1{ ˜W/˜x} τ=⇒ Λ′ +1; ∆′ +1 ⊢ P2 and P2 S Q2. +Lemma 4.9. Assume P1{ ˜W/˜x} is a process and P1{ ˜W/˜x} S Q1. +1. Whenever Γ2; Λ2; ∆2 ⊢ Q1 +(ν � +m2) ˘n!⟨V2⟩ +�−−−−−−−−→ Λ′ +2; ∆′ +2 ⊢ Q2 then there exist P2, V1, ∆′ +1, and Λ′ +1 such +that Γ1; Λ1; ∆1 ⊢ P1{ ˜W/˜x} +(ν � +m1) n!⟨V1⟩ +�========⇒ Λ′ +1; ∆′ +1 ⊢ P2 and, for a fresh t, +(ν � +m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν � +m2)(Q2 ∥ t1 ←�H V2) +2. Whenever Γ2; Λ2; ∆2 ⊢ Q1 +˘n?(V2) +�−−−−→ Λ′ +2; ∆′ +2 ⊢ Q2 then there exist P2, V1,Λ′ +1, and ∆′ +1 such that +Γ1; Λ1; ∆1 ⊢ P1{ ˜W/˜x} +n?(V1) +�====⇒ Λ′ +1, ∆′ +1 ⊢ P2 where V1 ▷◁ V2 and P2 S Q2, +3. Whenever Γ2; Λ2; ∆2 ⊢ Q1 +τ�−→ Λ′ +2; ∆′ +2 ⊢ Q2 then there exist P2, Λ′ +1, and ∆′ +1 such that +Γ1; Λ1; ∆1 ⊢ P1{ ˜W/˜x} τ�=⇒ Λ′ +1; ∆′ +1 ⊢ P2 and P2 S Q2. +Summary. +Together, Lemmas 4.6 and 4.7 imply that S is an MST-bisimilarity. In summary, we +have shown Theorem 4.1, i.e., that for any typed process P, we have that +Γ; Λ; ∆ ⊢ P ≈M G(Γ); G(Λ); G(∆) ⊢ D(P). +In this section we have defined a notion of MST bisimilarity, following the notion HO bisimilarity +for non-minimal processes. Following the strategy of Parrow in the untyped setting, we defined a +relation S containing all pairs (P, D(P)), which we proved to be an MST bisimulation. +5 +Optimizations of the Decomposition +In this section we discuss two optimizations that can be applied to the decomposition process. These +optimizations simplify the structure of the trios and the nature of the underlying communication +discipline. +The first optimization replaces trios in the decomposition with duos (i.e., processes with at +most two sequential prefixes). The decomposition in Section 3 follows Parrow’s approach in that it +converts a process into a parallel composition of trios. The use of trios seems to be necessary in +(plain) π-calculus; in our first optimization we show that, by exploiting the higher-order nature of +communications in HO, the trios can be replaced by duos. +The second optimization replaces polyadic communications (sending and receiving several values +at once) with monadic communications (sending and receiving only a single value per prefix). In +the decomposition, we use polyadic communications in order to propagate dependencies through +sub-processes. We show that the use of monadic communication prefixes is sufficient for that task. +43 + +From Trios to Duos. +In the first optimization we replace trios with duos, i.e., processes with at +most two sequential prefixes. This optimization is enabled by the higher-order nature of HO. In the +translation we make of thunk processes, i.e., inactive processes that can be activated upon reception. +We write {{P}} to stand for the thunk process λx : ⟨end→⋄⟩. P, for a fresh x ̸∈ fn(P). We write +run {{P}} to denote the application of a thunk to a (dummy) name of type end→⋄. This way, we +have a reduction run {{P}} −→ P. +The key idea behind replacing trios with duos is to transform a trio like +ck?(�x).u!⟨V ⟩.ck+1!⟨�z⟩ +into the composition of two duos, the second one being a “control” duo: +ck?(�x).c0! +� +{{u!⟨V ⟩.ck+1!⟨�z⟩}} +� +| c0?(y).(run y) +(24) +The first action (on ck) is as before; the two remaining prefixes (on u and ck+1) are encapsulated +into a thunk. This thunk is sent via an additional propagator (denoted c0) to the control duo that +activates it upon reception. Because of this additional propagator, this transformation involves +minor modifications in the definition of the degree function �−� (cf. Definition 3.6). +In some cases, the breakdown function in Section 3.2 already produces duos. Breaking down input +and output prefixes and parallel composition involves proper trios; following the scheme illustrated +by (24), we can define a map {|−|} to transform these trios into duos: +{|ck?(�x).ui!⟨V ⟩.ck+1!⟨�z⟩|} = ck?(�x).ck+1! +� +{{ui!⟨V ⟩.ck+2!⟨�z⟩}} +� +| ck+1?(y).(run y) +{|ck?(�x).ui?(y).ck+1!⟨�x′⟩|} = ck?(�x).ck+1! +� +{{ui?(y).ck+2!⟨�x′⟩}} +� +| ck+1?(y).(run y) +{|ck?(�x).ck+1!⟨�y⟩.ck+l+1!⟨�z⟩|} = ck?(�x).ck+1! +� +{{ck+2!⟨�y⟩.ck+l+2!⟨�z⟩}} +� +| ck+1?(y).(run y) +In breaking down prefixes involving tail-recursive names (Table 1) we encounter trios of the +following form: +B +� +ui?(y).Q +� += ck?(�x).cu! +� +Ny +� +| Bk+1 +˜w +� +Q +� +where +Ny = λ�z. z[S⟩?(y). +� +ck+1!⟨ �w⟩ | cu?(x).x �z +� +) +Here we can see that the top-level process is a duo and that only Ny packs a proper trio process. By +applying the same idea we can translate this trio into the following composition of duos: +{|z[S⟩?(y). +� +ck+1!⟨ �w⟩ | cu?(x).x �z +� +|} = z[S⟩?(y).ck+1!⟨{{ck+2!⟨ �w⟩ | cu?(x).x �z}}⟩ | ck+1?(y).run y +This is the idea behind the breakdown of a process starting with an input prefix; the breakdown of a +process with an output prefix follows the same lines. +From Polyadic to Monadic Communication. +Our second optimization replaces polyadic +communications, used for the propagators, with monadic communications. Recall that propagators +in B +� +− +� +serve two purposes: they (i) encode sequentiality by properly activating trios and (ii) +propagate bound values. By separating propagators along those two roles, we can we can dispense +with polyadic communication in the breakdown function. +We define monadic breakdown, B +� +− +� +, and monadic decomposition, D(−), which use two kinds of +propagators: (i) propagators for only activating trios of form ck (where k > 0 is an index) and (ii) +for propagating bound values of form cx (where x is some variable). We depict the mechanism of the +monadic breakdown in Figure 8. The main idea is to establish a direct link between trio that binds +the variable x and trios that make use of x on propagator channel cx. Thus, propagators on ck only +serve to activate next trios: they do so by receiving an abstraction that contains the next trio. +Formally, we define a monadic decomposition, D(P), that simplifies Definition 3.9 as follows: +D(P) = (ν �c) +� +ck!⟨⟩ | Bk� +Pσ +�� +where k > 0, �c = (ck, . . . , ck+�P�−1), and the initializing substitution σ = {index(�u)/�u} is the same as +in Definition 3.9. +44 + +Source process P1: +P1 +P2 +P3 +0 +u :?(str) +u :?(int) +u :!⟨bool⟩ +Monadic decomposition D(P1): +Q1 +Q′ +1 +u1 :?(str) +∥ +Q2 +Q′ +2 +u2 :?(int) +∥ +Q3 +Q′ +3 +u3 :!⟨bool⟩ +∥ +Q4 +x : str +y : int +Figure 8: Our monadic decomposition function D(−), illustrated. As in Figure 4, nodes represent process +states, ‘∥’ represents parallel composition of processes, black arrows stand for actions, and red arrows +indicate synchronizations that preserve the sequentiality of the source process; also, blue arrows indicates +synchronizations that propagate (bound) values. +Vx = λy. y?(z).cx!⟨x⟩.(ν s) (z s | s!⟨z⟩) +W ⇝ +x = +� +cx! +� +x +� +if ⇝=⊸ +(ν s) (Vx s | s!⟨Vx⟩) +if ⇝=→ +Bk� +ui?(x : C ⇝ ⋄).Q +� += (ν cx) +� +ck?().ui?(x).(ck+1!⟨⟩ | W ⇝ +x ) +� +| Bk+1� +Qσ +�� +Bk� +ui!⟨x⟩.Q +� += ck?().cx?(x).ui!⟨x⟩.ck+1!⟨⟩ | Bk+1� +Qσ +� +Bk� +ui!⟨V ⟩.Q +� += ck?().ui!⟨V +� +V σ +� +⟩.ck+1!⟨⟩ | Bk+1� +Qσ +� +Bk� +x ui +� += ck?().cx?(x).x �m +Bk� +V ui +� += ck?().V +� +V +� +�m +Bk� +(ν s) P ′� += (ν �s) Bk� +P ′σ +� +Bk� +Q | R +� += ck?().ck+1!⟨⟩.ck+�Q�+1!⟨⟩ | Bk+1� +Q +� +| Bk+�Q�+1� +R +� +V +� +y +� += y +V +� +λy : C⇝. P +� += λ(y1, . . . , y|G(C)|) : G(C)⇝. (ν c1, . . . , c�P�) +� +c1!⟨⟩ | B1� +P{y1/y} +�� +Figure 9: Monadic breakdown of processes and values +The monadic break down function Bk� +− +� +, given in Figure 9, simplifies the one in Table 1 by +using only one parameter, namely k. In Figure 9 we use σ to denote the subsequent substitution +next(ui), the same as in Table 1, and use �m to denote the breakdown (ui, . . . , ui+|G(C)|−1) of the +name ui. +The breakdown function Bk� +− +� +uses propagators ck (k > 0) for encoding sequentiality and +dedicated propagators cx for each variable x. As propagators ck now only serve to encode sequentiality, +only dummy values are being communicated along these channels (see Remark 3.2). +Let us describe the breakdown of a process with an input prefix, as it illustrates the key points +common to all the other cases. The breakdown Bk� +ui?(x).Q +� +consists of a trio in parallel with the +breakdown of the continuation Bk+1� +Qσ +� +with name cx restricted. The trio is first activated on ck. +This is followed by the prefix that mimics original input action on indexed name ui. Upon receiving +value x, two things will happen in parallel. First, the next trio will be activated on name ck+1. +45 + +Second, the value x received on ui is propagated further by the dedicated process W ⇝ +x . +The specific mechanism of propagation depends on whether a received value is linear (⇝=⊸) or +shared (⇝=→). In the former case, we simply propagate a value along the linear name cx once. +In the later case, we cannot propagate the value only once, because a shared variable can be used +in multiple trios. Thus, W → +x +implements a recursive mechanism that repeatedly sends a value on +the shared name cx. The recursion is encoded in the same way as in Example 3.4: action cx!⟨x⟩ is +enclosed in value V that gets appropriately duplicated upon a synchronization. +The breakdown function for values, V +� +− +� +, is accordingly changed to invoke B1� +− +� +for breaking +down a function body. +For simplicity, we defined the decomposition of the output process using a subprocess with four +prefixes. Alternatively, we could have used a decomposition that relies on two trios, by introducing +abstraction passing as in the previous section. +Let us illustrate the monadic breakdown by the means of an example: +Example 5.1 (Monadic Decomposition). We again consider process P = (ν u) (Q | R) as in Exam- +ple 3.7 where: +Q = u?(x). +Q′ +� +�� +� +u?(y).(ν s) +� +x s | s!⟨y⟩ +� +R = u!⟨V ⟩.u!⟨true⟩.0 +V = λz. z?(w).0 +Let us recall the reductions of P: +P −→ u?(y).(ν s) +� +V s | s!⟨y⟩ +� +| u!⟨true⟩.0 −→ (ν s) +� +V s | s!⟨true⟩ +� +−→ (ν s) +� +s?(w).0 | s!⟨true⟩ +� += P ′ +The monadic decomposition of P is as follows: +D(P) = (ν c1, . . . , c10) (ν u1, u2) +� +c1!⟨⟩ | B1� +Pσ +�� +where σ = {u1u1/uu}. We have: +B1� +Pσ +� += c1?().c2!⟨⟩.c8!⟨⟩ | B2� +Qσ +� +| B8� +Rσ +� +where: +B2� +Qσ +� += (ν cx) +� +c2?().u1?(x).(c3!⟨⟩ | cx!⟨x⟩ +� +| B3� +Q′σ′�� +B3� +Q′σ′� += (ν cy) +� +c3?().u2?(y).(c4!⟨⟩ | Wy +� +| B4� +(ν s) +� +x s | s!⟨y⟩ +��� +B4� +(ν s) +� +x s | s!⟨y⟩ +�� += (ν s1) c4?().c5!⟨⟩.c6!⟨⟩ | c5?().cx?(x).x s1 | +c6?().cy?(y).s1!⟨y⟩.c7!⟨⟩ | c7?().0 +B8� +Rσ +� += c8?().u1!⟨V +� +V +� +⟩.c9!⟨⟩ | B9� +u2!⟨true⟩.0 +� +B9� +u2!⟨true⟩.0 +� += c9?().u2!⟨true⟩.c10!⟨⟩ | c10?().0 +V +� +V +� += λz1. (ν cV +1 , cV +2 ) cV +1 !⟨⟩ | +(ν cw) cV +1 ?(z).z1?(w).(cV +2 !⟨⟩ | Ww) | cV +2 ?().0 +where Wx = (ν s) (Vx s | s!⟨Vx⟩) with Vx = λy. y?(z).cx!⟨x⟩.(ν s) (z s | s!⟨z⟩). We may observe that +D(P) correctly implements u1 and u2 typed with MSTs M1 and M2 (resp.) as given in Example 3.7. +Now, we inspect the reductions of D(P). First we have three reductions on propagators: +D(P) −→ (ν c2, . . . , c10) (ν u1, u2) c2!⟨⟩.c8!⟨⟩ | B2� +Qσ +� +| B8� +Rσ +� +−→2 (ν c3, . . . , c7, c9, c10) (ν cx) +� +u1?(x). (c3!⟨⟩ | cx!⟨x⟩ +� +| B3� +Q′σ′�� +| u1!⟨V +� +V +� +⟩. c9!⟨⟩ | B9� +u2!⟨true⟩.0 +� += D1 +46 + +Now, the synchronization on u1 can take a place in D1 (on the prefixes highlighted above). We can +see that value V +� +V +� +received on u1 can be propagated along cx to a trio using it. Following up on +that, propagators c3 and c9 are synchronized. +D1 −→ (ν c3, . . . , c7, c9, c10) (ν cx) +� +c3!⟨⟩ | cx!⟨V +� +V +� +⟩ | +| (ν cy) +� +c3?().u2?(y).(c4!⟨⟩ | Wy +� +| B4� +(ν s) +� +x s | s!⟨y⟩ +���� +| c9!⟨⟩ | B9� +u2!⟨true⟩.0 +� +−→2 (ν c4, . . . , c7, c10) (ν cx) +� +cx!⟨V +� +V +� +⟩ | +| (ν cy) +� +u2?(y). (c4!⟨⟩ | Wy +� +| B4� +(ν s) +� +x s | s!⟨y⟩ +���� +| u2!⟨true⟩. c10!⟨⟩ | c10?().0 = D2 +Similarly, D2 can mimic the synchronization on name u2. Again, this is followed by synchronizations +on propagators. +D2 −→ (ν c4, . . . , c7, c10) (ν cx) +� +cx!⟨V +� +V +� +⟩ | (ν cy) +� +c4!⟨⟩ | Wy{true/y} | B4� +(ν s) +� +x s | s!⟨y⟩ +���� +| c10!⟨⟩ | c10?().0 +−→4 (ν c7) (ν cx) +� +cx!⟨V +� +V +� +⟩ | (ν cy) +� +Wy{true/y} | (ν s1) cx?(x).x s1 +| cy?(y).s1!⟨y⟩.c7!⟨⟩ | c7?().0 +�� += D3 +The subprocess Wy{true/y} is dedicated to providing the value true on a shared name cy. Specifically, +it reduces as follow Its reductions are as follows: +Wy{true/y} −→2 cy!⟨true⟩.Wy{true/y} +In this example, the shared value received on y is used only once; in the general case, a process +could use a shared value multiple times: thus there could be multiple trios requesting the shared +value on cy. +With this information, we have the following reductions of the decomposed process: +D3 −→2 (ν c7) (ν cx) +� +cx!⟨V +� +V +� +⟩ | (ν cy) +� +cy!⟨true⟩.Wy{true/y} | (ν s1) cx?(x).x s1 +| cy?(y).s1!⟨y⟩.c7!⟨⟩ | c7?().0 +�� += D4 +In D4 a value for x is requested on name cx before it is applied to name s1. Similarly, a value for y is +gathered by the communication on cy. These values are retrieved in two reductions steps as follows: +D4 −→2 (ν c7) (ν s1) V +� +V +� +s1 | s1!⟨true⟩.c7!⟨⟩ | c7?().0 | (ν cy) Wy{true/y} = D5 +We remark that (ν cy) Wy{true/y} reduces to (ν cy) cy!⟨true⟩.Wy{true/y} which is behaviorally equiva- +lent to the inactive process. +Next, the application of the value is followed by the synchronization on propagator cV +1 : +D5 −→ (ν c7) (ν s1) (ν cV +1 , cV +2 ) cV +1 !⟨⟩ | (ν cw) cV +1 ?().s1?(w).(cV +2 !⟨⟩ | Ww) | cV +2 ?()0 +| s1!⟨true⟩.c7!⟨⟩ | c7?().0 | (ν cy) Wy{true/y} +−→ (ν c7) (ν s1) (ν cV +2 ) (ν cw) s1?(w).(cV +2 !⟨⟩ | Ww) | cV +2 ?()0 +| s1!⟨true⟩.c7!⟨⟩ | c7?().0 | (ν cy) Wy{true/y} = D6 +Here, we can see that D6 can simulate P ′, and its internal communication on the channel s. +6 +Extension with Labeled Choice +In this section we discuss how to extend our approach to include sessions with selection and branching +– constructs which are used commonly in session types to express deterministic choices. Forgoing +formal proofs, we illustrate by examples how to harness the expressive power of abstraction-passing +to decompose these constructs at the process level. First, we demonstrate how to break down +47 + +(Sel) +Γ; Λ; ∆, u : Sj ⊢ P ▷ ⋄ +j ∈ I +Γ; Λ; ∆, u : ⊕{li : Si}i∈I ⊢ u ◁ lj.P ▷ ⋄ +(Bra) +∀i ∈ I +Γ; Λ; ∆, u : Si ⊢ Pi ▷ ⋄ +Γ; Λ; ∆, u : &{li : Si}i∈I ⊢ u ▷ {li : Pi}i∈I ▷ ⋄ +Figure 10: Typing rules for selection and branching. +selection and branching constructs in absence of recursion in Section 6.1. Then, in Section 6.2 we +explore the interplay of recursion and labeled choice, as it requires special attention. Finally, in +Section 6.3 we sketch how the operational correspondence proof can be adapted to account for +branching and selection. +Let us briefly recall the labeled choice constructs in HO, following [17]. On the level of processes, +selection and branching are modeled using labeled choice: +P, Q ::= . . . | u ◁ l.P | u ▷ {li : Pi}i∈I +The process u◁l.P selects the label l on channel u and then proceeds as P. The process u▷{li : Pi}i∈I +receives a label on the channel u and proceeds with the continuation branch Pi based on the received +label. Selection and branching constructs can synchronize with each other, as represented in the +operational semantics by the following reduction rule: +u ◁ lj.Q | u ▷ {li : Pi}i∈I −→ Q | Pj +(j ∈ I) [Sel] +At the level of types, selection and branching are represented with the following types: +S ::= . . . | ⊕ {li : Si}i∈I | &{li : Si}i∈I +The selection type ⊕{li : Si}i∈I and the branching type &{li : Si}i∈I are used to type, respectively, +the selection and branching process constructs. +Note the implicit sequencing in the sessions +involving selection and branching: the exchange of a label li precedes the execution of one of the +stipulated protocol Si. The typing rules for type-checking branching and selection processes are +given in Figure 10. +Given these process constructs and types, what are the minimal versions of the session types +with labeled choice? We do not consider branching and selection as atomic actions as their purpose +is to make a choice of a stipulated protocol. In other words, it is not meaningful to type a channel +with branching type in which all protocols are end. Thus, we extend the minimal syntax types +Definition 3.1 with branching and selection constructs as follows: +M ::= . . . | ⊕ {li : Mi}i∈I | &{li : Mi}i∈I +That is, MSTs also include branching and selection types with MSTs nested in branches. +Next we explain our strategy for extending the breakdown function to account for selection and +branching. +6.1 +Breaking Down Selection and Branching +Notice that in a branching process u ▷ {li : Pi}i∈I each subprocess Pi can have a different session +with a different degree. Abstraction-passing allows to uniformly handle these kinds of processes. We +extend the breakdown function in Definition 3.3 to selection and branching as follows: +G(&{li : Si}i∈I) = &{li :!⟨G(Si)⊸⋄⟩}i∈I +G(⊕{li : Si}i∈I) = ⊕{li :?(G(Si)⊸⋄)}i∈I +This decomposition follows the intuition that branching and selection correspond to the input and +output of labels, respectively. For example, in the case of branching, once a particular branch li +48 + +has been selected, we would like to input names on which to provide sessions from the branch +G(Si). In our higher-order setting, we do not input or output names directly. Instead, we send +out an abstraction of the continuation process, which binds those names. It is then the job of the +(complementary) selecting process to activate that abstraction with the names we want to select. +To make this more concrete, let us consider decomposition of branching and selection at the level +of processes through the following extended example. +Example 6.1. Consider a mathematical server Q that offers clients two operations: addition and +negation of integers. The server uses name u to implement the following session type: +S = &{add : ?(int);?(int);!⟨int⟩;end +� +�� +� +Sadd +, neg : ?(int);!⟨int⟩;end +� +�� +� +Sneg +} +The branches have session types with different lengths: one receives two integers and sends over +their sum, the other has a single input of an integer followed by an output of its negation. Let us +consider a possible implementation for the server Q and for a client R that selects the first branch +to add integers 16 and 26: +Q ≜ u ▷ {add : Qadd, neg : Qneg} +R ≜ u ◁ add.u!⟨16⟩.u!⟨26⟩.u?(r) +Qadd ≜ u?(a).u?(b).u!⟨a + b⟩ +Qneg ≜ u?(a).u!⟨−a⟩ +The composed process P ≜ (ν u) (Q | R) can reduce as follows: +P −→ (ν u) (u?(a).u?(b).u!⟨a + b⟩ | u!⟨16⟩.u!⟨26⟩.u?(r)) −→2 (ν u) (u!⟨16 + 26⟩ | u?(r)) = P ′ +Let us discuss the decomposition of P. First, the decomposition of S is the minimal session type M, +defined as follows: +M = G(S) = &{add :!⟨ +� +?(int), ?(int), !⟨int⟩ +� +⊸⋄⟩, +neg :!⟨ +� +?(int), !⟨int⟩ +� +⊸⋄⟩} +Following Definition 3.9, we decompose P as follows: +D(P) = (ν c1 . . . c7) +� +c1!⟨⟩ | (ν u1) (c1?().c2!⟨⟩.c3!⟨⟩ | B2 +ϵ +� +Qσ2 +� +| B3 +ϵ +� +Rσ2 +� +) +� +where σ2 = {u1u1/uu}. The breakdown of the server process Q, which implements the branching, is +as follows: +B2 +ϵ +� +Qσ2 +� += c2?().u1 ▷ {add : u1! +� +λ(y1, y2, y3). (ν cV +1 . . . cV +4 ) cV +1 !⟨⟩ | B1 +ϵ +� +Qadd{y1/u} +� +σV +� +�� +� +V +� +, +neg : u1! +� +λ(y1, y2). (ν cW +1 . . . cW +3 ) cW +1 !⟨⟩ | B1 +ϵ +� +Qneg{y1/u} +� +σW +� +�� +� +W +� +} +where: +B1 +ϵ +� +Qadd{y1/u} +� += c1?().y1?(a).c2!⟨a⟩ | c2?(a).y2?(b).c3!⟨a, b⟩ | c3?(a, b).y3!⟨a + b⟩.c4!⟨⟩ | c4?() +B1 +ϵ +� +Qneg{y1/u} +� += c1?().y1?(a).c2!⟨a⟩ | c2?(a).y2!⟨−a⟩.c3!⟨⟩ | c3?() +with σV = {cV +1 , . . . , cV +4/c1, . . . , c4} and σW = {cW +1 , cW +2 , cW +3 /c1, c2, c3}. In process B2 +ϵ +� +Qσ2 +� +, name u1 +implements the minimal session type M. Following the common trio structure, the first prefix awaits +activation on c2. The next prefix mimics the branching action of Q on u1. Then, each branch +consists of the output of an abstraction along u1. This output does not have a counterpart in Q; it +is meant to synchronize with process B3 +ϵ +� +Rσ2 +� +, the breakdown of the corresponding selection process +(see below). +49 + +The abstractions sent along u1 encapsulate the breakdown of subprocesses in the two branches +(Qadd and Qneg). An abstraction in the branch has the same structure as the breakdown of a value +λy : C→. P in Table 1: it is a composition of a control trio and the breakdown of a subprocess; the +generated propagators are restricted. In the first branch the server needs three actions to perform +the session, and in the second branch the server needs to perform two actions. Because of that the +first abstraction binds three names y1, y2, y3, and the second abstraction binds two names y1, y2. +In the bodies of the abstractions we break down Qadd and Qneg, but not before adjusting the +names on which the broken down processes provide the sessions. For this, we substitute u with y1 in +both processes, ensuring that the broken down names are bound by the abstractions. By binding +decomposed names in abstractions we account for different session types of the original name in +branches, while preserving typability: this way the decomposition of different branches can use +(i) the same names but typed with different minimal types and (ii) a different number of names, as +it is the case in this example. +The decomposition of the client process R, which implements the selection, is as follows: +B3 +ϵ +� +Rσ2 +� += (ν u2, u3, u4) c3?().u1 ◁ add.u1?(z).c4!⟨⟩.z (u2, u3, u4) | B4 +ϵ +� +u2!⟨16⟩.u2!⟨26⟩.u2?(r) +� +where: +B4 +ϵ +� +u2!⟨16⟩.u2!⟨26⟩.u2?(r) +� += c4?().u2!⟨16⟩.c5!⟨⟩ | c5?().u3!⟨26⟩.c6!⟨⟩ | c6?().u4?(r).c7!⟨⟩ | c7?() +After receiving the context on c3 (empty in this case), the selection action on u1 is mimicked; then, +an abstraction (an encapsulation of the selected branch) is received and applied to (u2, u3, u4), which +are locally bound. The intention is to use these names to connect the received abstraction and the +continuation of a selection process: the subprocess encapsulated within the abstraction will use +(u2, u3, u4), while the dual names (u2, u3, u4) are present in the breakdown of the continuation. +For simplicity, we defined B3 +ϵ +� +Rσ2 +� +using a subprocess with four prefixes. Alternatively, we could +have used a decomposition that relies on two trios, by introducing abstraction passing as in Section 5. +We will now examine the reductions of the decomposed process D(P). First, c1, c2, and c3 will +synchronize. We have D(P) −→4 D1, where +D1 = (ν c4 . . . c7) (ν u1) +� +u1 ▷ {add : u1! +� +V +� +, neg : u1! +� +W +� +} +| (ν u2, u3, u4) (λ(y1, y2, y3). u1 ◁ add.u1?(z).c4!⟨⟩.z (y1, y2, y3)) (u2, u3, u4) | +B4 +ϵ +� +u!⟨26⟩.u?(r) +�� +In D1, (u2, u3, u4) will be applied to the abstraction; after that, the process chooses the label add on +u1. Process D1 will reduce further as D1 −→2 D2 −→2 D3, where: +D2 = (ν c4 . . . c7) (ν u1) +� +u1! +� +V +� +| (ν u2, u3, u4) (u1?(z).c4!⟨⟩.z (u2, u3, u4) | B4 +ϵ +� +u!⟨26⟩.u?(r) +� +) +� +D3 = (ν c4 . . . c7) (ν u1, u2, u3, u4) +� +c4!⟨⟩.V (u2, u3, u4) | +c4?().u2!⟨16⟩.c5!⟨⟩ | c5?().u3!⟨26⟩.c6!⟨⟩ | c6?().u4?(r).c7!⟨⟩ | c7?() +� +Then D3 reduces as D3 −→ D4 −→ D5, where: +D4 = (ν c5 . . . c7) (ν u2, u3, u4) +� +(ν cV +1 . . . cV +4 ) (cV +1 !⟨⟩ | cV +1 ?().u2?(a).cV +2 !⟨a⟩ | cV +2 ?(a).u3?(b).cV +3 !⟨a, b⟩ | +cV +3 ?(a, b).u4!⟨a + b⟩.cV +4 !⟨⟩ | cV +4 ?()) | +u2!⟨16⟩.c5!⟨⟩ | c5?().u3!⟨26⟩.c6!⟨⟩ | c6?().u4?(r).c7!⟨⟩ | c7?() +� +D5 = (ν c5 . . . c7) (ν u2, u3, u4) +� +(ν cV +2 . . . cV +4 ) (u2?(a).cV +2 !⟨a⟩ | cV +2 ?(a).u3?(b).cV +3 !⟨a, b⟩ | +cV +3 ?(a, b).u4!⟨a + b⟩.cV +4 !⟨⟩ | cV +4 ?()) | +u2!⟨16⟩.c5!⟨⟩ | c5?().u3!⟨26⟩.c6!⟨⟩ | c6?().u4?(r).c7!⟨⟩ | c7?() +� +50 + +Now, process D5 can mimic the original transmission of the integer 16 on channel u2 as follows: +D5 −→ (ν c5 . . . c7) (ν u2, u3, u4) +� +(ν cV +2 . . . cV +4 ) (cV +2 !⟨16⟩ | cV +2 ?(a).u3?(b).cV +3 !⟨a, b⟩ | +cV +3 ?(a, b).u4!⟨a + b⟩.cV +4 !⟨⟩ | cV +4 ?()) | +c5!⟨⟩ | c5?().u3!⟨26⟩.c6!⟨⟩ | c6?().u4?(r).c7!⟨⟩ | c7?() +� += D6 +Finally, process D6 reduces to D7 in three steps, as follows: +D6 −→3 (ν c5 . . . c7) (ν u4) +� +(ν cV +4 ) (u4!⟨16 + 26⟩.cV +4 !⟨⟩ | cV +4 ?()) | u4?(r).c7!⟨⟩ | c7?() +� += D7 +Clearly, process D7 correctly simulates the synchronizations of the process P ′. +◁ +6.2 +The Interplay of Selection/Branching and Recursion +Now, we discuss by example how recursive session types involving branching/selection are broken +down. For simplicity, we consider recursive types without nested recursion and in which the recursive +step is followed immediately by branching or selection, without any intermediate actions, i.e. types +of the following form: +µt.&{li : Si}i∈I +µt. ⊕ {li : Si}i∈I +where none of Si contain branching/selection or recursion. +In this case, the decomposition of branching recursive types should be defined differently than +for tail-recursive types: a type such as µt.&{li : Si}i∈I does not necessarily describe a channel +with an infinite behavior, because some of the branches Si can result in termination. In such case, +decomposing all actions in the type &{li : Si}i∈I as their own recursive types using the R(−) function +would be incorrect. +Instead, we decompose the body of the recursive type with G(−) itself: +G(µt.&{li : Si}i∈I) = µt.&{li :!⟨G(Si)⊸⋄⟩}i∈I +G(µt. ⊕ {li : Si}i∈I) = µt. ⊕ {li :?(G(Si)⊸⋄)}i∈I +If some branch Si contains the recursion variable t, then it will appear in G(Si), because G(t) = t. +That is, recursion variables will appear as part of the abstraction G(Si)⊸⋄. That means that the +decomposition of a tail-recursive type form can produce a minimal non-tail-recursive types. +Now, we illustrate this decomposition on the level of processes. +Example 6.2. We consider a process P with a name r that is typed as follows: +S = µt.&{l1 :?(str);!⟨int⟩;t, l2 : end}. +For simplicity, we give P in HOπ (which includes HO with recursion as sub-calculus): +P = R | Q +R = µX.r ▷ {l1 : r?(t).r!⟨len(t)⟩.X, l2 : 0} +Q = r ◁ l1.r!⟨“Hello”⟩.r?(a1).r ◁ l1.r!⟨“World”⟩.r?(a2).r ◁ l2.0 +That is, P contains a server R which either accepts a new request to calculate a length of a string, +or to terminate. Dually, P contains a client Q, which uses the server twice before terminating. +We can give an equivalent process in HO by encoding the recursion (as done in [17]): +�P� = �R� | Q +�R� = (ν s) (V r, s | ¯s!⟨V ⟩) +V = λ(xr, xs). xs?(y).xr ▷ {l1 : xr?(t).xr!⟨len(t)⟩.(ν s) (y (xr, s) | s!⟨y⟩), l2 : 0} +51 + +The decomposition of S, denoted M∗, is the following minimal session type: +M∗ = G(S) = µt.&{l1 :!⟨(?(str), !⟨int⟩, t)⊸⋄⟩, l2 : end} +As in the previous example (Example 6.1), the continuation of a selected branch will be packed in +an abstraction and sent over. This abstraction binds names on which the session actions should be +performed. In addition, if a branch contains a recursive call, then the last argument of the abstraction +will be a name on which the next instance of the recursion will be mimicked. We illustrate this +mechanism by giving the decomposition of �P� and inspecting its reductions. +D(�P�) = (ν c1, . . . , c12) c1!⟨⟩ | c1?().c2!⟨⟩.c5!⟨⟩ | B2 +ϵ +� +�R� +� +| B5 +ϵ +� +Q +� +B2 +ϵ +� +�R� +� += (ν s1) (c2?().c3!⟨⟩.c4!⟨⟩ | c3?().Vϵ +� +V +� +(r1, s1) | c4?().s1!⟨Vϵ +� +V +� +⟩) +Vϵ +� +V +� += λ(xr1, xs1). (ν cV +1 cV +2 ) cV +1 !⟨⟩ | cV +1 ?().xs1?(y).cV +2 !⟨y⟩ | cV +2 ?(y).xr1 ▷ {l1 : xr1!⟨W⟩, l2 : 0} +W = λ(z1, z2, z3). (ν cW +1 . . . cW +5 ) cW +1 !⟨⟩ | cW +1 ?().z1?(t).cW +2 !⟨t⟩ | cW +2 ?(t).z2!⟨len(t)⟩.cW +3 !⟨⟩ +| (ν s1) (cW +3 ?().cW +4 !⟨⟩.cW +5 !⟨⟩ | cW +4 ?().y (z3, s1) | cW +5 ?().s1!⟨y⟩) +B5� +Q +� += (ν r2 :?(str), r3 :!⟨int⟩, r4 : M∗) +c5?().r1 ◁ l1.c6!⟨⟩.r1?(y).y (r2, r3, r4) | +c6?().r2!⟨“Hello”⟩.c7!⟨⟩ | c7?().r3?(t).c11!⟨⟩ | +(ν r5 :?(str), r6 :!⟨int⟩, r7 : M∗) +c8?().r4 ◁ l1.c12!⟨⟩.r4?(y).y (r5, r6, r7) | c9?().r5!⟨“World”⟩.c10!⟨⟩ | +c10?().r6?(t).c11!⟨⟩ | c11?().r7 ◁ l2.c12!⟨⟩ | c12?() +In the process B5� +Q +� +, the restricted names (r2, r3, r4) are the decomposition of the name r for the +branch l1. To calculate their types, we unfold S: +S = µt.&{l1 :?(str);!⟨int⟩;t, l2 : end} ≡ &{l1 :?(str);!⟨int⟩;t, l2 : end}{S/t} += &{l1 :?(str);!⟨int⟩;S, l2 : end}, +and we look at the decomposition of the type corresponding to the branch l1: +G(?(str);!⟨int⟩;S) = (?(str), !⟨int⟩, M∗) +Now we inspect a few reductions of D(P). First, we have synchronizations on c1, . . . , c4. This is +followed by the application of the exchanged value Vϵ +� +V +� +to names r1, s1: +D(�P�) −→∗(ν cV +1 cV +2 ) cV +1 !⟨⟩ | cV +1 ?().s1?(y).cV +2 !⟨y⟩ | cV +2 ?(y).r1 ▷ {l1 : xr1!⟨W⟩, l2 : 0} +| s1!⟨Vϵ +� +V +� +⟩ | c5!⟨⟩ | B5 +ϵ +� +Q +� += D1 +Then, after synchronizations on cV +1 , s1, and cV +2 in D1 we have the following: +D1 −→∗(ν c6, . . . , c12) r1 ▷ {l1 : r1!⟨W{Vϵ +� +V +� +/y}⟩, l2 : 0} | +(ν r2 :?(str), r3 :!⟨int⟩, r4 : M∗) +r1 ◁ l1.c6!⟨⟩.r1?(y).y (r2, r3, r4) | +c6?().r2!⟨“Hello”⟩.c7!⟨⟩ | c7?().r3?(t).c11!⟨⟩ | +(ν r5 :?(str), r6 :!⟨int⟩, r7 : M∗) +c8?().r4 ◁ l1.c12!⟨⟩.r4?(y).y (r5, r6, r7) | c9?().r5!⟨“World”⟩.c10!⟨⟩ | +c10?().r6?(t).c11!⟨⟩ | c11?().r7 ◁ l2.c12!⟨⟩ | c12?() = D2 +52 + +D2 can mimic a silent select action on r1; this is followed by a reception of value W{Vϵ +� +V +� +/y} on +name r1, which is then applied to names (r2, r3, r4). The resulting process is as follows: +D2 −→∗(ν c8, . . . , c12) (ν r2 :?(str), r3 :!⟨int⟩, r4 : M∗) +(ν cW +1 . . . cW +5 ) cW +1 !⟨⟩ | cW +1 ?().r2?(t).cW +2 !⟨t⟩ | cW +2 ?(t).r3!⟨len(t)⟩.cW +3 !⟨⟩ +| (ν s1) (cW +3 ?().cW +4 !⟨⟩.cW +5 !⟨⟩ | cW +4 ?().Vϵ +� +V +� +(r4, s1) | cW +5 ?().s1!⟨Vϵ +� +V +� +⟩) | +r2!⟨“Hello”⟩.c7!⟨⟩ | c7?().r3?(t).c11!⟨⟩ | +(ν r5 :?(str), r6 :!⟨int⟩, r7 : M∗) +c8?().r4 ◁ l1.c12!⟨⟩.r4?(y).y (r5, r6, r7) | c9?().r5!⟨“World”⟩.c10!⟨⟩ | +c10?().r6?(t).c11!⟨⟩ | c11?().r7 ◁ l2.c12!⟨⟩ | c12?() = D3 +The next interesting process emerges once silent actions on r are mimicked by r2 and r3: +D3 −→∗(ν c8, . . . , c12) (ν r4 : M∗) (ν s1) Vϵ +� +V +� +(r4, s1) | s1!⟨Vϵ +� +V +� +⟩) | +(ν r5 :?(str), r6 :!⟨int⟩, r7 : M∗) +c8?().r4 ◁ l1.c12!⟨⟩.r4?(y).y (r5, r6, r7) | c9?().r5!⟨“World”⟩.c10!⟨⟩ | +c10?().r6?(t).c11!⟨⟩ | c11?().r7 ◁ l2.c12!⟨⟩ | c12?() = D4 +In D4, name r4 with type M∗, is applied to the abstraction Vϵ +� +V +� +, which encapsulates a “new +instance” of the recursive branch process. After application, we obtain the following process: +D4 −→∗(ν c8, . . . , c12) (ν r4 : M∗) (ν s1) (ν cV +1 cV +2 ) cV +1 !⟨⟩ | cV +1 ?().s1?(y).cV +2 !⟨y⟩ | +cV +2 ?(y).r4 ▷ {l1 : r4!⟨V1⟩, l2 : 0} | s1!⟨Vϵ +� +V +� +⟩) | +(ν r5 :?(str), r6 :!⟨int⟩, r7 : M∗) +c8?().r4 ◁ l1.c12!⟨⟩.r4?(y).y (r5, r6, r7) | c9?().r5!⟨“World”⟩.c10!⟨⟩ | +c10?().r6?(t).c11!⟨⟩ | c11?().r7 ◁ l2.c12!⟨⟩ | c12?() = D5 +Thus, we can see that after few administrative reductions (on cV +1 , s1, and cV +2 ) the process is able to +mimic the a next selection on r on name r4. As the process again selects l1, we can see that the +next selection will occur on name r7, again typed with M∗. +◁ +We would like to finish this subsection with the following remark. So far we have only considered +recursive types which did not contain any actions between recursion and branching/selection. +However, types with prefixed branching +µt.α1. . . . .αn.&{li : Si}i∈I, +where α1, . . . , αn are some session prefixes, can also be accommodated in the same framework, as +these types can be written equivalently without prefixed branching: +α1. . . . .αn.µt.&{li : Si{α1....αn.t/t}}i∈I. +6.3 +Adapting Operational Correspondence +We briefly remark on how to adapt the operational correspondence result from Section 4. For the +operational correspondence result, and the related lemmas, we must enforce additional constraints +on the processes that we break down. These concerns arise from the following fact. When a type +&{li : Si}i∈I is broken down as +G(&{li : Si}i∈I) = &{li :!⟨G(Si)⊸⋄⟩}i∈I, +an additional action gets introduced on the level of MST processes. After performing the branching, +an abstraction needs to be sent out. This additional action will be matched by a corresponding +53 + +abstraction-input action on the side of selection, if present. However, this abstraction-sending action +does not correspond to any action of the source process. +Therefore, to show the operational correspondence between the source term and its decomposition, +we need to restrict our attention to processes in which branching and selection types are both present +in (matching) pairs. Specifically, we assume the following conditions on the source process P: +• P is a well-typed, that is Γ; ∆; Λ ⊢ P ▷ ⋄ with balanced(∆); +• for any name u, u ∈ fn(P) with u : S such that S involves selection or branching constructs if +and only if u ∈ fn(P). +Intuitively, these two conditions ensure that every branching action in P has its complement (and +vice-versa). Note that for closed typeable processes both the balancedness condition and the second +condition on names are vacuously true. +With this condition in place, we need to enlarge the relation S in order to account for silent +actions that are introduced by the breakdown of selection and branching constructs. That is, when +matching the original silent action involving selection/branching, the corresponding broken down +process need to perform several silent actions, in order to be able to mimic the process continuation. +7 +Related Work +We draw inspiration from insights developed by Parrow [21], who showed that every process in the +untyped, summation-free π-calculus with replication is weakly bisimilar to its decomposition into +trios (i.e., P ≈ D(P)). As already mentioned, we are concerned with a different technical setting: +our decomposition treats processes from a calculus without name-passing but with higher-order +concurrency (abstraction-passing), supports recursive types, and can accommodate labeled choices. +Our goals are different than those of Parrow [21]: for us, trios processes are a relevant instrument +for defining and justifying minimal session types, but they are not an end in themselves. Still, we +retain the definitional style and terminology for trios from [21], which are elegant and clear. +Our main results connect the typability and the behaviour of a process with its decomposition, +as witnessed by the static and dynamic correctness theorems. Static correctness was not considered +by Parrow, as he worked in an untyped setting. As for dynamic correctness, a similar result was +established in [21], linking the process and its decomposition through weak bisimilarity. In our +setting we had to use a different, typed notion of bisimilarity. An obstacle here is that known +notions of typed bisimilarity for session-typed processes, such as those given by Kouzapas et al. [18], +only relate processes typed under the same typing environments. To that extent, our notion of +equivalence (MST bisimulations) is more flexible than prior related notions as it (i) relates processes +typable under different environments (e.g., ∆ and G(∆)) and (ii) admits that actions along a name s +from P can be matched by D(P) using actions along indexed names sk, for some k (and viceversa). +As mentioned in the introduction, our approach is broadly related to works that relate session +types with other type systems for the π-calculus (cf. [16, 5, 6, 7, 9]). Hence, these works target +the relative expressiveness of session-typed process languages, by encoding processes between two +different systems. By contrast, we relate a session types system with its subsystem of minimal types. +Thus, by explaining session types in terms of themselves, our work emerges as the first study of +absolute expressiveness in the context of session types. +In this context, works by Kobayashi [16] and Dardha et al. [5, 6] are worth discussing. Kobayashi [16] +encoded a finite session π-calculus into a π-calculus with linear types with usages (without sequenc- +ing); this encoding uses a continuation-passing style to codify a session name using multiple linear +channels. Dardha et al. [5, 6] formalize and extend Kobayashi’s approach. They use two separate +encodings, one for processes and one for types. The encoding of processes uses a freshly generated +linear name to mimic each session action; this fresh name becomes an additional argument in +communications. The encoding of types codifies sequencing in session types by nesting payload types. +In contrast, we “slice” the n actions occurring in a session s : S along indexed names s1, . . . , sn +54 + +with minimal session types—n slices of S. Hence, Dardha et al.’s could be described as codifying +sequencing in a “dynamic style”, via the freshly generated names, whereas we follow a “static style” +using names that are indexed according to the corresponding session type. +Recently, Jacobs [15] developed a small programming calculus with a single fork-like construct +and a linear type system, which can be used to encode session-typed communications. His system +can be seen as a distillation of Wadler’s GV [23] which is, in essence, a λ-calculus with session-based +concurrency; in contrast, HO can be seen as a π-calculus in which abstractions can be exchanged. +While similar in spirit, our work and the developments by Jacobs are technically distant; we +observe that the operational correspondences developed in [15] are strictly simpler than our dynamic +correspondence result (Theorem 4.1) although they are mechanized in the Coq proof assistant. +Finally, we elaborate further on our choice of HO as source language for minimal session types. +HO is one of the sub-calculi of HOπ, a higher-order process calculus with recursion and both name- +and abstraction-passing. The basic theory of HOπ was studied by Kouzapas et al. [17, 18] as a +hierarchy of session-typed calculi based on relative expressiveness. Our results enable us to place +HO with minimal session types firmly within this hierarchy. Still, the definition of minimal session +types does not rely on having HO as source language, as they can be defined on top of other process +languages. In fact, in separate work we have defined minimal session types on top of the first-order +sub-calculus of HOπ [2]. This development attests that minimal session types admit meaningful +formulations independently from the kind of communicated objects (abstractions or names). +8 +Concluding Remarks +We have presented a minimal formulation of session types, one of the most studied classes of +behavioral types for message-passing programs. This minimal formulation forgoes sequencing on +the level of types. We formally connect standard and minimal session types (MSTs), through a +decomposition of session-typed processes, adopting the higher-order process calculus HO as target +language. Following Parrow [21], we defined the decomposition of a process P, denoted D(P), as a +collection of trio processes (processes with at most three actions) that trigger each other mimicking +the sequencing in the original process. We proved that typability of P using standard session types +implies the typability of D(P) with minimal session types; we also established that P and D(P) +are behaviourally equivalent through an MST bisimulation. Our results hold for all session types +constructs, including labeled choices and recursive types. +From a foundational standpoint, our study of minimal session types is a conceptual contribution +to the theory of behavioral types, in that we clarify the status of sequencing in theories of session +types. As remarked in Section 1, there are many session types variants, and their expressivity often +comes at the price of an involved underlying theory. Our work contributes in the opposite direction, +as we identified a simple yet expressive fragment of an established session-typed framework [17, 18], +which allows us to justify session types in terms of themselves. Understanding further the underlying +theory of minimal session types (e.g., notions such as type-based compatibility) is an exciting +direction for future work. +As mentioned above, one insight derived from our results is that sequentiality in session types is +convenient but not indispensable. Convenience is an important factor in the design of type systems +for message-passing programs, because types are abstract specifications of communication structures. +By identifying sequencing as a source of redundancy, our minimal formulation of session types does +not contradict or invalidate the prior work on standard session types and their extensions; rather, it +contributes to our understanding of the sources of convenience of those advanced type systems. +In formulating minimal session types we have committed to a specific notion of minimality, tied to +sequencing constructs in types—arguably the most distinctive feature in session types. There could +be other notions of minimality, unrelated to sequencing but worth exploring nevertheless. Consider, +for instance, the framework of context-free session types [22], which extend standard session types +by allowing sequencing of the form S; T. This form of sequential composition is quite powerful, +and yet it could be seen as achieving a form of minimality different from the one we studied here: +55 + +as illustrated in [22, Section 5], context-free session types allow to describe the communication of +tree-structured data while minimizing the need for channel creation and avoiding channel passing. +Our work can be seen as a new twist on Parrow’s decomposition results in the untyped setting [21]. +While Parrow’s work indeed does not consider types, in fairness we must observe that when Parrow’s +work appeared (1996) the study of types (and typed behavioral equivalences) for the π-calculus was +rather incipient (for instance, the widely known formulation of binary session types, given in [12], +appeared in 1998). That said, we would like to stress that our results are not merely an extension +of Parrow’s work with session types, for types in our setting drastically narrow down the range of +conceivable decompositions. Additionally, in this work we exploit features not supported in [21], +most notably higher-order concurrency (cf. Section 5). +Finally, from a practical standpoint, we believe that our approach paves a new avenue to the +integration of session types in programming languages whose type systems lack sequencing, such as +Go. It is natural to envision program analysis tools which, given a message-passing program that +should conform to protocols specified as session types, exploit our decomposition as an intermediate +step in the verification of communication correctness. Remarkably, our decomposition lends itself +naturally to an implementation—in fact, we generated our examples automatically using MISTY, an +associated artifact written in Haskell [4]. +Acknowledgments +We are grateful to Erik Voogd, who as a BSc student was one of the authors +in the conference version of this paper [3]. +References +[1] D. Ancona, V. Bono, M. Bravetti, J. Campos, G. Castagna, P. Deniélou, S. J. Gay, N. Gesbert, +E. Giachino, R. Hu, E. B. Johnsen, F. Martins, V. Mascardi, F. Montesi, R. Neykova, N. Ng, +L. Padovani, V. T. Vasconcelos, and N. Yoshida. Behavioral types in programming languages. +Foundations and Trends in Programming Languages, 3(2-3):95–230, 2016. +[2] A. Arslanagic, A. Palamariuc, and J. A. Pérez. Minimal session types for the π-calculus. In +N. Veltri, N. Benton, and S. Ghilezan, editors, PPDP 2021: 23rd International Symposium on +Principles and Practice of Declarative Programming, Tallinn, Estonia, September 6-8, 2021, +pages 12:1–12:15. ACM, 2021. +[3] A. Arslanagić, J. A. Pérez, and E. Voogd. Minimal Session Types (A Pearl). In 33rd European +Conference on Object-Oriented Programming, ECOOP 2019, July 15-19, 2019, London, UK, +2019. To appear. +[4] A. Arslanagic, J. A. Pérez, and E. Voogd. Minimal session types (artifact). Dagstuhl Artifacts +Ser., 5(2):05:1–05:3, 2019. +[5] O. Dardha, E. Giachino, and D. Sangiorgi. Session types revisited. In Proc. of PPDP 2012, +pages 139–150. ACM, 2012. +[6] O. Dardha, E. Giachino, and D. Sangiorgi. Session types revisited. Inf. Comput., 256:253–286, +2017. +[7] R. Demangeon and K. Honda. Full abstraction in a subtyped pi-calculus with linear types. In +Proc. of CONCUR 2011, volume 6901 of LNCS, pages 280–296. Springer, 2011. +[8] M. Dezani-Ciancaglini and U. de’ Liguoro. Sessions and Session Types: an Overview. In +WS-FM’09, volume 6194 of LNCS, pages 1–28. Springer, 2010. +[9] S. J. Gay, N. Gesbert, and A. Ravara. Session types as generic process types. In J. Borgström +and S. Crafa, editors, Proceedings Combined 21st International Workshop on Expressiveness in +Concurrency and 11th Workshop on Structural Operational Semantics, EXPRESS 2014, and +56 + +11th Workshop on Structural Operational Semantics, SOS 2014, Rome, Italy, 1st September +2014., volume 160 of EPTCS, pages 94–110, 2014. +[10] S. J. Gay, P. Thiemann, and V. T. Vasconcelos. Duality of session types: The final cut. +In S. Balzer and L. Padovani, editors, Proceedings of the 12th International Workshop on +Programming Language Approaches to Concurrency- and Communication-cEntric Software, +PLACES@ETAPS 2020, Dublin, Ireland, 26th April 2020, volume 314 of EPTCS, pages 23–33, +2020. +[11] D. Gorla. Towards a unified approach to encodability and separation results for process calculi. +Inf. Comput., 208(9):1031–1053, 2010. +[12] K. Honda, V. T. Vasconcelos, and M. Kubo. Language primitives and type disciplines for +structured communication-based programming. In ESOP’98, volume 1381 of LNCS, pages +22–138. Springer, 1998. +[13] K. Honda, N. Yoshida, and M. Carbone. Multiparty Asynchronous Session Types. In POPL’08, +pages 273–284. ACM, 2008. +[14] H. Hüttel, I. Lanese, V. T. Vasconcelos, L. Caires, M. Carbone, P. Deniélou, D. Mostrous, +L. Padovani, A. Ravara, E. Tuosto, H. T. Vieira, and G. Zavattaro. Foundations of session +types and behavioural contracts. ACM Comput. Surv., 49(1):3, 2016. +[15] J. Jacobs. A self-dual distillation of session types. In K. Ali and J. Vitek, editors, 36th European +Conference on Object-Oriented Programming, ECOOP 2022, June 6-10, 2022, Berlin, Germany, +volume 222 of LIPIcs, pages 23:1–23:22. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, +2022. +[16] N. Kobayashi. Type systems for concurrent programs. In Formal Methods at the Crossroads, +volume 2757 of LNCS, pages 439–453. Springer, 2003. +[17] D. Kouzapas, J. A. Pérez, and N. Yoshida. On the relative expressiveness of higher-order +session processes. In P. Thiemann, editor, Programming Languages and Systems - 25th European +Symposium on Programming, ESOP 2016, Held as Part of the European Joint Conferences on +Theory and Practice of Software, ETAPS 2016, Eindhoven, The Netherlands, April 2-8, 2016, +Proceedings, volume 9632 of Lecture Notes in Computer Science, pages 446–475. Springer, 2016. +Extended version to appear in Information and Computation (Elsevier). +[18] D. Kouzapas, J. A. Pérez, and N. Yoshida. Characteristic bisimulation for higher-order session +processes. Acta Inf., 54(3):271–341, 2017. +[19] J. Lange, N. Ng, B. Toninho, and N. Yoshida. A static verification framework for message passing +in go using behavioural types. In M. Chaudron, I. Crnkovic, M. Chechik, and M. Harman, +editors, Proceedings of the 40th International Conference on Software Engineering, ICSE 2018, +Gothenburg, Sweden, May 27 - June 03, 2018, pages 1137–1148. ACM, 2018. +[20] N. Ng and N. Yoshida. Static deadlock detection for concurrent go by global session graph +synthesis. In A. Zaks and M. V. Hermenegildo, editors, Proceedings of the 25th International +Conference on Compiler Construction, CC 2016, Barcelona, Spain, March 12-18, 2016, pages +174–184. ACM, 2016. +[21] J. Parrow. Trios in concert. In G. D. Plotkin, C. Stirling, and M. Tofte, editors, Proof, Language, +and Interaction, Essays in Honour of Robin Milner, pages 623–638. The MIT Press, 2000. Online +version, dated July 22, 1996, available at http://user.it.uu.se/~joachim/trios.pdf. +[22] P. Thiemann and V. T. Vasconcelos. Context-free session types. In J. Garrigue, G. Keller, +and E. Sumii, editors, Proceedings of the 21st ACM SIGPLAN International Conference on +57 + +Functional Programming, ICFP 2016, Nara, Japan, September 18-22, 2016, pages 462–475. +ACM, 2016. +[23] P. Wadler. Propositions as sessions. In P. Thiemann and R. B. Findler, editors, ACM SIG- +PLAN International Conference on Functional Programming, ICFP’12, Copenhagen, Denmark, +September 9-15, 2012, pages 273–286. ACM, 2012. +58 + +Contents +1 +Introduction +1 +2 +The Source Language +4 +2.1 +Syntax and Semantics +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +4 +2.2 +Session Types for HO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +7 +3 +Decomposing Session-Typed Processes +11 +3.1 +Key Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +12 +3.2 +The Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +13 +3.2.1 +Minimal Session Types and Decomposing Types +. . . . . . . . . . . . . . . . +14 +3.2.2 +Decomposing Processes +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +16 +3.3 +The Decomposition by Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +21 +3.3.1 +Decomposing Processes with Non-Recursive Names . . . . . . . . . . . . . . . +21 +3.3.2 +Decomposing Processes with Recursive Names . . . . . . . . . . . . . . . . . . +23 +3.4 +Static Correctness +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +25 +4 +Dynamic Correctness +26 +4.1 +Behavioral Equivalence in HO and its Limitations . . . . . . . . . . . . . . . . . . . . +27 +4.2 +MST Bisimilarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +28 +4.3 +The Bisimulation Relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +30 +4.3.1 +A Motivating Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +30 +4.3.2 +The relation S +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +34 +4.4 +Proving Operational Correspondence . . . . . . . . . . . . . . . . . . . . . . . . . . . +40 +5 +Optimizations of the Decomposition +43 +6 +Extension with Labeled Choice +47 +6.1 +Breaking Down Selection and Branching . . . . . . . . . . . . . . . . . . . . . . . . . +48 +6.2 +The Interplay of Selection/Branching and Recursion +. . . . . . . . . . . . . . . . . . +51 +6.3 +Adapting Operational Correspondence . . . . . . . . . . . . . . . . . . . . . . . . . . +53 +7 +Related Work +54 +8 +Concluding Remarks +55 +A Appendix to Section 3.2 +60 +A.1 Auxiliary Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +60 +B Appendix to Section 3.4 +61 +B.1 +Proof of Lemma 3.1 +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +61 +B.2 +Proof of Theorem 3.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +74 +C Appendix to Section 4 +76 +C.1 Proof of Lemma 4.3 +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +76 +C.2 Proof of Lemma 4.4 +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +78 +C.3 Proof of Lemma 4.7 +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +91 +59 + +A +Appendix to Section 3.2 +A.1 +Auxiliary Results +Remark A.1. We derive polyadic rules for typing HOπ as an expected extension of HO typing rules: +PolyVar +Γ, �x : �Ux; �y : �Uy; ∅ ⊢ �x�y : �Ux �Uy +PolySess +Γ; ∅; �u : �S ⊢ �u ▷ �S +Γ; Λ1; ∆, u : S ⊢ P ▷ ⋄ +Γ; Λ2; ∅ ⊢ �x ▷ �U +PolyRcv +Γ \ �x; Λ1 \ Λ2; ∆, u :?(�U);S ⊢ u?(�x).P ▷ ⋄ +u : S ∈ ∆ +Γ; Λ1; ∆ ⊢ P +Γ; Λ2; ∅ ⊢ �x ▷ �U +PolySend +Γ; Λ1, Λ2; (∆ \ u : S), u :!⟨�U⟩;S ⊢ u!⟨�x⟩.P +⇝∈ {⊸, →} +Γ; Λ; ∆1 ⊢ V ▷ �C ⇝ ⋄ +Γ; ∅; ∆2 ⊢ �u ▷ �C +PolyApp +Γ; Λ; ∆1, ∆2 ⊢ V �u +Γ; Λ; ∆1 ⊢ P ▷ ⋄ +Γ; ∅; ∆2 ⊢ �x ▷ �C +PolyAbs +Γ \ �x; Λ; ∆1 \ ∆2 ⊢ λ�x. P ▷ �C ⊸⋄ +Γ, �a : � +⟨U⟩; Λ; ∆ ⊢ P +PolyRes +Γ; Λ; ∆ ⊢ (ν �a) P +Γ; Λ; ∆, �s : �S1, �s : �S2 ⊢ P +�S1 dual +�S2 +PolyResS +Γ; Λ; ∆ ⊢ (ν �s) P +Lemma A.1 (Substitution Lemma [17]). Γ; Λ; ∆, x : S ⊢ P ▷ ⋄ and u /∈ dom(Γ, Λ, ∆) implies +Γ; Λ; ∆, u : S ⊢ P{u/x} ▷ ⋄. +Lemma A.2 (Shared environment weakening). If Γ; Λ; ∆ ⊢ P ▷ ⋄ then Γ, x : C →⋄; Λ; ∆ ⊢ P ▷ ⋄ +and Γ, u : ⟨U⟩; Λ; ∆ ⊢ P ▷ ⋄. +Lemma A.3 (Shared environment strengthening). +• If Γ; Λ; ∆ ⊢ P ▷ ⋄ and x /∈ fv(P) then +Γ \ x; Λ; ∆ ⊢ P ▷ ⋄. +• If Γ; Λ; ∆ ⊢ P ▷ ⋄ and u /∈ fn(P) then Γ \ u; Λ; ∆ ⊢ P ▷ ⋄. +60 + +B +Appendix to Section 3.4 +We use the following auxiliary lemma: +Lemma B.1. Let �z be tuple of channel names, U a higher-order type, and S a recursive session +type. If �z : R⋆(!⟨U⟩;S) and k = [!⟨U⟩;S⟩ then zk : µt.!⟨G(U)⟩;t. +B.1 +Proof of Lemma 3.1 +Lemma 3.1. Let P be an indexed HO process and V be a value. +1. If Γ; Λ; ∆ ◦ ∆µ ⊢ P ▷ ⋄ then G(Γ1), Φ; ∅; G(∆), Θ ⊢ Bk +˜x +� +P +� +▷ ⋄, where: +• k > 0 +• �r = dom(∆µ) +• Φ = � +r∈˜r cr : ⟨R⋆(∆µ(r))⊸⋄⟩ +• �x = fv(P) +• Γ1 = Γ \ �x +• dom(Θ) = {ck, . . . , ck+�P�−1} ∪ {ck+1, . . . , ck+�P�−1} +• Θ(ck) =?(U1, . . . , Un), where (G(Γ), G(Λ))(�x) = (x1 : U1, . . . , xn : Un) +• balanced(Θ) +2. If Γ; Λ; ∆ ◦ ∆µ ⊢ V ▷ �T ⊸⋄ then G(Γ), Φ; G(Λ); G(∆) ⊢ V˜x +� +V +� +▷ G( �T)⊸⋄, where: +• �x = fv(V ) +• Φ = � +r∈˜r cr : ⟨R⋆(∆µ(r))⊸⋄⟩ +Proof. By mutual induction on the structure of P and V . Here, we analyze only Part (1) of the +theorem, as Part (2) and Part (3) are proven similarly: +1. By assumption Γ; Λ; ∆, ∆µ ⊢ P ▷ ⋄. There are four cases, depending on the shape of P. We +consider two representative cases. We omit other cases as they are similar. +(a) Case P = 0. The only rule that can be applied here is Nil. By inversion of this rule, we +have: Γ; ∅; ∅ ⊢ 0. We shall then prove the following judgment: +G(Γ); ∅; Θ ⊢ Bk +˜x +� +0 +� +▷ ⋄ +(25) +where �x = fv(0) = ∅ and Θ = {ck :?(end ⊸ ⋄)}. By Table 1: Bk +ϵ +� +0 +� += ck?().0. By +convention we know that ck?().0 stands for ck?(y).0 with ck :?(end→⋄). The following +tree proves this case: +Nil Γ′; ∅; ∅ ⊢ 0 ▷ ⋄ +ck /∈ dom(Γ) +End +Γ′; ∅; ck : end ⊢ 0 ▷ ⋄ +LVar G(Γ); y ▷ end⊸⋄; ∅ ⊢ y ▷ end⊸⋄ +EProm +Γ′; ∅; ∅ ⊢ y ▷ end⊸⋄ +Prom Γ′; ∅; ∅ ⊢ y ▷ end→⋄ +Rcv +G(Γ); ∅; Θ ⊢ ck?().0 ▷ ⋄ +where Γ′ = G(Γ), y : end → ⋄. We know ck /∈ dom(Γ) since we use reserved names for +propagators channels. +(b) Case P = ui!⟨V ⟩.P ′. We distinguish three sub-cases: (i) ui ∈ dom(∆) and (ii) ui ∈ dom(Γ), +and (iii) ui ∈ dom(∆µ). +We consider sub-case (i) first. For this case Rule Send can be applied: +Γ; Λ1; ∆1, ∆µ1 ⊢ P ′ ▷ ⋄ +Γ; Λ2; ∆2, ∆µ2 ⊢ V ▷ U +ui : S ∈ ∆1, ∆2 +Send +Γ; Λ1, Λ2; ((∆1, ∆2) \ {ui : S}), ui :!⟨U⟩;S, ∆µ1, ∆µ2 ⊢ ui!⟨V ⟩.P ′ ▷ ⋄ +(26) +61 + +Let �w = fv(P ′). Also, let Γ′ +1 = Γ \ �w and Θ1 be a balanced environment such that +dom(Θ1) = {ck+1, . . . , ck+�P ′�} ∪ {ck+2, . . . , ck+�P ′�} +and Θ1(ck+1) =?(� +M1) where � +M1 = (G(Γ), G(Λ1))( �w). We define: +Φi = +� +r∈dom(∆µi) +cr : ⟨R⋆(∆µi(r))⊸⋄⟩ for i ∈ {1, 2} +(27) +Then, by IH on the first assumption of (26) we have: +G(Γ′ +1), Φ1; ∅; G(∆1), Θ1 ⊢ Bk+1 +˜z +� +P ′� +▷ ⋄ +(28) +Let �y = fv(V ) and Γ′ +2 = Γ \ �y. Then, by IH (Part 2) on the second assumption of (26) +we have: +G(Γ), Φ2; G(Λ2); G(∆2) ⊢ V˜y +� +V +� +▷ G(U) +(29) +We may notice that if U = C →⋄ then Λ2 = ∅ and ∆2 = ∅. Let �x = fv(P). We define +Θ = Θ1, Θ′, where: +Θ′ = ck :?(� +M), ck+1 :!⟨� +M2⟩ +with � +M = (G(Γ), G(Λ1, Λ2))(�x). By Definition 3.6, we know �P� = �P ′� + 1, so +dom(Θ) = {ck, . . . , ck+�P�−1} ∪ {ck+1, . . . , ck+�P�−1} +By construction Θ is balanced since Θ(ck+1) dual Θ(ck+1) and Θ1 is balanced. By Table 1, +we have: +Bk +˜x +� +ui!⟨V ⟩.P ′� += ck?(�x).ui! +� +V˜y +� +V {ui+1/ui} +�� +.ck+1!⟨ �w⟩.0 | Bk+1 +˜w +� +P ′{ui+1/ui} +� +We know fv(P ′) ⊆ fv(P) and fv(V ) ⊆ fv(P) that is �w ⊆ �x and �y ⊆ �x. Let Γ1 = Γ \ �x +and Φ = Φ1, Φ2. We shall prove the following judgment: +G(Γ1), Φ; ∅; G(((∆1, ∆2) \ {ui : S}), ui :!⟨U⟩;S), Θ ⊢ Bk +˜x +� +ui!⟨V ⟩.P ′� +▷ ⋄ +(30) +Let σ = {ui+1/ui}. To type the left-hand side component of Bk +˜x +� +ui!⟨V ⟩.P ′� +we use some +auxiliary derivations: +Nil G(Γ), Φ; ∅; ∅ ⊢ 0 ▷ ⋄ +End G(Γ), Φ; ∅; ck+1 : end ⊢ 0 ▷ ⋄ +PolyVar +G(Γ), Φ; G(Λ1); ∅ ⊢ �w ▷ � +M2 +PolySend +G(Γ), Φ; G(Λ1); ck+1 :!⟨� +M2⟩;end ⊢ ck+1!⟨ �w⟩.0 ▷ ⋄ +End +G(Γ), Φ; G(Λ1); ck+1 :!⟨� +M2⟩;end, ui : end ⊢ ck+1!⟨ �w⟩.0 ▷ ⋄ +(31) +(29) +(Lemma A.1) with {˜n/˜u} G(Γ), Φ2; G(Λ2); G(∆2σ) ⊢ V˜y +� +V σ +� +▷ G(U) +(Lemma A.3) with Φ1 +G(Γ), Φ; G(Λ2); G(∆2σ) ⊢ V˜y +� +V σ +� +▷ G(U) +(32) +ui :!⟨G(U)⟩;end ∈ G(∆2σ), ui :!⟨G(U)⟩;end, ck+1 :!⟨� +M2⟩;end +(31) +(32) +Send +G(Γ), Φ; G(Λ1, Λ2); G(∆2σ), ui :!⟨G(U)⟩;end, ck+1 :!⟨� +M2⟩;end ⊢ +ui! +� +V˜y +� +V σ +�� +.ck+1!⟨ �w⟩.0 ▷ ⋄ +End +G(Γ), Φ; G(Λ1, Λ2); G(∆2σ), ui :!⟨G(U)⟩;end, ck+1 :!⟨� +M2⟩;end, ck : end ⊢ +ui! +� +V˜y +� +V σ +�� +.ck+1!⟨ �w⟩.0 ▷ ⋄ +(33) +62 + +(33) +PolyVar +G(Γ), Φ; G(Λ2); ∅ ⊢ �x : � +M +PolyRcv +G(Γ1), Φ; ∅; G(∆2σ), ui :!⟨G(U)⟩;end, Θ′ ⊢ +ck?(�x).ui! +� +V˜y +� +V σ +�� +.ck+1!⟨ �w⟩.0 ▷ ⋄ +(34) +The following tree proves this case: +(34) +(28) +(Lemma A.1) with {˜n/˜u} +G(Γ′ +1), Φ1; ∅; G(∆1σ), Θ1 ⊢ Bk+r+1 +˜w +� +P ′σ +� +▷ ⋄ +(Lemma A.3) with ˜x \ ˜w and Φ2 +G(Γ1), Φ; ∅; G(∆1σ), Θ1 ⊢ Bk+r+1 +˜w +� +P ′σ +� +▷ ⋄ +Par +G(Γ1), Φ; ∅; G(((∆1, ∆2) \ {ui : S}), ui :!⟨U⟩;S), Θ ⊢ Bk +˜x +� +ui!⟨V ⟩.P ′� +▷ ⋄ +(35) +where �n = (ui+1, . . . , ui+|G(S)|) and �u = (ui, . . . , ui+|G(S)|−1). This concludes sub-case (i). +Now, we consider sub-case (ii). For this sub-case Rule Req can be applied: +Γ; ∅; ∅ ⊢ u ▷ ⟨U⟩ +Γ; Λ; ∆1, ∆µ1 ▷ P ′ ▷ ⋄ +Γ; ∅; ∆2, ∆µ2 ⊢ V ▷ U +Req +Γ; Λ; ∆1, ∆2, ∆µ1, ∆µ2 ⊢ u!⟨V ⟩.P ′ ▷ ⋄ +(36) +Let �w = fv(P ′). Further, let Γ′ +1 = Γ \ �w and let Θ1, Φ1, and Φ2 be environments defined +as in sub-case (i). By IH on the second assumption of (36) we have: +G(Γ′ +1), Φ1; ∅; G(∆1), Θ1 ⊢ Bk+1 +˜w +� +P ′� +▷ ⋄ +(37) +Let �y = fv(V ). By IH on the second assumption of (26) we have: +G(Γ), Φ2; ∅; G(∆2) ⊢ V˜y +� +V +� +▷ G(U) +(38) +Let �x = fv(P) and Γ1 = Γ \ �x. We define Θ = Θ1, Θ′, where: +Θ′ = ck :?(� +M), ck+1 :!⟨� +M2⟩ +with � +M = (G(Γ), G(Λ))(�x). By Definition 3.6, we know �P� = �P ′� + 1, so +dom(Θ) = (ck, . . . , ck+�P�−1) ∪ (ck+1, . . . , ck+�P�−1) +By construction Θ is balanced since Θ(ck+1) dual Θ(ck+1) and Θ1 is balanced. By Table 1, +we have: +Bk +˜x +� +ui!⟨V ⟩.P ′� += ck?(�x).ui! +� +V˜y +� +V +�� +.ck+1!⟨ �w⟩.0 | Bk+1 +˜w +� +P ′� +We know fv(P ′) ⊆ fv(P) and fv(V ) ⊆ fv(P) that is �w ⊆ �x and �y ⊆ �x. +To prove +G(Γ1), Φ; ∅; G(∆1, ∆2), Θ ⊢ Bk +˜x +� +ui!⟨V ⟩.P ′� +we use some auxiliary derivations: +Nil G(Γ), Φ; ∅; ∅ ⊢ 0 ▷ ⋄ +End G(Γ), Φ; ∅; ck+1 : end ⊢ 0 ▷ ⋄ +PolyVar +G(Γ), Φ; G(Λ); ∅ ⊢ �w : � +M2 +PolySend +G(Γ), Φ; G(Λ); ck+1 :!⟨� +M2⟩;end ⊢ ck+1!⟨ �w⟩.0 ▷ ⋄ +(39) +(39) +(38) +(Lemma A.3) with Φ1 G(Γ), Φ; ∅; G(∆2) ⊢ V˜y +� +V +� +▷ G(U) +Req +G(Γ), Φ; G(Λ); G(∆2), ck+1 :!⟨� +M2⟩;end ⊢ ui! +� +V˜y +� +V +�� +.ck+1!⟨ �w⟩.0 ▷ ⋄ +(40) +63 + +(40) +PolyVar +G(Γ), Φ; G(Λ); ∅ ⊢ �x ▷ � +M +PolyRcv +G(Γ1), Φ; ∅; G(∆2), Θ′ ⊢ ck?(�x).ui! +� +V˜y +� +V +�� +.ck+1!⟨ �w⟩.0 ▷ ⋄ +(41) +The following tree proves this case: +(41) +(37) +(Lemma A.3) with ˜x \ ˜w and Φ2 +G(Γ1), Φ; ∅; G(∆1), Θ1 ⊢ Bk+1 +˜w +� +P ′� +▷ ⋄ +Par +G(Γ1), Φ; ∅; G(∆1, ∆2), Θ ⊢ Bk +˜x +� +ui!⟨V ⟩.P ′� +▷ ⋄ +(42) +This concludes sub-case (ii). +Now, we consider sub-case (iii). Here we know P = ui!⟨V ⟩.P ′ and ui : S ∈ ∆µ. For this +case Rule Send can be applied: +Γ; Λ1; ∆1, ∆µ1 ⊢ P ′ ▷ ⋄ +Γ; Λ2; ∆2, ∆µ2 ⊢ V ▷ U +ui : S′ ∈ ∆µ1, ∆µ2 +Send +Γ; Λ1, Λ2; ∆1, ∆2, ((∆µ1, ∆µ2) \ {ui : S′}), ui :!⟨U⟩;S′ ⊢ ui!⟨V ⟩.P ′ ▷ ⋄ +(43) +Let �w = fv(P ′). Let Θ1, Θ′, Θ, Φ1, and Φ2 be defined as in the previous sub-case. Also, +let Γ′ +1 = Γ \ �w. Then, by IH on the first assumption of (43) we have: +G(Γ′ +1), Φ1; ∅; G(∆1), Θ1 ⊢ Bk+1 +˜w +� +P ′� +▷ ⋄ +(44) +Let Γ′ +2 = Γ \ �y. Then, by IH (Part 2) on the second assumption of (43) we have: +G(Γ′ +2), Φ2; G(Λ2); G(∆2) ⊢ V˜y +� +V +� +▷ G(U) +(45) +By Table 1 we have: +Bk +˜x +� +P +� += ck?(�x).cu! +� +NV +� +.0 | Bk+1 +˜w +� +P ′� +where NV = λ�z. z[S⟩!⟨V˜y +� +V +� +⟩. +� +ck+1!⟨ �w⟩ | cu?(x).x �z +� +We notice that ui ∈ rn(V ), rn(P) since ui has tail-recursive type S. Hence, by (27) +we know (Φ1, Φ2)(cu) = ⟨R⋆(S) ⊸ ⋄⟩. +Further, we know that S =!⟨U⟩;S′ and by +Definition 3.3, R⋆(S) = R⋆(S′). +So we define Φ = Φ1, Φ2. +Let Γ1 = Γ \ �x where +�x = fv(P). We shall prove the following judgment: +G(Γ1), Φ; ∅; G(∆1, ∆2), Θ ⊢ Bk +˜x +� +ui!⟨V ⟩.P ′� +▷ ⋄ +We use auxiliary derivations: +LVar +G(Γ1), Φ; x : R⋆(S)⊸⋄; ∅ ⊢ +x ▷ R⋆(S)⊸⋄ +PolySess +G(Γ1), Φ; ∅; �z : R⋆(S) ⊢ +�z ▷ R⋆(S) +PolyApp +G(Γ1), Φ; x : R⋆(S)⊸⋄; �z : R⋆(S) ⊢ x �z ▷ ⋄ +(46) +(46) +Sh +G(Γ), Φ; ∅; ∅ ⊢ +cu ▷ ⟨R⋆(S)⊸⋄⟩ +LVar +G(Γ), Φ; x : R⋆(S)⊸⋄; ∅ ⊢ +x ▷ R⋆(S)⊸⋄ +Acc +G(Γ), Φ; ∅; Θ′, �z : R⋆(S) ⊢ cu?(x).x �z ▷ ⋄ +(47) +Nil G(Γ), Φ; ∅; ∅ ⊢ 0 ▷ ⋄ +ck+1 ̸∈ dom(Γ, Φ) +End +G(Γ), Φ; ∅; ck+1 : end ⊢ 0 ▷ ⋄ +(48) +64 + +ck+1 :!⟨� +M2⟩;end ∈ Θ′ +(48) +PolyVar +G(Γ), Φ; G(Λ2); ∅ ⊢ �w ▷ � +M2 +PolySend +G(Γ), Φ; G(Λ1); ck+1 :!⟨� +M2⟩ ⊢ ck+1!⟨ �w⟩ ▷ ⋄ +(49) +(49) +(47) +Par +G(Γ), Φ; G(Λ1); ck+1 :!⟨� +M2⟩, �z : R⋆(S) ⊢ ck+1!⟨ �w⟩ | cu?(x).x �z ▷ ⋄ +(50) +(50) +(44) +(Lemma A.2) with Φ1 +G(Γ′ +2), Φ; G(Λ2); ∅ ⊢V˜y +� +V +� +▷ G(U) +(Lemma A.2) with ˜z +G(Γ), Φ; G(Λ2); ∅ ⊢ V˜y +� +V +� +▷ G(U) +Send +G(Γ), Φ; G(Λ1, Λ2); G(∆2), �z : R⋆(S), ck+1 :!⟨� +M2⟩ ⊢ +z[S⟩!⟨V˜y +� +V +� +⟩. +� +ck+1!⟨ �w⟩ | cu?(x).x �z +� +(51) +By Lemma B.1 we know that if �z : R⋆(S) then z[S⟩ : µt.!⟨G(U)⟩;t. +(51) +PolySess G(Γ), Φ; ∅; �z : R⋆(S) ⊢ �z ▷ R⋆(S) +PolyAbs +G(Γ), Φ; G(Λ1, Λ2); G(∆2), ck+1 :!⟨� +M2⟩ ⊢ NV ▷ R⋆(S)⊸⋄ +(52) +LVar G(Γ), Φ; ∅; ∅ ⊢ cu ▷ ⟨R⋆(S)⊸⋄⟩) +Nil G(Γ), Φ; ∅; ∅ ⊢ 0 ▷ ⋄ +(52) +Req +G(Γ), Φ; G(Λ1, Λ2); G(∆2), ck+1 :!⟨� +M2⟩ ⊢ cu! +� +NV +� +.0 ▷ ⋄ +(53) +(53) +PolyVar +G(Γ), Φ; G(Λ1, Λ2); ∅ ⊢ �x ▷ � +M +PolyRcv +G(Γ1), Φ; ∅; G(∆2), Θ′ ⊢ ck?(�x).cu! +� +NV +� +.0 ▷ ⋄ +(54) +The following tree proves this case: +(54) +(44) +(Lemma A.2) with Φ2 +G(Γ′ +1), Φ; ∅; G(∆1), Θ1 ⊢ Bk+1 +˜w +� +P ′� +▷ ⋄ +(Lemma A.3) with ˜y +G(Γ1), Φ; ∅; G(∆1), Θ1 ⊢ Bk+1 +˜w +� +P ′� +▷ ⋄ +Par +G(Γ1), Φ; ∅; G(∆1, ∆2), Θ ⊢ Bk +˜x +� +r!⟨V ⟩.P ′� +▷ ⋄ +(55) +This concludes the analysis for the output case P = ui!⟨V ⟩.P ′. We remark that the +proof for the case when V = y is specialization of above the proof where ˜y = fv(y) = y, +V˜y +� +y +� += y and it holds that yσ = y. +(c) Case P = ui?(y).P ′. We distinguish two sub-cases: (i) ui ∈ dom(∆), (ii) ui ∈ dom(Γ), +and (iii) ui ∈ dom(∆µ). We consider sub-cases (i) and (ii); we omit sub-case (iii) as it +follows the same reasoning as the corresponding sub-case of the previous (Send) case. +We consider sub-case (i) first. For this case Rule Rcv can be applied: +Γ; Λ1; ∆′, ui : S, ∆µ ⊢ P ′ ▷ ⋄ +Γ; Λ2; ∅ ⊢ y ▷ U +Rcv Γ \ y; Λ1 \ Λ2; ∆′, ui :?(U);S, ∆µ ⊢ ui?(y).P ′ ▷ ⋄ +(56) +Let �x = fv(P) and �w = fv(P ′). Also, let Γ′ +1 = Γ \ �w and Θ1 be a balanced environment +such that +dom(Θ1) = {ck+1, . . . , ck+�P ′�} ∪ {ck+2, . . . , ck+�P ′�} +65 + +and Θ1(ck+1) =?(� +M′) where � +M′ = (G(Γ), G(Λ1))( �w). We define: +Φ = +� +r∈dom(∆µ) +cr : ⟨R⋆(∆µi(r))⊸⋄⟩ +(57) +Then, by IH on the first assumption of (56) we know: +G(Γ′ +1), Φ; ∅; G(∆′, ui : S), Θ1 ⊢ Bk+1 +˜w +� +P ′� +▷ ⋄ +(58) +By Definition 3.3 and Definition 3.10 and the second assumption of (56) we have: +G(Γ); G(Λ2); ∅ ⊢ y ▷ G(U) +(59) +We define Θ = Θ1, Θ′, where +Θ′ = ck :?(� +M), ck+1 :!⟨� +M′⟩ +with � +M = (G(Γ), G(Λ1 \ Λ2))(�x). By Definition 3.6, �P� = �P ′� + 1 so +dom(Θ) = {ck, . . . , ck+�P�−1} ∪ {ck+1, . . . , ck+�P�−1} +and Θ is balanced since Θ(ck+1) dual Θ(ck+1) and Θ1 is balanced. By Table 1: +Bk +˜x +� +ui?(y).P ′� += ck?(�x).ui?(y).ck+1!⟨ �w⟩.0 | Bk+1 +˜w +� +P ′{ui+1/ui} +� +Let Γ1 = Γ \ �x. We shall prove the following judgment: +G(Γ1 \ y), Φ; ∅; G(∆′, ui :?(U);S), Θ ⊢ Bk +˜x +� +ui?(y).P ′� +The left-hand side component of Bk +˜x +� +ui?(y).P ′� +is typed using some auxiliary derivations: +Nil G(Γ), Φ; ∅; ∅ ⊢ 0 ▷ ⋄ +End G(Γ), Φ; ∅; ck+1 : end ⊢ 0 ▷ ⋄ +PolyVar +G(Γ), Φ; G(Λ1); ∅ ⊢ �w ▷ � +M′ +PolySend +G(Γ), Φ; G(Λ1), G(Λ2); ck+1 :!⟨� +M′⟩;end ⊢ ck+1!⟨ �w⟩.0 ▷ ⋄ +End +G(Γ), Φ; G(Λ1), G(Λ2); ck+1 :!⟨� +M′⟩;end, ui : end ⊢ ck+1!⟨ �w⟩.0 ▷ ⋄ +(60) +(60) +(59) +Rcv +G(Γ \ y), Φ; G(Λ1 \ Λ2); ui :?(G(U));end, ck+1 :!⟨� +M′⟩;end ⊢ +ui?(y).ck+1!⟨ �w⟩.0 ▷ ⋄ +End +G(Γ \ y), Φ; G(Λ1 \ Λ2); ui :?(G(U));end, ck+1 :!⟨� +M′⟩;end, ck : end ⊢ +ui?(y).ck+1!⟨ �w⟩.0 ▷ ⋄ +(61) +(61) +PolyVar +G(Γ \ y), Φ; G(Λ1); ∅ ⊢ �x ▷ � +M +PolyRcv +G(Γ1 \ y), Φ; ∅; ui :?(G(U));end, Θ′ ⊢ ck?(�x).ui?(y).ck+1!⟨ �w⟩.0 ▷ ⋄ +(62) +The following tree proves this case: +(62) +(58) +(Lemma A.1) with {˜n/˜u} +G(Γ1 \ y), Φ; ∅; G(∆′, ui+1 : S), Θ1 ⊢ +Bk+1 +˜w +� +P ′{ui+1/ui} +� +▷ ⋄ +Par +G(Γ1\y), Φ; ∅; G(∆′, ui :?(U);S), Θ ⊢ +ck?(�x).ui?(y).ck+1!⟨ �w⟩.0 | Bk+1 +˜w +� +P ′{ui+1/ui} +� +▷ ⋄ +(63) +66 + +where �n = (ui+1, . . . , ui+|G(S)|) and �u = (ui, . . . , ui+|G(S)|−1). We may notice that if +y ∈ fv(P ′) then Γ′ +1 = Γ1 \ y. On the other hand, when y /∈ fv(P ′) then Γ′ +1 = Γ1 so we +need to apply Lemma A.3 with y after Lemma A.1 to (58) in (63). Note that we have +used the following for the right assumption of (63): +G(∆′, ui : S){˜n/˜u} = G(∆′, ui+1 : S) +Bk+1 +˜w +� +P ′� +{˜n/˜u} = Bk+1 +˜w +� +P ′{ui+1/ui} +� +This concludes sub-case (i). We now consider sub-case (ii), i.e., ui ∈ dom(Γ). Here +Rule Acc can be applied: +Γ; ∅; ∅ ⊢ ui ▷ ⟨U⟩ +Γ; Λ1; ∆, ∆µ ⊢ P ′ ▷ ⋄ +Γ; Λ2; ∅ ⊢ y ▷ U +Acc +Γ \ y; Λ1 \ Λ2; ∆, ∆µ ⊢ ui?(y).P ′ ▷ ⋄ +(64) +Let �x = fv(P) and �w = fv(P ′). Furthermore, let Θ1, Θ, Γ1, Γ′ +1, and Φ be defined as in +sub-case (i). By IH on the second assumption of (64) we have: +G(Γ′ +1), Φ; ∅; G(∆), Θ1 ⊢ Bk+1 +˜w +� +P ′� +▷ ⋄ +(65) +By Definition 3.3 and Definition 3.10 and the first assumption of (64) we have: +G(Γ), Φ; ∅; ∅ ⊢ ui ▷ ⟨G(U)⟩ +(66) +By Definition 3.3, Definition 3.10, and the third assumption of (64) we have: +G(Γ), Φ; G(Λ2); ∅ ⊢ y ▷ G(U) +(67) +By Table 1, we have: +Bk +˜x +� +ui?(y).P ′� += ck?(�x).ui?(y).ck+1!⟨ �w⟩.0 | Bk+1 +˜w +� +P ′{ui+1/ui} +� +(68) +We shall prove the following judgment: +G(Γ1 \ y), Φ; ∅; G(∆), Θ ⊢ Bk +˜x +� +ui?(y).P ′� +▷ ⋄ +(69) +To this end, we use some auxiliary derivations: +Nil G(Γ), Φ; ∅; ∅ ⊢ 0 ▷ ⋄ +End G(Γ), Φ; ∅; ck+1 : end ⊢ 0 ▷ ⋄ +PolyVar +G(Γ), Φ; G(Λ1); ∅ ⊢ �w ▷ � +M′ +PolySend +G(Γ), Φ; G(Λ1); ck+1 :!⟨� +M′⟩;end ⊢ ck+1!⟨ �w⟩.0 ▷ ⋄ +(70) +(66) +(70) +(67) +Acc +G(Γ \ y), Φ; G(Λ1); ck+1 :!⟨� +M′⟩;end ⊢ ui?(y).ck+1!⟨ �w⟩.0 ▷ ⋄ +End +G(Γ \ y), Φ; G(Λ1 \ Λ2); ck+1 :!⟨� +M′⟩;end, ck : end ⊢ ui?(y).ck+1!⟨ �w⟩.0 ▷ ⋄ +(71) +(71) +PolyVar +G(Γ \ y), Φ; G(Λ1 \ Λ2); ∅ ⊢ �x ▷ � +M +PolyRcv +G(Γ1 \ y), Φ; ∅; Θ′ ⊢ ck?(�x).ui?(y).ck+1!⟨ �w⟩.0 ▷ ⋄ +(72) +The following tree proves this sub-case: +(72) +(65) +Par +G(Γ1 \ y), Φ; ∅; G(∆), Θ ⊢ ck?(�x).ui?(y).ck+1!⟨ �w⟩.0 | Bk+1 +˜w +� +P ′� +▷ ⋄ +(73) +67 + +As in sub-case (i), we may notice that if y ∈ fv(P ′) then Γ′ +1 = Γ1 \ y. On the other hand, +if y /∈ fv(P ′) then Γ′ +1 = Γ1 so we need to apply Lemma A.3 with y to (65) in (73). This +concludes the analysis for the input case P = ui?(y).P ′. This concludes sub-case (ii). +Now, we consider sub-case (iii). Here we know P = ui?(V ).P ′ and ui : S ∈ ∆µ. +Γ; Λ1; ∆′, ∆µ, ui : S′ ⊢ P ′ ▷ ⋄ +Γ; Λ2; ∅ ⊢ y ▷ U +Rcv Γ \ y; Λ1 \ Λ2; ∆′, ∆µ, ui :?(U);S′ ⊢ ui?(y).P ′ ▷ ⋄ +(74) +Let �w = fv(P ′). Let Θ1,Θ2, Θ′, and Φ be defined as in the sub-case (i). Also, let +Γ′ +1 = Γ \ �w. Then, by IH on the first assumption of (74) we have: +G(Γ′ +1), Φ; ∅; G(∆′), Θ1 ⊢ Bk+1 +˜w +� +P ′� +▷ ⋄ +(75) +Further, by IH on the second assumption of (74) we have: +G(Γ), Φ; G(Λ2); ∅ ⊢ y ▷ G(U) +(76) +By Table 1 we have: +Bk +˜x +� +P +� += ck?(�x).cu! +� +Ny +� +| Bk+1 +˜w +� +P ′� +where Ny = λ�z. z[S⟩?(y). +� +ck+1!⟨ �w⟩ | cu?(x).x �z +� +Notice that ui ∈ rn(P) as tr(ui). Hence, by (57) we know Φ(cu) = ⟨R⋆(S)⊸⋄⟩. Further, +we know that S =?(U);S′ and by Definition 3.3, R⋆(S) = R⋆(S′). Let Γ1 = Γ \ �x where +�x = fv(P). Thus, we shall prove the following judgment: +G(Γ1 \ y), Φ; ∅; G(∆′), Θ ⊢ Bk +˜x +� +ui?(y)P ′� +▷ ⋄ +We use auxiliary derivations: +LVar +G(Γ1), Φ; x : R⋆(S)⊸⋄; ∅ ⊢ +x ▷ R⋆(S)⊸⋄ +PolySess +G(Γ1), Φ; ∅; �z : R⋆(S) ⊢ +�z ▷ R⋆(S) +PolyApp +G(Γ1), Φ; x : R⋆(S)⊸⋄; �z : R⋆(S) ⊢ x �z ▷ ⋄ +(77) +(77) +Sh +G(Γ), Φ; ∅; ∅ ⊢ +cu ▷ ⟨R⋆(S)⊸⋄⟩ +LVar +G(Γ), Φ; x : R⋆(S)⊸⋄; ∅ ⊢ +x ▷ R⋆(S)⊸⋄ +Acc +G(Γ), Φ; ∅; �z : R⋆(S) ⊢ cu?(x).x �z ▷ ⋄ +(78) +Nil G(Γ), Φ; ∅; ∅ ⊢ 0 ▷ ⋄ +ck+1 ̸∈ dom(Γ, Φ) +End +G(Γ), Φ; ∅; ck+1 : end ⊢ 0 ▷ ⋄ +(79) +ck+1 :!⟨� +M′⟩;end ∈ Θ′ +(79) +PolyVar +G(Γ), Φ; G(Λ1); ∅ ⊢ �w ▷ � +M′ +PolySend +G(Γ), Φ; G(Λ1); ck+1 :!⟨� +M′⟩ ⊢ ck+1!⟨ �w⟩ ▷ ⋄ +(80) +(80) +(78) +Par G(Γ), Φ; G(Λ1); Θ′, �z : R⋆(S) ⊢ ck+1!⟨ �w⟩ | cu?(x).x �z ▷ ⋄ +(81) +68 + +(81) +(76) +Rcv +G(Γ \ y), Φ; G(Λ1 \ Λ2); ck+1 :!⟨� +M′⟩, �z : R⋆(S) ⊢ z[S⟩?(y). +� +ck+1!⟨ �w⟩ | cu?(x).x �z +� +(82) +By Lemma B.1 we know that if �z : R⋆(S) then z[S⟩ : µt.?(G(U));t. +(51) +PolySess G(Γ \ y), Φ; ∅; �z : R⋆(S) ⊢ �z ▷ R⋆(S) +PolyAbs +G(Γ \ y), Φ; G(Λ1 \ Λ2); ck+1 :!⟨� +M′⟩ ⊢ Ny ▷ R⋆(S)⊸⋄ +(83) +LVar G(Γ \ y), Φ; ∅; ∅ ⊢ cu ▷ ⟨R⋆(S)⊸⋄⟩ +Nil G(Γ \ y), Φ; ∅; ∅ ⊢ 0 ▷ ⋄ +(83) +Req +G(Γ \ y), Φ; G(Λ1 \ Λ2); ck+1 :!⟨� +M′⟩ ⊢ cu! +� +Ny +� +.0 ▷ ⋄ +(84) +(84) +PolyVar +G(Γ \ y), Φ; G(Λ); ∅ ⊢ �x ▷ � +M +PolyRcv +G(Γ1 \ y), Φ; ∅; Θ′ ⊢ ck?(�x).cu! +� +Ny +� +.0 ▷ ⋄ +(85) +The following tree proves this case: +(85) +(75) +(Lemma A.3) with ˜y +G(Γ1 \ y), Φ; ∅; G(∆′), Θ1 ⊢ Bk+1 +˜w +� +P ′� +▷ ⋄ +Par +G(Γ1 \ y), Φ; ∅; G(∆′), Θ ⊢ Bk +˜x +� +ui?(y)P ′� +▷ ⋄ +(86) +This concludes sub-case (iii). +(d) Case P = V (�r, ui). We assume a certain order in the tuple (�r, ui): names in �r have +recursive session types �r = (r1, . . . , rn) : (S1, . . . , Sn), and ui has non-recursive session +type ui : C. We distinguish two sub-cases: (i) V : �SC ⊸⋄ and (ii) V : �SC →⋄. We will +consider only sub-case (i) since the other is similar. For this case Rule PolyApp can be +applied: +Γ; Λ; ∆1, ∆µ1 ⊢ V ▷ �SC ⊸⋄ +Γ; ∅; ∆2, ∆µ2 ⊢ (�r, ui) ▷ �SC +PolyApp +Γ; Λ; ∆1, ∆2, ∆µ1, ∆µ2 ⊢ V (�r, ui) +(87) +Let �x = fv(V ) and Γ1 \ �x. Let �x = fv(V ) and let Θ1 be a balanced environment such +that +dom(Θ1) = {ck+1, . . . , ck+�V �} ∪ {ck+1, . . . , ck+�V �} +and Θ1(ck+1) =?(� +M) and Θ1(ck+1) =!⟨� +M⟩ where � +M = (G(Γ), G(Λ))(�x). +We define: +Φ1 = +� +r∈dom(∆µ1) +cr : ⟨R⋆(∆µ1(r))⊸⋄⟩ +(88) +Then, by IH (Part 2) on the first assumption of (87) we have: +G(Γ1), Φ1; ∅; G(∆1), Θ1 ⊢ V˜x +� +V +� +▷ G(�SC)⊸⋄ +(89) +By Definition 3.10 and Definition 3.3 and the second assumption of (87) we have: +G(Γ); ∅; G(∆2), G(∆µ2) ⊢ (�r1, . . . , �rn, �m) : G(�SC) +(90) +69 + +where �ri = (ri +i, . . . , ri +i+|G(Si)|−1) for i ∈ {1, . . . , n} and �m = (ui, . . . , ui+|G(C)|−1). +We define Φ = Φ1, Φ2 where: +Φ2 = +� +r∈dom(∆µ2) +cr : ⟨R⋆(∆µ2(r))⊸⋄⟩ +We define Θ = Θ1, ck :?(� +M). +We will first consider the case where n = 3; the proof is then generalized for any n ≥ 1: +• If n = 3 then P = V (r1, r2, r3, ui). By Table 1 we have: +Bk +˜x +� +V (r1, r2, r3, ui) +� += ck?(˜x).cr1!⟨λ�z1. cr2!⟨λ�z2. cr3!⟨λ�z3. Q⟩.0⟩.0⟩.0 +where Q = V˜x +� +V +� +(�z1, . . . , �zn, �m); �zi = (zi +1, . . . , zi +|G(Si)|) for i = {1, 2, 3}; �m = +(ui, . . . , ui+|G(C)|−1). +We shall prove the following judgment: +G(Γ), Φ; ∅; G(∆1∆2), Θ ⊢ Bk +˜x +� +V (�r, ui) +� +▷ ⋄ +(91) +We use auxiliary derivations: +(89) +(Lemma A.2) with Φ2 +G(Γ), Φ; G(Λ); G(∆1), Θ1 ⊢ V˜x +� +V +� +▷ G(�SC)⊸⋄ +(92) +(90) +(Lemma A.1) with σ +G(Γ), Φ; ∅; G(∆2), G(∆µ2) ⊢ (�z1, �z2, �z3, �m) ▷ G(�SC) +(93) +(92) +(93) +PolyApp +G(Γ), Φ; G(Λ); G(∆1, ∆2), Θ1, G(∆µ2) ⊢ V˜x +� +V +� +(�z1, �z2, �z3, �m) +(94) +where σ = {�n1/�z1} · {�n2/�z2} · {�n3/�z3} with �ni = (ri +i, . . . , ri +i+|G(Si)|−1) for i = {1, 2, 3}. +(94) +PolySess G(Γ), Φ; ∅; �z3 : G(S3) ⊢ �z3 ▷ G(S3) +PolyAbs G(Γ), Φ; G(Λ); G(∆1∆2), Θ1 ⊢ λ�z3. Q ▷ G(S3)⊸⋄ +(95) +(95) +Nil G(Γ), Φ; ∅; ∅ ⊢ 0 +LVar G(Γ), Φ; ∅; ∅ ⊢ cr3 ▷ ⟨G(S3)⊸⋄⟩ +Req G(Γ), Φ; G(Λ); G(∆1∆2), Θ1, �z1 : G(S1), �z2 : G(S2) ⊢ cr3!⟨λ�z3. Q⟩.0 ▷ ⋄ +(96) +(96) +PolySess G(Γ), Φ; ∅; �z2 : G(S2) ⊢ �z2 ▷ G(S2) +PolyAbs G(Γ), Φ; G(Λ); G(∆1∆2), Θ1, �z1 : G(S1) ⊢ λ�z2. cr3!⟨λ�z3. Q⟩.0 ▷ G(S2)⊸⋄ +(97) +(97) +Nil G(Γ), Φ; ∅; ∅ ⊢ 0 +LVar G(Γ), Φ; ∅; ∅ ⊢ cr2 ▷ ⟨G(S2)⊸⋄⟩ +Req G(Γ), Φ; G(Λ); G(∆1∆2), Θ1, �z1 : G(S1) ⊢ cr2!⟨λ�z2. cr3!⟨λ�z3. Q⟩.0⟩.0 ▷ ⋄ +(98) +(98) +PolySess G(Γ), Φ; ∅; �z1 : G(S1) ⊢ �z1 ▷ G(S1) +PolyAbs G(Γ), Φ; G(Λ); G(∆1∆2), Θ1 ⊢ λ�z1. cr2!⟨λ�z2. cr3!⟨λ�z3. Q⟩.0⟩.0 ▷ G(S1)⊸⋄ +(99) +70 + +(99) +Nil G(Γ), Φ; ∅; ∅ ⊢ 0 +LVar G(Γ), Φ; ∅; ∅ ⊢ cr1 ▷ ⟨G(S1)⊸⋄⟩ +Req +G(Γ), Φ; G(Λ); G(∆1∆2), Θ1 ⊢ cr1!⟨λ�z1. cr2!⟨λ�z2. cr3!⟨λ�z3. Q⟩.0⟩.0⟩.0 +(100) +The following tree proves this case: +(100) +PolyVar +G(Γ1), Φ; G(Λ); ∅ ⊢ �x ▷ � +M +PolyRcv +G(Γ1), Φ; ∅; G(∆1, ∆2), Θ ⊢ Bk +˜x +� +V (�r, ui) +� +▷ ⋄ +• Now we consider the general case for any n ≥ 1: +By Table 1 we have: +Bk +˜x +� +V �r +� += ck?(�x). +n=|�r| +cr1!⟨λ�z1. . . . crn!⟨λ�zn. Q⟩ . . .⟩ +where Q = V˜x +� +V +� +(�r1, . . . , �rn, �m) with: �zi = (zi +1, . . . , zi +|G(Si)|) for i = {1, . . . , n}; and +�m = (ui, . . . , ui+|G(C)|−1). +We shall prove the following judgment: +G(Γ), Φ; ∅; G(∆1∆2), Θ ⊢ Bk +˜x +� +V (�r, ui) +� +▷ ⋄ +(101) +We construct auxiliary derivations parametrized by k and denoted by d(k). If k = n, +derivation d(n) is defined as: +(89) +(Lemma A.2) with Φ2 +G(Γ), Φ; G(Λ); G(∆1), Θ1 ⊢ V˜x +� +V +� +▷ G(�SC)→⋄ +(102) +(102) +(90) +(Lemma A.1) with σ +G(Γ), Φ; ∅; G(∆µ2) ⊢ (�r1, . . . , �rn, �m) ▷ G(�SC) +PolyAbs +G(Γ), Φ; G(Λ); G(∆1, ∆2), Θ1, G(∆µ2) ⊢ λ�zn. Q ▷ G(Sn)⊸⋄ +(103) +where σ = � +i∈{1,...,n}{�ni/�zi} with �ni = (ri +i, . . . , ri +i+|G(Si)|−1) for i = {1, . . . , n}. +(103) +Nil G(Γ), Φ; ∅; ∅ ⊢ 0 +LVar G(Γ), Φ; ∅; ∅ ⊢ crn ▷ ⟨G(Sn)⊸⋄⟩ +Req +G(Γ), Φ; G(Λ); G(∆1, ∆2), Θ1, G(∆µ2) ⊢ crn!⟨λ�zn. Q⟩.0 +(104) +Otherwise, if k ∈ {1, ..., n − 1}, derivation d(k) is as follows: +d(k + 1) +PolyVar G(Γ), Φ; ∅; �zk : G(Sk) ⊢ �zk ▷ G(Sk) +PolyAbs +G(Γ), Φ; G(Λ); G(∆1, ∆2), Θ1, (�z1, . . . , �zk−1) : (G(S1), . . . , G(Sk−1)) ⊢ +λ�zk. +n−k +crk+1!⟨λ�zk+1. . . . crn!⟨λ�zn. Q +n−k +⟩.0 . . .⟩.0 ▷G(S1)⊸⋄ +(105) +(105) +G(Γ), Φ; ∅; ∅ ⊢ cr1 ▷ ⟨G(S1)⊸⋄⟩ +Acc +G(Γ), Φ; G(Λ); G(∆1, ∆2), Θ1, (�z1, . . . , �zk−1) : (G(S1), . . . , G(Sk−1)) ⊢ +n−k+1 +crk!⟨λ�zk. . . . crn!⟨λ�zr. Q +n−k+1 +⟩.0 . . .⟩.0 +(106) +The following tree proves this case: +d(1) +PolyVar +G(Γ1), Φ; G(Λ); ∅ ⊢ �x ▷ � +M +PolyRcv +G(Γ1), Φ; ∅; G(∆1, ∆2), Θ ⊢ Bk +˜x +� +V (�r, ui) +� +▷ ⋄ +71 + +2. This part concerns values. +Without a los of generality we assume �T = �S, C with �S = +(S1, . . . , Sn) such that tr(Si) for i ∈ {1, . . . , n}. We can distinguish two sub-cases: (i) V = y +and (ii) V = λ�y, z. P. +We first consider sub-case (i). By assumption Γ; Λ; ∆ ⊢ y ▷ C ⇝ ⋄. +Further, we can distinguish two sub-sub-cases (a) ⇝=⊸ and (b) ⇝=→. In sub-sub-case (a), +when ⇝=⊸, only Rule LVar can be applied and by inversion Λ = {y : �T ⊸ ⋄} and +∆ = ∅. By Table 1 we have V˜x +� +y +� += y and by Definition 3.3 and Definition 3.10 we have +G(∆) = {G( �T ⊸⋄)}. Hence, we prove the following judgment by applying Rule LVar: +G(Γ); G(∆); ∅ ⊢ V˜x +� +y +� +▷ G( �T ⊸⋄) +In sub-sub-case (b) only Rule Sh can be applied and by inversion we have Γ = {y : �T →⋄}, +Λ = ∅, and ∆ = ∅. Similarly to (a), by Definition 3.3 and Definition 3.10 we have G(Γ) = +{G( �T →⋄)}. Hence, we prove the following judgment by applying Rule SH: +G(Γ); ∅; ∅ ⊢ V˜x +� +y +� +▷ G( �T →⋄) +This concludes sub-case (i). Now, we consider sub-case (ii). +This is the second sub-case concerning values when V = λ�y, z. P where �y = y1, . . . , yn. By +assumption we have Γ; Λ; ∆, ∆µ ⊢ V ▷ �S, C ⇝ ⋄. Here we distinguish two sub-sub-cases (a) +⇝=⊸ and (b) ⇝=→: +• ⇝=⊸. By assumption, Γ; Λ; ∆, ∆µ ⊢ V ▷ �S, C ⊸⋄. In this case Rule Abs can be applied. +Firstly, we α-convert value V as follows: +V ≡α λ�y, z1. P{z1/z} +(107) +For this case only Rule Abs can be applied: +Γ; Λ; ∆1, ∆µ1 ⊢ P{z1/z} ▷ ⋄ +Γ; ∅; ∆2, ∆µ2 ⊢ �y, z1 ▷ �S, C +Abs +Γ \ z1; Λ; ∆1 \ ∆2, ∆µ1 \ ∆µ2 ⊢ λ�y, z1. P{z1/z} ▷ �S, C ⊸⋄ +(108) +Let �x = fv(P) and Γ1 = Γ \ �x. Also, let Θ1 be a balanced environment such that +dom(Θ1) = {c1, . . . , c�P�} ∪ {c2, . . . , c�P�} +and Θ1(c1) =?(� +M);end with � +M = (G(Γ \ y1), G(Λ))(�x). We define: +Φi = +� +r∈dom(∆µi) +cr : ⟨R⋆(∆µi(r))⊸⋄⟩ for i ∈ {1, 2} +Then, by IH (Part 1) on the first assumption of (108) we have: +G(Γ1), Φ1; ∅; G(∆1), Θ1 ⊢ B1 +˜x +� +P{y1/y} +� +▷ ⋄ +(109) +Let �T = G(S1), . . . , G(Sn), G(C). By Definition 3.3 and Definition 3.10 and the second +assumption of (108) we have: +G(Γ); ∅; G(∆2) ⊢ �y1, . . . , �yn, �z ▷ �T +(110) +where �z = (z1, . . . , z|G(C)|) and �yi = (yi +1, . . . , yi +|G(Si)|)) for i ∈ {1, . . . , n}. +We define Θ = Θ1, ck :!⟨� +M⟩. By Table 1, we have: +V˜x +� +λy1, . . . , yn, z. P +� += λ( �y1, . . . , � +yn, �z) : ( �T) +⇝. N +72 + +where +N = (ν �c) (ν �cr) +� +i∈|�y| +(cyi?(x).x �yi) | c1!⟨�x⟩ | B1 +˜x +� +P{z1/z} +� +with �c = (c1, . . . , c�P�) and �cr = � +r∈˜y cr. +We use an auxiliary derivation: +Nil G(Γ), Φ1; ∅; ∅ ⊢ 0 ▷ ⋄ +End G(Γ), Φ1; ∅; ck : end ⊢ 0 ▷ ⋄ +PolyVar +G(Γ), Φ1; G(Λ); ∅ ⊢ �x ▷ � +M +Send +G(Γ), Φ1; G(Λ); c1 :!⟨� +M⟩;end ⊢ c1!⟨�x⟩.0 ▷ ⋄ +(111) +LVar +G(Γ), Φ1; x : R⋆(∆µ2(yi))⊸⋄; ∅ ⊢ +x ▷ R⋆(∆µ2(yi))⊸⋄ +(112) +(112) +PolySess +G(Γ), Φ1; ∅; �yi : R⋆(∆µ2(yi)) ⊢ +�yi ▷ R⋆(∆µ2(yi)) +PolyApp +G(Γ), Φ1; x : R⋆(∆µ2(yi))⊸⋄; �yi : R⋆(∆µ2(yi)) ⊢ (b �yi) +(113) +(113) +Sh +G(Γ), Φ1; ∅; ∅ ⊢ cyi▷ +⟨R⋆(∆µ(yi))⊸⋄⟩ +LVar +G(Γ), Φ1; x : R⋆(∆µ(yi))⊸⋄; ∅ +⊢ x ▷ R⋆(∆µ(yi))⊸⋄ +Acc +G(Γσ), Φ1; ∅; �yi : R⋆(∆µ1(yi)) ⊢ cyi?(x).x �yi +(114) +for yi ∈ �y +(114) +Par (|�y| − 1 times) +G(Γ), Φ1; G(Λ); G(∆1), G(∆µ2) ⊢ � +i∈|�y|(cyi?(x).x �yi) ▷ ⋄ +(115) +(115) +(111) +(109) +(Lemma A.2) with ˜x +G(Γ), Φ1; ∅; G(∆1), Θ1 ⊢ B1 +˜x +� +P{z1/z} +� +▷ ⋄ +Par +G(Γ), Φ1; G(Λ); G(∆1), Θ ⊢ c1!⟨�x⟩ | B1 +˜x +� +P{z1/z} +� +▷ ⋄ +G(Γ), Φ1; G(Λ); G(∆1), G(∆µ2), Θ ⊢ +� +i∈|�y|(cyi?(x).x �yi) | c1!⟨�x⟩ | B1 +˜x +� +P{z1/z} +� +▷ ⋄ +PolyRes +G(Γ), Φ1 \ Φ2; G(Λ); G(∆1), G(∆µ2), Θ ⊢ +(ν �cr) � +i∈|�y|(cyi?(x).x �yi) | c1!⟨�x⟩ | B1 +˜x +� +P{z1/z} +� +▷ ⋄ +PolyResS +G(Γ), Φ1 \ Φ2; G(Λ); G(∆1), G(∆µ2) ⊢ N ▷ ⋄ +(116) +The following tree proves this part: +(116) +(110) +Abs +G(Γ \ z1), Φ1 \ Φ2; G(Λ); G(∆1 \ ∆2) ⊢ λ( �y1, . . . , � +yn, �z) : ( �T)⊸. N ▷ ⋄ +(117) +• ⇝=→. By assumption, Γ; ∅; ∅ ⊢ V ▷ C →⋄. In this case Rule Prom can be applied: +Γ; ∅; ∆ ⊢ P{y1/y} ▷ ⋄ +Γ; ∅; ∆ ⊢ y1 ▷ C +Abs +Γ \ z1; ∅; ∅ ⊢ λ�y, z1. P{z1/z} ▷ C ⊸⋄ +Prom Γ \ z1; ∅; ∅ ⊢ λ�y, z1. P{z1/z} ▷ C →⋄ +(118) +73 + +Now, we can see that we can specialize previous sub-case by taking ∆1 \ ∆2 = ∅ (resp. +∆µ1 \ ∆µ2 = ∅), that is ∆1 = ∆2 (resp. ∆µ1 = ∆µ2) and Λ = ∅. Subsequently, we have +Φ1 \ Φ2 = ∅, G(Λ) = ∅, and G(∆1 \ ∆2) = ∅. Thus, we can apply Rule Prom to (117) to +prove this sub-case as follows: +(117) +Prom +G(Γ \ z1); ∅; ∅ ⊢ λ( �y1, . . . , � +yn, �z) : ( �T)→. N ▷ ⋄ +This concludes this part (and the proof). +B.2 +Proof of Theorem 3.1 +Theorem 3.1 (Static Correctness). Let P be a closed HO process (i.e. fv(P) = ∅) with �u = fn(P). +If Γ; ∅; ∆ ◦ ∆µ ⊢ P ▷ ⋄, then G(Γσ); ∅; G(∆σ), G(∆µσ) ⊢ D(P) ▷ ⋄, where σ = {init(�u)/�u}. +Proof. By assumption Γ; ∅; ∆ ◦ ∆µ ⊢ P ▷ ⋄. Then, by applying Lemma A.1 we have: +Γσ; ∅; ∆σ ◦ ∆µσ ⊢ Pσ ▷ ⋄ +(119) +By Lemma 3.1 on (119) we have: +G(Γ1σ), Φ; ∅; G(∆σ), Θ ⊢ Bk +ϵ +� +Pσ +� +▷ ⋄ +(120) +where Θ is balanced with dom(Θ) = {ck, ck+1, . . . , ck+�P�−1}∪{ck+1, . . . , ck+�P�−1}, and Θ(ck) =?(·), +and Φ = � +r∈dom(∆µ) cr : ⟨R⋆(∆µ(r))⊸⋄⟩. By assumption, fv(P) = ∅. +By Definition 3.9, we shall prove the following judgment: +G(Γσ); ∅; G(∆σ) ◦ G(∆µσ) ⊢ (ν �c) (ν �cr) +� � +r∈˜v +cr?(x).x �r | ck!⟨⟩.0 | Bk +ϵ +� +Pσ +�� +where: k > 0; �v = rn(P); �r = (r1, . . . , r|G(S)|) for each r ∈ �v. +We know dom(∆µ) = �v. We assume that recursive session types are unfolded. By Definition 3.10 +and Definition 3.3, for r ∈ dom(∆µ) we have: +G(∆µ)(r) = R(∆µ(r)) = R⋆(∆µ(r)) +We use a family of auxiliary derivations parametrized by r ∈ �v. +LVar +G(Γσ), Φ; x : R⋆(∆µ(r))⊸⋄; ∅ ⊢ +x ▷ R⋆(∆µ(r))⊸⋄ +PolySess +G(Γσ), Φ; ∅; �r : R⋆(∆µ(r)) ⊢ +�r ▷ R⋆(∆µ(r)) +PolyApp +G(Γσ), Φ; x : R⋆(∆µ(r))⊸⋄; �r : R⋆(∆µ(r)) ⊢ (x �r) +(121) +(121) +Sh +G(Γσ), Φ; ∅; ∅ ⊢ cr▷ +⟨R⋆(∆µ(r))⊸⋄⟩ +LVar +G(Γσ), Φ; x : R⋆(∆µ(r))⊸⋄; ∅ +⊢ x ▷ R⋆(∆µ(r))⊸⋄ +Acc +G(Γσ), Φ; ∅; �r : R⋆(∆µ(r)) ⊢ cr?(x).x �r +(122) +We will then use: +for r ∈ �v +(122) +Par (|�v| − 1 times) G(Γσ), Φ; ∅; G(∆µσ) ⊢ � +r∈˜v cr?(x).x �r +(123) +74 + +where we apply Rule Par |�v| − 1 times and for every r ∈ �v we apply derivation (122). Notice +that by Definition 3.10 and Definition 3.3 we have G(∆µσ) = � +r∈˜v �r : R⋆(∆µ(r)). +Sess G(Γσ), Φ; ∅; ck :!⟨·⟩;end ⊢ ck!⟨⟩.0 +(120) +Par +G(Γσ), Φ; ∅; G(∆σ), Θ, ck :!⟨·⟩;end ⊢ ck!⟨⟩.0 | Bk +ϵ +� +Pσ +� +(124) +The following tree proves this case: +(123) +(124) +Par +G(Γσ), Φ; ∅; G(∆σ), Θ, ck :!⟨·⟩;end ◦ G(∆µσ) ⊢ +� +r∈˜v(cr?(x).x �r) | ck!⟨⟩.0 | Bk +ϵ +� +Pσ +� +PolyRes +G(Γσ); ∅; G(∆σ), Θ, ck :!⟨·⟩;end ◦ G(∆µσ) ⊢ +(ν �cr) (� +r∈˜v(cr?(x).x �z) | ck!⟨⟩.0 | Bk +ϵ +� +Pσ +� +) +PolyResS +G(Γσ); ∅; G(∆σ) ◦ G(∆µσ) ⊢ (ν �c) (ν �cr) (� +r∈˜v(cr?(x).x �r) | ck!⟨⟩.0 | Bk +ϵ +� +Pσ +� +) +(125) +75 + +C +Appendix to Section 4 +C.1 +Proof of Lemma 4.3 +Lemma 4.3. Given an indexed process P1{ ˜W/˜x}, the set C ˜ +W +˜x +� +P1 +� +is closed under τ-transitions +on non-essential prefixes. That is, if R1 ∈ C ˜ +W +˜x +� +P1 +� +and R1 +τ−→ R2 is inferred from the actions on +non-essential prefixes, then R2 ∈ C ˜ +W +˜x +� +P1 +� +. +Proof. By the induction on the structure of P1. We consider two base cases: +• Case P1 = 0. Let �B such that � +W⊠ �B. Then, the elements of C ˜ +W +˜x +� +0 +� +are R1 = (ν ck) ck!⟨ �B⟩ | ck?(�x).0 +and R2 = 0. Clearly, R1 +τ−→ R2. +• Case P1 = V1 (�r, u). Let n = |�r|. Then, we have +C +˜ +W +˜x +� +P1 +� += N1 ∪ N4 ∪ +� +∪1≤l≤n Nl +2 +� +∪ +� +∪1≤l≤n−1 Nl +3 +� +where +N1 = {R˜v,˜r | ck!⟨ �B⟩ | Bk +˜x +� +P1 +� +: � +W ⊠ �B} +Nl +2 = {R˜v,rl,...,rn | +|˜r|−l+1 +crl! +� +λ�zl.crl+1!⟨λ�zl+1. · · · .crn!⟨λ�zn. QV2 +l ⟩ ⟩ +� +: V1{ ˜W/˜x} ⊠ V2} +Nl +3 = {R˜v,rl+1,...,rn | λ�zl. +|˜r|−l +crl+1!⟨λ�zl+1. · · · .crn!⟨λ�zn. QV2 +l ⟩ +� +�rl : V1{ ˜W/˜x} ⊠ V2} +N4 = {R˜v | V2 (�r1, . . . , �rn, �m) : V1{ ˜W/˜x} ⊠ V2} +with +QV2 +l += V2 (�r1, . . . , �rl−1, �zl, . . . , �zn, �m) +We can see that for R1 ∈ N1 there exist R0 +2 ∈ N0 +2 such that R1 +τ−→ R0 +2. Further, we could see +that for Rl +2 ∈ Nl +2 there is Rl +3 ∈ Nl +3 such that Rl +2 +τ−→ Rl +3. Now, we can see that for Rl +3 ∈ Nl +3 +there is Rl+1 +2 +∈ Nl+1 +2 +such that Rl +3 +τ−→ Rl+1 +2 +. Finally, we have for +Rn +3 ∈ Nn +3 = {R˜v | λ�zn. QV2 +n �rn : V1{ ˜W/˜x} ⊠ V2} +there is R4 ∈ N4 such that Rn +3 +τ−→ R4. +We consider two inductive cases as remaining cases are similar: +• Case P1 = ui!⟨V1⟩.P2. We distinguish two sub-case: (i) ¬tr(ui) and (ii) tr(ui). In both sub- +cases, we distinguish two kinds of an object value V1: (a) V1 ≡ x, such that {Vx/x} ∈ { ˜W/˜x} +and (b) V1 = λy : C. P ′, that is V1 is a pure abstraction. +First, we consider sub-case (i). Let �y = fv(V1), �w = fv(P2), � +W1, and � +W2 such that {� +W/�x} = +{� +W1/�y} · {� +W2/ �w}. Further, let �v = rn(P1{ ˜W/˜x}) and σ = {ui+1/ui}. Then, by the definition of +C− +− +� +− +� +(Table 3), we have that C ˜ +W +˜x +� +ui!⟨V1⟩.P2 +� += N1 ∪ N2 where: +N1 = {R˜v | ck!⟨ �B⟩ | Bk +˜x +� +P1 +� +: � +W ⊠ �B} +N2 = {R˜v | ui!⟨V2⟩.ck!⟨ �B2⟩ | Bk2 +˜w +� +P2σ +� +: V1σ{� +W1/�y} ⊠ V2, � +W2 ⊠ �B2} +We can see that in both cases of V1, a variable or a pure abstraction, we have that for R1 ∈ N1 +there is R2 ∈ N2 such that R1 +τ−→ R2. In the sub-case (a) by {Vx/x} ∈ { ˜W/˜x} we have V2 ∈ �B, +76 + +such that Vx ⊠ V2, that by τ-move substitutes x in Bk +˜x +� +P1 +� +. Thus, by xσ{ ˜W1/˜y} = Vx we have +V1σ{ ˜W1/˜y} ⊠ V2. In the sub-case (b), by definition of B− +− +� +− +� +we have that by τ-move �B1 ⊆ �B +substitute �y in V˜y +� +V1σ +� +so we have R1 +τ−→ R2 where +V2 = V˜y +� +V1σ +� +{ ˜B1/˜y} +Now, we may notice that by Table 3 we have +V2 ∈ C +˜ +W1 +˜y +� +V1σ +� +Hence, by Definition 4.11 and Definition 4.13 we have V1σ{ ˜W1/˜y} ⊠ V2. Further, we may +notice that there is no τ-transition involving non-essential prefixes in R2. This concludes this +sub-case. +Now, we consider sub-case (ii). Let �y = fv(V1), �w = fv(P2), � +W1, and � +W2 such that {� +W/�x} = +{� +W1/�y} · {� +W2/ �w}. Then, we have C ˜ +W +˜x +� +P1 +� += N1 ∪ N2 ∪ N3 ∪ N4 where +N1 = {R˜v | ck!⟨ �B⟩ | Bk +˜x +� +P1 +� +: � +W ⊠ �B} +N2 = {R˜v | cu! +� +M +˜B2 +V2 +� +| Bk +˜w +� +P2 +� +: V1{ ˜W1/˜y} ⊠ V2, � +W2 ⊠ �B2} +N3 = {R˜v\u | M +˜B2 +V2 �u | Bk +˜w +� +Q +� +: V1{ ˜W1/˜y} ⊠ V2, � +W2 ⊠ �B2} +N4 = {R˜v\u | u[S⟩! +� +V2 +� +.ck!⟨ �B2⟩.cu?(b).(b �u) | Bk +˜w +� +P2 +� +: V1{ ˜W1/˜y} ⊠ V2, � +W2 ⊠ �B2} +where +M +˜B2 +V2 = λ�z. z[S⟩! +� +V2 +� +.ck!⟨ �B2⟩ | cu?(b).(b �z) +As in the previous sub-case, we can see that in both cases of V1, a variable or a pure abstraction, +we have that for R1 ∈ N1 there is R2 ∈ N2 such that R1 +τ−→ R2, for appropriate choice of �B, �B2, +and k. Similarly, by the communication on shared name cu for R2 ∈ N2 there is R3 ∈ N3 such +that R2 +τ−→ R3. Finally, for R3 ∈ N3 there is R4 ∈ N4 such that R3 +τ−→ R4 by the application. +This concludes output case. +• Case P1 = Q1 | Q2. Let �y = fv(Q1), �w = fv(Q2), � +W1, and � +W2 such that {� +W/�x} = { ˜W1/˜y} · +{ ˜W2/ ˜w}. Then, by the definition of C− +− +� +− +� +(Table 3), we have that C ˜ +W +˜x +� +Q1 | Q2 +� += N1∪N2∪N3 +where: +N1 = {ck!⟨ �B⟩ | Bk +˜x +� +Q1 | Q2 +� +: � +W ⊠ �B} +N2 = {ck!⟨ �B1⟩.ck+l!⟨ �B2⟩ | Bk +˜y +� +Q1 +� +| Bk+l +˜w +� +Q2 +� +: � +W1 ⊠ �B1, � +W2 ⊠ �B2} +N3 = {R1 | R2 : R1 ∈ C +˜ +W1 +˜y +� +Q1 +� +, R2 ∈ C +˜ +W2 +˜w +� +Q2 +� +} +with l = �Q1�. +We show that the thesis holds for processes in each of these three sets: +1. Clearly, by picking appropriate �B, �B1, and �B2, for any R1 +1 ∈ N1 there is R1 +2 such that +R1 +1 +τ−→ R1 +2 and R1 +2 ∈ N2. +2. Now, we consider set N3. Let us pick R3 = R1 | R2 ∈ N3, for some R1 ∈ C +˜ +W1 +˜y +� +Q1 +� +and +R2 ∈ C +˜ +W2 +˜w +� +Q2 +� +. By the definition of C− +− +� +− +� +(Table 3) we know all propagator names are +restricted element-wise in R3, and so there is no communication between R1 and R2 on +propagator prefixes. This ensures that any τ-actions emanating from R3 arise from R1 +or R2 separately, not from their interaction. The thesis then follows by IH, for we know +that if R1 +τ−→ R′ +1 then R′ +1 ∈ C +˜ +W1 +˜y +� +Q1 +� +; similarly, if R2 +τ−→ R′ +2 then R′ +2 ∈ C +˜ +W2 +˜w +� +Q2 +� +. Thus, +by the definition R′ +1 | R′ +2 ∈ N3. +77 + +3. Finally, we show that for any R2 ∈ N2 if R2 +τ−→ R′ +2 then R′ +2 ∈ C ˜ +W +˜x +� +Q1 | Q2 +� +. We know +that R2 = ck!⟨ �B1⟩.ck+l!⟨ �B2⟩ | Bk +˜y +� +Q1 +� +| Bk+l +˜w +� +Q2 +� +, where �Bi are such that � +Wi ⊠ �Bi for +i ∈ {1, 2}. Clearly, by a synchronization on ck, we have +R2 +τ−→ ck+l!⟨ �B2⟩ | BQ1 | Bk+l +˜w +� +Q2 +� += R′ +2 +where BQ1 stands for the derivative of Bk +˜y +� +Q1 +� +after the synchronization (and substitution +of �B1). +To show that R′ +2 is already in C ˜ +W +˜x +� +Q1 | Q2 +� +, we consider an R3 ∈ N3 such that +R3 = ck!⟨ �B1⟩ | Bk +˜y +� +Q1 +� +| ck+l!⟨ �B2⟩ | Bk+l +˜w +� +Q2 +� +Note that there is a τ-transition on ck such that R3 +τ−→ R′ +2. Because processes in N3 +satisfy the thesis (cf. the previous sub-sub-case), we have that R′ +2 ∈ N3. Therefore, +R′ +2 ∈ C ˜ +W +˜x +� +Q1 | Q2 +� +, as desired. This concludes parallel composition case. +This concludes the proof. +C.2 +Proof of Lemma 4.4 +For the proof we will use the following syntactic sugar. +Definition C.1 (Function �C− +− +� +− +� +). Let P be a HO process, ρ be a values substitution, and σ be +an indexed name substitution. We define �Cρ +σ +� +P +� +as follows: +�Cρ +σ +� +P1 +� += C +˜ +Wσ +˜x +� +P1σ +� +with ρ = { ˜W/˜x} +Lemma 4.4. Assume P1{ ˜W/˜x} is a process such that Γ1; Λ1; ∆1 ⊢ P1{ ˜W/˜x} ▷ ⋄ with balanced(∆1) +and P1{ ˜W/˜x} S Q1. +1. Whenever P1{ ˜W/˜x} +(ν �m1) n!⟨V1⟩ +−−−−−−−−→P2 , such that n ̸∈ fn(P1{ ˜W/˜x}), then there exist Q2 and V2 +such that Q1 +(ν �m2) ˘n!⟨V2⟩ +========⇒Q2 and, for a fresh t, +(ν �m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν �m2)(Q2 ∥ t1 ←�H V2) +2. Whenever P1{ ˜W/˜x} +n?(V1) +−−−−→P2 , such that n ̸∈ fn(P1{ ˜W/˜x}), then there exist Q2, V2, and σ +such that Q1 +˘n?(V2) +====⇒Q2 where V1σ ⊠ V2 and P2 S Q2, +3. Whenever P1 +τ−→P2 then there exists Q2 such that Q1 +τ=⇒Q2 and P2 S Q2. +Proof. By transition induction. Let ρ1 = { ˜W/˜x}. By inversion of P1ρ1 S Q1 we know there is +σ1 ∈ index(fn(Pρ1)) such that Q1 ∈ �Cρ1 +σ1 +� +P1 +� +. Then, we need the following assertion on the index +substitution. If P1ρ1 +ℓ−→ P2ρ2 and subj(ℓ) = n such that ¬tr(n) then there exists Q2 such that +Q1 +˘ℓ=⇒ Q2 with subj(˘ℓ) = ni and Q2 ∈ �Cρ2 +σ2 +� +P2 +� +such that σ2 ∈ index(P2ρ2) and next(ni) ∈ σ2. +First, we consider three base cases: Rules Snd, Rv, and App. Then, we distinguish five inductive +cases and analyze three cases (as cases ParR and ParL, and New and Res are similar). Thus, in total +we consider six cases: +1. Case ⟨Snd⟩. Then P1 = n!⟨V1⟩.P2. We first consider the case when P1 is not a trigger collection, +and then briefly discuss the case when it is a trigger collection. +We distinguish two sub-cases: (i) ¬tr(n) and (ii) tr(n). In both sub-cases, we distinguish two +kinds of an object value V1: (a) V1 ≡ x, such that {Vx/x} ∈ { ˜W/˜x} and (b) V1 = λy : C. P ′, +that is V1 is a pure abstraction. Next, we consider two sub-cases: +78 + +i) Sub-case ¬tr(n). Let � +W1, � +W2, �y, and �w such that +P1{ ˜W/˜x} = n!⟨V1{ ˜W1/˜y}⟩.P2{ ˜W2/ ˜w} +We have the following transition: +⟨Snd⟩ +P1{ ˜W/˜x} +n!⟨V1{ ˜W1/˜y}⟩ +−−−−−−−−−→ P2{ ˜W2/ ˜w} +Let σ1 ∈ index(�u) where �u = fn(P1{ ˜W/˜x}) such that {ni/n} ∈ σ1. +Also, let σ2 = +σ1 · next(ni). Further, let �v = rn(P1{ ˜W/˜x}), �cr = ∪r∈˜vcr, �ck = (ck, . . . , ck+�P1�−1), and +�ck+1 = (ck+1, . . . , ck+�P1�−1). When P1 is not a trigger, by the definition of S (Table 3), +for both sub-cases, we have Q1 ∈ N1 ∪ N2 where: +N1 = +� +(ν �cr) (ν �ck) R˜v | ck!⟨ �B⟩ | Bk +˜x +� +P1σ1 +� +: � +W ⊠ �B +� +N2 = +� +(ν �cr) (ν �ck+1) R˜v | ni!⟨V2⟩.ck+1!⟨ �B2⟩ | Bk+1 +˜w +� +P2σ2 +� +: +V1σ{� +W1/�y} ⊠ V2, � +W2 ⊠ �B2 +� +If Q1 ∈ N1, then there is some Q2 ∈ N2 such that Q1 reduces to Q2 through communication +on non-essential prefixes. By Lemma 4.3 it is then sufficient to consider the situation when +Q2 ∈ N2. Let �v1 = rn(P2{ ˜W2/˜z}), �v2 = rn(V2{ ˜W1/˜y}), �cr1 = ∪r∈˜v1cr, and �cr2 = ∪r∈˜v2cr. +By Definition 4.16 and the assumption that P1{ ˜W/˜x} is well-typed we have �cr = �cr1 · �cr2 +and �cr1 ∩ �cr2 = ∅. In that case we have the following transition: +⟨Snd⟩ +ni!⟨V2⟩.ck+1!⟨ �B2⟩ +ni!⟨V2⟩ +−−−−→ ck+1!⟨ �B2⟩ +⟨ParL⟩ +ni!⟨V2⟩.ck+1!⟨ �B2⟩ | Bk+1 +˜w +� +P2σ2 +� ni!⟨V2⟩ +−−−−→ R1 +⟨ParR⟩ +R˜v | ni!⟨V2⟩.ck+1!⟨ �B2⟩ | Bk+1 +˜w +� +P2σ2 +� ni!⟨V2⟩ +−−−−→ R1 +�cr · �ck+1 ∩ fn(ni!⟨V2⟩) = ∅ +⟨New⟩ +(ν �cr) (ν �ck+1) (R˜v | ni!⟨V2⟩.ck+1!⟨ �B2⟩ | Bk+1 +˜z +� +P2σ2 +� +) +(ν �cr2) ni!⟨V2⟩ +−−−−−−−−→ Q′ +2 +(126) +where Q′ +2 = (ν �cr1) (ν �ck+1) R˜v | ck+1!⟨ �B2⟩ | Bk+1 +˜w +� +P2σ2 +� +with V1{ ˜W1/˜y}σ2 ⊠ V2 and +� +W2σ1 ⊠ �B2. Then, we shall show the following: +(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν �cr2) (Q′ +2 ∥ t1 ←�H V2) +(127) +By assumption that P1{ ˜W/˜x} is well-typed, we know �v = �v1 · �v2 and �v1 ∩ �v2 = ∅. Thus, +by Definition 4.16 we know R˜v = R˜v1 | R˜v2, that is +(ν �cr2) (Q′ +2 ∥ t1 ←�H V2) +≡ (ν �cr1) (ν �cr2) (ν �ck+1)(R˜v1 | ck+1!⟨ �B⟩ | Bk+1 +˜w +� +P2σ1 +� +| R˜v2 ∥ t1 ←�H V2) +≡ (ν �cr) (ν �ck+1)(R˜v1 | ck+1!⟨ �B⟩ | Bk+1 +˜w +� +P2σ1 +� +| R˜v2 ∥ t1 ←�H V2) += (ν �cr) (ν �ck+1) R +From the definition of S (Definition 4.17) we have that n ̸∈ fn(� +W2) and thus � +W2σ1 = � +W2σ2. +Thus, by the definition of �B2 (� +W2σ2 ⊠ �B2) we can see that +R˜v1 | ck+1!⟨ �B⟩ | Bk+1 +˜w +� +P2σ1 +� +| R˜v2 ∈ C +˜ +W2σ2 +˜w +� +P2σ2 +� +(128) +79 + +Now, we can see that assertion next(ni) ∈ σ2 holds, as by definition σ2 = σ1 · next(ni). +Let σ′ +2 = σ2 · {t1/t}. Then, we have +C +˜ +W1σ′ +2 +˜y +� +t1 ←�H V1σ2 +� += {P ′ : (t1 ←�H V1){ ˜W1/˜y}σ2 ⋄ P ′} +As (t1 ←�H V1){ ˜W1/˜y}σ2 = t1 ←�H V1{ ˜W1/˜y}σ2 and V1{ ˜W1/˜y}σ2 ⊠ V2 we have +(t1 ←�H V1){ ˜W1/˜y}σ2 ⋄ (t1 ←�H V2) +(129) +that is +R˜v2 ∥ t1 ←�H V2 ∈ C +˜ +W1σ′ +2 +˜y +� +t1 ←�H V1σ2 +� +Finally, by Table 3 we have +C +˜ +Wσ′ +2 +˜x +� +P2σ2 ∥ t1 ←�H V1σ2 +� += +� +R1 ∥ R2 : R1 ∈ C +˜ +W2σ′ +2 +˜w +� +P2σ2 +� +, R2 ∈ C +˜ +W1σ′ +2 +˜y +� +t1 ←�H V1σ2 +�� +So, by this, (128), and (129) we have: +R ∈ C +˜ +Wσ′ +2 +˜x +� +P2σ′ +2 ∥ t1 ←�H V1σ2 +� +Further, by σ′ +2 = σ1 · next(ni) · {tj/t} and Definition 4.10, we have +σ′ +2 ∈ index(fn((P2 ∥ t ←�H V1){ ˜W/˜x})) +Hence, the goal (127) follows. This concludes sub-case ¬tr(n). +ii) Sub-case tr(n). Let � +W1, � +W2, �y, and �w be such that +P1{ ˜W/˜x} = n!⟨V1{ ˜W1/˜y}⟩.P2{ ˜W2/ ˜w} +The transition inference tree is as follows: +⟨Snd⟩ +P1{ ˜W/˜x} +n!⟨V1{ ˜W1/˜y}⟩ +−−−−−−−−−→ P2{ ˜W2/ ˜w} +Let σ1 ∈ index(�u) where �u = fn(P1{ ˜W/˜x}). Also, let �v = rn(P1), �cr = ∪r∈˜vcr, �ck = +(ck, . . . , ck+�P1�−1), �ck+1 = (ck+1, . . . , ck+�P1�−1), and let S be such that n : S. Then, by +the definition of S (Definition 4.17) we have Q1 ∈ N1 ∪ N2 ∪ N3 ∪ N4 where +N1 = {(ν �cr) (ν �ck) R˜v | ck!⟨ �B⟩ | Bk +˜x +� +P1σ1 +� +: � +Wσ1 ⊠ �B} +N2 = {(ν �cr) (ν �ck+1) R˜v | cn! +� +M +˜B2 +V2 +� +| Bk+1 +˜w +� +P2σ1 +� +: � +W2σ1 ⊠ �B2} +N3 = {(ν �cr) (ν �ck+1) R˜v | M +˜B2 +V2 �n | Bk+1 +˜w +� +P2σ1 +� +: V1{ ˜W1/˜y}σ1 ⊠ V2, � +W2σ1 ⊠ �B2} +N4 = +� +(ν �cr) (ν �ck+1) R˜v\n | n[S⟩! +� +V2 +� +.(ck+1!⟨ �B2⟩ | cn?(x).x �z | Bk+1 +˜w +� +P2σ1 +� +: V1{ ˜W1/˜y}σ1 ⊠ V2, � +W2σ1 ⊠ �B2 +� +with +M +˜B2 +V2 = λ�z. z[S⟩! +� +V2 +� +. +� +ck+1!⟨ �B2⟩ | cn?(x).x �z +� +If Q1 ∈ N1 ∪ N2 ∪ N3, then Q1 reduces to some Q4 ∈ N4 through communication on +non-essential prefixes. By Lemma 4.3 it suffices to consider the case when Q4 ∈ N4. Let +�v1 = rn(P2), �v2 = rn(V2), �cr1 = ∪r∈˜v1cr, and �cr2 = ∪r∈˜v2cr. By Definition 4.16 and the +80 + +assumption that P1{ ˜W/˜x} is well-typed we have �cr = �cr1 · �cr2 and �cr1 ∩ �cr2 = ∅. We then +infer the following transition: +Q4 +(ν �cr2) n[S⟩!⟨V2⟩ +−−−−−−−−−−→ Q′ +4 +where Q′ +4 = (ν �cr1) (ν �ck+1) R˜v\n | ck+1!⟨ �B2⟩ | cn?(b).(b �n) | Bk+1 +˜w +� +P2σ1 +� +. Then, we shall +show the following +(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν �cr2) +� +Q′ +4 ∥ t1 ←�H V2 +� +(130) +By assumption that P1{ ˜W/˜x} is well-typed, we know �v = �v1 · �v2 and �v1 ∩ �v2 = ∅. Hence, +by Definition 4.16 we know R˜v = R˜v1 | R˜v2, that is +Q′ +4 ≡ (ν �cr1) (ν �ck+1) R˜v\n | cn?(x).x �n | ck+1!⟨ �B2⟩ | Bk+1 +˜w +� +P2σ1 +� += (ν �cr1) (ν �ck+1) R˜v | ck+1!⟨ �B2⟩ | Bk+1 +˜w +� +P2σ1 +� += (ν �cr1) (ν �ck+1) R˜v1 | R˜v2 | ck+1!⟨ �B2⟩ | Bk+1 +˜w +� +P2σ1 +� +That is, we have +(ν �cr2) +� +Q′ +4 ∥ t1 ←�H V2 +� +≡ (ν �cr2) +� +(ν �cr1) (ν �ck+1) R˜v1 | R˜v2 | ck+1!⟨ �B2⟩ | Bk+1 +˜w +� +P2σ1 +� +∥ t1 ←�H V2 +� +≡ (ν �cr1) (ν �cr2) (ν �ck+1)(R˜v1 | ck+1!⟨ �B⟩ | Bk+1 +˜w +� +P2σ1 +� +| R˜v2 ∥ t1 ←�H V2) +≡ (ν �cr) (ν �ck+1)(R˜v1 | ck+1!⟨ �B⟩ | Bk+1 +˜w +� +P2σ1 +� +| R˜v2 ∥ t1 ←�H V2) = (ν �cr) (ν �ck+1) R +Now, by Definition 4.8 we may notice that �v2 = rn(t ←�H V2). Let σ′ +1 = σ1 · {t1/t}. So, by +Table 3 we have +R˜v1 | ck+1!⟨ �B⟩ | Bk+1 +˜w +� +P2σ1 +� +∈ C +˜ +W2σ1 +˜w +� +P2σ1 +� +and +R˜v2 ∥ t1 ←�H V2 ∈ C +˜ +W1σ1 +˜y +� +t1 ←�H V1σ′ +1 +� +(131) +Thus, by the definition of the parallel composition case of C− +− +� +− +� +(Table 3) we have +R ∈ C +˜ +Wσ′ +1 +˜x +� +(P2 ∥ t ←�H V1)σ′ +1 +� +Now, we can notice that �cr = cr(R) and �ck+1 = fpn(R). Further, we have +σ′ +1 ∈ index(fn((P2 ∥ t ←�H V1){ ˜W/˜x})) +Thus, (130) follows. This concludes sub-case tr(n) of case ⟨Snd⟩. +Finally, we briefly analyze the case when P1 is a trigger collection. Let σ1 be defined as above. +Let H′ +1 be such that P1{ ˜W/˜x}σ1 ⋄ H′ +1. Then, by Table 3, Q1 is as follows: +Q1 = R˜v ∥ H′ +1 +where �v = rn(P1{ ˜W/˜x}). Further, by Definition 4.15 we know H′ +1 = ni!⟨V2⟩.H′ +2 such that +V1{ ˜W1/˜y}σ2 ⊠ V2 and P2{ ˜W2/ ˜w}σ2 ⋄ H′ +2 with σ2 = σ1 · next(ni). We can see that +H′ +1 +ni!⟨V2⟩ +−−−−→ H′ +2 +81 + +So, we should show +(P2 ∥ t ←�H V1){ ˜W/˜x} S (R˜v ∥ H′ +2 | t1 ←�H V2) +(132) +Similarly to previous sub-cases, we have +R˜v ∥ H′ +2 | t1 ←�H V2 ≡ R˜v1 ∥ H′ +2 ∥ R˜v2 ∥ t1 ←�H V2 +By P2{ ˜W2/ ˜w}σ2 ⋄ H′ +2 and �v1 = rn(P2{ ˜W2/ ˜w}) we have +R˜v1 ∥ H′ +2 ∈ C +˜ +W2σ2 +˜w +� +P2σ2 +� +(133) +Let σ′ +2 = σ2 · {t1/t}. By (133), (131), and definition of C− +− +� +− +� +(Table 3) for the parallel +composition case we have +R˜v1 ∥ H′ +2 ∥ R˜v2 ∥ t1 ←�H V2 ∈ C +˜ +Wσ′ +2 +˜x +� +P2 ∥ t ←�H V1 +� +Thus, we reach goal (132). This concludes case ⟨Snd⟩. +2. Case ⟨Rv⟩. In this case we know P1 = n?(y).P2. We first consider cases when P1 is not a +trigger collection, and then briefly discuss the case when it is a trigger collection. As in the +previous case, we distinguish two sub-cases: (i) ¬tr(n) and (ii) tr(n): +i) Sub-case ¬tr(n). We have the following transition: +⟨Rv⟩ +(ni?(y).P2){ ˜W/˜x} +n?(V1) +−−−−→ P2{ ˜W/˜x}{V1/y} +Here we assume y ∈ fv(P2). +Let σ1 ∈ index(�u) with �u = fn(P1{ ˜W/˜x}) such that +{ni/n} ∈ σ1. Also, let σ2 = σ1 · next(ni). Further, let �v = rn(P1{ ˜W/˜x}), �cr = ∪r∈˜vcr, �ck = +(ck, . . . , ck+�P1�−1), and �ck+1 = (ck+1, . . . , ck+�P1�−1). By the definition of S (Table 3) we +have Q1 ∈ N1 ∪ N2 where +N1 = +� +(ν �cr) (ν �ck) R˜v | ck!⟨ �B⟩ | Bk +˜x +� +P1σ1 +� +: � +Wσ1 ⊠ �B +� +N2 = +� +(ν �cr) (ν �ck+1) R˜v | ni?(y).ck+1!⟨ �By⟩ | Bk+1 +˜xy +� +P2σ2 +� +: � +Wσ1 ⊠ �B +� +Similar to the other cases, if Q1 ∈ N1, then Q1 reduces to some Q′ +1 ∈ N2 through +communication on non-essential prefixes. Now, we pick V2 such that V1σv · σ2 ⊠ V2 where +σv ∈ index(fn(V ) \ �u) such that +σv · σ2 ∈ index(fn(P2{ ˜WV1/˜xy})) +(134) +By Lemma 4.3 it suffices to consider the case when Q′ +1 ∈ N2, under which we have the +following transition: +⟨Rv⟩ +ni?(y).ck+1!⟨ �By⟩ +ni?(V2) +−−−−→ ck+1!⟨ �BV2⟩ +(135) +(135) +bn(ni?(V2)) ∩ fn(Bk+1 +˜xy +� +P2σ +� +) = ∅ +⟨ParL⟩ +ni?(y).ck+1!⟨ �By⟩ | Bk+1 +˜xy +� +P2σ2 +� ni?(V2) +−−−−→ ck+1!⟨ �BV2⟩ | Bk+1 +˜xy +� +P2σ2 +� +(136) +(136) +�cr · �ck+1 ∩ fn(ni?(V2)) = ∅ +⟨Res⟩ +(ν �cr) (ν �ck+1) R˜v | ni?(y).ck+1!⟨ �By⟩ | Bk+1 +˜xy +� +P2σ2 +� ni?(V2) +−−−−→ R +82 + +where R = (ν �cr) (ν �ck+1) ck+1!⟨ �BV2⟩ | Bk+1 +˜xy +� +P2σ2 +� +with � +Wσ1 ⊠ �B. We can see that +assertion next(ni) ∈ σ2 holds by the definition. We should show that +P2{ ˜WV1/˜xy} S R +(137) +We know n ̸∈ fn(� +W) and n ̸∈ fn(V1). Thus, � +WV1σv · σ1 = � +WV1σv · σ2. That is, we may +notice that � +WV1σv · σ2 ⊠ �BV2. Further, by the definition of σv, we have P2σ2 = P2σv · σ2. +Thus, we have +R ∈ C +˜ +WV1σv·σ2 +˜xy +� +P2σv · σ2 +� +Finally, by this and (134) the goal (137) follows. This concludes sub-case ¬tr(n). +ii) Sub-case tr(n). The transition inference tree is as follows: +⟨Rv⟩ +(n?(y).P2){ ˜W/˜x} +n?(V1) +−−−−→ P2{ ˜W/˜x}{V1/y} +Let σ1 = index(�u) where �u = fn(P1{ ˜W/˜x}). Also, let �v = rn(P1), �cr = ∪r∈˜vcr, �ck = +(ck, . . . , ck+�P1�−1), �ck+1 = (ck+1, . . . , ck+�P1�−1), and let S be such that n : S. Then, by +the definition of S (Definition 4.17) we have Q1 ∈ N1 ∪ N2 ∪ N3 ∪ N4 where +N1 = {(ν �cr) (ν �ck) R˜v | ck!⟨ �B⟩ | Bk +˜x +� +P1σ1 +� +: � +Wσ1 ⊠ �B} +N2 = {(ν �cr) (ν �ck) R˜v | cn! +� +M +˜B +V +� +| Bk+1 +˜xy +� +P2σ1 +� +: � +Wσ1 ⊠ �B} +N3 = {(ν �cr) (ν �ck) R˜v\n | M +˜B +V �n | Bk+1 +˜xy +� +P2σ1 +� +: � +Wσ1 ⊠ �B} +N4 = {(ν �cr) (ν �ck+1) R˜v\n | n[S⟩?(y).(ck+1!⟨ �By⟩ | cn?(x).x �n | Bk+1 +˜xy +� +P2σ1 +� +: � +Wσ1 ⊠ �B} +with +M +˜B +V = λ�z. z[S⟩?(y). +� +ck+1!⟨ �By⟩ | cn?(x).x �z +� +Similar to the other cases, if Q1 ∈ N1 ∪ N2 ∪ N3, then there exists some Q′ +1 ∈ N4 such +that Q1 reduces to Q′ +1 through communication on non-essential prefixes. By Lemma 4.3 +it suffice to consider the case when Q1 ∈ N4. We infer the following transition: +Q1 +n[S⟩?(V2) +−−−−−−→ (ν �cr) (ν �ck+1) R +where R = R˜v\n | ck+1!⟨ �BV2⟩ | cn?(b).(b �n) | Bk+1 +˜xy +� +P2σ1 +� +and V1σ ⊠ V2 for some σ. We +should show that +P2{ ˜WV1/˜xy} S (ν �cr) (ν �ck+1) R +(138) +We may notice that we have �v = rn(P1) = rn(P2) and as tr(n) we have n ∈ �v. Thus, we +have the following structural equivalence +R ≡ R˜v | ck+1!⟨ �BV2⟩ | Bk+1 +˜xy +� +P2σ1 +� +Further, we have V1σ ⊠ V2, � +Wσ1 ⊠ �B. Thus by the definition of C− +− +� +− +� +(Table 3) the +goal (138) follows. This concludes sub-case tr(n) of case ⟨Rv⟩. +Now, we briefly consider the case when P1 is a trigger collection. Let σ1 be defined as above. +Let H′ +1 be such that P1{ ˜W/˜x}σ1 ⋄ H′ +1. Then, by definition of S , we know Q1 has the following +shape: +Q1 = R˜v ∥ H1 +83 + +where �v = rn(P1{ ˜W/˜x}). Further, by Definition 4.15 we know H′ +1 = ni?(y).H′ +2 such that +P2{ ˜W/˜x}σ2 ⋄ H′ +2, where σ2 = σ1 · next(ni). Now, let V2 be such that V1σ ⊠ V2, for some σ. We +could see that +H′ +1 +ni?(V2) +−−−−→ H′ +2{V2/y} +We should show that +P2{ ˜W/˜x}{V1/y} S R˜v ∥ H2{V2/y} +(139) +By P2{ ˜W/˜x}σ2 ⋄ H′ +2 and noticing that ⋄ is closed under the substitution of ⊠-related values +we have +P2{ ˜W/˜x}{V1/y}σ2 ⋄ H′ +2{V2/y} +Thus, goal (139) follows. This concludes case ⟨Rv⟩. +3. Case ⟨App⟩. Here we know P1 = V1 (�r, u) where �r = (r1, . . . , rn). We distinguish two sub-cases: +(i) V1 = x where {Vx/x} ∈ { ˜W/˜x} and (ii) V1 is an abstraction. Let V1{ ˜W/˜x} = λ(�y, z). P2 +where �y = �y1, . . . , �yn. The inference tree is as follows +⟨App⟩ +(V1 (�r, u)){ ˜W/˜x} τ−→ P2{˜r, u/˜y, z} +Let σ1 = index(fn(P1ρ1)) such that {ui/u} ∈ σ1. Further, let �v = rn(V1), �cvr = � +r∈˜v,˜r cr, +�ck = (ck, . . . , ck+�P1�−1), and �ck+1 = (ck+1, . . . , ck+�P1�−1). Also, let �m = (ui, . . . , ui+|G(C)|−1) +with ui : C and �ri = (ri +1, . . . , ri +|R⋆(Si)|)) with ri : Si for i = {1, . . . , n}. Then, by the definition +of S we have Q1 ∈ N where N is defined as follows: +N = N1 ∪ N4 ∪ +� +∪1≤l≤n Nl +2 +� +∪ +� +∪1≤l≤n−1 Nl +3 +� +where +N1 = {(ν �ck) (ν �cvr) R˜v,˜r | ck!⟨ �B⟩ | Bk +˜x +� +P1σ1 +� +: � +Wσ1 ⊠ �B} +Nl +2 = {(ν �ck+1) (ν �cvr) R˜v,rl,...,rn | +|˜r|−l+1 +crl! +� +λ�zl.crl+1!⟨λ�zl+1. · · · .crn!⟨λ�zn. QV2 +l ⟩ ⟩ +� +: V1{ ˜W/˜x}σ1 ⊠ V2} +Nl +3 = {(ν �ck+1) (ν �cvr) R˜v,rl+1,...,rn | λ�zl. +|˜r|−l +crl+1!⟨λ�zl+1. · · · .crn!⟨λ�zn. QV2 +l ⟩ +� +�rl +: V1{ ˜W/˜x}σ1 ⊠ V2} +N4 = {(ν �ck+1) (ν �cvr) R˜v | V2 (�r1, . . . , �rn, �m) : V1{ ˜W/˜x}σ1 ⊠ V2} +where +QV2 +l += V2 (�r1, . . . , �rl−1, �zl, . . . , �zn, �m) +Note that for any +Q1 ∈ N1 ∪ N4 ∪ +� +∪1≤l≤n Nl +2 +� +∪ +� +∪1≤l≤n−1 Nl +3 +� +there exist Q′ +1 ∈ N5 such that Q1 reduces to Q′ +1 through communication on non-essential +prefixes. By Lemma 4.3 it then suffices to consider the case Q′ +1 ∈ N5. +Let V2 = λ�y1, . . . , �yn, �z. Q2 where �z = (z1, . . . , z|G(C)|). Then, we have the following transition: +Q′ +1 +τ−→ (ν �ck+1) (ν �cr) R +84 + +where R = R˜v | Q2{˜r1, . . . , ˜rn, ˜m/˜y1, . . . , ˜yn, ˜z}. We should show that +P2{˜r, u/˜y, z} S (ν �ck+1) (ν �cvr) R +(140) +By V1ρ1σ1 ⊠ V2 (with ρ1 = { ˜W/˜x}) and Definition 4.13 either V2 ∈ C +� +V1ρ1σ1 +� +or V1ρ1 ▷◁ V2. +In the former case, we know V2 ∈ �Cρ′ +1 +σ′ +1 +� +V ′ +1 +� +where ρ′ +1 = { ˜W ′/˜x′} is such that V ′ +1ρ′ +1σ′ +1 = V1ρ1σ1. +Let �B′ be such that � +W ′σ′ +1 ⊠ �B′. By Table 3 we have +V2 = V˜x′ +� +λ(�y, z). P ′ +2 +� +{ ˜B′/˜x′} = λ( �y1, . . . , � +yn, �z). Q2{ ˜B′/˜x′} +where +Q2 = (ν �cy) +� +i∈|�y| +(cyi?(b).(b �yi)) | ck+1!⟨ �B′⟩ | Bk+1 +˜x′ +� +P ′ +2{z1/z} +� +with �cy = � +i∈|˜y| cyi and P ′ +2 is such that +P ′ +2{ ˜W ′/˜x′} = P2 +Thus, we know +R ≡ R˜v | (ν �cy) +� +i∈|�y| +(cyi?(b).(b �ri)) | ck+1!⟨ �B′⟩ | Bk+1 +˜x′ +� +P ′ +2{z1/z} +� +Now, we know (ν �cvr) R ≡ (ν �cv) R where �cv = � +r∈˜v cr since �cvr \ �cv ̸⊆ fn(R). Further, by +renaming bound names we have +R ≡ R˜v | (ν �cr) +� +r∈�r +(cr?(b).(b �r)) | ck+1!⟨ �B′⟩ | Bk+1 +˜x′ +� +P ′ +2{z1/z} +� +{˜cr/˜cy} +where �cr = � +r∈˜r cr. Now, by the definition of R˜v (Definition 4.16) we know +R˜v,˜r = R˜v | +� +r∈�r +(cn?(x).x �r) +Thus, we have +R ≡ (ν �cr) R˜v,˜r | ck+1!⟨ �B′⟩ | Bk+1 +˜x′ +� +P ′ +2{z1/z} +� +{˜cr/˜cy} = (ν �cr) R′ +and by the definition we have R′ ∈ C ˜ +W ′ +˜x′ +� +P ′ +2 +� +. We may notice that �v, �r = rn(P ′ +2) and (ν cvr) R ≡ +(ν cv) (ν cr) R′. +The later case, when V1ρ1 ▷◁ V2, follows by the fact that bodies of characteristic and triggers +values are ⋄-related to their minimal counterparts as shown in Lemma 4.2 and that relation ⋄ +is closed under names substitutions. +So, the goal (140) follows. This concludes case ⟨App⟩ (and base cases). Next, we consider +inductive cases. +4. Case ⟨ParL⟩. +In this case we distinguish two sub-cases: (i) P1ρ = P ′ +1ρ′ +1 | P ′′ +1 ρ′′ +1 and (ii) +P1ρ = P ′ +1ρ′ +1 ∥ P ′′ +1 ρ′′ +1 where P ′ +1 is a triggers collection. The final rule in the inference tree is: +P ′ +1ρ′ +1 +ℓ−→ P ′ +2ρ′ +2 +bn(ℓ) ∩ fn(P ′′ +1 ) = ∅ +⟨ParL⟩ +P ′ +1ρ′ +1 | P ′′ +1 ρ′′ +1 +ℓ−→ P ′ +2ρ′ +2 | P ′′ +1 ρ′′ +1 +85 + +Let σ1 ∈ index(�u) where �u = fn(P1{ ˜W/˜x}). Further, we know ρ′ +1 = { ˜W1/˜y} and ρ′′ +1 = { ˜W2/˜z}. +Further, let σ′ +1 and σ′′ +1 such that +P1ρ1σ1 = P ′ +1ρ′ +1σ′ +1 | P ′′ +1 ρ′′ +1σ′′ +1 +In sub-case (i), by the definition of S (Table 3) we have Q1 ∈ N1 ∪ N2 ∪ N3 where +N1 ={(ν �ck) (ν �cr) (ck!⟨ �B⟩ | Bk +˜x +� +P ′ +1σ′ +1 | P ′′ +1 σ′′ +1 +� +) : � +Wσ1 ⊠ �B} +N2 ={(ν �ck+1) (ν �cr) (ck+1!⟨ �B1⟩.ck+2!⟨ �B2⟩ | Bk+1 +˜y +� +P ′ +1σ′ +1 +� +| Bk+2 +˜z +� +P ′′ +1 σ′′ +1 +� +) +: � +Wiσ1 ⊠ �Bi, i ∈ {1, 2}} +N3 ={(ν �c) (ν �cr) R′ +1 | R′′ +1 : R′ +1 ∈ C +˜ +W1 +˜y +� +P ′ +1σ′ +1 +� +, R′′ +1 ∈ C +˜ +W2 +˜z +� +P ′′ +1 σ′′ +1 +� +} +where �ck = (ck, . . . , ck+�P1�−1), �ck+1 = (ck+1, . . . , ck+�P1�−1), and �c = fpn(R′ +1 | R′′ +1). Note that +for Q1 ∈ N1 ∪ N2 there exists some Q′ +1 and Q′′ +1 such that Q1 reduces to Q′ +1 | Q′′ +1 ∈ N3 through +communication on non-essential prefixes, with +Q′ +1 ∈ �Cρ′ +1 +σ′ +1 +� +P ′ +1 +� +(141) +Q′′ +1 ∈ �Cρ′′ +1 +σ′′ +1 +� +P ′′ +1 +� +(142) +Then, by Lemma 4.3 it suffices to consider the case of Q′ +1 | Q′′ +1 ∈ N3. By the definition of S +we have +P ′ +1ρ′ +1 S Q′ +1 +(143) +P ′′ +1 ρ′′ +1 S Q′′ +1 +(144) +To apply IH we do the case analysis on the action ℓ: +• Sub-case ℓ ̸≡ (ν �m1) n!⟨V1⟩. By (143) and IH we know there is Q′ +2 such that Q′ +1 +ℓ=⇒ Q′ +2 +and +P ′ +2ρ′ +2 S Q′ +2 +(145) +We should show that +P ′ +2ρ′ +2 | P ′′ +1 ρ′′ +1 S Q′ +2 | Q′′ +1 +(146) +We know that there is R′ such that +Q′ +1 +τ=⇒ R′ +˘ℓ−→ Q′ +2 +(147) +Thus, by Rule ⟨ParL⟩ we can infer the following: +Q′ +1 | Q′′ +1 +τ=⇒ R′ | Q′′ +1 +Further, we can infer +R′ +˘ℓ−→ Q′ +2 +⟨ParL⟩ +R′ | Q′′ +1 +˘ℓ−→ Q′ +2 | Q′′ +1 +Then, by the IH (145) and the definition of S (Definition 4.17) we know +Q′ +2 ∈ �Cρ′ +2 +σ′ +1·σ′ +2 +� +P ′ +2 +� +86 + +So, we may notice that +Cρ′′ +1 +σ′′ +1 ·σ′ +2 +� +P ′′ +1 +� += Cρ′′ +1 +σ′′ +1 +� +P ′′ +1 +� +So, by (142) and definition of C− +− +� +− +� +we have +Q′ +2 | Q′′ +1 ∈ �Cρ′ +2·ρ′′ +1 +σ′ +2·σ′′ +1 +� +P ′ +2 | P ′′ +1 +� +By IH and assertion, we know that if ℓ = n?⟨V1⟩ then next(ni) ∈ σ′ +2. So, assertion +next(ni) ∈ σ′ +2 · σ′′ +1 holds in this case. Now, by (143) we have σ′′ +1 ∈ index(fn(P ′′ +1 ρ′′ +1)) and +by (145) we have σ′ +2 ∈ index(fn(P ′ +2ρ′ +2)). We may notice that if ℓ = n?⟨V1⟩, by transition +rule ⟨SRv⟩ we have ¯n ̸∈ fn(P ′ +2ρ′ +2 | P ′′ +1 ρ′′ +1) so by 4.10 we have {nj/n} ̸∈ σ′′ +1 for any j > 0. +So, we have +σ′ +2 · σ′′ +1 ∈ index(fn(P ′ +2ρ′ +2 | P ′′ +1 ρ′′ +1)) +Thus, the goal (146) follows. This concludes this sub-case. +• Sub-case ℓ ≡ (ν �m1) n!⟨V1⟩. This sub-case follows the essential steps of the previous +sub-case. By (143) and IH we know there is Q′ +2 such that Q′ +1 +(ν ˜m2) ni!⟨V2⟩ +=========⇒ Q′ +2 and +(ν �m1) (P ′ +2 ∥ t ←�H V1)ρ′ +1 S (ν �m2) (Q′ +2 ∥ t ←�H V2) +(148) +We should show that +(ν �m1) (P ′ +2 | P ′′ +1 ∥ t ←�H V1)ρ1 S (ν �m2) (Q′ +2 | Q′′ +1 ∥ t ←�H V2) +(149) +We pick R′ as in the previous sub-case. So, we can infer the following transition: +R′ (ν ˜m2) ni!⟨V2⟩ +−−−−−−−−→ Q′ +2 +⟨ParL⟩ +R′ | Q′′ +1 +(ν ˜m2) ni!⟨V2⟩ +−−−−−−−−→ Q′ +2 | Q′′ +1 +Next, by Table 3 we can infer the following. First, by (148) we know +Q′ +2 ∥ t ←�H V2 ∈ �Cρ′ +1 +σ′ +2 +� +P ′ +2 ∥ t ←�H V1 +� +By IH and assertion, we know next(ni) ∈ σ′ +2. So, assertion next(ni) ∈ σ′ +2 · σ′′ +1 holds. +Similarly to the previous sub-case, we have +�Cρ′′ +1 +σ′′ +1 ·σ′ +2 +� +P ′′ +1 +� += Cρ′′ +1 +σ′′ +1 +� +P ′′ +1 +� +Thus, we have +(ν �m2) (Q′ +2 | Q′′ +1 ∥ t ←�H V2) ∈ �Cρ1 +σ′′ +1 ·σ′ +2 +� +(ν �m1) (P ′ +2 | P ′′ +1 ∥ t ←�H V1) +� +Now, by (143) we have σ′′ +1 ∈ index(fn(P ′′ +1 ρ′′ +1)) and by (148) we have σ′ +2 ∈ index(P ′ +2ρ′ +2). +We may notice that if ℓ = n!⟨V1⟩, by transition rule SSnd we have ¯n ̸∈ fn(P ′ +2ρ′ +2 | P ′′ +1 ρ′′ +1) +so by Definition 4.10 we have {nj/n} ̸∈ σ′′ +1 for any j > 0. So, we have +σ′ +2 · σ′′ +1 ∈ index(fn(P ′ +2ρ′ +2 | P ′′ +1 ρ′′ +1)) +Thus, (149) follows. +This concludes case ⟨ParL⟩. +87 + +5. Case ⟨Tau⟩. We distinguish two sub-cases: (i) P1ρ1 = P ′ +1ρ′ +1 | P ′′ +1 ρ′′ +1 and (ii) P1ρ1 = P ′ +1ρ′ +1 ∥ P ′′ +1 ρ′′ +1 +where one of parallel components is a trigger collection. Without loss of generality, we assume +ℓ1 = (ν �m1) n!⟨V1⟩ and ℓ2 = n?(V1). The final rule in the inference tree is then as follows: +P ′ +1ρ′ +1 +ℓ1 +−→ P ′ +2ρ′ +2 +P ′′ +1 ρ′′ +1 +ℓ2 +−→ P ′′ +2 ρ′′ +2 +ℓ1 ≍ ℓ2 +⟨Tau⟩ +P ′ +1ρ′ +1 | P ′′ +1 ρ′′ +1 +τ−→ (ν �m1) (P ′ +2ρ′ +2 | P ′′ +2 ρ′′ +2) +Let σ1 = index(�u) where �u = fn(P1{ ˜W/˜x}). Further, let σ′ +1 and σ′′ +1 such that +P1ρ1σ1 = P ′ +1ρ′ +1σ′ +1 | P ′′ +1 ρ′′ +1σ′′ +1 +We know ρ′ +1 = { ˜W1/˜y} and ρ′′ +1 = { ˜W2/ ˜w}. By the definition of S (Table 3) we have Q1 ∈ +N1 ∪ N2 ∪ N3 where +N1 = {(ν �ck) (ck!⟨ �B⟩ | Bk +˜x +� +P ′ +1σ′ +1 | P ′′ +1 σ′′ +1 +� +) : � +Wσ1 ⊠ �B} +N2 = {(ν �ck+1) (ck+1!⟨ �B1⟩.ck+l+1!⟨ �B2⟩ | Bk+1 +˜y +� +P ′ +1σ′ +1 +� +| Bk+l+1 +˜w +� +P ′′ +1 σ′′ +1 +� +) +: � +Wiσ1 ⊠ �Bi, i ∈ {1, 2}} +N3 = {R′ +1 | R′′ +1 : R′ +1 ∈ C +˜ +W1 +˜y +� +P ′ +1σ′ +1 +� +, R′′ +1 ∈ C +˜ +W2 +˜w +� +P ′′ +1 σ′′ +1 +� +} +By Lemma 4.3, for Q1 +1 ∈ N1 there exists Q2 +1 ∈ N2 such that +Q1 +1 +τ=⇒ Q2 +1 +τ=⇒ Q′ +1 | Q′′ +1 +where Q′ +1 | Q′′ +1 ∈ N3, that is +Q′ +1 ∈ �Cρ′ +1 +σ′ +1 +� +P ′ +1 +� +(150) +Q′′ +1 ∈ �Cρ′′ +1 +σ′′ +1 +� +P ′′ +1 +� +(151) +Thus, in both cases we only consider how Q′ +1 | Q′′ +1 evolves. By the definition of S we have +P ′ +1ρ′ +1 S Q′ +1 +(152) +P ′′ +1 ρ′′ +1 S Q′′ +1 +(153) +We have the following IH: +(a) By (152) and IH there is Q′ +2 such that Q′ +1 +(ν �m1) ni!⟨V2⟩ +=========⇒ Q′ +2 and +(ν �m1) (P ′ +2 ∥ t ←�H V1)ρ′ +1 S (ν �m2) (Q′ +2 ∥ t1 ←�H V2) +(154) +By Definition 4.17 we know there is σv · σ′ +2 ∈ index(fn((P ′ +2 ∥ t ←�H V1)ρ′ +1)) such that +σv ∈ index(fn(t ←�H V1ρ′ +1)) and σ′ +2 ∈ index(fn(P ′ +2ρ′ +2)) and +Q′ +2 ∥ t1 ←�H V2 ∈ �Cρ′ +1 +σv·σ′ +2 +� +P ′ +2 ∥ t1 ←�H V1 +� +So, we can infer +Q′ +2 ∈ �Cρ′ +2 +σ′ +2 +� +P ′ +2 +� +(155) +88 + +(b) By (153) and IH there is Q′′ +2 such that Q′′ +1 +nj?(V2) +=====⇒ Q′′ +2 and +P ′′ +2 ρ′′ +2 S Q′′ +2 +(156) +By 4.17 and (156) we know there is σ′′ +2 ∈ index(fn(P ′′ +2 ρ′′ +2)) such that +Q′′ +2 ∈ Cρ′′ +2 +σ′′ +2 +� +P ′′ +2 +� +(157) +Similarly to the ParL case, we know there is R′ such that +Q′ +1 +τ=⇒ R′ (ν �m2) ni!⟨V2⟩ +−−−−−−−−→ Q′ +2 +where ˘ℓ1 = (ν �m2) ni!⟨V2⟩. Further, there is R′′ such that +Q′′ +1 +τ=⇒ R′′ nj?(V2) +−−−−−→ Q′′ +2 +where ˘ℓ2 = nj?(V2). By Rule ParL and Rule ParR we can infer the following: +Q′ +1 | Q′′ +1 +τ=⇒ R′ | R′′ +Now, to proceed we must show ˘ℓ1 ≍ ˘ℓ2, which boils down to showing that indices of ni and +nj match. For this, we distinguish two sub-cases: (i) ¬tr(ni) and ¬tr(nj) and (ii) tr(ni) and +tr(nj). In the former sub-case, we have {ni/n} ∈ σ1 and {nj/n} ∈ σ1, where σ1 = index(�u). +Further, by this and and Definition 4.10 we know that i = j. Now, we consider the later +case. By assumption that P1{ ˜W/˜x} is well-typed, we know there Γ1, Λ1, and ∆1 such that +Γ1; Λ1; ∆1 ⊢ P1{ ˜W/˜x} ▷ ⋄ with balanced(∆1), Thus, we have n : S ∈ ∆1 and n : T ∈ ∆1 such +that S dual T. Hence, by the definition of [−⟩ (Definition 3.5) we have i = [S⟩ = [T⟩ = j. +Hence, we can infer the following transition: +R′ (ν �m2) ni!⟨V2⟩ +−−−−−−−−→ Q′ +2 +R′′ ni?(V2) +−−−−→ Q′′ +2 +˘ℓ1 ≍ ˘ℓ2 +⟨Tau⟩ +(R′ | R′′) τ−→ (ν �m2) (Q′ +2 | Q′′ +2) +Now, we should show that +(ν �m1) (P ′ +2ρ′ +2 | P ′′ +2 ρ′′ +2) S (ν �m2) (Q′ +2 | Q′′ +2) +(158) +Further, we have (P ′ +2 | P ′′ +2 )ρ′ +2 · ρ′′ +2 = P ′ +2ρ′ +2 | P ′ +2ρ′′ +2. So, by (155) and (157) we have +(ν �m2) (Q′ +2 | Q′′ +2) ∈ �Cρ′ +2·ρ′′ +2 +σ′ +2·σ′′ +2 +� +(ν �m1) (P ′ +2ρ′ +2σ′ +2 | P ′′ +2 ρ′′ +2σ′′ +2) +� +Finally, we need to show σ′ +2 · σ′′ +2 ∈ index(�u), where �u = fn(P ′ +2ρ′ +2 | P ′′ +2 ρ′′ +2). By IH we have +σ′ +2 ∈ index(fn(P ′ +2ρ′ +2)) and σ′′ +2 ∈ index(fn(P ′′ +2 ρ′′ +2)). +Further, as P is well-typed, we have +n ∈ fn(P ′ +2ρ′ +2), n ̸∈ fn(P ′ +2ρ′ +2), n ∈ fn(fn(P ′′ +2 ρ′′ +2)), and n ̸∈ fn(P ′′ +2 ρ′′ +2). Thus, by Definition 4.10 +in sub-case ¬tr(n) we only need to show that for some k > 0 we have {nk/n} ∈ σ′ +2 and +{nk/n} ∈ σ′′ +2. +This follows by the assertion as we know next(ni) = {ni+1/ni} ∈ σ′ +2 and +next(ni) = {ni+1/ni} ∈ σ′′ +2. The sub-case tr(n) follows directly by the Definition 4.10 as we +have {n1/n} ∈ σ′ +2 and {n1/n} ∈ σ′′ +2. So, we have σ′ +2 ·σ′′ +2 ∈ index(�u). Thus, the goal (158) follows. +This concludes case ⟨Tau⟩. +89 + +6. Case ⟨New⟩. In this case we know P1 = (ν m : C) P ′ +1. The final rule in the transition inference +tree is as follows: +P ′ +1ρ1 +(ν �n1) u!⟨V1⟩ +−−−−−−−→ P2ρ2 +m ∈ fn(V1) +⟨New⟩ +(ν m) P ′ +1ρ1 +(ν m·�n1) u!⟨V1⟩ +−−−−−−−−−→ P2ρ1 +(159) +Let σ1 = index(fn(P1ρ1)). By the definition of S (Table 3) we have Q1 ∈ N1 where +N1 ={(ν �cr) (ν �c) (ν �m2) (ν ˜cm) R : R ∈ C +˜ +Wσ1 +˜x +� +P ′ +1σ1 · {m1m1/mm} +� +} +where �cr = cr(R), �m2 = (m1, . . . , m|G(C)|), and ˜cm = cm · cm if tr(C), otherwise ˜cm = ϵ. By +IH, if P ′ +1ρ1 S Q′ +1 there are Q2 and V2 such that +Q′ +1 +(ν �n2) ui!⟨V2⟩ +========⇒ Q2 +and +(ν �n1) (P2 ∥ t ←�H V1)ρ1 S (ν �n2) (Q2 ∥ t ←�H V2) +(160) +For Q1 ∈ N1 we should show that +Q1 +(ν �m2·�n2) ui!⟨V2⟩ +===========⇒ Q2 +(161) +such that +(ν m · �n1) (P2 ∥ t ←�H V1)ρ1 S (ν �c′ +r · �m2 · �n2) (Q2 ∥ t ←�H V2) +(162) +where �c′ +r = cr(V2). Note that by the definition we have fpn(V2) = ∅. By Lemma 4.3, we know +there is R such that P ′ +1ρ1 S R and +Q′ +1 +τ=⇒ R +(ν ˜n2) ui!⟨V2⟩ +−−−−−−−−→ Q2 +(163) +Now, by rule ⟨New⟩ we have +Q1 +τ=⇒ (ν �c′ +r) (ν �m2) R +Now, we need to apply Rule ⟨New⟩ | �m2| times to (163) to infer the following: +R′ (ν �n2) ui!⟨V2⟩ +−−−−−−−−→ Q2 +�m2 ⊆ fn(V2) +⟨New⟩ +(ν �m2) R +(ν �m2·�n2) ui!⟨V2⟩ +−−−−−−−−−−→ Q2 +Therefore, the sub-goal (161) follows. Now, by (160) and by Definition 4.17 we can infer the +following: +(ν �n2) (Q2 ∥ t ←�H V2) ≡ (ν �c′ +r) (ν �n) (R˜v | R2 | R ˜w ∥ t ←�H V2) +where �v = rn(R2), �w = rn(V2), �c′ +r = cr(V2), and +(ν �n) (R˜v | R2 | R ˜w ∥ t ←�H V2) ∈ �Cρ1 +σ1 +� +(ν �n1) (P2 ∥ t ←�H V1) +� +By this and the definition of C− +− +� +− +� +(Table 3) we have +(ν �m) (ν ˜cm) (ν �n) (R˜v | R2 | R ˜w ∥ t ←�H V2) ∈ �Cρ1 +σ1 +� +(ν m) (ν �n1) (P2 ∥ t ←�H V1) +� +Further, we may notice +(ν �m2 · �n2) (Q2 ∥ t ←�H V2) ≡ (ν �cr) (ν �m2) (ν �n) (R˜v | R2 | R ˜w ∥ t ←�H V2) +Therefore, the sub-goal (162) follows. This concludes case ⟨New⟩ and the proof. +90 + +C.3 +Proof of Lemma 4.7 +Lemma 4.7. Assume P1{ ˜W/˜x} is a process and P1{ ˜W/˜x} S Q1. +1. Whenever Q1 +(ν � +m2) ni!⟨V2⟩ +−−−−−−−−→Q2 , such that ni ̸∈ fn(Q1), then there exist P2 and V2 such that +P1{ ˜W/˜x} +(ν � +m2) n!⟨V2⟩ +−−−−−−−−→P2 and, for a fresh t, +(ν � +m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν � +m2)(Q2 ∥ t1 ←�H V2). +2. Whenever Q1 +ni?(V2) +−−−−→Q2 , such that ni ̸∈ fn(Q1), there exist P2, V2, and σ such that P1{ ˜W/˜x} +n?(V1) +−−−−→P2 +where V1σ ⊠ V2 and P2 S Q2. +3. Whenever Q1 +τ−→ Q2 either (i) P1{ ˜W/˜x} S Q2 or (ii) there exists P2 such that P1 +τ−→P2 and +P2 S Q2. +Proof (Sketch). By transition induction. First, we analyze the case of non-essential prefixes, which +induce τ-actions that do not correspond to actions in P1. This concerns the sub-case (i) of Part 3. +This directly follows by Lemma 4.3, that is by the fact that C ˜ +W +˜x +� +P1 +� +is closed under transitions on +non-essential prefixes. +Now, assume Q1 +ℓ−→ Q2 when ℓ is an essential prefix. This is mainly the converse of the proof of +Lemma 4.4 noting that there are no essential actions in C ˜ +W +˜x +� +P1 +� +not matched in P1. We consider +only one case: +• Case ⟨Snd⟩. In this case we know P1 = n!⟨V1⟩.P2. We distinguish two sub-cases: (i) ¬tr(ui) +and (ii) tr(ui). In both sub-cases, we distinguish two kinds of an object value V1: (a) V1 ≡ x, +such that {Vx/x} ∈ { ˜W/˜x} and (b) V1 = λy : C. P ′, that is V1 is a pure abstraction. We only +consider sub-case (a). +Let � +W1, � +W2, �y, and �w such that +P1{ ˜W/˜x} = n!⟨V1{ ˜W1/˜y}⟩.P2{ ˜W2/ ˜w} +Let σ1 ∈ index(�u) where �u = fn(P1{ ˜W/˜x}) such that {ni/n} ∈ σ1. Also, let σ2 = σ1 · next(ni). +When P1 is not a trigger, by the definition of S (Table 3), for both sub-cases, we have Q1 ∈ N1 +where: +N1 = +� +(ν �cr) (ν �ck+1) R˜v | ni!⟨V2⟩.ck+1!⟨ �B2⟩ | Bk+1 +˜w +� +P2σ2 +� +: V1σ{� +W1/�y} ⊠ V2, � +W2 ⊠ �B2 +� +For Q1 ∈ N1 we have the following transition inference tree: +⟨Snd⟩ +Q1 +ni!⟨V1⟩ +−−−−→ Q2 +where +Q2 = (ν �cr) (ν �ck+1) ck+1!⟨ �B2⟩ | Bk +˜w +� +P2σ2 +� +We have +⟨Snd⟩ +P1{ ˜W/˜x} +n!⟨V1{ ˜W1/˜y}⟩ +−−−−−−−−−→ P2{ ˜W2/ ˜w} +We should show that +(ν � +m1)(P2 ∥ t ←�H V1) S (ν � +m2)(Q2 ∥ t1 ←�H V2) +This immediately follows by the definition of S and Table 3. This concludes Snd case. +As can be seen the proof of this part is essentially the inverse of the proof of Lemma 4.4. We just +need to show that C ˜ +Wσ +˜x +� +P1σ +� +does not introduce extra actions on essential prefixes not present in +P1. This is evident by the inspection of the definition of C− +− +� +− +� +. Briefly, only in the case of the +input and the output prefix J − +− +� +− +� +introduce actions that mimic those prefixes. Remaining cases +only introduce actions on non-essential prefixes (τ-actions on propagator names). +91 + diff --git a/8dE4T4oBgHgl3EQf2w3D/content/tmp_files/load_file.txt b/8dE4T4oBgHgl3EQf2w3D/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..06c8cee32b56ee2146cd84eb868919fc1d4163ec --- /dev/null +++ b/8dE4T4oBgHgl3EQf2w3D/content/tmp_files/load_file.txt @@ -0,0 +1,8139 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf,len=8138 +page_content='A Minimal Formulation of Session Types Alen Arslanagić1, Jorge A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Pérez1, and Dan Frumin1 1University of Groningen, The Netherlands January 16, 2023 Abstract Session types are a type-based approach to the verification of message-passing programs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' They specify communication structures essential for program correctness;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' a session type says what and when should be exchanged through a channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Central to session-typed languages are sequencing constructs in types and processes that explicitly specify the order of actions in a protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In this paper we study session types without sequencing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The resulting framework of minimal session types is arguably the simplest form of session types one could conceive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the context of a core process calculus with sessions and higher-order concurrency (abstraction-passing), we establish two main technical results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, we prove that every process P typable with standard session types can be compiled down into a process D(P) typable with minimal session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Second, we prove that P and D(P) are behaviorally equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' These results indicate that having sequencing constructs in processes and session types is convenient but redundant: only sequentiality in processes is truly indispensable, as it can correctly codify sequentiality in types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Our developments draw inspiration from work by Parrow on behavior-preserving decompo- sitions of untyped processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By casting Parrow’s results in the realm of typed processes, our developments reveal a conceptually simple formulation of session types and a principled avenue to the integration of session types into programming languages without sequencing in types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 1 Introduction Session types are a type-based approach to the verification of message-passing programs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A session type specifies what and when should be exchanged through a channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This makes session types a useful tool to enforce safety and liveness properties related to communication correctness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Originated in the realm of concurrency theory, session types have had a significant impact on the foundations of programming languages [14], but also on their practice [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Our goal in this work is to understand to what extent session types can admit simpler, more fundamental formulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This foundational question has concrete practical ramifications, as we discuss next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In session-typed languages, sequencing constructs in types and processes specify the intended structure of message-passing protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For example, in the session type S =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, sequencing (denoted ‘;’' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=') allows us to specify a protocol for a channel that first receives (?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=') two integers, then sends (!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=') a boolean, and finally ends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As such, S could type a service that checks for integer equality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Sequencing in types goes hand-in-hand with sequencing in processes, which is specified using prefix constructs (denoted ‘.’).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The π-calculus process P = s?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x1 = x2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 is an implementation of the equality service: it first expects two values on name s, then outputs a boolean on s, and finally stops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, name s in P conforms to the session type S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Session types can also specify sequencing within labeled choices and recursion;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' these typed constructs are also in close match with their respective process expressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Session types have been originally developed as a typing discipline for π-calculus for the analysis of message-passing protocols between exactly two parties [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Since then session types have been extended in many directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We find, for instance, multiparty session types [13], and extensions 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='05301v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='PL] 12 Jan 2023 P = s?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x1 = x2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 s : ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' end D(P) c2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x1⟩ ∥ c3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y1, x2⟩ ∥ c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x1, x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x1 = x2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ s1 : ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' end c2 : ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ();' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' end s2 : ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' end c3 : ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' end s3 : !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' end c4 : ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int, int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' end Figure 1: The process decomposition, illustrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Arrows in magenta indicate synchronizations orchestrated by the decomposition D(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' with dependent types, assertions, exceptions, and time (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [8, 14] for surveys).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' All these extensions seek to address natural research questions on the expressivity and applicability of session types theories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Here we address a different, if opposite, question: is there a minimal formulation of session types?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This is an appealing question from a theoretical perspective, but seems particularly relevant to the practice of session types: identifying the “core” of session types could enable their integration in languages whose type systems do not have certain advanced constructs present in session types, such as sequencing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For instance, the Go programming language offers primitive support for message- passing concurrency;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' it comes with a static verification mechanism which can only enforce that messages exchanged along channels correspond with their declared payload types—it cannot ensure essential correctness properties associated with the ordering of messages and the structure of the protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This observation has motivated the development of advanced static verification tools based on session types for Go programs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', [20, 19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This paper identifies and studies the properties of an elementary formulation of session types, which we call minimal session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Minimal session types are session types without sequencing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' That is, in session types such as ‘!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S’ and ‘?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S’, we stipulate that S can only correspond to end, the type of the terminated protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Adopting minimal session types entails dispensing with sequencing, which is arguably the most distinctive feature of session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' While this may appear as a far too drastic restriction, it turns out that it is not: we show that for every process P typable under standard (non minimal) session types, there is a decomposition of P, denoted D(P), a process that codifies the sequencing information given by the session types (protocols) of P using additional synchronizations, extracted from its protocols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Figure 1 illustrates the key idea of the decomposition using the process P and session type S motivated above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Because P contains three actions in sequence (as stipulated by S), its decomposition D(P) consists of three processes in parallel—each of them implementing one action of P—as well as of mechanisms for orchestrating these parallel processes: the synchronizations on names c2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c5 ensure that the sequencing in P is preserved and that received names are properly propagated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' These three parallel processes are typable with minimal session types (in the figure, they are given below each process), which are obtained by suitably “slicing” S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Our main finding is that D(P) satisfies two important properties: first, it is well-typed using minimal session types (static correctness);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' second, it is behaviorally equivalent to P (dynamic correctness).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' These properties ensure that having sequencing in both types and processes is convenient but redundant: only sequencing at the level of processes is truly indispensable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 2 The definition of D(P) is interesting on its own, as it draws inspiration from a known result by Parrow [21], who showed that any untyped π-calculus process can be decomposed as a collection of trio processes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', processes with at most three nested prefixes [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The question of how to relate session types with other type systems has attracted interest in the past.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Session types have been encoded into, for instance, generic types [9] and linear types [7, 5, 6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As such, these prior studies concern the relative expressiveness of session types, where the expressivity of session types stands with respect to that of some other type system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In sharp contrast, we study the absolute expressiveness of session types: how session types can be explained in terms of themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To our knowledge, this is the first study of its kind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Session types have been developed on top of different process languages (mainly, dialects of the π-calculus), and so choosing the target language for minimal session types is an important decision in our developments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In this paper, our target language is HO, the core process calculus for session-based concurrency studied by Kouzapas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [17, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' HO is a very small language, which only supports passing of abstractions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', functions from names to processes) and lacks name-passing and recursion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Nonetheless, HO is very expressive, because both features can be encoded in HO in a fully abstract way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Moreover, HO has a well-developed theory of behavioral equivalences [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The combination of minimal number of features and expressivity makes HO an excellent candidate for studying a minimal formulation of session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Indeed, as we will see, several aspects of our decomposition take advantage of the higher-order nature of HO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Being a higher-order language, HO is very different from the (untyped, first-order) π-calculus considered by Parrow [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Therefore, our technical results arise in a context very different from Parrow’s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Contributions & Outline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In summary, in this paper we present the following contributions: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We identify the class of minimal session types (MST) as a simple fragment of standard session types for HO without sequencing that retains its absolute expressiveness (Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We show how to decompose standard session types into minimal session types, and how to decompose processes typable with standard session types into processes typable with minimal session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This is a result of static correctness (Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We show that the decomposition of a process is behaviorally equivalent to the original process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This is a result of dynamic correctness, formalized in terms of MST bisimulations, a typed behavioral equivalence that we introduce here (Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We develop optimizations and extensions of our decomposition that bear witness to its robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The rest of the paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In Section 2 we recall the preliminaries on the session type system for HO, which is the core process calculus for session-based concurrency on which we base our developments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In Section 3 we present minimal session types, and the decomposition of well-typed HO processes into minimal session types processes, accompanied by explanations and examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In Section 4 we show the correctness of the decomposition, by establishing an MST bisimulation between an HO process and its decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In Section 5 we examine two optimizations of the decomposition that are enabled by the higher-order nature of our setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In Section 6 we discuss extensions of our approach to consider constructs for branching and selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, in Section 7 we elaborate further on related work and in Section 8 we present some closing remarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The appendix contains omitted definitions and proofs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Differences with the conference version.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' An earlier version of this paper was presented at ECOOP 2019 [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The current paper revises the conference version, includes further examples, and incorporates a major addition: Section 4 on dynamic correctness, including the notion of an MST bisimulation and the constructed bisimulation relation, is completely new to this presentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 3 Colors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Throughout the paper we use different colors (such as pink and green) to improve readability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' However, the usage of colors is not indispensable, and the paper can be followed in black-and-white.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 2 The Source Language We start by recalling the syntax, semantics, and type system for HO, the higher-order process calculus for session-based concurrency studied by Kouzapas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [17, 18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Our presentation of HO follows the aforementioned papers, which concern definitions and results for HOπ, the super-calculus of HO with name-passing, abstraction-passing, and recursion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' HO is arguably the simplest language for session types: it supports passing of abstractions (functions from names to processes) but does not support name-passing nor process recursion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Still, HO is very expressive: it can encode name-passing, recursion, and polyadic communication via type-preserving encodings that are fully-abstract with respect to contextual equivalence [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Syntax and Semantics Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 (HO processes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The syntax of names, variables, values, and HO processes is defined as follows: n, m ::= a, b | s, s u, w ::= n | x, y, z V, W ::= x, y, z | λx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P P, Q ::= u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P | u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P | V u | P | Q | (ν n) P | 0 We use a, b, c, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' to range over shared names, and s, s, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' to range over session names.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Shared names are used for unrestricted, non-deterministic interactions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' session names are used for linear, deterministic interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We write n, m to denote session or shared names, and assume that the sets of session and shared names are disjoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The dual of a name n is denoted n;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' we define s = s and a = a, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', duality is only relevant for session names.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Variables are denoted with x, y, z, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' An abstraction λx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P is a process P with parameter x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Values V, W, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' include variables and abstractions, but not names.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Process V u is the application which substitutes name u on abstraction V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Constructs for inaction 0, parallel composition P1 | P2, and name restriction (ν n) P are standard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' HO lacks name-passing and recursion, but they are expressible in the language (see Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To enhance readability, we often omit trailing 0’s, so we write, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩ instead of u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Also, we write u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P and u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P whenever the exchanged value is not relevant (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Restriction for shared names (ν a) P is as usual;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' session name restriction (ν s) P simultaneously binds session names s and s in P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Functions fv(P), fn(P), and fs(P) denote, respectively, the sets of free variables, names, and session names in P, and are defined as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' If fv(P) = ∅, we call P closed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We write P{u/y} (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', P{V/y}) for the capture-avoiding substitution of name u (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', value V ) for y in process P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We identify processes up to consistent renaming of bound names, writing ≡α for this congruence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We shall rely on Barendregt’s variable convention, under which free and bound names are different in every mathematical context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The operational semantics of HO is defined in terms of a reduction relation, denoted −→.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Reduction is closed under structural congruence, denoted ≡, which is defined as the smallest congruence on processes such that: P | 0 ≡ P P1 | P2 ≡ P2 | P1 P1 | (P2 | P3) ≡ (P1 | P2) | P3 (ν n) 0 ≡ 0 P | (ν n) Q ≡ (ν n) (P | Q) (n /∈ fn(P)) P ≡ Q if P ≡α Q We assume the expected extension of ≡ to values V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The reduction relation expresses the behavior 4 t!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⌜˜u⌝⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ≜ t!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='z?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x ˜u)⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P t?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (⌜˜x⌝).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q ≜ t?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � (ν z) (y z | z!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ˜x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q⟩) � ⌜�S⌝ ≜ (?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (��S�⊸⋄);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end)⊸⋄ ⌜⟨�S⟩⌝ ≜ (?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (⟨��S�⟩⊸⋄);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end)⊸⋄ ⌜ �C ⊸⋄⌝ ≜ � �C�⊸⋄ ⌜ �C →⋄⌝ ≜ � �C�→⋄ �!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S� ≜ !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⌜U⌝⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='�S� �?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S� ≜ ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (⌜U⌝);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='�S� �C1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , Cn� ≜ �C1�, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �Cn� Figure 2: Encoding name passing in HO of processes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' it is defined as follows: (λx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P) u −→ P{u/x} [App] n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P | n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q −→ P | Q{V/x} [Pass] P −→ P ′ ⇒ (ν n) P −→ (ν n) P ′ [Res] P −→ P ′ ⇒ P | Q −→ P ′ | Q [Par] P ≡ Q −→ Q′ ≡ P ′ ⇒ P −→ P ′ [Cong] Rule [App] defines name application (β-reduction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Rule [Pass] defines a shared or session interaction, depending on the nature of n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Other rules are standard π-calculus rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We write −→k for a k-step reduction, and −→∗ for the reflexive, transitive closure of −→.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We illustrate HO processes and their semantics by means of an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 (Encoding Name-Passing).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The HO calculus lacks the name-passing primitives of HOπ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hence, it cannot express reductions of the form n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P | n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q −→ P | Q{m/x} (1) Fortunately, name-passing can be encoded in HO in a fully-abstract way: as shown in [17], one can use abstraction passing to “pack” a name.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To this end, Figure 2 defines the required syntactic sugar, at the level of processes and types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, the reduction (1) can be mimicked as n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⌜m⌝⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P | n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (⌜x⌝).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q = n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x m) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P | n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s)(y s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q⟩) −→ P | (ν s)(λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x m) s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q⟩) −→ P | (ν s)(s?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x m) | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q⟩) −→ P | (λx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q) m −→ P | Q{m/x} ◁ Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 (Polyadic Communication).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' HO as presented above allows only for monadic commu- nication, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', the exchange of tuples of values with length 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We will find it convenient to use HO with polyadic communication, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', the exchange of tuples of values �V = (V1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , Vk), with length |�V | = k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We will use similar notation for tuples of names and variables, and we will use ϵ to denote the empty tuple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 5 In HO, polyadicity appears in session synchronizations and applications, but not in synchroniza- tions on shared names.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This entails having the following reduction rules: (λ�x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P) �u −→ P{�u/�x} s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P | s?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q −→ P | Q{�V/�x} where the simultaneous substitutions P{�u/�x} and P{�V/�x} are as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This polyadic HO can be readily encoded into (monadic) HO [18];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' for this reason, by a slight abuse of notation we will often write HO when we actually mean “polyadic HO”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We discuss two simple examples that illustrate how HO can implement mechanisms resembling servers and forms of partial instantiation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' these mechanisms shall come in handy later, when defining the process decomposition in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 (A Server of a Kind).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let Sa denote the process a?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x r), which receives an abstraction on the shared name a and then applies it to r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Consider the following process composition: P = (ν r) (ν a) � a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Sa | r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � V = λy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ′⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Sa{y/r}) W = λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (z!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W ′⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Sa{z/r}) where V ′ and W ′ are some unspecified shared values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In P, process Sa operates as a server that provides r upon an invocation on a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Dually, the outputs on a are requests to this server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' One possible reduction sequence for P is the following: P −→ (ν r) (ν a) � a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | V r | r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � −→ (ν r) (ν a) � a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | r!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ′⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Sa | r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � −→ (ν r) (ν a) � a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Sa | r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q{V ′/x1} � = P ′ In this reduction sequence, the value V in the first request is instantiated with the name r by consuming a copy of Sa available in P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' However, a copy of the server Sa is restored through the value V , after an communication on r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This way, in P ′ the exchange of W ′ on r can take place: P ′ −→∗ (ν r) (ν a) � Sa | Q{V ′/x1}{W ′/x2} � Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 (Partial Instantiation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let Sa and Sb be servers as defined in the previous example: Sa = a?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x r) Sb = b?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x v) Further, let R be a process in which requests to Sa and Sb are nested within abstractions: R = a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � λy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' b!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' V (y, z)⟩ � Notice how the polyadic application ‘V (y, z)’ is enclosed in the innermost abstraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now consider the following composition: P = (ν a, b) R | Sa | Sb The structure of R induces a form of partial instantiation for y, z, implemented by combining synchronizations and β-reductions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To see this, let us inspect one possible reduction chain for P: P −→ (ν b) (λy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' b!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' V (y, z)⟩ r) | Sb −→ (ν b) b!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' V (r, z)⟩ | Sb = P ′ The first request of R, aimed to obtain name r, is realized by the first reduction, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', the communica- tion with Sa on name a: the result is the application of the top-level abstraction to r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Subsequently, the application step substitutes y with r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hence, in P ′, names in the nested application are only partially instantiated: at this point, we have ‘V (r, z)’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Process P ′ can then execute the same steps to instantiate z with name v by interacting with Sb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' After two reductions, we obtain the fully instantiated application V (r, v): P ′ −→ λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' V (r, z) v −→ V (r, v) 6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 Session Types for HO We give essential definitions and properties for the session type system for HO, following [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 (Session Types for HO).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let us write ⋄ to denote the process type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The syntax of value types U, channel types C, and session types S for HO is defined as follows: U ::= C →⋄ | C ⊸⋄ C ::= S | ⟨U⟩ S ::= !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S | ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S | µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S | t | end As we have seen, HO only admits the exchange of abstractions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' accordingly, value types include C →⋄ and C ⊸⋄, which denote shared and linear higher-order types, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Channel types include session types and the shared types ⟨U⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Session types follow the standard binary session type syntax [12], in which sequencing specifies communication structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This way, the output type !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S describes a session in which first a value of type U is sent, and then the session proceeds as S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Dually, the input type ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S describes a session in which first a value of type U is received, and then the session proceeds as S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In examples, we often assume basic types (such as int, bool, str) are exchanged in communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Session types also include recursive types µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S, in which the variable t is assumed to occur guarded in S, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', types such as µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t are not allowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In most cases, recursive types will be tail-recursive, although instances of non-tail-recursive session types will also be relevant (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, type end is the type of the terminated protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Notation 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As mentioned in the introduction, we shall study session types in which the continu- ation S in !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S and ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S is always end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Given this, we may sometimes omit trailing end’s and write !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩ and ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U) rather than !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end and ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In theories of session types duality is a key notion: implementations derived from dual session types will respect their protocols at run-time, avoiding communication errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Intuitively, duality is obtained by exchanging !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' by ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (and vice versa), including the fixed point construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We write S dual T if session types S and T are dual according to this intuition;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' the formal definition is coinductive, and given in [18] (see also [10]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We consider shared, linear, and session environments, denoted Γ, Λ, and ∆, resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' : Γ ::= ∅ | Γ, x : C →⋄ | Γ, u : ⟨U⟩ Λ ::= ∅ | Λ, x:C ⊸⋄ ∆ ::= ∅ | ∆, u:S Γ maps variables and shared names to value types;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ maps variables to linear higher-order types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ maps session names to session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' While Γ admits weakening, contraction, and exchange principles, both Λ and ∆ are only subject to exchange.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The domains of Γ, Λ, and ∆ are assumed pairwise distinct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We write ∆1 · ∆2 to denote the disjoint union of ∆1 and ∆2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We write Γ\\x to denote the environment obtained from Γ by removing the assignment x : C →⋄, for some C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Notations ∆\\u and Γ\\�x are defined similarly and have the expected readings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' With a slight abuse of notation, given a tuple of variables �x, we sometimes write (Γ, ∆)(�x) to denote the tuple of types assigned to the variables in �x by the environments Γ and ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The typing judgements for values V and processes P are denoted Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ V ▷ U and Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P ▷ ⋄ Figure 3 shows the typing rules;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' we briefly describe them and refer the reader to [18] for a full account.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The shared type C →⋄ is derived using Rule (Prom) only if the value has a linear type with an empty linear environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Rule (EProm) allows us to freely use a shared type variable as linear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Abstraction values are typed with Rule (Abs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Application typing is governed by Rule (App): the type C of an application name u must match the type of the application variable x (C ⊸⋄ or 7 (Sess) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' {u : S} ⊢ u ▷ S (Sh) Γ, u : U;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ u ▷ U (LVar) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' {x : C ⊸⋄};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ x ▷ C ⊸⋄ (RVar) Γ, X : ∆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ X ▷ ⋄ (Abs) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ x ▷ C Γ\\x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1\\∆2 ⊢ λx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P ▷ C ⊸⋄ (App) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ V ▷ C ⇝⋄ ⇝ ∈ {⊸, →} Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ u ▷ C Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1, ∆2 ⊢ V u ▷ ⋄ (Prom) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ V ▷ C ⊸⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ V ▷ C →⋄ (EProm) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ, x : C ⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P ▷ ⋄ Γ, x : C →⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P ▷ ⋄ (End) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P ▷ T u ̸∈ dom(Γ, Λ, ∆) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, u : end ⊢ P ▷ ⋄ (Rec) Γ, X : ∆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ µX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ▷ ⋄ (Par) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆i ⊢ Pi ▷ ⋄ i = 1, 2 Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1, Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1, ∆2 ⊢ P1 | P2 ▷ ⋄ (Nil) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 ▷ ⋄ (Req) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ u ▷ ⟨U⟩ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ V ▷ U Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1, ∆2 ⊢ u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ▷ ⋄ (Acc) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ u ▷ ⟨U⟩ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ x ▷ U Γ\\x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1\\Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1\\∆2 ⊢ u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ▷ ⋄ (Send) u : S ∈ ∆1, ∆2 Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ V ▷ U Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1, Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ((∆1, ∆2) \\ u : S), u :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S ⊢ u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ▷ ⋄ (Rcv) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1, u : S ⊢ P ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ x ▷ U Γ\\x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1\\Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1\\∆2, u :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S ⊢ u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ▷ ⋄ (ResS) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, s : S1, s : S2 ⊢ P ▷ ⋄ S1 dual S2 Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ (ν s) P ▷ ⋄ (Res) Γ, a : ⟨S⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ (ν a) P ▷ ⋄ Figure 3: Typing Rules for HO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' C →⋄).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Rules (Req) and (Acc) type interaction along shared names;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' the type of the sent/received object V (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', U) should match the type of the subject s (⟨U⟩).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In Rule (Send), the type U of the value V should appear as a prefix in the session type !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S of u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Rule (Rcv) is its dual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To state type soundness, we require two auxiliary definitions on session environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, a session environment ∆ is balanced (written balanced(∆)) if whenever s : S1, s : S2 ∈ ∆ then S1 dual S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Second, we define the reduction relation −→ on session environments as: ∆, s :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S1, s :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S2 −→ ∆, s : S1, s : S2 ∆, s : ⊕{li : Si}i∈I, s : &{li : S′ i}i∈I −→ ∆, s : Sk, s : S′ k (k ∈ I) Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 (Type Soundness [18]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Suppose Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P ▷ ⋄ with balanced(∆).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then P −→ P ′ implies Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ ⊢ P ′ ▷ ⋄ and ∆ = ∆′ or ∆ −→ ∆′ with balanced(∆′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 8 Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 (Typed Polyadic Communication).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' When using processes with polyadic communication (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Remark 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1), we shall assume the extension of the type system defined in [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4 (Typing name-passing constructs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 we recalled how to encode name- passing constructs in HO;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' now we show that this translation is typed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Following the name-passing encoding from [17] we define a syntactic sugar for types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The following typing rules for name-passing are derivable: (SendN) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ �b ▷ �C Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1, Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1, ∆2, t :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⌜ �C⌝⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ⊢ t!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⌜�b⌝⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ▷ ⋄ (RcvN) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ �x ▷ �C Γ\\x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1\\Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1\\∆2, t :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (⌜ �C⌝);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ⊢ t?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (⌜�x⌝).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ▷ ⋄ Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='5 (Typing Recursive Servers).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Here we show how to type the processes from Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let us define: T = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t C = ⟨T ⊸⋄⟩ where U is some value type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We recall process P from Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 with the additional typing information on bound names r and a: P = (ν r : T) (ν a : C) � a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Sa | r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � V = λy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ′⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Sa{y/r}) W = λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (z!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W ′⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Sa{z/r}) where Sa stands for a?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let us assume there is a shared environment Γ under which V ′ and W ′ implement type U: Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ V ′ ▷ U (2) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ W ′ ▷ U (3) Also, we assume that process r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q is well-typed under the following environments: Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' r : T ⊢ r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q ▷ ⋄ (4) Under these assumptions, it holds that the body of process P correctly implements name a with type C, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' r : T ⊢ (ν a : C) � a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Sa � ▷ ⋄ We detail the corresponding typing derivations: (LVar) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' x : T ⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ x ▷ T ⊸⋄ (Sess) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y : T ⊢ y ▷ T (App) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' x : T ⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y : T ⊢ x y ▷ ⋄ (5) (5) (Sh) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ a ▷ ⟨T ⊸⋄⟩ (LVar) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' x : T ⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ x ▷ T ⊸⋄ (Acc) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y : T ⊢ a?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x y) ▷ ⋄ (6) (6) (2) (Send) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y : T ⊢ y!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ′⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Sa{y/r} ▷ ⋄ (Sess) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y : T ⊢ y ▷ T (Abs) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ V ▷ T ⊸⋄ (7) (Nil) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 ▷ ⋄ (Sh) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ a ▷ ⟨T ⊸⋄⟩ (7) (Req) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (8) 9 In the following derivation tree the right-hand side is shown similarly to (8) using assumption (3) instead of (2): (8) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (Par) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (9) Finally we have: (9) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' r : T ⊢ Sa ▷ ⋄ (Par) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' r : T ⊢ a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Sa | r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q ▷ ⋄ (4) (Par) Γ, a : C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' r : T, r : T ⊢ a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Sa | r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q ▷ ⋄ (Res) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' r : T, r : T ⊢ (ν a : C) � a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Sa | r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � ▷ ⋄ (ResS) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ (ν r : T) (ν a : C) � a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Sa | r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � ▷ ⋄ Above, we have omitted details of the right-hand side derivation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' it the same as (6) with name y substituted with r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6 (Typing Nested Abstractions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Here we show how to type process P from Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let types C1 and C2 be defined as Ci = ⟨Si ⊸⋄⟩ where i ∈ {1, 2} and Si stands for a tail-recursive type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For simplicity, we assume that value V has the following typing: a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ V ▷ (S1, S2)⊸⋄ (10) The following holds: ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ (ν a : C1) (ν b : C2) R | Sa | Sb ▷ ⋄ (11) In the following typing derivations, we rely on the following two typing rules for polyadic elements;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' they can be derived from monadic typing rules from Figure 3 (see Remark A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 for details): (PolySess) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �u : �S ⊢ �u ▷ �S ⇝∈ {⊸, →} Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ V ▷ �C ⇝ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ �u ▷ �C (PolyApp) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1, ∆2 ⊢ V �u Now, we detail the typing derivations that show (11): (10) (PolySess) a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y : S1, z : S2 ⊢ y, z ▷ S1, S2 (PolyApp) a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y : S1, z : S2 ⊢ V (y, z) ▷ ⋄ (12) (12) (Sess) a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z : S2 ⊢ z ▷ S2 (Abs) a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y : S1 ⊢ λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' V (y, z) ▷ S2 ⊸⋄ (13) (Nil) a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 ▷ ⋄ (Sh) a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ b ▷ ⟨S2 ⊸⋄⟩ (13) (Req) a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y : S1 ⊢ b!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' V (y, z)⟩ ▷ ⋄ (14) (14) (Sess) a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y : S1 ⊢ y ▷ S1 (Abs) a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ λy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' b!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' V (y, z)⟩ ▷ S1 ⊸⋄ (15) 10 a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 ▷ ⋄ (Sh) a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ a ▷ ⟨S1 ⊸⋄⟩ (15) (Req) a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � λy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' b!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' V (y, z)⟩ � ▷ ⋄ (16) Finally we have: (16) a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ Sa ▷ ⋄ (Par) a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ R | Sa ▷ ⋄ a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ Sb ▷ ⋄ (Par) a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ R | Sa | Sb ▷ ⋄ (Res) a : C1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ (ν b : C2) R | Sa | Sb ▷ ⋄ (Res) ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ (ν a : C1) (ν b : C2) R | Sa | Sb ▷ ⋄ In the above typing derivation, we remark that the judgments a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ Sa ▷ ⋄ (17) a : C1, b : C2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ Sb ▷ ⋄ (18) are shown similarly as in (6) from Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Indeed, to derive (17) reusing the derivation tree from (6) we need to substitute y with r and then weaken the shared environment (6) with b : C2 (see Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Similarly, by substituting a with b and y with r in the derivation tree (6) and then by weakening the shared environment with a : C1 in its conclusion we can obtain (18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Notation 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 (Type Annotations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We shall often annotate bound names and variables with their respective type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We will write, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', (ν s : S) P to denote that the type of s in P is S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Similarly for values: we shall write λu : C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Also, letting ⇝∈ {⊸, →}, we may write λu : C⇝.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P to denote that the value is linear (if ⇝=⊸) or shared (if ⇝=→).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' That is, we write λu : C⇝.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P if Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ λu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P ▷ C ⇝ ⋄, for some Γ, Λ, and ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Having introduced the core session process language HO, we now move to detail its type-preserving decomposition into minimal session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 3 Decomposing Session-Typed Processes In this section we define minimal session types and present a decomposition of well-typed processes: given a process P typable with (standard) session types, our decomposition returns a process denoted D(P), typable with minimal session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The definition of D(P) follows Parrow’s trio processes for the π-calculus [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A trio process is a process with at most three sequential prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Roughly speaking, if P is a process with k sequential actions, then D(P) will contain k trios running in parallel: each of them will enact exactly one action from P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The decomposition is carefully designed to ensure that trios trigger each other by preserving the sequencing in P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This section is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1, we use examples to discuss some key ideas of the decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2, we give the full definitions of minimal session types and the decomposition functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define decomposition functions for types G(−) and for processes D(−).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The former “slices” a session type S and returns a list of minimal session types, corresponding to individual actions in S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' the latter breaks down an HO process into a parallel composition of processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We demonstrate these notions on a number of examples in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4 we establish the static correctness result (Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1): if P is well-typed under session types S1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , Sn, then D(P) is typable using the minimal session types G(S1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , G(Sn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The issue of dynamic correctness, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', the operational correspondence between P and D(P), is treated separately in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 (Color Convention).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We use colors to differentiate the operations on processes (in pink) and on types (in green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The usage of the colors is for visual aid only, and is not important for the mathematical content of the presented material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 11 Source process P1: P1 P2 P3 0 u :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str) u :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int) u :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩ Decomposed process D(P1): Q1 Q′ 1 u1 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str) ∥ Q2 Q′ 2 u2 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int) ∥ Q3 Q′ 3 u3 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩ ∥ Q4 x : str x : str, y : int Figure 4: Our decomposition function D(−), illustrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Nodes represent process states, ‘∥’ represents parallel composition of processes, black arrows stand for actions, and red arrows indicate synchronizations that preserve the sequentiality of the source process by activating trios and propagating (bound) values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Key Ideas Consider a process P1 that implements the (standard) session type S =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(str);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end along name u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In process P1, name u is not a single-use resource;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' rather, it is used several times to implement the communication actions in S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Figure 4 (top) graphically depicts the actions and the corresponding states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The decomposition D(P1) is illustrated in the bottom part of Figure 4: it is defined as the parallel composition of four processes Qi (for i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , 4}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Each process Q1, Q2, and Q3 mimic one action of P1 on an indexed name ui, while Q4 simulates the termination of the session.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This way, a single name u in P1 is decomposed into a sequence of names u1, u2, u3 in D(P1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The processes Q1, Q2, Q3, and Q4 are composed in parallel, but we would like to retain the same sequentiality of actions on the channels ui as we have on the channel u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To that end, each process Qi, with the exception of Q1, does not perform its designated action on ui until it gets activated by the previous process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In turn, after Qi performs an action on ui it evolves to a state Q′ i, which is responsible for activating the next process Qi+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In Figure 4, the activations are indicated by red arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In general, the decomposition orchestrates the activation of sub-processes, following the sequencing prescribed by the session types of the given process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Therefore, assuming a well-typed source process, our decomposition codifies the sequentiality in session types into the process level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The activation mechanism includes the propagation of values across sub-processes (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' the labels on red arrows).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This establishes a flow of values from sub-processes binding them to those that use them (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', it makes variable bindings explicit).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For example, in P1, the Boolean value being sent over as part of the session S might depend on the previously received string and integer values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Therefore, both of those values have to be propagated to the process Q3, which is responsible for sending out the Boolean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In this example a single name u : S is decomposed into a sequence �u = (u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , un): each ui ∈ �u is a single-use resource, as prescribed by its minimal session type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Such is the case for non-recursive types S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' When S is recursive, the situation is more interesting: each action of S can be repeated many times, and therefore the names �u should be propagated across trios to enable potentially many uses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As an example, consider the recursive session type S = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t, in which an input and an output actions are repeated indefinitely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Consider the following process R1 = r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � �� � T1 r!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨−z⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � �� � T2 r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � �� � T3 r!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨z⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � �� � T4 V r ���� T5 which makes use of the channel r : S and where V has type S →⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Figure 5 (top) gives the first four 12 actions of R1 and the corresponding sates: the body of type S prescribes two actions on name r, performed sequentially in R1 and R2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' subsequent actions (enabled in R3 and R4) correspond to a “new instance” of the body of S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The decomposition D(R1), depicted in Figure 5 (bottom), generates a trio process for each prefix in R1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' we denote prefixes with their corresponding trios T1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , T5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The type decomposition function on types, G(−), slices S into two minimal tail-recursive types: M1 = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t and M2 = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the recursive case, a key idea is that trios that mimic actions prescribed by a recursive session types should reuse names, which should be propagated across trios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This way, for instance, trios T1 and T3 mimic the same (input) action, and so they both should use the same name (r1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To achieve this, we devise a mechanism that propagates names with tail-recursive types (such as (r1, r2)) through the trios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' These propagation actions are represented by blue arrows in Figure 5 (bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In our example, T3 gathers the complete decomposition of names from preceding trios (r1, r2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' it mimics an input action on r1 and makes (r1, r2) available to future trios (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', T4 and T5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Since the same tail-recursive names can be (re)used infinitely often, we propagate tail-recursive names through the following process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' All the names �r corresponding to the decomposition of a tail-recursive name r are bound in the process cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �r, which is similar to the servers discussed in Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We call these processes recursive propagators, and each tail-recursive name in the original process P has a dedicated propagator in D(P) on the channel cr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever a trio has to perform an action α(ri) on one of the decomposed tail-recursive names (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', a decomposition of an input action ‘r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).’ or an output action ‘r!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.’ on the name r), it first has to request the name from the corresponding recursive propagator by performing an output action cr!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � N � , where value N is the abstraction N = λ�z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' α(zi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A synchronization on cr will result in the reduction: cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �r | cr!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � N � −→ α(ri).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �r � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The resulting process first simulates α(r) and subsequently reinstates the recursive propagator on cr, for the benefit of the other trios requiring access to the names �r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' See Examples 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 below (Page 24) for further illustration of this method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This decomposition strategy handles HO processes with recursive types which are simple and contractive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' That is, recursive types of the form µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S, where the body S ̸= t does not itself contain recursive types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Unless stated otherwise, we consider tail-recursive session types such as, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', S = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(bool);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Non-tail-recursive session types such as µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (( �T, t)→⋄);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, used in the fully-abstract encoding of HOπ into HO [17], can also be accommodated;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' see Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 The Decomposition Here we formally present the decomposition of HO processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We start introducing some preliminary definitions, including the definition of an auxiliary function, called the breakdown function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Following Parrow [21] we adopt some useful terminology and notation on trios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The context of a trio is a tuple of variables �x, possibly empty, which makes variable bindings explicit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We use a reserved set of propagator names (or simply propagators), denoted with ck, ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', to carry contexts and trigger the subsequent trio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A process with less than three sequential prefixes is called a degenerate trio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Also, a leading trio is the one that receives a context, performs an action, and triggers the next trio;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' a control trio only activates other trios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The breakdown function works on both processes and values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The breakdown of process P is denoted by Bk ˜x � P � , where k is the index for the propagators ck, and �x is the context to be received by the previous trio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Similarly, the breakdown of a value V is denoted by V˜x � V � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 13 Source process R1: R1 R2 R3 R4 R5 r :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int) r :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩ r :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int) r :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩ Decomposed process D(R1): T1 T ′ 1 r1 : ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int) ∥ T2 T ′ 2 r2 : !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩ ∥ T3 T ′ 3 r1 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int) ∥ T4 T ′ 4 r2 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩ ∥ T5 r1,r2 r1,r2 r1,r2 r1,r2 Figure 5: Decomposition of processes with recursive session types, illustrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Dashed blue arrows represent the propagation of tail-recursive names (r1,r2) across trios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Minimal Session Types and Decomposing Types We start by introducing minimal session types as a fragment of Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2: Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 (Minimal Session Types).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The syntax of minimal session types for HO is defined as follows: U ::= �C →⋄ | �C ⊸⋄ C ::= M | ⟨U⟩ M ::= γ | !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='γ | ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='γ | µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='M γ ::= end | t The above definition is minimal in its use of sequencing, which is only present in recursive session types such as µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t and µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t—these are tail-recursive session types with exactly one session prefix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Clearly, this minimal type structure induces a reduced set of typable HO processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A type system for HO based on minimal session types can be straightforwardly obtained by specializing the definitions, typing rules, and results summarized in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We refer to HO processes and terms typeable with minimal session types as MST processes and terms, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We now define how to “slice” a standard session type into a list of minimal session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We need the following auxiliary definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 (Predicates on Types and Names).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let C be a channel type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We write tr(C) to indicate that C is a tail-recursive session type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Given u : C, we write lin(u) if a session type (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' C = S for some S) that is not tail recursive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' With a slight abuse of notation, we write tr(u) to mean u : C and tr(C) (and similarly for ¬tr(u)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 (Decomposing Session Types).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Given the session, higher-order, and shared types of Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2, the type decomposition function G(−) is defined using the auxiliary function R(−) as in Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We write |G(S)| to denote the length of G(S) (and similarly for R(−)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The decomposition is self-explanatory;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' intuitively, if a session type S contains k input/output actions, the list G(S) will contain k minimal session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For a tail recursive µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S, G(µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S) is a list of minimal recursive session types, obtained using the auxiliary function R(−) on S: if S has k prefixes then the list G(µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S) will contain k minimal recursive session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We illustrate Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 with three examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 14 G(!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S) = � !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨G(U)⟩ if S = end !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨G(U)⟩ , G(S) otherwise G(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S) = � ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (G(U)) if S = end ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (G(U)) , G(S) otherwise G(µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S) = � R(S) if tr(µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S) µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='G(S) if ¬tr(µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S) and G(S) is a singleton G(end) = end G(t) = t G(C ⊸⋄) = G(C)⊸⋄ G(C →⋄) = G(C)→⋄ G(⟨U⟩) = ⟨G(U)⟩ R(t) = ϵ R(!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S) = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨G(U)⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t, R(S) R(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S) = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (G(U));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t, R(S) Figure 6: Decomposing session types into minimal session types (Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3) Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 (Decomposition a Non-recursive Type).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let S =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end be the session type given in Section 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then G(S) denotes the list ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int) , ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int) , !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ◁ Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 (Decomposing a Recursive Type).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let S = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S′ be a recursive session type, with S′ =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(bool);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3, since S is tail-recursive, G(S) = R(S′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, R(S′) = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (G(int));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t, R(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(bool);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By definition of R(−), we obtain G(S) = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t, µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (bool);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t, µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t, R(t) (using G(int) = int and G(bool) = bool).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Since R(t) = ϵ, we obtain G(S) = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t, µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (bool);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t, µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t ◁ In addition to tail-recursive types that are handled by R(−), we need to support non-tail-recursive types of form µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (( �T, t)→⋄);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end that are essential for the encoding of recursion in HOπ into HO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The following example illustrates such a decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 (Decomposing a Non-tail-recursive Type).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let S = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='((?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨str⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, t)→⋄);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end be a non-tail-recursive type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We obtain the following decomposition: G(S) = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='G(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='((?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨str⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, t)→⋄);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end) = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(G((?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨str⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, t)→⋄)) = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='((?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str), !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨str⟩, t)→⋄) = M We can see that we have generated minimal non-tail-recursive type M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ◁ Now, we illustrate the encoding of HOπ recursive processes into HO from [17] using the non-tail- recursive type S given in the above example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4 (Encoding Recursion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Consider the process P = µX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='a?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='X, which contains recursion and so it is not an HO process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Still, P can be encoded into HO as follows [17]: �P� = a?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s) (V (a, s) | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩) 15 where the value V is an abstraction that potentially reduces to �P�: V = λ(xa, y1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(zx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='xa?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='xa!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s) (zx (xa, s) | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨zx⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0) As detailed in [17], this encoding relies on non-tail-recursive types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In particular, the bound name s in �P� is typed with the following type, discussed above in Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3: S = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='((?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨str⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, t)→⋄);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end We compose �P� with an appropriate client process to illustrate the encoding of recursion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Below R stands for some unspecified process such that a ∈ rn(R): �P� | a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='a?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='R −→2 (ν s) (V (a, s) | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩) | R −→ (ν s) (s?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(zx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='a?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s′) (zx (a, s′) | s′!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨zx⟩) | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩) | R −→ a?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s′) (V (a, s′) | s′!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩) | R = �P� | R 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 Decomposing Processes As we have seen, each session type S is decomposed into G(S), a list of minimal session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Accordingly, given an assignment s : S, we decompose s into a series of names, one for each action in S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We use indexed names to formalize the names used by minimally typed processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Formally, an indexed name is a pair (n, i) with i ∈ N, which we denote as ni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We refer to processes with indexed names as indexed processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The decomposition of processes is defined in Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9, and it relies on a breakdown function, denoted Bk ˜x � − � , which operates on indexed processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Before we dive into those functions we present some auxiliary definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Preliminaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To handle the unfolding of recursive types, we shall use the following auxiliary function, which decomposes guarded recursive types, by first ignoring all the actions until the recursion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4 (Decomposing an Unfolded Recursive Type).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let S be a session type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The function R⋆(−): is defined as follows R⋆(µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S) = R(S) R⋆(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S) = R⋆(S) R⋆(!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S) = R⋆(S) Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let T =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (bool);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S be a derived unfolding of S from Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, by Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3, R⋆(T) is the list of minimal recursive types obtained as follows: first, R⋆(T) = R⋆(!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S′) and after one more step, R⋆(!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S′) = R⋆(µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, we have R⋆(µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S′) = R(S′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We get the same list of minimal types as in Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2: R⋆(T) = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t, µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (bool);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t, µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ◁ Given an unfolded recursive session type S, the auxiliary function [S⟩ returns the position of the top-most prefix of S within its body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='5 (Index function).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let S be an (unfolded) recursive session type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The function [S⟩ is defined as follows: [S⟩ = � [S′{S/t}⟩⋆ 0 if S = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S′ [S⟩⋆ 0 otherwise 16 where [S⟩⋆ l : [µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S⟩⋆ l = |R(S)| − l + 1 [!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S⟩⋆ l = [S⟩⋆ l+1 [?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S⟩⋆ l = [S⟩⋆ l+1 Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let S′ =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (bool);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S where S is as in Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then [S′⟩ = 2 since the top-most prefix of S′ (‘?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (bool);’' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=') is the second prefix in the body of S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ◁ In order to determine the required number of propagators (ck, ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=') required in the breakdown of processes and values, we define the degree of a process: Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6 (Degree of a Process).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let P be an HO process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The degree of P, denoted �P�, is defined as follows: �P� = � � � � � � � � � � � �Q� + 1 if P = ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q or P = ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q �P ′� if P = (ν s : S) P ′ �Q� + �R� + 1 if P = Q | R 1 if P = V ui or P = 0 We define an auxiliary function that “initializes” the indices of a tuple of names, for turning a regular process into an indexed process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='7 (Initializing an indexed process).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let �u = (a, b, s, s′, r, r′, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=') be a finite tuple of names.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We shall write init(�u) to denote the tuple of indexed names (a1, b1, s1, s′ 1, r1, r′ 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='8 (Subsequent index substitution).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let ni be an indexed name.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define next(ni) = (lin(ni)) ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' {ni+1/ni}: {}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Recall that we write ‘ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()’ and ‘ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩’ to denote input and output prefixes in which the value communicated along ck is not relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' While ‘ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()’ stands for ‘ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x)’, ‘ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩’ stands for ‘ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 0⟩’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Their corresponding minimal types are ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (end→⋄) and !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨end→⋄⟩, which are denoted by ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (−) and !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨−⟩, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Given a typed process P, we write rn(P) to denote the set of free names of P whose types are recursive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As mentioned above, for each r ∈ rn(P) with r : S we shall rely on a control trio of the form cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �r, where �r = r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , r|G(S)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9 (Decomposition of a Process).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let P be a closed HO process with �u = fn(P) and �v = rn(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The decomposition of P, denoted D(P), is defined as: D(P) = (ν �c) (ν �cr) � ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Bk ϵ � Pσ � | � r∈˜v cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �r � where: k > 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �c = (ck, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P�−1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �cr = � r∈˜v cr;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' σ = {init(�u)/�u}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Notice that when rn(P) = ∅, then D(P) = (ν �c) (ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Bk ϵ � Pσ � ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We now discuss the breakdown of process P, denoted Bk ˜x � P � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The Breakdown Function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Given a context �x and a k > 0, the breakdown of an indexed process P, denoted Bk ˜x � P � , is defined recursively on the structure of processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The definition of Bk ˜x � − � relies on an auxiliary breakdown function on values, denoted V˜x � − � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' When V = y, then the breakdown function is simply the identity: V˜x � y � = y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The breakdown function relies on type information, in two ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, names are decomposed based on their session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Second, for most constructs the shape of decomposed process depends on whether the associated session type is tail-recursive or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The definition of the breakdown function is given in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Next, we describe each of the cases of the definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 (Page 21) we develop several examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 17 P Bk ˜x � P � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q ¬tr(S): ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V˜y � V σ �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | Bk+1 ˜w � Qσ � tr(S): ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � NV � | Bk+1 ˜w � Q � where: NV = λ�z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z[S⟩!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V˜y � V �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z � ui : S �y = fv(V ) �w = fv(Q) σ = next(ui) �z = (z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , z|R⋆(S)|) ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q tr(S): ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | Bk+1 ˜w � Qσ � ¬tr(S): ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � Ny � | Bk+1 ˜w � Q � where: Ny = λ�z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z[S⟩?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z � ui : S �w = fv(Q) σ = next(ui) �z = (z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , z|R⋆(S)|) V (�r, ui) ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' n=|˜r| cr1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � λ�z1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cr2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�z2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='crn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q⟩ ⟩ � where: Q = V˜x � V � (�z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �zn, �m) ui : C ∀ri ∈ �r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ri : Si ∧ tr(Si)∧ �zi = (zi 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , zi |R⋆(Si)|)) �m = (ui, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ui+|G(C)|−1) (ν s : C) P ′ ¬tr(C) : (ν �s : G(C)) Bk ˜x � P ′σ � tr(C) : (ν �s : G(C)) (ν cs) cs?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �s | (ν c¯s) c¯s?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x�s | Bk ˜x � P ′σ � �x = fv(P ′) �s = (s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , s|G(C)|) �s = (s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , s|G(C)|) σ = {s1s1/ss} Q | R ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+l+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | Bk+1 ˜y � Q � | Bk+l+1 ˜w � R � �y = fv(Q) �w = fv(R) l = �Q� 0 ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 V V˜x � V � y y λ(�yz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P λ( �y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , � yn, �z) : (� M) ⇝.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' N where: � M = (G(S1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , G(Sn), G(C)) N = (ν �c) (ν �cr) � i∈|�y|(cyi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �yi) | c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�x⟩ | B1 ˜x � P{z1/z} � �yz : �SC ∀yi ∈ �y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (yi : Si ∧ tr(Si)∧ �yi = (yi 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , yi |G(Si)|)) �z = (z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , z|G(C)|) �c = (c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c�P�) �cr = � r∈˜y cr Table 1: The breakdown function for processes and values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Output: The decomposition of ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q is arguably the most interesting case, as both the sent value V and the continuation Q have to be decomposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We distinguish two cases: If ¬tr(ui) then ui is linear or shared, and then we have: Bk ˜x � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V˜y � V σ �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | Bk+1 ˜w � Qσ � This decomposition consists of a leading trio that mimics an output action in parallel with the breakdown of Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The context �x must include the free variables of V and Q, which are denoted 18 �y and �w, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' These tuples are not necessarily disjoint: variables with shared types can appear free in both V and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The value V is then broken down with parameters �y and k + 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' the latter serves to consistently generate propagators for the trios in the breakdown of V , denoted V˜y � V σ � (see below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The substitution σ increments the index of session names;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' it is applied to both V and Q before they are broken down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By taking σ = next(ui) we distinguish two cases (see Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='8): – If name ui is linear (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', it has a session type) then its future occurrences are renamed into ui+1, and σ = {ui+1/ui};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' – Otherwise, if ui is shared, then σ = {}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Note that if ui is linear then it appears either in V or Q and σ affects only one of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The last prefix activates the breakdown of Q with its corresponding context �w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In case V = y, the same strategy applies;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' because V˜y � yσ � = y, we have: Bk ˜x � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | Bk+1 ˜w � Qσ � Notice that variable y is not propagated further if it does not appear free in Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' If tr(ui) then ui is tail-recursive and then we have: Bk ˜x � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � NV � | Bk+1 ˜w � Q � where: NV = λ�z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z[S⟩!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V˜y � V �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z � The decomposition consists of a leading trio that mimics the output action running in parallel with the breakdown of Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' After receiving the context �x, the leading trio sends an abstraction NV along cu, which performs several tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, NV collects the sequence of names ˜u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' then, it mimics the output action of P along one of such names (u[S⟩) and triggers the next trio, with context �w;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' finally, it reinstates the server on cu for the next trio that uses u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Notice that indexing is not relevant in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In case V = y, we have V˜y � yσ � = y and �y� = 0, hence: Bk ˜x � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � λ�z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z[S⟩!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z �� | Bk+1 ˜w � Q � Input: To decompose a process ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q we distinguish two cases, as before: (i) name ui is linear or shared or (ii) tail-recursive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In case (i), the breakdown is defined as follows: Bk ˜x � ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | Bk+1 ˜w � Qσ � where �w = fv(Q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A leading trio mimics the input action and possibly extends the context with the received variable y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The substitution σ is defined as in the output case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In case (ii), when ui has tail-recursive session type S, the decomposition is as in the output case: Bk ˜x � ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � λ�z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z[S⟩?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z �� | Bk+1 ˜w � Q � Application: For simplicity we consider the breakdown of applications of the form V (�r, ui), where every ri ∈ �r is such that tr(ri) and only ui is such that ¬tr(ui).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The general case (involving different orders in names and multiple names with non-recursive types) is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We have: Bk ˜x � V (�r, ui) � =ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' n=|˜r| cr1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � λ�z1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cr2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�z2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='crn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' V˜x � V � (�z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �zn, �m)⟩ ⟩ � 19 Let us first discuss how names in (�r, ui) are decomposed using types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Letting |˜r| = n and i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , n}, for each ri ∈ �r (with ri : Si) we generate a sequence �zi = (zi 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , zi |R⋆(Si)|) as in the output case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We decompose name ui (with ui : C) as �m = (ui, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ui+|G(C)|−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The decomposition first receives a context �x for value V : we break down V with �x as a context since these variables need to be propagated to the abstracted process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Subsequently, an output on cr1 sends a value containing n abstractions that occur nested within output prefixes—this is similar to the mechanism for partial instantiation shown in Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For each j ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , n − 1}, each abstraction binds �zj and sends the next abstraction along crj+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The innermost abstraction abstracts over �zn and encloses the process V˜x � V � (�z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �zn, �m), which effectively mimics the application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This abstraction nesting binds all variables �zi, the decompositions of all tail-recursive names (�r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The breakdown of a value application of the form y (�r, ui) results into the following specific case: Bk ˜x � y (�r, ui) � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' n=|˜r| cr1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � λ�z1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cr2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�z2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='crn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y (�z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �zn, �m)⟩ ⟩ � Restriction: The decomposition of (ν s : C) P ′ depends on C: If ¬tr(C) then Bk ˜x � (ν s : C) P ′� = (ν �s : G(C)) Bk ˜x � P ′σ � By construction, �x = fv(P ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Similarly as in the decomposition of ui into �m discussed above, we use the type C of s to obtain the tuple �s of length |G(C)|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We initialize the index of s in P ′ by applying the substitution σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This substitution depends on C: if it is a shared type then σ = {s1/s};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' otherwise, if C is a session type, then σ = {s1s1/ss}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Otherwise, if tr(C) then we have: Bk ˜x � (ν s : C) P ′� = (ν �s : R(S)) (ν cs) cs?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �s | (ν c¯s) c¯s?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x�s | Bk ˜x � P ′� We decompose s into �s = (s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , s|G(S)|) and s into �s = (s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , s|G(S)|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Notice that as tr(C) we have C ≡ µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S, therefore G(C) = R(S).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The breakdown introduces two servers in parallel with the breakdown of P ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' they provide names for s and s along cs and cs, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The server on cs (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cs) receives a value and applies it to the sequence �s (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We restrict over �s and propagators cs and cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Composition: The breakdown of a process Q | R is as follows: Bk ˜x � Q | R � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+l+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | Bk+1 ˜y � Q � | Bk+l+1 ˜w � R � A control trio triggers the breakdowns of Q and R;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' it does not mimic any action of the source process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The tuple �y ⊆ �x (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �w ⊆ �x) collects the free variables in Q (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To avoid name conflicts, the trigger for the breakdown of R is ck+l+1, with l = �Q�.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Inaction: To breakdown 0, we define a degenerate trio with only one input prefix that receives a context that by construction will always be empty (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', �x = ϵ, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2): Bk ˜x � 0 � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 Value: For simplicity, let us consider values of the form V = λ(�y, z) : (�S, C) ⇝.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P, where tr(yi) holds for every yi ∈ �y and ¬tr(z), and ⇝∈ {⊸, →}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The general case is defined similarly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We have: V˜x � λ(�y, z) : (�S, C) ⇝.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P � = λ( �y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , � yn, �z) : (� M) ⇝.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' N where: � M = G(S1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , G(Sn), G(C) N = (ν �c) (ν �cr) � i∈|�y| cyi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �yi | c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�x⟩ | B1 ˜x � P{z1/z} � 20 Every yi (with yi : Si) is decomposed into �yi = (y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , y|G(Si)|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We use C to decompose z into �z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We abstract over �y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �yn, �z;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' the body of the abstraction (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' N) is the composition of recursive names propagators, the control trio, and the breakdown of P, with name index initialized with the substitution {z1/z}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For every yi ∈ �y there is a server cyi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �yi as a subprocess in the abstracted composition—the rationale for these servers is as in previous cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We restrict the propagators �c = (c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c�P�): this enables us to type the value in a shared environment when ⇝=→.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Also, we restrict special propagator names �cr = � r∈˜v cr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 The Decomposition by Example We illustrate the decompositions by means of several examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Decomposing Processes with Non-Recursive Names Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Consider process P = (ν u) (Q | R) whose body implements end-points of channel u with session type S =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (bool);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, with U = (?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (bool);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end)⊸⋄, where: Q = u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q′ � �� � u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s) � x s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ � R = u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 V = λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 The process P reduces as follows: P −→ (ν u) � u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s) � V s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ � | u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 � −→ (ν s) � V s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩ � −→ (ν s) � s?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩ � = P ′ By Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9 we have that the decomposition of P is as follows: D(P) = (ν c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c10) (c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B1 ϵ � Pσ � ) where σ = {u1u1/uu}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We have: B1 ϵ � Pσ � = (ν u1, u2) c1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B2 ϵ � Qσ � | B8 ϵ � Rσ � The breakdowns of sub-processes Q and R are as follows: B2 ϵ � Qσ � = c2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩ | B3 ϵ � Q′σ′� B3 x � Q′σ′� = c3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x, y⟩ | B4� (ν s) � x s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ �� B4 x,y � (ν s) � x s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ �� = (ν s1) � c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x, y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x s1 | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 � B8 ϵ � Rσ � = c8?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c9!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B9 ϵ � u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 � B9 ϵ � u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 � = c9?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 Vϵ � V � = λz1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ((ν cV 1 , cV 2 ) cV 1 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cV 1 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='z1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cV 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cV 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0) where σ′ = {u2u2/uu}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By G(−) from Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 we decompose S into M1 and M2 given as follows: M1 =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (G(U));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end M2 =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (bool);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end Above we may notice that G(U) = U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We remark that D(P) accordingly implements indexed names u1, u2 typed with M1, M2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 21 Let us inspect the reductions of D(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, there are three synchronizations on c1, c2, and c8: D(P) −→ (ν c2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c10) (ν u1, u2) c2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c8!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B2 ϵ � Qσ � | B8 ϵ � Rσ � −→2 (ν c3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c7, c9, c10) u1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩ | B3 ϵ � Q′σ′� | u1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' c9!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B9 ϵ � u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 � = D1 After reductions on propagators, D1 is able to mimic the original synchronization on channel u (highlighted above).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' It is followed by two administrative reductions on c3 and c9: D1 −→ (ν c3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c7, c9, c10) c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � ⟩ | c3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x, y⟩ | B4� (ν s) � x s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ �� | c9!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c9?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 −→2 (ν c4, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c7, c10) u2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � , y⟩ | (ν s1) � c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x, y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x s1 | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 � | u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 = D2 Similarly, D2 can mimic the next synchronization of the original process on name u2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Following up on that, syncronization on c10 takes place: D2 −→2 (ν c4, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c7) c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � , true⟩ | (ν s1) � c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x, y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x s1 | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 � = D3 Now, we can see that the next three reductions on c4, c5, and c6 appropriately propagate values Vϵ � V � and true to the breakdown of sub-processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Subsequently, value Vϵ � V � is applied to name s1: D3 −→ (ν c5, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c7) (ν s1) � c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x s1 | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 � −→2 (ν c7) (ν s1) � Vϵ � V � s1 | s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 � −→ (ν c7) (ν s1) ((ν cV 1 , cV 2 ) cV 1 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cV 1 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cV 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cV 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0) | s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 = D4 Finally, after syncronization on cV 1 we reach the process D5 that is clearly able to simulate P ′, and its internal communication on the channel s: D4 −→ (ν c7) (ν s1) ((ν cV 2 ) s1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cV 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cV 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0) | s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 = D5 ◁ Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='8 (Breaking Down Name-Passing).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Consider the following process P, in which a channel m is passed, through which a boolean value is sent back: P = (ν u) (u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⌜m⌝⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='m?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b) | u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (⌜x⌝).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩) After expanding the syntactic sugar of name-passing, we get a process P = (ν u) (Q | R), where Q = u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='m?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s) (y s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 0⟩) V = λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x m) R = u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s) (y s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩) W = λx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' x!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W ′⟩ with W ′ = λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x true) Note that to mimic the name-passing synchronization, we require exactly four reduction steps: P −→4 �m?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b) | m!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩� −→4 0 (19) We will now investigate the decomposition of P and its reduction chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, we use Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6 to compute �Q� = 6, and similarly, �R� = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Therefore, �P� = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Following Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9, we see that σ = {m1m1/mm}, which we silently apply.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Taking k = 1, the breakdown of P and its subprocesses is shown in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 22 D(P) = (ν c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c12) � c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | (ν u1) � c1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c8!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B2 ϵ � Q � | B8 ϵ � R ��� B2 ϵ � Q � = c2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='m1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ | (ν s1) (c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y s1) | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � λb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 0 � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()) B8 ϵ � R � = c8?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c9!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ | (ν s1) � c9?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c11!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y s1) | c11?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � W � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c12!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c12?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () � Vϵ � V � = λz1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν cV 1 , cV 2 ) (cV 1 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cV 1 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='z1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cV 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩ | cV 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x m1)) Vϵ � λb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 0 � = λb1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν cb 1) (cb 1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cb 1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()) Vϵ � W � = λx1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν cW 1 , cW 2 ) (cW 1 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cW 1 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � W ′� ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cW 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cW 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()) Vϵ � W ′� = λz1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν cW ′ 1 , cW ′ 2 ) (cW ′ 1 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cW ′ 1 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='z1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cW ′ 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩ | cW ′ 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x true)) Table 2: The decomposition on processes discussed in Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In Table 2 we have omitted substitutions that have no effect and trailing 0s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The first interesting action appears after synchronizations on c1, c2, and c8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' At that point, the process will be ready to mimic the first action that is performed by P, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', u1 will send Vϵ � V � , the breakdown of V , from the breakdown of Q to the breakdown of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Next, c9 and c10 will synchronize, and Vϵ � V � is passed further along, until s1 is ready to be applied to it in the breakdown of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' At this point, we know that P −→7 (ν �c) P ′, where �c = (c3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c12), and P ′ = c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='m1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ | (ν s1) (c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y s1 | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � λb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 0 � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()) | (ν s1) � Vϵ � V � s1 | s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � W � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c12!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c12?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () � After s1 is applied, the trio guarded by c3 will be activated, where z1 has been substituted by s1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then s1 and s1 will synchronize, and the breakdown of W is passed along.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then c4 and c19 synchronize, and now m1 is ready to be applied to Vϵ � W � , which was the input for c4 in the breakdown of V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' After this application, c3 and cW 1 can synchronize with their duals, and we know that (ν �c) P ′ −→8 (ν �c′) P ′′, where �c′ = (c4, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c7, cW ′ 2 ), and P ′′ = m1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ | m1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � W ′� ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cW ′ 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cW ′ 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () | (ν s1) (c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y s1 | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � λb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 0 � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()) Remarkably, P ′′ is standing by to mimic the encoded exchange of value true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Indeed, the decomposi- tion of the four-step reduced process in (19) will reduce in three steps to a process that is equal (up to ≡α) to the process we obtained here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This strongly suggests a tight operational correspondence between a process and its decomposition, which we will explore in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ◁ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 Decomposing Processes with Recursive Names Next, we illustrate the decomposition of processes involving names with tail-recursive types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Recall process R1, which we used in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 to motivate the need for recursive propagators: R1 = r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨−z⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨z⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='V r Two following examples illustrate the low-level workings of the propagation mechanism of the decomposition in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The first example illustrates how the propagation of recursive names works in the case of input and output actions on names with recursive types (the “first part” of R1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The second example shows how an application where a value is applied to a tuple of names with recursive names is broken down (the “second part” of R1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 23 Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9 (Decomposing Processes with Recursive Names (I)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let P = r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′ be a process where r has type S = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t and r ∈ fn(P ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9 we have: D(P) = (ν �c) (ν cr) � c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B1 ϵ � P � | cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (r1, r2) � where �c = (c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c|P|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The control trio in the parallel composition provides a decomposition of r on name cr, which is shared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The decomposition B1 ϵ � P � is defined as follows: B1 ϵ � P � = c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cr!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨N1⟩ | c2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cr!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨N2⟩ | B3 ϵ � P ′�� N1 = λ(z1, z2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (z1, z2) N2 = λ(z1, z2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (z1, z2) Each trio in B1 ϵ � P � that mimics some action on r requests the sequence ˜r from the server on cr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We can see that this request is realized by a higher-order communication: trios send abstractions (N1 and N2) to the server;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' these abstractions contain further actions of trios and it will be applied to the sequence ˜r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hence, the formal arguments for these values are meant to correspond to ˜r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' After two reductions (the trio activation on c1 and the communication on cr), we have: D(P) −→2 (ν c2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c�P�) r1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (r1, r2) | c2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cr!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨N2⟩ | B3 ϵ � P ′� = P1 By synchronizing with the top-level server on cr, the bound names in N1 are instantiated with r1, r2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, the first trio in P1 is able to mimic the action on r1 that is followed by the activation of the next trio on c2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, the server on cr gets reinstantiated making names r1, r2 available for future trios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The break down of the output action follows the same pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ◁ Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 (Decomposing Processes with Recursive Names (II)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let S = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t and T = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (bool);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t, and define Q = V (u, v) as a process where u : S and v : T, where V is some value of type (S, T)→⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9, the decomposition of Q is as in the previous example, except that now there are two servers, one for u and one for v: D(Q) = (ν c1˜c) (ν cucv) � cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (u1, u2) | cv?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (v1, v2) | c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B1 ϵ � Q �� B1 ϵ � Q � = c1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � λ(x1, x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cv!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ(y1, y2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Vϵ � V � (x1, x2, y1, y2)⟩ � with ˜c = (c2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c�Q�).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Process Q is broken down in such a way that it communicates with both servers to collect ˜u and ˜v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To this end, B1 ϵ � Q � is a process in which abstractions are nested using output prefixes and whose innermost process is an application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' After successive communications with multiple servers this innermost application will have collected all names in ˜u and ˜v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Observe that we use two nested outputs, one for each name with recursive types in Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We now look at the reductions of D(Q) to analyze how the communication of nested abstractions allows us to collect all name sequences needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' After the first reduction along c1 we have: D(Q) −→(ν ˜c) (ν cucv) � cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (u1, u2) | cv?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (v1, v2) | cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � λ(x1, x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cv!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ(y1, y2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Vϵ � V � (x1, x2, y1, y2)⟩ �� = R1 From R1 we have a synchronization along name cu: R1 −→(ν ˜c) (ν cucv) � (λ(x1, x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cv!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ(y1, y2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Vϵ � V � (x1, x2, y1, y2)⟩) (u1, u2) | cv?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (v1, v2) � = R2 Upon receiving the value, the server applies it to (u1, u2), thus obtaining the following process: R2 −→(ν ˜c) (ν cucv) � cv!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ(y1, y2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Vϵ � V � (u1, u2, y1, y2)⟩ | cv?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (v1, v2) � = R3 Up to here, we have partially instantiated name variables of a value with the sequence ˜u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Next, the first trio in R3 can communicate with the server on name cv: R3 −→(ν ˜c) (ν cucv) � λ(y1, y2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Vϵ � V � (u1, u2, y1, y2) (v1, v2) � −→(ν ˜c) (ν cucv) � Vϵ � V � (u1, u2, v1, v2) � This completes the instantiation of name variables with appropriate sequences of names with recursive types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' At this point, D(Q) can proceed to mimic the application in Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ◁ 24 Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='11 (Breakdown of Recursion Encoding).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We recall process �P� from Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4: �P� = a?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='a!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s) (V (a, s) | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩) V = λ(xa, y1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(zx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='xa?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='xa!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s) (zx (xa, s) | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨zx⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0) Here, bound name s is typed with S, from Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3, defined as: S = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='((?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨str⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, t)→⋄);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end We now analyze D(�P�) and its reduction chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6, we have ��P�� = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, we choose k = 1 and observe that σ = {a1a1/aa}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Following Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9, we get: D(�P�) = (ν c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c7) (ν ca) (ca?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (a1, a2) | c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B1 ϵ � �P�σ � ) B1 ϵ � �P� � = c1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ca!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ(z1, z2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ca?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (z1, z2)⟩ | c2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ca!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ(z1, z2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ca?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (z1, z2)⟩ | (ν s1) � c3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ca!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ(z1, z2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Vϵ � V � (z1, z2, s1)⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () � In accordance with Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3, the type of s1 in the decomposed process is M = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='((?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str), !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨str⟩, t)→⋄).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The decomposition relies twice on Vϵ � V � , the breakdown of value V , which we give below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For this, we observe that V is an abstraction of a process Q with |Q| = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We also α-convert the process abstracted in Vϵ � V � renaming bound propagators c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c7 to cV 1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , cV 7 to avoid name clashes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Vϵ � V � = λ(xa1, xa2, y1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν cV 1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , cV 7 ) � cV 1 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B1 ϵ � Q � {cV 1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , cV 7/c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c7} | cxa?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (xa1, xa2) � B1 ϵ � Q � = c1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (zx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨zx⟩ | c2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (zx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ca!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ(z1, z2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨zx, m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ca?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (z1, z2)⟩ | c3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (zx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ca!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ(z1, z2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨zx⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ca?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (z1, z2)⟩ | (ν s1) � c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (xz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨zx⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨zx⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (zx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ca!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ(z1, z2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' zx (z1, z2, s1)⟩ | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (zx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨zx⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () � We follow the reduction chain on D(�P�) until it is ready to mimic the first action with channel a, which is an input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, c1 will synchronize, after which ca sends the abstraction to which then (a1, a2) is applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We obtain D(�P�) −→3 (ν c2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c7, ca) P ′, where P ′ = a1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ca?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (a1, a2) | c2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (m).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ca!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ(z1, z2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨m⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ca?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x (z1, z2)⟩ | (ν s1) � c3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' | c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ca!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ(z1, z2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Vϵ � V � (z1, z2, s1)⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () � Note that this process is awaiting an input on channel a1, after which c2 can synchronize with its dual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' At that point, ca is ready to receive another abstraction that mimics an input on a1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This strongly suggests a tight operational correspondence between a process P and its decomposition in the case where P performs higher-order recursion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ◁ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4 Static Correctness Having presented and illustrated our decomposition, we may now state its technical results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Given an environment ∆ = ∆1, ∆2, below we write ∆1 ◦ ∆2 to indicate the split of ∆ into a ∆1 containing non-recursive names and a ∆2 containing recursive names.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We extend the decomposition function G(−) to typing environments in the obvious way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We rely on the following notation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Given a tuple of names �s = s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , sn and a tuple of (session) types �S = S1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , Sn of the same length, we write �s : �S to denote a list of typing assignments s1 : S1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , sn : Sn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 25 Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 (Decomposition of Environments).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let Γ, Λ, and ∆ be typing environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define G(Γ), G(Λ), and G(∆) inductively as follows: G(∆, ui : S) = G(∆), (ui, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ui+|G(S)|−1) : G(S) G(Γ, ui : ⟨U⟩) = G(Γ), ui : G(⟨U⟩) G(Γ, x : U) = G(Γ), x : G(U) G(Λ, x : U) = G(Λ), x : G(U) G(∅) = ∅ Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let P be an indexed HO process and V be a value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' If Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ◦ ∆µ ⊢ P ▷ ⋄ then G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆), Θ ⊢ Bk ˜x � P � ▷ ⋄, where: k > 0 �r = dom(∆µ) Φ = � r∈˜r cr : ⟨R⋆(∆µ(r))⊸⋄⟩ �x = fv(P) Γ1 = Γ \\ �x dom(Θ) = {ck, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P�−1} ∪ {ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P�−1} Θ(ck) =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , Un), where (G(Γ), G(Λ))(�x) = (x1 : U1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , xn : Un) balanced(Θ) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' If Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ◦ ∆µ ⊢ V ▷ �T ⊸⋄ then G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆) ⊢ V˜x � V � ▷ G( �T)⊸⋄, where: �x = fv(V ) Φ = � r∈˜r cr : ⟨R⋆(∆µ(r))⊸⋄⟩ Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By mutual induction on the structure of P and V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' See Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Using the above lemma we can prove our static correctness result, which explains how our decomposition induces minimal session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 (Static Correctness).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let P be a closed HO process (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' fv(P) = ∅) with �u = fn(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' If Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ◦ ∆µ ⊢ P ▷ ⋄, then G(Γσ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆σ), G(∆µσ) ⊢ D(P) ▷ ⋄, where σ = {init(�u)/�u}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Directly from the definitions, using Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' See Appendix B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 for details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 4 Dynamic Correctness In this section, we establish the dynamic correctness of our decomposition, stated in terms of a typed behavioral equivalence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' More specifically, we would like to show that any typed process P is equivalent to its decomposition D(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' But how do we even state it formally?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Both P and D(P) are typed HO processes (as any minimally typed process is also an HO process), so we can consider compare them as HO terms inside the HO type system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The conventional notion of typed equivalence for HO processes is contextual equivalence, which is given a local characterization in terms of higher-order bisimulations [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In our case, however, contextual equivalence is not the right choice: contextual equivalence applies to processes of the same type, whereas the process P and its decomposition D(P) have different types and typing contexts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Instead of using contextual equivalence, we generalize the notion of higher-order bisimilarity to a notion that we call MST bisimilarity, which relates processes of (potentially) different types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This section is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 we recall the notion of higher-order bisimulation, used for characterizing behavioral equivalence in HO, and discuss its limitations for our purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 26 We use higher-order bisimulation as a basis to give a formal definition of MST bisimulation in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2, which we will use as a notion of behavioral equivalence for comparing P and D(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In order to show that our decomposition is correct, in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 we exhibit a bisimulation relation S which relates a process and its decomposition, containing a number of intermediate pairs, working from a motivating example in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4 we show that S is indeed an MST bisimulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Behavioral Equivalence in HO and its Limitations Let us begin by recalling the notion of HO bisimulation, defined in [18] to characterize contextual equivalence of HO processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 (Definition 17 in [18]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A typed relation ℜ is an HO bisimulation if for all Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1 ℜ Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1, 1) Whenever Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1 (ν � m1) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩ �−−−−−−−−→ Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2 then there exist Q2, ∆′ 2, and Λ′ 2 such that Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1 (ν � m2) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ �========⇒ Λ′ 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 2 ⊢ Q2 where, for a fresh t, Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′′ 1 ⊢ (ν � m1)(P2 | t ←�H V1) ℜ Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′′ 2 ⊢ (ν � m2)(Q2 | t ←�H V2) 2) Whenever Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1 ℓ�−→ Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2, with ℓ not an output, then there exist Q2, Λ′ 2, and ∆′ 2 such that Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1 ˆℓ�=⇒ Λ′ 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 2 ⊢ Q2 and Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2 ℜ Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ′ 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 2 ⊢ Q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 3) The symmetric cases of 1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The largest such bisimulation is called HO bisimilarity, denoted by ≈H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' There are two points worth highlighting in this definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Firstly, the labeled transition system ℓ�−→ used in the definition of ≈H is what is called the refined transition system, different from the standard labeled transition system for the higher-order π-calculus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The idea behind the refined transition system is that we want to disallow arbitrary inputs P x(V ) �−−−→ P ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' having to consider such transitions in the definition of bisimilarity is undesirable, because it involves input of an arbitrary (higher-order) value V , making the definition very much non-local and ensuring that the bisimulations are very large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As it turns out, due to the typed nature of the system, it suffices to consider inputs of the processes of a very particular kind—characteristic values, defined based on the type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Secondly, because the inputs are restricted in the refined LTS, there is some price to pay in the handling of the outputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' If an output action P1 (ν � m1) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩ �−−−−−−−−→ P2 is matched by an output action Q1 (ν � m2) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ �========⇒ Q2, then we need to ensure that that the output processes V1 and V2 are somehow related.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We have to ensure this in the output clause, because on the receiving end transitions inputing values V1 or V2 might not even be considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To that extent, we package the values V1 or V2 in trigger processes (denoted t ←�H V1 and t ←�H V2), which are defined based on the typing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We then make them part of the processes that are considered at the “next step” of the bisimulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This notion of HO bisimilarity works for processes of the same type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For our case, we need to compare processes of different, but related types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To that extent we make several changes to the definition above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Firstly, during the decomposition a single name x in a source process is decomposed into a sequence of names x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , xk in the target process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' So in the definition of MST bisimilarity we match an action on a name x with an action on an indexed name xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Secondly, such discrepancy between names might arise in input and output values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This also needs to be considered as part of the definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For this, we need to accommodate the difference between characteristic values and trigger processes for MST and HO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the next subsection we work out the details sketched above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 27 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 MST Bisimilarity In this section we define a generalized version of HO bisimilarity allowing for comparing MST and HO process terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Our goal is to define MST bisimilarity (denoted ≈M), a typed behavioral equivalence, which we give in Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To define ≈M, we require some auxiliary definitions, in particular: A refined LTS on typed processes (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='5);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A relation ▷◁ on values (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6) and on names (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='14);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A revised notion of trigger processes (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Refined LTS and characteristic values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The idea behind defining the refined LTS is to restrict the input of arbitrary processes (values) and make the transition system image-finite (modulo names).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The refined LTS for HO is defined in [18] in three layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First comes the untyped LTS P ℓ−→ P ′, which describes reductions of untyped processes in the usual style of the LTS semantics for π-calculus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Secondly, there is a notion of the environmental LTS (Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1) ℓ−→ (Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2), which describes reductions of typing environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This LTS describes the way a typing context can evolve in accordance with its session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' On top of these layers there are notions of refined environmental LTS and refined LTS for processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The former restricts the environmental LTS to inputs on characteristic values, as we discussed in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, the refined LTS for processes restricts the untyped LTS to those actions which are supported by the refined environmental LTS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We follow this approach for defining the refined LTS for MST processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Both the untyped LTS for processes and the environmental LTS for MST processes coincides with the same LTSs for HO (or, to be more precise, with its restriction to minimal session types).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' It remains, then, to define the refined environmental LTS for MST processes, with the idea that the refined LTS restricts inputs to the inputs on minimal characteristic values and minimal trigger values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 (Minimal trigger value).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Given a value type C ⇝ ⋄ and fresh (indexed) name t1, the minimal trigger value on t1 of type G(C) ⇝ ⋄ is defined as the abstraction λ�x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' t1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y �x where �x = (x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , x|G(C)|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 (Minimal characteristic values).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let u be a name and i > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define ⟨−⟩u i and ⟨−⟩ on types as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ⟨?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (L);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S⟩u i def = ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⌜ui+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ui+|G(S)|⌝⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | ⟨L⟩x i ) ⟨S⟩ def = �s (|�s| = |G(S)|, �s fresh) ⟨!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨L⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S⟩u i def = ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟨L⟩⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⌜ui+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ui+|G(S)|⌝⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ⟨⟨L⟩⟩ def = a1 (a1 fresh) ⟨end⟩u i def = 0 ⟨C →⋄⟩ def = λ(x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , x|G(C)|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ⟨C⟩x 1 ⟨µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S⟩u i def = ⟨S{end/t}⟩u i ⟨C ⊸⋄⟩ def = λ(x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , x|G(C)|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ⟨C⟩x 1 ⟨⟨L⟩⟩u i def = u1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟨L⟩⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⌜u1⌝⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ⟨C →⋄⟩x i def = x ⟨C⟩ ⟨C ⊸⋄⟩x i def = x ⟨C⟩ where t1 is a fresh (indexed) name.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In this definition we use name-passing constructs, as outlined in Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4 (Refined environmental LTS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The refined LTS, denoted ℓ �−−→m, is defined on top of the environmental LTS using the following rules: [MTr] (Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1) ℓ−→ (Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2) ℓ ̸= n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩ (Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1) ℓ �−−→m (Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2) 28 [MRcv] (Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1) n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩ −−−−→ (Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2) (V ≡ ⟨L⟩) ∨ (V ≡ λ�x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' t1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y �x)) with t1 fresh (Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1) n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩ �−−−−→m (Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2) where λ�x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' t1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y �x) is a minimal trigger value of type G(C) (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, the refined LTS for MST processes is just a combination of the untyped LTS with the refined environmental LTS: Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='5 (Refined LTS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The environmental refined LTS extends to the typed refined LTS on processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We write Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1 ℓ �−−→m Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2 when P1 ℓ−→ P2, and (Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1) ℓ �−−→m (Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We write ℓ�=⇒m for the weak version of the transition ℓ�−→m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Notice that while the untyped LTS and the non-refined environmental LTS coincide with that of HO, the refinement that we impose on the environmental LTS is different from its HO counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Specifically in Rule [MRcv] we take special care to use minimal characteristic processes ⟨−⟩, instead of general HO characteristic process [(−)]c as defined in [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Relating trigger and characteristic values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As we mentioned earlier, the notion of bisimulation that we consider requires matching transitions of the source HO term with the transitions of the target MST term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' However, the two transitions might differ on the inputs of characteristic values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We accommodate for that difference by establishing a relation between the trigger and characteristic values of HO and MST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define the relation ▷◁ between HO processes and indexed processes inductively as: |˜x| = |G(C)| λx : C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' t?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y x ▷◁ λ˜x : G(C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' t1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y ˜x [(C ⇝ ⋄)]c ▷◁ ⟨C ⇝ ⋄⟩ where λ�x : G(C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' t1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y �x) is a minimal trigger value of type G(C) ⇝ ⋄ (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2) and [(−)]c denotes the characteristic values defined in [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We write λx : C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' t1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y x to mean that value λx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' t1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y x is of type C ⇝ ⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Trigger processes and MST bisimilarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Before we give the definition of MST bisimilarity, we establish the following notations: Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='7 (Indexed name).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Given a name n, we write ˘n to either denote n or any indexed name ni, with i > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='8 (Trigger process).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Given a value V , a trigger process for a fresh (indexed) name t1 is defined as: t1 ←�H V def = t1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V �x) where |�x| = | �C| for V : �C ⇝ ⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' If Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ V ▷ �C ⇝ ⋄, then Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, t1 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ( �C) ⊢ t1 ←�H V ▷ ⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, we are ready to formally define MST bisimilarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9 (MST Bisimilarity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A typed relation ℜ is an MST bisimulation if for all Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1 ℜ Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1, 29 1) Whenever Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1 (ν � m1) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩ �−−−−−−−−→ Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2 then there exist Q2, ∆′ 2, and Λ′ 2 such that Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1 (ν � m2) ˘n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ �========⇒m Λ′ 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 2 ⊢ Q2 where, for a fresh t, Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′′ 1 ⊢ (ν � m1)(P2 | t ←�H V1) ℜ Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′′ 2 ⊢ (ν � m2)(Q2 | ˘t ←�H V2) 2) Whenever Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1 n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V1) �−−−−→ Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2 then there exist Q2, Λ′ 2, and ∆′ 2 such that Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1 ˘n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) �====⇒m Λ′ 2, ∆′ 2 ⊢ Q2 where V1 ▷◁ V2 and Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2 ℜ Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ′ 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 2 ⊢ Q2, 3) The symmetric cases of 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The largest such bisimulation is called MST bisimilarity, denoted by ≈M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In all clauses, we use the refined LTS (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='5) and rely on notation ˘n (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the output clause, we use the triggers (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the input clause, we use the relation ▷◁ on values (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We discuss differences between MST bisimilarity and higher-order bisimilarity as defined in [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, an action in P1 must be matched by an action on an indexed name in Q1, and refined LTS actions in P1 are matched by minimal refined LTS actions in Q1 (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As a consequence of the latter, in the input case the observed values are not identical but related by ▷◁ (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In other words, whenever P1 receives a trigger or a characteristic value, then Q1 should receive their minimal counterparts (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 and Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, as names could be indexed on the right-hand side, the typing environments could differ for open processes, so the MST bisimilarity assumes different typing environments on both sides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 The Bisimulation Relation Our goal is to complement our static correctness result (Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1) by proving the following statement about the decomposition of processes (Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9): Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let P be an HO process such that Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ ⊢ P ▷ ⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We have Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P ≈M G(Γ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆) ⊢ D(P) To show that P and D(P) are MST-bisimilar, we provide a concrete bisimulation relation S that contains (P, D(P)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Defining S to be just the set of such pairs is, however, not going to work;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' instead, the relation S should also contain pairs corresponding to “intermediate” states in which the process and its decomposition may get “desynchronized”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Before we give the concrete definition of S we look at an example, illustrating the need for such intermediate pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 A Motivating Example Consider the following process: P1 = u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='v?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s : S) (u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | t s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0) | v!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 where u :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (⟨Ut⟩);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨UV ⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end and v : S with S = ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (UV ), Ut = S →⋄, and UV is some shared value type, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' UV = SV →⋄, for some session type SV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, V is some value, such that V = λy : SV .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, P1 is typed using the typing of its constituents: ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' v : S ⊢ v!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' u :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (⟨Ut⟩);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨UV ⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, v : S ⊢ u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='v?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s : S) (u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | t s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0) ▷ ⋄ ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' u :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (⟨Ut⟩);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨UV ⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, v : S, v : S ⊢ P1 ▷ ⋄ 30 P1 P2 P3 P4 P5 P6 P7 P8 u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (Vc) τ u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩ τ τ τ u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩ u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩ τ Q1 Q′ 1 Q′′ 1 Q2 Q′ 2 Q′′ 2 Q3 Q′ 3 Q′′ 3 Q4 Q′ 4 Q′′ 4 Q5 Q′ 5 Q′′ 5 Q6 Q′ 6 Q′′ 6 Q7 Q′ 7 Q′′ 7 Q8 u1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V m c ) τ τ τ τ τ u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V � V � ⟩ τ τ τ τ τ τ τ τ τ u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V � V � ⟩ u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V � V � ⟩ τ τ τ τ τ Figure 7: Transitions of P1 and Q1 = D(P1) in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The blue nodes represent processes that contain characteristic values and trigger processes induced by the bisimilarites defined in [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The decomposition of P1 is as follows: D(P1) = (ν �c) � c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B1 ϵ � P1 �� = (ν �c) � c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c11!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨t⟩ | c3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='v1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨t, x⟩ | (ν s1) (c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨t, x⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () | | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c8!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨t⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c9!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩ | c8?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t s1 | c9?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()) | c11?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='v1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c12!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c12?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () � , where �c = c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let us write Q1 for the decomposition D(P1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We wish to show P1 ≈M Q1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For this, we must exhibit a relation S included in ≈M such that (P1, D(P1)) ∈ S .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To illustrate the notions required to define the additional pairs, we consider 31 possible transitions of P1 and Q1, denoted schematically in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, let us consider a possible (refined) transition of P1, an input on u of a characteristic value: P1 u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨VC⟩ −−−−→ v?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s : S) (u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | VC s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0) | v!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 = P2 where VC = [(Ut)]c = λy : S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | x′ s′) is the characteristic value of Ut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Process Q1 can weakly match this input action on the indexed name u1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This input does not involve VC but the minimal characteristic value of type Ut (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We have: Q1 τ−→ Q′ 1 τ−→ Q′′ 1 u1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V m C ⟩ −−−−−→ (ν �c•) c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V m C ⟩ | c3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='v1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨t, x⟩ | c11!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | (ν s1) (c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨t, x⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () | | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c8!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨t⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c9!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩ | c8?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t s1 | c9?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()) | c11?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='v1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c12!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c12?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () = Q2 where V m C = ⟨Ut⟩ = λ(y1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | x′ �s′), with y1 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (S), |�s′| = |G(SV )|, and �c• = c3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hence, we should have P2 S Q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Observe that Q2 is not exactly the decomposition of P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, V m C is not the breakdown of VC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Second, V m C is not at the same position in Q2 as VC;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' the later being in the application position and the former being pushed through several propagators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Therefore, the relation S needs to (1) relate VC and V m C and (2) account for the fact that a value related to VC and thus it needs to be propagated (as in Q2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To address the first point, we establish a relation ⊠ between characteristic values and their minimal counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For the second point, we record this fact by “decomposing” the process as P2 = P ′ 2{VC/t}, and propagating the information about this substitution when computing the set of processes that are related to P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The same considerations we mentioned also apply to the value V , which is transmitted internally, via a synchronization: P2 τ−→ (ν s) (u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | VC s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0) = P3 Value V transmitted in P2 should be related to its corresponding breakdown Vϵ � V � , which should be propagated through the decomposition: Q2 τ−→ Q′ 2 τ−→ Q′′ 2 τ=⇒ (ν �c••) c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V m C , Vϵ � V � ⟩ | (ν s1) (c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨t, x⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () | | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c8!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨t⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c9!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩ | c8?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t s1 | c9?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()) | | c12!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c12?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () = Q3 where �c•• = c4, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c10, c12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, in P3 we can observe the output of V along u: P3 u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩ −−−→ (ν s) (0 | VC s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0) = P4 Process Q3 mimics this action by sending the process Vϵ � V � along name u2: Q3 u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � ⟩ =======⇒ (ν �c∗) c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V m C , Vϵ � V � ⟩ | c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () | | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t, x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c8!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨t⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c9!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩ | c8?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t s1 | c9?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()) = Q4 where �c∗ = c6, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Following the definition of higher-order bisimilarity, we should have: P4 ∥ t′ ←�H V S Q4 ∥ t′ 1 ←�H Vϵ � V � 1We use blue to denote characteristic values and trigger processes that do no occur in the original process, but which are induced by the bisimilarities defined in [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 32 for a fresh t′, where we have used ‘∥’ (rather than ‘|’) to denote process composition: we find it convenient to highlight those sub-processes in parallel that originate from trigger and characteristic processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We can see that the trigger process for V on the left-hand side should be matched with a trigger process for the breakdown of V on the right-hand side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Moreover, the definition of trigger processes should be generalized to polyadic values, as Vϵ � V � could be polyadic (see Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let us briefly consider how P4 ∥ t′ ←�H V evolves after due to the synchronization in sub-process Vc s within P4: P4 ∥ t′ ←�H V τ−→ (ν s) (s?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | x′ s′) ∥ s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0) ∥ t′ ←�H V = P6 ∥ t′ ←�H V We can see that Q4 can mimic this synchronization after a few administrative reductions on propagators: Q4 τ=⇒ (ν c9c10) c9!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � ⟩ | s1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | x′ �s′) | c9?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()) ∥ t′ 1 ←�H Vϵ � V � = Q6 ∥ t′ 1 ←�H Vϵ � V � Therefore, we need to have: P6 ∥ t′ ←�H V S Q6 ∥ t′ 1 ←�H Vϵ � V � To ensure that this pair is in S , we introduce an auxiliary relation, denoted ⋄ (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='15), which allows us to account for the sub-processes that originate from characteristic values or trigger processes (in blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We need to account for them separately, because one of them is not the decomposition of the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We thus decree: s?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | x′ s′) ⋄ s1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | x′ �s′) t′ ←�H V ⋄ t′ 1 ←�H Vϵ � V � Next, the synchronization on s in P6 is mimicked by Q6 with a synchronization on s1: P6 ∥ t ←�H V τ−→ (t!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | V s′) ∥ t′ ←�H V = P8 ∥ t′ ←�H V Q6 ∥ t′ 1 ←�H Vϵ � V � τ=⇒ (ν c10) (t1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | Vϵ � V � �s′) | c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()) = Q8 ∥ t′ 1 ←�H Vϵ � V � Finally, we can see that after the output on the trigger name t there is an application that activates R, the body of V : P8 t!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ −−→ V s′ τ−→ R{s′/y} Q8 t!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ −−→ Vϵ � V � �s′ τ−→ (ν �c∗∗) c12!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B12 ϵ � R � {�s′/�y} ≡ D(R{s′/y}) We reached the point where we relate process R{s′/y} with its decomposition D(R{s′/y}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hence, the remaining pairs in S are obtained in the same way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Key insights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We summarize some key insights from the example: A received value can either be a pure value or a characteristic value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the former case, the pure value has to be related to its decomposition, but in the later case the value should be related to an MST characteristic value of the same type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define the relation ⊠ on values to account for this (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Trigger processes mentioned in the output case of MST bisimilarity should be matched with their minimal counterparts, and the same applies to processes originating from such trigger processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The relation ⋄ accounts for this (see Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Any value in process P could have been previously received.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The definition of S takes this into account by explicitly relating processes with substitutions (see Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' That is, for P, it relates P ′{ ˜W/˜x} such that P ′{ ˜W/˜x} = P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Here, the substitution { ˜W/˜x} records values that should be propagated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 33 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 The relation S In this section we give the definition of the relation S (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='17), following the insights gathered from the example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' More specifically, we define a relation ⊠ on values, which includes the relation ▷◁ from Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6, (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='13);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' a relation ⋄ on processes, for relating characteristic and trigger processes with their MST counterparts, (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='15);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' a set C ˜ W ˜x � P � of processes correlated to a process P{ ˜W/˜x}, (Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Because we will be working extensively with indexed processes, we will use the following function, which returns a set of all valid indexing substitutions for a list of names.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 (Indexed names substitutions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let �u = (a, b, r, r, r′, r′, s, s, s′, s′, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=') be a finite tuple of names, where a, b, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' denote shared names, r, r, r′, r′, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' denote tail-recursive names , and s, s, s′, s′, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' denote linear (non tail-recursive names).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We write index(�u) to denote index(�u) = {a1, b1, r1, r1, r′ 1, r′ 1, si, si, s′ j, s′ j, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='/a, b, r, r, r′, r′, s, s, s′, s′, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' : i, j, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' > 0} Any substitution σ ∈ index(fn(P)) turns an HO process P into an indexed process Pσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Correlated values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The main ingredient in defining the relation S is the the set C ˜ W ˜x � P � , which contains processes correlated to process P with a substitution { ˜W/˜x}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The substitution, as discussed above, denotes previously received values, and we assume that fv(P) = �x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Essentially, C− − � − � computes a breakdown of P{ ˜W/˜x} in parallel with an activating trio, that mimics the original actions of P up to transitions on propagators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The activating trio propagates not the original values ˜W, but the values related to ˜W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To do that we introduce the set C− − � V � of correlated values and the relation ⊠ on values, which are defined mutually recursively in the three following definitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='11 (Broken down values).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Given a value V , the set C � V � is defined as follows: C � V � = � � C ˜ W ˜x � V ′� : V = V ′{ ˜W/˜x} and V ′ is not a variable � We extend C � − � to work on a list of values �V component-wise, that is: C � V1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , Vn � = {B1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , Bn : Bi ∈ C � Vi � for i ∈ 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This way, the elements in C � V � differ in the propagated values � W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Consider the following example: Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let V = λy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' There are four possibilities of V ′, � W, and �x such that V = V ′{ ˜W/˜x}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' That is, V = V 1{V1V2/x1x2} where V1 = λy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 V = V 2{V1/x1} where V 2 = λy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 V = V 3{V2/x2} where V 3 = λy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 Finally, we can take the identity substitution � W = ϵ and �x = ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, we have C � V � = � CV1V2 x1x2 � V 1� , CV1 x1 � V 2� , CV2 x2 � V 3� , Cϵ ϵ � V �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Given a value V , the set C ˜ W ˜x � V � , where fn(V ) = �x is defined as follows: C ˜ W ˜x � V � = � V˜x � V � { ˜B/˜x} | � W ⊠ �B � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 34 Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='13 (Relating values).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The relation ⊠ on values (with indexed names) is defined as follows: V1⊠V2 ⇐⇒ � ∃V ′ 1, σ ∈ index(fn(V ′ 1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' V1 = V ′ 1σ ∧ V ′ 1 ▷◁ V2 if V1 is a characteristic or a trigger value V2 ∈ C � V1 � otherwise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' where ▷◁ is the relation from Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, in the definition of C ˜ W ˜x � V � , the value V is related to the triggered break down values with �B substituted for �x such that � W ⊠ �B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Additionally, to define C ˜ W ˜x � − � for processes, we have to observe the behaviour of processes enclosed in the received trigger and characteristic values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, we have to observe the behaviour of trigger processes of shape t ←�H V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For this we need to define a relation ⋄ on processes that contains pairs ([(C)]x, ⟨C⟩x 1), (t?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y x, t1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y �x), (t ←�H V, t1 ←�H W) where x : C and |�x| = |G(C)| and V ⊠ W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Before we define ⋄ we need the following auxiliary definition: Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='14 (Relating names).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define ⋄ as the relation on names defined as ϵ ⋄ ϵ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ ni ▷ C ni ⋄ (ni, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ni+|G(C)|−1) ˜n ⋄ ˜m1 ni ⋄ ˜m2 ˜n, ni ⋄ ˜m1, ˜m2 where ϵ denotes the empty list.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, we are ready to relate processes, modulo indexed names (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='7), using the relation ⋄ defined as follows: Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='15 (⋄ Indexed process relation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define the relation ⋄ as [IPApp] V ⊠ W xi ⋄ ˜x V xi ⋄ W ˜x [IPPar] P ⋄ P ′ Q ⋄ Q′ P | Q ⋄ P ′ | Q′ [IPInact] 0 ⋄ 0 [IPSnd] Pσ ⋄ P ′ V σ ⊠ W σ = next(ni) ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ⋄ ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′ [IPRcv] Pσ ⋄ P ′ σ = next(ni) ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ⋄ ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′ [IPNews] P ⋄ P ′ ˜m1 ⋄ ˜m2 (ν ˜m1) P ⋄ (ν ˜m2) P ′ We can now show the property that we wanted, namely that: the bodies of trigger values and minimal trigger values (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2) are related;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' the bodies of characteristic values and minimal characteristic values (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3) are related;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' and that the trigger processes and minimal trigger processes (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='8) are related, with appropriate name substitutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We have: � ([(C)]x{xi, t1/x, t}, ⟨C⟩x i ), (t1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y x{xi/x}, t1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y �x), (t ←�H V σ, t1 ←�H W) � ⊂ ⋄ where i, j > 0, x : C, �x = (xi, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , xi+|G(C)|−1), σ ∈ index(�u), �u = fn(V ), and V σ ⊠ W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Proof (Sketch).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We may notice that ⋄ relates process up to incremented indexed names and values related by V σ ⊠ W for some σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' More precisely, free names as subject of actions are indexed and incremented accordingly in a related process, and names as objects of output actions are broken down in a related process, by V σ ▷◁ W when V σ = mi, that is mi ▷◁ ˜m where mi : C and ˜m = (mi, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , mi+|G(C)|−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For the first pair ([(C)]x{xi, t1/x, t}, ⟨C⟩x i ) by inspection of Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='7 we can observe that ⟨C⟩x i is essentially [(C)]x with its subject names indexed and incremented (starting with index i) and objects names broken down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, it is contained in ⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Similarly, (t?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y x{xi/x}, t1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y �x) is contained by observing that xi ⋄ �x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, for (t ←�H V σ, t1 ←�H W), by Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='8, V σ ⊠W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 35 Correlated processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, we can use the introduced notions to define the set C− − � − � of correlated processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As mentioned, the set C ˜ W ˜x � P � contains processes correlated to process P with a substitution { ˜W/˜x}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The definition of C− − � − � is given in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Before looking into the details, we first describe how the C− − � − � is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We introduce auxiliary notions for treating free (tail-recursive) names in processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='16 (Auxiliary Notions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let P be an HO process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We write fpn(P) to denote the set of free propagator names in P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define rfv(P) to denote free tail-recursive names in values in P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define cr(P) to denote free names of form cr in P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define rfni(P) such that r ∈ rfni(P) if and only if (ri, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , rj) ⊆ rn(P) for some i, j > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Given r : S and �r = (r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , r|G(S)|), we write R˜v to denote the process R˜v = � r∈˜v cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �r Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='17 (Relation S ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let P{ ˜W/˜x} be a well-typed process such that fn(P) ∩ fn(� W) = ∅, and let the C-set be as in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define the relation S as follows: S = �� P{ ˜W/˜x}, (ν �cr) (ν �c) R � : R ∈ C ˜ Wσ ˜x � Pσ � with �u = fn(P{ ˜W/˜x}), σ ∈ index(�u), �cr = cr(R), �c = fpn(R) � Now we describe the definition of C− − � − � in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Essentially, C− − � − � computes a breakdown of P{ ˜W/˜x} in parallel with an activating trio, that mimics the original actions of P up to transitions on propagators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This is done with the help of J − − � − � (also given in Table 3), which computes a closure of a process with respect to τ-transitions on propagators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To define the C-set we distinguish processes that do not appear in the given process, but that are composed in parallel by the clauses of MST bisimilarity (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For this we use the following notions: Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='18 (Trigger Collections).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We let H, H′ to range over trigger collections: processes of the form P1 | · · · | Pn (with n ≥ 1), where each Pi is a trigger process or a process that originates from a trigger or from a characteristic value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Example 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let H1 = t1 ←�H V | [(C)]u1 | t2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨u2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 where t1, t2, u1, u2 are channel names, V is a value, and C a channel type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, we could see that t2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨u2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 originates from a characteristic value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, H1 is a trigger collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Notice that we write P to denote a “pure” process that is not composed with a trigger collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For processes with trigger collections, the following notation is relevant: Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='19 (Process in parallel with a trigger or a characteristic process).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We write P ∥ Q to stand for P | Q where either P or Q is a trigger collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now we can describe all the cases in the definitions of the J -set and the C-set in Table 3 (Page 37).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Observe that the second and third columns in Table 3 are closely related: the third column lists side conditions for the definitions in the second column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Note that in each case we assume the substitution ρ = { ˜W/˜x}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We start with the cases for C ˜ W ˜x � P � : 36 P C ˜ W ˜x � P � Q1 ∥ Q2 � R1 ∥ R2 : R1 ∈ C ˜ W1 ˜y � Q1 � , R2 ∈ C ˜ W2 ˜w � Q2 �� �y = fv(Q1), �w = fv(Q2) { ˜W/˜x} = { ˜W1/˜y} · { ˜W2/ ˜w} (ν m : C) Q � (ν �m : G(C)) (ν ˜cm) R : R ∈ C ˜ W ˜x � Qσ �� �m = (m1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , m|G(C)|) σ = {m1m1/mm} ˜cm = (tr(C)) ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cm · cm: ϵ Q � R˜v | ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk ˜x � P � } ∪ � R˜v\\˜r | R : R ∈ J ˜ W ˜x � P � , �r = rfni(R) � � W ⊠ �B �v = rn(P{ ˜W/˜x}) H � R˜v ∥ H′ : H{ ˜W/˜x} ⋄ H′� ˜v = rn(H{ ˜W/˜x}) P J ˜ W ˜x � P � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q ¬tr(C): � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk ˜z � Qσ �� tr(C): � cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � M ˜B2 V2 � | Bk ˜w � Q � , M ˜B2 V2 �u | Bk ˜w � Q � , u[S⟩!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �u) | Bk ˜w � Q �� where: M ˜B V = λ�z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z[S⟩!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z) �y = fv(V1), �w = fv(Q) { ˜W/˜x} = { ˜W1/˜y} · { ˜W2/ ˜w} σ = next(ui) V1σ{ ˜W1/˜y} ⊠ V2, � W2 ⊠ �B2 �z = (z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , z|R⋆(S)|) �u = (u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , u|R⋆(S)|) ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q ¬tr(C): � ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �By⟩ | Bk ˜xy � Qσ �� tr(C): � cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � M ˜B y � | Bk ˜xy � Q � , M ˜B y �u | Bk ˜xy � Q � , u[S⟩?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �By⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �u) | Bk ˜xy � Q �� where: M ˜B y = λ�z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z[S⟩?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �By⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z) � W ⊠ �B σ = next(ui) �z = (z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , z|R⋆(S)|) �u = (u1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , u|R⋆(S)|) V1 (�r, ui) � |˜r|−l+1 crl!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � λ�zl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='crl+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zl+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='crn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Ql⟩ ⟩ � , λ�zl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' |˜r|−l crl+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zl+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='crn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Ql⟩ � �rl, : 1 ≤ l ≤ n, V1{ ˜W/˜x} ⊠ V2 � ∪ {V2 �r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �rn, �m : V1{ ˜W/˜x} ⊠ V2} where: Ql = V2 (�r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �rl−1, �zl, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �zn, �m) ∀ri ∈ �r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ri : Si ∧ tr(Si)∧ �zi = (zi 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , zi |R⋆(Si)|), �ri = (ri 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ri |R⋆(Si)|)) ui : C �m = (ui, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ui+|G(C)|−1) Q1 | Q2 � ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+l!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk ˜y � Q1 � | Bk+l ˜z � Q2 �� ∪� (R1 | R2) : R1 ∈ C ˜ W1 ˜y � Q1 � , R2 ∈ C ˜ W2 ˜z � Q2 �� l = �Q1�, � W1 ⊠ �B1, � W2 ⊠ �B2 �y = fv(Q1), �z = fv(Q2) { ˜W/˜x} = { ˜W1/˜y} · { ˜W2/˜z} 0 0 Table 3: The sets C ˜ W ˜x � P � and J ˜ W ˜x � P � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Parallel with a trigger collection: The C-set of Q1 ∥ Q2 is defined as: {R1 ∥ R2 : R1 ∈ C ˜ W1 ˜y � Q1 � , R2 ∈ C ˜ W2 ˜w � Q2 � } By Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='19, either Q1 or Q2 is a trigger collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Notice that a composition Q1 | Q2 37 (where both Q1 and Q2 are “pure”) is handled by J � − � , see below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We treat Q1 ∥ Q2 compositionally: we split the substitution into parts concerning Q1 and Q2, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', { ˜W/˜x} = { ˜W1/˜y} · { ˜W2/ ˜w} such that �y = fv(Q1) and �w = fv(Q2), and relate it to a parallel composition whose components come from a corresponding C-set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Restriction: The C-set of (ν m : C) Q is inductively defined as: � (ν �m : G(C)) R : (ν ˜cm) R ∈ C ˜ W ˜x � Qσ �� where σ = {m1m1/mm} and �m = (m1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , m|G(C)|) is the decomposition of m under C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The elements are processes from the C-set of Q with names �m restricted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the case when restricted name m is a tail-recursive then we also restrict the special propagator names cm and cm which appear in R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Notice that the processes of the form (ν m) (Q1 ∥ Q2), which are induced by the output clause of MST bisimilarity, are treated in this case in the definition of C � − � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Pure process: The C-set of a pure process Q is defined as follows: � R˜v | ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk ˜x � Q � : � W ⊠ �B � ∪ � R˜v\\˜r | R : R ∈ J ˜ W ˜x � Q � , �r = rfni(R) � where �v = rn(Q{ ˜W/˜x}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The elements in the first set are essentially the decomposition of Q (without restrictions of recursive propagators, which are handled in S ) up to different possibilities of values �B that are ⊠-related to � W (see Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Here, we remark that R˜v is recursive name providers for all tail-recursive names of Q and � W (by �v = rn(Q{ ˜W/˜x})).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The second set contains elements of the J -set of Q in parallel with R˜v\\˜r where �r = rfni(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='16 we can see that rfni(R) denotes tail-recursive names already gathered in R by communications that consumed R˜r : thus, we have R˜v\\˜r as providers at top level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In this sense, the processes from the second set can be seen as reducts of the processes from the first set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For example, if we examine the C-set corresponding to the process P2 from Figure 7, we note that the process Q2 belongs to the first set, and the processes Q′ 2 and Q′′ 3 belong to the second set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Trigger collection: The C-set of a trigger collection H contains its minimal counterparts, defined using the relation ⋄ (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='15): � R˜v ∥ H′ : H{ ˜W/˜x} ⋄ H′� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' where �v = rn(H{ ˜W/˜x}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In this case we do not use the information on the substitution { ˜W/˜x}, because the substitution information is needed for values that are, or were, propagated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' However, because H is a trigger collection, it will only contain propagators as part of values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The substitutions related the propagators in values are already handled by the relation ⊠, invoked by ⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As in the case with pure processes, the process R˜r is the recursive names provider for the tail-recursive names of H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We now discuss the cases for J ˜ W ˜x � P � : Output: The J -set of ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q depends on whether (i) ui is linear or shared name (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', ¬tr(ui)) or (ii) ui is a tail-recursive name (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', tr(ui)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In sub-case (i) J -set is defined as follows: � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk ˜z � Qσ � : V1σ{ ˜W1/˜y} ⊠ V2, � W2 ⊠ �B2 � where σ = next(ui).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By the definition, the substitution σ depends on whether ui is linear or shared: in the former case, we use a substitution that increments ui;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' in the latter case we use 38 an identity substitution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We split � W into � W1 and � W2, associated to the emitted value V1 and the continuation Q, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Instead of the emitted value V1 we consider values V2 that are ⊠-related to V1σ{ ˜W1/˜y}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This way, we uniformly handle cases when (i) V1 is a pure value, (ii) variable, and (iii) a characteristic value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In particular, if V1 is a pure value, the set C ˜ W1 ˜y � V1σ � is included in all the values ⊠-related to V1σ{ ˜W1/˜y}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, the propagator ck actives the next trio with the values �B2 such that � W2 ⊠ �B2: as � W2 denotes previously received values, we take a context of ⊠-related values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Again, received values could be either trigger and characteristic values (required to be observed by MST bisimilarity, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9) or pure values originated from internal actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Again, by ⊠ (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='13) we account for both cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In sub-case (ii), when ui is a tail-recursive name, the elements are as follows: � cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � M ˜B2 V2 � | Bk ˜w � Q � , M ˜B2 V2 �u | Bk ˜w � Q � , u[S⟩!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �u) | Bk ˜w � Q � : V1{ ˜W1/˜y} ⊠ V2, � W2 ⊠ �B2 � where M ˜B V = λ�z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z[S⟩!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z) The first element is a process obtained by the activation from the preceding trio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The second element is a result of a communication of the first element with top-level provider Rui (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='16) on channel cu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By this synchronization, the decomposition of recursive name u, that is �u, is gathered in application M ˜B2 V2 �u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, the third element represents the result of the application: it is a process ready to mimic the original output action on u[S⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Differently from sub-case (i), here we do not have to increment index of ui in Q and V1 as indices of recursive names are obtained based on the type S, that is [S⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Input: The J -set of ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q depends on whether (i) ui is linear or shared name (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', ¬tr(ui)) or (ii) ui is a tail-recursive name (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', tr(ui)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In both sub-cases J -set is defined similarly to the output case, with only one caveat: we need to expand the context for the continuation with a newly received value y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The J -set in sub-case (i) is defined as follows: � ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �By⟩ | Bk ˜xy � Qσ � : � W ⊠ �B � where σ = next(ui).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The J -set in sub-case (ii) is defined as follows: � cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � M ˜B y � | Bk ˜xy � Q � , M ˜B y �u | Bk ˜xy � Q � , u[S⟩?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �By⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z) | Bk ˜xy � Q � : � W ⊠ �B � where: M ˜B y = λ�z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z[S⟩?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �By⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The elements of the set represent steps of obtaining name u[S⟩, along which the original action is mimicked, by synchronizing with the top-level provider Rui, obtained in the corresponding C-set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Application: The J -set of V1 (�r, ui) where �r are tail-recursive names, is a union of two sets as follows: � |˜r|−l+1 crl!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � λ�zl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='crl+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zl+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='crn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Ql⟩ ⟩ � , (λ�zl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' |˜r|−l crl+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zl+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='crn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Ql⟩ � ) �rl : 1 ≤ l ≤ n, V1{ ˜W/˜x} ⊠ V2 � ∪ � V2 �r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �rn, �m : V1{ ˜W/˜x} ⊠ V2 � where: Ql = V2 (�r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �rl−1, �zl, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �zn, �m) 39 The first set contains intermediate processes emerging while collecting recursive names using synchronizations with recursive name providers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We can see that the body of the inner-most abstraction, Ql, is an application of V2 (such that V1{ ˜W/˜y} ⊠ V2) to partially instantiated recursive names: l denotes that decompositions of first l − 1 recursive names are retrieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The final tuple in arguments of Ql, �m = (ui, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ui+|G(C)|−1), is a full decomposition of non-recursive (linear or shared) name ui.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Just like in the previous cases, by taking V2 as a ⊠-related value to V1{ ˜W/˜y}, we uniformly handle all the three possibilities for V1 (pure value, variable, and characteristic value).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the first set, the first element is a process is ready to send an abstraction to an appropriate name provider, in order to retrieve the decomposition of l-th recursive name.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The second element is a process that results from a communication of the first element with a provider: an application which will instantiate l-th recursive name in Ql.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, the second set contains application processes in which the decompositions of all n recursive names are gathered, and it is ready to mimic the silent action (application reduction) of the original process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Parallel composition: The J -set of Q1 | Q2 is defined using two sets: � ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+l!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk ˜y � Q1 � | Bk+l ˜z � Q2 � : � W1 ⊠ �B1, � W2 ⊠ �B2 � ∪� (R1 | R2) : R1 ∈ C ˜ W1 ˜y � Q1 � , R2 ∈ C ˜ W2 ˜z � Q2 �� The first set contains a control trio that is ready to activate the decomposition of the two components in parallel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Just like in the other cases, the control trio propagates values that are ⊠-related to ˜W1 and ˜W2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In order to close the set with respect to the τ-actions on propagators, the second set contains the composition of processes drawn from the C-sets of Q1 and Q2, with appropriate substitutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4 Proving Operational Correspondence Recall that we aim to establish Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To that end, we prove that S (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='17) is an MST bisimulation, by establishing two results: Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6 covers the case in which the given process performs an action, which is matched by an action of the decomposed process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In terms of operational correspondence (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', [11]), this establishes completeness of the decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='7 covers the converse direction, in which the decomposed process performs an action, which is matched by the initial process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This established the soundness of the decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For proving both operational completeness and soundness, we will need the following result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Following Parrow [21], we refer to prefixes that do not correspond to prefixes of the original process, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' prefixes on propagators ci, as non-essential prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then the relation S is closed under reductions that involve non-essential prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Given an indexed process P1{ ˜W/˜x}, the set C ˜ W ˜x � P1 � is closed under τ-transitions on non-essential prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' That is, if R1 ∈ C ˜ W ˜x � P1 � and R1 τ−→ R2 is inferred from the actions on non-essential prefixes, then R2 ∈ C ˜ W ˜x � P1 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By the induction on the structure of P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' See Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Operational completeness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We first consider transitions using the unrestricted and untyped LTS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' in Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6 we will consider transitions with the refined LTS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 40 Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Assume P1{ ˜W/˜x} is a process such that Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1{ ˜W/˜x} ▷ ⋄ with balanced(∆1) and P1{ ˜W/˜x} S Q1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever P1{ ˜W/˜x} (ν �m1) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩ −−−−−−−−→P2 , such that n ̸∈ fn(P1{ ˜W/˜x}), then there exist Q2 and V2 such that Q1 (ν �m2) ˘n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ ========⇒Q2 and, for a fresh t, (ν �m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν �m2)(Q2 ∥ t1 ←�H V2) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever P1{ ˜W/˜x} n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V1) −−−−→P2 , such that n ̸∈ fn(P1{ ˜W/˜x}), then there exist Q2, V2, and σ such that Q1 ˘n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) ====⇒Q2 where V1σ ⊠ V2 and P2 S Q2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever P1 τ−→P2 then there exists Q2 such that Q1 τ=⇒Q2 and P2 S Q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By transition induction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' See Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The following statement builds upon the previous one to address the case of the typed LTS (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='5): Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Assume P1{ ˜W/˜x} is a process and P1{ ˜W/˜x} S Q1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1{ ˜W/˜x} (ν � m1) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩ −−−−−−−−→ Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2 then there exist Q2, V2, ∆′ 2, and Λ′ 2 such that Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1 (ν � m2) ˘n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ ========⇒ Λ′ 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 2 ⊢ Q2 and, for a fresh t, (ν � m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν � m2)(Q2 ∥ t1 ←�H V2) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1{ ˜W/˜x} n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V1) −−−−→ Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2 then there exist Q2, V2, σ, Λ′ 2, and ∆′ 2 such that Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1 ˘n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) ====⇒ Λ′ 2, ∆′ 2 ⊢ Q2 where V1σ ⊠ V2 and P2 S Q2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1{ ˜W/˜x} τ−→ Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2 then there exist Q2, Λ′ 2, and ∆′ 2 such that Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1 τ=⇒ Λ′ 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 2 ⊢ Q2 and P2 S Q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The proof uses results of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We consider the first case, the other two being similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By the definition of the typed LTS we have: Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1{ ˜W/˜x} (20) (Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1) (ν �m) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩ −−−−−−−→ (Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2) (21) By (21) we further have Γ, Γ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ ⊢ V ▷ U ∆′\\(∪j∆j) ⊆ (∆, n : S) Γ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆j ⊢ mj ▷ Uj Γ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ j ⊢ mj ▷ U ′ j n /∈ dom(∆) Λ′ ⊆ Λ [SSnd] (Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, s :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S) (ν �m) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩ −−−−−−−→ (Γ, Γ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ\\Λ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (∆, n : S, ∪j∆′ j)\\∆′) By (20) and the condition n /∈ dom(∆) we have n ̸∈ fn(P1{ ˜W/˜x}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Therefore, we can apply Item 1 of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, we are in a position to address the case of the refined typed LTS (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='5): Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Assume P1{ ˜W/˜x} is a process and P1{ ˜W/˜x} S Q1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 41 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1{ ˜W/˜x} (ν � m1) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩ �−−−−−−−−→ Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2 then there exist Q2, V2, ∆′ 2, and Λ′ 2 such that Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1 (ν � m2) ˘n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ �========⇒m Λ′ 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 2 ⊢ Q2 and, for a fresh t, (ν � m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν � m2)(Q2 ∥ t1 ←�H V2) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1{ ˜W/˜x} n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V1) �−−−−→ Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2 then there exist Q2, V2, Λ′ 2, and ∆′ 2 such that Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1 ˘n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) �====⇒m Λ′ 2, ∆′ 2 ⊢ Q2 where V1 ▷◁ V2 and P2 S Q2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1{ ˜W/˜x} τ�−→ Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2 then there exist Q2, Λ′ 2, and ∆′ 2 such that Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1 τ�=⇒m Λ′ 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 2 ⊢ Q2 and P2 S Q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By case analysis of the transition label ℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' It uses results of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We consider two cases: (i) ℓ ≡ n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V1) and (ii) ℓ ̸≡ n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (i) Case ℓ ≡ n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(V1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This case concerns Part (2) of the lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In this case we know P1 = n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We have the following transition inference tree: ⟨Rv⟩ (n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P2){ ˜W/˜x} n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V1) −−−−→ P2 (22) (22) V1 ≡ [(U)]c ∨ V1 ≡ λx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' t?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y x) t fresh ⟨RRcv⟩ (n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P2){ ˜W/˜x} n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V1) �−−−−→ P2 (23) From (22) and Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='5 we know that there exist Q2, and V2 such that Q1 ˘n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) ====⇒ Q2 and P2 S Q2 where V1σ ⊠ V2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Since V1 is a characteristic or a trigger value, we have V1 ▷◁ V2 and that V2 is a minimal characteristic or a trigger value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hence, Q1 ˘n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) �====⇒m Q2 using the Rule MTr (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Case ℓ ̸≡ n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This case concerns Parts (1) and (3) of the lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We only consider the first part, when ℓ ≡ (ν �m1) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩, since the other part is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We apply Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4 to obtain Q2 such that Q1 (ν � m2) ˘n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ �========⇒Q2, and, for a fresh t, (ν � m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν � m2)(Q2 ∥ t1 ←�H V2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Since we are dealing with an output action, we can immediately conclude that Q1 (ν � m2) ˘n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ �========⇒mQ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Operational soundness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For the proof of operational soundness we follow the same strategy of stratifying it into three lemmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Assume P1{ ˜W/˜x} is a process and P1{ ˜W/˜x} S Q1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Q1 (ν � m2) ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−−−−−→Q2 , such that ni ̸∈ fn(Q1), then there exist P2 and V2 such that P1{ ˜W/˜x} (ν � m2) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−−−−−→P2 and, for a fresh t, (ν � m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν � m2)(Q2 ∥ t1 ←�H V2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Q1 ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) −−−−→Q2 , such that ni ̸∈ fn(Q1), there exist P2, V2, and σ such that P1{ ˜W/˜x} n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V1) −−−−→P2 where V1σ ⊠ V2 and P2 S Q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 42 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Q1 τ−→ Q2 either (i) P1{ ˜W/˜x} S Q2 or (ii) there exists P2 such that P1 τ−→P2 and P2 S Q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Proof (Sketch).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By transition induction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' See Appendix C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 for more details.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Assume P1{ ˜W/˜x} is a process and P1{ ˜W/˜x} S Q1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1 (ν � m2) ˘n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−−−−−→ Λ′ 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 2 ⊢ Q2 then there exist P2, V1, ∆′ 1, and Λ′ 1 such that Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1{ ˜W/˜x} (ν � m1) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩ ========⇒ Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2 and, for a fresh t, (ν � m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν � m2)(Q2 ∥ t1 ←�H V2) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1 ˘n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) −−−−→ Λ′ 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 2 ⊢ Q2 then there exist P2, V1, σ, Λ′ 1, and ∆′ 1 such that Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1{ ˜W/˜x} n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V1) ====⇒ Λ′ 1, ∆′ 1 ⊢ P2 where V1σ ⊠ V2 and P2 S Q2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1 τ−→ Λ′ 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 2 ⊢ Q2 then there exist P2, Λ′ 1, and ∆′ 1 such that Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1{ ˜W/˜x} τ=⇒ Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2 and P2 S Q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Assume P1{ ˜W/˜x} is a process and P1{ ˜W/˜x} S Q1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1 (ν � m2) ˘n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ �−−−−−−−−→ Λ′ 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 2 ⊢ Q2 then there exist P2, V1, ∆′ 1, and Λ′ 1 such that Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1{ ˜W/˜x} (ν � m1) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩ �========⇒ Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2 and, for a fresh t, (ν � m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν � m2)(Q2 ∥ t1 ←�H V2) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1 ˘n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) �−−−−→ Λ′ 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 2 ⊢ Q2 then there exist P2, V1,Λ′ 1, and ∆′ 1 such that Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1{ ˜W/˜x} n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V1) �====⇒ Λ′ 1, ∆′ 1 ⊢ P2 where V1 ▷◁ V2 and P2 S Q2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Γ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ Q1 τ�−→ Λ′ 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 2 ⊢ Q2 then there exist P2, Λ′ 1, and ∆′ 1 such that Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1{ ˜W/˜x} τ�=⇒ Λ′ 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′ 1 ⊢ P2 and P2 S Q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Summary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Together, Lemmas 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='7 imply that S is an MST-bisimilarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In summary, we have shown Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', that for any typed process P, we have that Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P ≈M G(Γ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆) ⊢ D(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In this section we have defined a notion of MST bisimilarity, following the notion HO bisimilarity for non-minimal processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Following the strategy of Parrow in the untyped setting, we defined a relation S containing all pairs (P, D(P)), which we proved to be an MST bisimulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 5 Optimizations of the Decomposition In this section we discuss two optimizations that can be applied to the decomposition process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' These optimizations simplify the structure of the trios and the nature of the underlying communication discipline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The first optimization replaces trios in the decomposition with duos (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', processes with at most two sequential prefixes).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The decomposition in Section 3 follows Parrow’s approach in that it converts a process into a parallel composition of trios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The use of trios seems to be necessary in (plain) π-calculus;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' in our first optimization we show that, by exploiting the higher-order nature of communications in HO, the trios can be replaced by duos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The second optimization replaces polyadic communications (sending and receiving several values at once) with monadic communications (sending and receiving only a single value per prefix).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the decomposition, we use polyadic communications in order to propagate dependencies through sub-processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We show that the use of monadic communication prefixes is sufficient for that task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 43 From Trios to Duos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the first optimization we replace trios with duos, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', processes with at most two sequential prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This optimization is enabled by the higher-order nature of HO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the translation we make of thunk processes, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', inactive processes that can be activated upon reception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We write {{P}} to stand for the thunk process λx : ⟨end→⋄⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P, for a fresh x ̸∈ fn(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We write run {{P}} to denote the application of a thunk to a (dummy) name of type end→⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This way, we have a reduction run {{P}} −→ P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The key idea behind replacing trios with duos is to transform a trio like ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�z⟩ into the composition of two duos, the second one being a “control” duo: ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c0!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � {{u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�z⟩}} � | c0?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (run y) (24) The first action (on ck) is as before;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' the two remaining prefixes (on u and ck+1) are encapsulated into a thunk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This thunk is sent via an additional propagator (denoted c0) to the control duo that activates it upon reception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Because of this additional propagator, this transformation involves minor modifications in the definition of the degree function �−� (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In some cases, the breakdown function in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 already produces duos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Breaking down input and output prefixes and parallel composition involves proper trios;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' following the scheme illustrated by (24), we can define a map {|−|} to transform these trios into duos: {|ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�z⟩|} = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � {{ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�z⟩}} � | ck+1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (run y) {|ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�x′⟩|} = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � {{ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�x′⟩}} � | ck+1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (run y) {|ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+l+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�z⟩|} = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � {{ck+2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+l+2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�z⟩}} � | ck+1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (run y) In breaking down prefixes involving tail-recursive names (Table 1) we encounter trios of the following form: B � ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � Ny � | Bk+1 ˜w � Q � where Ny = λ�z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z[S⟩?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z � ) Here we can see that the top-level process is a duo and that only Ny packs a proper trio process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By applying the same idea we can translate this trio into the following composition of duos: {|z[S⟩?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z � |} = z[S⟩?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨{{ck+2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z}}⟩ | ck+1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='run y This is the idea behind the breakdown of a process starting with an input prefix;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' the breakdown of a process with an output prefix follows the same lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' From Polyadic to Monadic Communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Our second optimization replaces polyadic communications, used for the propagators, with monadic communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Recall that propagators in B � − � serve two purposes: they (i) encode sequentiality by properly activating trios and (ii) propagate bound values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By separating propagators along those two roles, we can we can dispense with polyadic communication in the breakdown function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define monadic breakdown, B � − � , and monadic decomposition, D(−), which use two kinds of propagators: (i) propagators for only activating trios of form ck (where k > 0 is an index) and (ii) for propagating bound values of form cx (where x is some variable).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We depict the mechanism of the monadic breakdown in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The main idea is to establish a direct link between trio that binds the variable x and trios that make use of x on propagator channel cx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, propagators on ck only serve to activate next trios: they do so by receiving an abstraction that contains the next trio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Formally, we define a monadic decomposition, D(P), that simplifies Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9 as follows: D(P) = (ν �c) � ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | Bk� Pσ �� where k > 0, �c = (ck, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P�−1), and the initializing substitution σ = {index(�u)/�u} is the same as in Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 44 Source process P1: P1 P2 P3 0 u :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str) u :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int) u :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩ Monadic decomposition D(P1): Q1 Q′ 1 u1 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str) ∥ Q2 Q′ 2 u2 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int) ∥ Q3 Q′ 3 u3 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨bool⟩ ∥ Q4 x : str y : int Figure 8: Our monadic decomposition function D(−), illustrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As in Figure 4, nodes represent process states, ‘∥’ represents parallel composition of processes, black arrows stand for actions, and red arrows indicate synchronizations that preserve the sequentiality of the source process;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' also, blue arrows indicates synchronizations that propagate (bound) values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Vx = λy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cx!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s) (z s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨z⟩) W ⇝ x = � cx!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � x � if ⇝=⊸ (ν s) (Vx s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vx⟩) if ⇝=→ Bk� ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x : C ⇝ ⋄).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � = (ν cx) � ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | W ⇝ x ) � | Bk+1� Qσ �� Bk� ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cx?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | Bk+1� Qσ � Bk� ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V � V σ � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | Bk+1� Qσ � Bk� x ui � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cx?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �m Bk� V ui � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='V � V � �m Bk� (ν s) P ′� = (ν �s) Bk� P ′σ � Bk� Q | R � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+�Q�+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | Bk+1� Q � | Bk+�Q�+1� R � V � y � = y V � λy : C⇝.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P � = λ(y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , y|G(C)|) : G(C)⇝.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c�P�) � c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B1� P{y1/y} �� Figure 9: Monadic breakdown of processes and values The monadic break down function Bk� − � , given in Figure 9, simplifies the one in Table 1 by using only one parameter, namely k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In Figure 9 we use σ to denote the subsequent substitution next(ui), the same as in Table 1, and use �m to denote the breakdown (ui, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ui+|G(C)|−1) of the name ui.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The breakdown function Bk� − � uses propagators ck (k > 0) for encoding sequentiality and dedicated propagators cx for each variable x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As propagators ck now only serve to encode sequentiality, only dummy values are being communicated along these channels (see Remark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let us describe the breakdown of a process with an input prefix, as it illustrates the key points common to all the other cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The breakdown Bk� ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q � consists of a trio in parallel with the breakdown of the continuation Bk+1� Qσ � with name cx restricted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The trio is first activated on ck.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This is followed by the prefix that mimics original input action on indexed name ui.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Upon receiving value x, two things will happen in parallel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, the next trio will be activated on name ck+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 45 Second, the value x received on ui is propagated further by the dedicated process W ⇝ x .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The specific mechanism of propagation depends on whether a received value is linear (⇝=⊸) or shared (⇝=→).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the former case, we simply propagate a value along the linear name cx once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the later case, we cannot propagate the value only once, because a shared variable can be used in multiple trios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, W → x implements a recursive mechanism that repeatedly sends a value on the shared name cx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The recursion is encoded in the same way as in Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4: action cx!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩ is enclosed in value V that gets appropriately duplicated upon a synchronization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The breakdown function for values, V � − � , is accordingly changed to invoke B1� − � for breaking down a function body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For simplicity, we defined the decomposition of the output process using a subprocess with four prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Alternatively, we could have used a decomposition that relies on two trios, by introducing abstraction passing as in the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let us illustrate the monadic breakdown by the means of an example: Example 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 (Monadic Decomposition).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We again consider process P = (ν u) (Q | R) as in Exam- ple 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='7 where: Q = u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q′ � �� � u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s) � x s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ � R = u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 V = λz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 Let us recall the reductions of P: P −→ u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s) � V s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ � | u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 −→ (ν s) � V s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩ � −→ (ν s) � s?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩ � = P ′ The monadic decomposition of P is as follows: D(P) = (ν c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c10) (ν u1, u2) � c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B1� Pσ �� where σ = {u1u1/uu}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We have: B1� Pσ � = c1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c8!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B2� Qσ � | B8� Rσ � where: B2� Qσ � = (ν cx) � c2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cx!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩ � | B3� Q′σ′�� B3� Q′σ′� = (ν cy) � c3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | Wy � | B4� (ν s) � x s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ ��� B4� (ν s) � x s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ �� = (ν s1) c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cx?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x s1 | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cy?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 B8� Rσ � = c8?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V � V � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c9!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B9� u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 � B9� u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 � = c9?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 V � V � = λz1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν cV 1 , cV 2 ) cV 1 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | (ν cw) cV 1 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='z1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (cV 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | Ww) | cV 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 where Wx = (ν s) (Vx s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vx⟩) with Vx = λy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cx!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s) (z s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨z⟩).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We may observe that D(P) correctly implements u1 and u2 typed with MSTs M1 and M2 (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=') as given in Example 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, we inspect the reductions of D(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First we have three reductions on propagators: D(P) −→ (ν c2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c10) (ν u1, u2) c2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c8!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B2� Qσ � | B8� Rσ � −→2 (ν c3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c7, c9, c10) (ν cx) � u1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cx!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨x⟩ � | B3� Q′σ′�� | u1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V � V � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' c9!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B9� u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 � = D1 46 Now, the synchronization on u1 can take a place in D1 (on the prefixes highlighted above).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We can see that value V � V � received on u1 can be propagated along cx to a trio using it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Following up on that, propagators c3 and c9 are synchronized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' D1 −→ (ν c3, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c7, c9, c10) (ν cx) � c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cx!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V � V � ⟩ | | (ν cy) � c3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | Wy � | B4� (ν s) � x s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ ���� | c9!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B9� u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 � −→2 (ν c4, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c7, c10) (ν cx) � cx!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V � V � ⟩ | | (ν cy) � u2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | Wy � | B4� (ν s) � x s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ ���� | u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 = D2 Similarly, D2 can mimic the synchronization on name u2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Again, this is followed by synchronizations on propagators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' D2 −→ (ν c4, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c7, c10) (ν cx) � cx!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V � V � ⟩ | (ν cy) � c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | Wy{true/y} | B4� (ν s) � x s | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ ���� | c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 −→4 (ν c7) (ν cx) � cx!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V � V � ⟩ | (ν cy) � Wy{true/y} | (ν s1) cx?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x s1 | cy?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 �� = D3 The subprocess Wy{true/y} is dedicated to providing the value true on a shared name cy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Specifically, it reduces as follow Its reductions are as follows: Wy{true/y} −→2 cy!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Wy{true/y} In this example, the shared value received on y is used only once;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' in the general case, a process could use a shared value multiple times: thus there could be multiple trios requesting the shared value on cy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' With this information, we have the following reductions of the decomposed process: D3 −→2 (ν c7) (ν cx) � cx!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V � V � ⟩ | (ν cy) � cy!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Wy{true/y} | (ν s1) cx?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x s1 | cy?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 �� = D4 In D4 a value for x is requested on name cx before it is applied to name s1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Similarly, a value for y is gathered by the communication on cy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' These values are retrieved in two reductions steps as follows: D4 −→2 (ν c7) (ν s1) V � V � s1 | s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | (ν cy) Wy{true/y} = D5 We remark that (ν cy) Wy{true/y} reduces to (ν cy) cy!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Wy{true/y} which is behaviorally equiva- lent to the inactive process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Next, the application of the value is followed by the synchronization on propagator cV 1 : D5 −→ (ν c7) (ν s1) (ν cV 1 , cV 2 ) cV 1 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | (ν cw) cV 1 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (cV 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | Ww) | cV 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()0 | s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | (ν cy) Wy{true/y} −→ (ν c7) (ν s1) (ν cV 2 ) (ν cw) s1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (cV 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | Ww) | cV 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()0 | s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨true⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | (ν cy) Wy{true/y} = D6 Here, we can see that D6 can simulate P ′, and its internal communication on the channel s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 6 Extension with Labeled Choice In this section we discuss how to extend our approach to include sessions with selection and branching – constructs which are used commonly in session types to express deterministic choices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Forgoing formal proofs, we illustrate by examples how to harness the expressive power of abstraction-passing to decompose these constructs at the process level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, we demonstrate how to break down 47 (Sel) Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, u : Sj ⊢ P ▷ ⋄ j ∈ I Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, u : ⊕{li : Si}i∈I ⊢ u ◁ lj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ▷ ⋄ (Bra) ∀i ∈ I Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, u : Si ⊢ Pi ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, u : &{li : Si}i∈I ⊢ u ▷ {li : Pi}i∈I ▷ ⋄ Figure 10: Typing rules for selection and branching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' selection and branching constructs in absence of recursion in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 we explore the interplay of recursion and labeled choice, as it requires special attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, in Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 we sketch how the operational correspondence proof can be adapted to account for branching and selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let us briefly recall the labeled choice constructs in HO, following [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' On the level of processes, selection and branching are modeled using labeled choice: P, Q ::= .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' | u ◁ l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P | u ▷ {li : Pi}i∈I The process u◁l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P selects the label l on channel u and then proceeds as P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The process u▷{li : Pi}i∈I receives a label on the channel u and proceeds with the continuation branch Pi based on the received label.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Selection and branching constructs can synchronize with each other, as represented in the operational semantics by the following reduction rule: u ◁ lj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Q | u ▷ {li : Pi}i∈I −→ Q | Pj (j ∈ I) [Sel] At the level of types, selection and branching are represented with the following types: S ::= .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' | ⊕ {li : Si}i∈I | &{li : Si}i∈I The selection type ⊕{li : Si}i∈I and the branching type &{li : Si}i∈I are used to type, respectively, the selection and branching process constructs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Note the implicit sequencing in the sessions involving selection and branching: the exchange of a label li precedes the execution of one of the stipulated protocol Si.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The typing rules for type-checking branching and selection processes are given in Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Given these process constructs and types, what are the minimal versions of the session types with labeled choice?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We do not consider branching and selection as atomic actions as their purpose is to make a choice of a stipulated protocol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In other words, it is not meaningful to type a channel with branching type in which all protocols are end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, we extend the minimal syntax types Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 with branching and selection constructs as follows: M ::= .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' | ⊕ {li : Mi}i∈I | &{li : Mi}i∈I That is, MSTs also include branching and selection types with MSTs nested in branches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Next we explain our strategy for extending the breakdown function to account for selection and branching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Breaking Down Selection and Branching Notice that in a branching process u ▷ {li : Pi}i∈I each subprocess Pi can have a different session with a different degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Abstraction-passing allows to uniformly handle these kinds of processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We extend the breakdown function in Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 to selection and branching as follows: G(&{li : Si}i∈I) = &{li :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨G(Si)⊸⋄⟩}i∈I G(⊕{li : Si}i∈I) = ⊕{li :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (G(Si)⊸⋄)}i∈I This decomposition follows the intuition that branching and selection correspond to the input and output of labels, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For example, in the case of branching, once a particular branch li 48 has been selected, we would like to input names on which to provide sessions from the branch G(Si).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In our higher-order setting, we do not input or output names directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Instead, we send out an abstraction of the continuation process, which binds those names.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' It is then the job of the (complementary) selecting process to activate that abstraction with the names we want to select.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To make this more concrete, let us consider decomposition of branching and selection at the level of processes through the following extended example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Example 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Consider a mathematical server Q that offers clients two operations: addition and negation of integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The server uses name u to implement the following session type: S = &{add : ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end � �� � Sadd , neg : ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end � �� � Sneg } The branches have session types with different lengths: one receives two integers and sends over their sum, the other has a single input of an integer followed by an output of its negation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let us consider a possible implementation for the server Q and for a client R that selects the first branch to add integers 16 and 26: Q ≜ u ▷ {add : Qadd, neg : Qneg} R ≜ u ◁ add.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨16⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨26⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (r) Qadd ≜ u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨a + b⟩ Qneg ≜ u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨−a⟩ The composed process P ≜ (ν u) (Q | R) can reduce as follows: P −→ (ν u) (u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨a + b⟩ | u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨16⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨26⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (r)) −→2 (ν u) (u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨16 + 26⟩ | u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (r)) = P ′ Let us discuss the decomposition of P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, the decomposition of S is the minimal session type M, defined as follows: M = G(S) = &{add :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ � ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int), ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int), !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩ � ⊸⋄⟩, neg :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ � ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (int), !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩ � ⊸⋄⟩} Following Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9, we decompose P as follows: D(P) = (ν c1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' c7) � c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | (ν u1) (c1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B2 ϵ � Qσ2 � | B3 ϵ � Rσ2 � ) � where σ2 = {u1u1/uu}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The breakdown of the server process Q, which implements the branching, is as follows: B2 ϵ � Qσ2 � = c2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u1 ▷ {add : u1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � λ(y1, y2, y3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν cV 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cV 4 ) cV 1 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B1 ϵ � Qadd{y1/u} � σV � �� � V � , neg : u1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � λ(y1, y2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν cW 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cW 3 ) cW 1 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B1 ϵ � Qneg{y1/u} � σW � �� � W � } where: B1 ϵ � Qadd{y1/u} � = c1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨a⟩ | c2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨a, b⟩ | c3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (a, b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨a + b⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () B1 ϵ � Qneg{y1/u} � = c1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨a⟩ | c2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨−a⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () with σV = {cV 1 , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , cV 4/c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c4} and σW = {cW 1 , cW 2 , cW 3 /c1, c2, c3}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In process B2 ϵ � Qσ2 � , name u1 implements the minimal session type M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Following the common trio structure, the first prefix awaits activation on c2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The next prefix mimics the branching action of Q on u1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, each branch consists of the output of an abstraction along u1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This output does not have a counterpart in Q;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' it is meant to synchronize with process B3 ϵ � Rσ2 � , the breakdown of the corresponding selection process (see below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 49 The abstractions sent along u1 encapsulate the breakdown of subprocesses in the two branches (Qadd and Qneg).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' An abstraction in the branch has the same structure as the breakdown of a value λy : C→.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P in Table 1: it is a composition of a control trio and the breakdown of a subprocess;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' the generated propagators are restricted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the first branch the server needs three actions to perform the session, and in the second branch the server needs to perform two actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Because of that the first abstraction binds three names y1, y2, y3, and the second abstraction binds two names y1, y2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the bodies of the abstractions we break down Qadd and Qneg, but not before adjusting the names on which the broken down processes provide the sessions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For this, we substitute u with y1 in both processes, ensuring that the broken down names are bound by the abstractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By binding decomposed names in abstractions we account for different session types of the original name in branches, while preserving typability: this way the decomposition of different branches can use (i) the same names but typed with different minimal types and (ii) a different number of names, as it is the case in this example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The decomposition of the client process R, which implements the selection, is as follows: B3 ϵ � Rσ2 � = (ν u2, u3, u4) c3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u1 ◁ add.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='z (u2, u3, u4) | B4 ϵ � u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨16⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨26⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (r) � where: B4 ϵ � u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨16⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨26⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (r) � = c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨16⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨26⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () After receiving the context on c3 (empty in this case), the selection action on u1 is mimicked;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' then, an abstraction (an encapsulation of the selected branch) is received and applied to (u2, u3, u4), which are locally bound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The intention is to use these names to connect the received abstraction and the continuation of a selection process: the subprocess encapsulated within the abstraction will use (u2, u3, u4), while the dual names (u2, u3, u4) are present in the breakdown of the continuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For simplicity, we defined B3 ϵ � Rσ2 � using a subprocess with four prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Alternatively, we could have used a decomposition that relies on two trios, by introducing abstraction passing as in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We will now examine the reductions of the decomposed process D(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, c1, c2, and c3 will synchronize.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We have D(P) −→4 D1, where D1 = (ν c4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' c7) (ν u1) � u1 ▷ {add : u1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V � , neg : u1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � W � } | (ν u2, u3, u4) (λ(y1, y2, y3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' u1 ◁ add.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='z (y1, y2, y3)) (u2, u3, u4) | B4 ϵ � u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨26⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (r) �� In D1, (u2, u3, u4) will be applied to the abstraction;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' after that, the process chooses the label add on u1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Process D1 will reduce further as D1 −→2 D2 −→2 D3, where: D2 = (ν c4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' c7) (ν u1) � u1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V � | (ν u2, u3, u4) (u1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='z (u2, u3, u4) | B4 ϵ � u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨26⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (r) � ) � D3 = (ν c4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' c7) (ν u1, u2, u3, u4) � c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='V (u2, u3, u4) | c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨16⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨26⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () � Then D3 reduces as D3 −→ D4 −→ D5, where: D4 = (ν c5 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' c7) (ν u2, u3, u4) � (ν cV 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cV 4 ) (cV 1 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cV 1 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cV 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨a⟩ | cV 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cV 3 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨a, b⟩ | cV 3 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (a, b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨a + b⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cV 4 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cV 4 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()) | u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨16⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨26⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () � D5 = (ν c5 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' c7) (ν u2, u3, u4) � (ν cV 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cV 4 ) (u2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cV 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨a⟩ | cV 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cV 3 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨a, b⟩ | cV 3 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (a, b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨a + b⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cV 4 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cV 4 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()) | u2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨16⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨26⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () � 50 Now, process D5 can mimic the original transmission of the integer 16 on channel u2 as follows: D5 −→ (ν c5 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' c7) (ν u2, u3, u4) � (ν cV 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cV 4 ) (cV 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨16⟩ | cV 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cV 3 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨a, b⟩ | cV 3 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (a, b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨a + b⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cV 4 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cV 4 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()) | c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨26⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='u4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () � = D6 Finally, process D6 reduces to D7 in three steps, as follows: D6 −→3 (ν c5 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' c7) (ν u4) � (ν cV 4 ) (u4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨16 + 26⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cV 4 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cV 4 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ()) | u4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () � = D7 Clearly, process D7 correctly simulates the synchronizations of the process P ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ◁ 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 The Interplay of Selection/Branching and Recursion Now, we discuss by example how recursive session types involving branching/selection are broken down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For simplicity, we consider recursive types without nested recursion and in which the recursive step is followed immediately by branching or selection, without any intermediate actions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' types of the following form: µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='&{li : Si}i∈I µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ⊕ {li : Si}i∈I where none of Si contain branching/selection or recursion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In this case, the decomposition of branching recursive types should be defined differently than for tail-recursive types: a type such as µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='&{li : Si}i∈I does not necessarily describe a channel with an infinite behavior, because some of the branches Si can result in termination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In such case, decomposing all actions in the type &{li : Si}i∈I as their own recursive types using the R(−) function would be incorrect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Instead, we decompose the body of the recursive type with G(−) itself: G(µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='&{li : Si}i∈I) = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='&{li :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨G(Si)⊸⋄⟩}i∈I G(µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ⊕ {li : Si}i∈I) = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ⊕ {li :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (G(Si)⊸⋄)}i∈I If some branch Si contains the recursion variable t, then it will appear in G(Si), because G(t) = t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' That is, recursion variables will appear as part of the abstraction G(Si)⊸⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' That means that the decomposition of a tail-recursive type form can produce a minimal non-tail-recursive types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, we illustrate this decomposition on the level of processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Example 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We consider a process P with a name r that is typed as follows: S = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='&{l1 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t, l2 : end}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For simplicity, we give P in HOπ (which includes HO with recursion as sub-calculus): P = R | Q R = µX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r ▷ {l1 : r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨len(t)⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='X, l2 : 0} Q = r ◁ l1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨“Hello”⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (a1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r ◁ l1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨“World”⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (a2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r ◁ l2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 That is, P contains a server R which either accepts a new request to calculate a length of a string, or to terminate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Dually, P contains a client Q, which uses the server twice before terminating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We can give an equivalent process in HO by encoding the recursion (as done in [17]): �P� = �R� | Q �R� = (ν s) (V r, s | ¯s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩) V = λ(xr, xs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' xs?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='xr ▷ {l1 : xr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='xr!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨len(t)⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν s) (y (xr, s) | s!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩), l2 : 0} 51 The decomposition of S, denoted M∗, is the following minimal session type: M∗ = G(S) = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='&{l1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str), !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩, t)⊸⋄⟩, l2 : end} As in the previous example (Example 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1), the continuation of a selected branch will be packed in an abstraction and sent over.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This abstraction binds names on which the session actions should be performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In addition, if a branch contains a recursive call, then the last argument of the abstraction will be a name on which the next instance of the recursion will be mimicked.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We illustrate this mechanism by giving the decomposition of �P� and inspecting its reductions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' D(�P�) = (ν c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c12) c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B2 ϵ � �R� � | B5 ϵ � Q � B2 ϵ � �R� � = (ν s1) (c2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Vϵ � V � (r1, s1) | c4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � ⟩) Vϵ � V � = λ(xr1, xs1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν cV 1 cV 2 ) cV 1 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cV 1 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='xs1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cV 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ | cV 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='xr1 ▷ {l1 : xr1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩, l2 : 0} W = λ(z1, z2, z3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ν cW 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cW 5 ) cW 1 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cW 1 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='z1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cW 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨t⟩ | cW 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='z2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨len(t)⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cW 3 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | (ν s1) (cW 3 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cW 4 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cW 5 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cW 4 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y (z3, s1) | cW 5 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩) B5� Q � = (ν r2 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str), r3 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩, r4 : M∗) c5?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r1 ◁ l1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y (r2, r3, r4) | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨“Hello”⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c11!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | (ν r5 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str), r6 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩, r7 : M∗) c8?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r4 ◁ l1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c12!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y (r5, r6, r7) | c9?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨“World”⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c11!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c11?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r7 ◁ l2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c12!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c12?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () In the process B5� Q � , the restricted names (r2, r3, r4) are the decomposition of the name r for the branch l1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To calculate their types, we unfold S: S = µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='&{l1 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t, l2 : end} ≡ &{l1 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t, l2 : end}{S/t} = &{l1 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S, l2 : end}, and we look at the decomposition of the type corresponding to the branch l1: G(?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S) = (?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str), !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩, M∗) Now we inspect a few reductions of D(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, we have synchronizations on c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This is followed by the application of the exchanged value Vϵ � V � to names r1, s1: D(�P�) −→∗(ν cV 1 cV 2 ) cV 1 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cV 1 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cV 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ | cV 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r1 ▷ {l1 : xr1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W⟩, l2 : 0} | s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � ⟩ | c5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | B5 ϵ � Q � = D1 Then, after synchronizations on cV 1 , s1, and cV 2 in D1 we have the following: D1 −→∗(ν c6, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c12) r1 ▷ {l1 : r1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨W{Vϵ � V � /y}⟩, l2 : 0} | (ν r2 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str), r3 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩, r4 : M∗) r1 ◁ l1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c6!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y (r2, r3, r4) | c6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨“Hello”⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c11!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | (ν r5 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str), r6 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩, r7 : M∗) c8?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r4 ◁ l1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c12!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y (r5, r6, r7) | c9?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨“World”⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c11!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c11?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r7 ◁ l2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c12!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c12?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () = D2 52 D2 can mimic a silent select action on r1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' this is followed by a reception of value W{Vϵ � V � /y} on name r1, which is then applied to names (r2, r3, r4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The resulting process is as follows: D2 −→∗(ν c8, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c12) (ν r2 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str), r3 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩, r4 : M∗) (ν cW 1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cW 5 ) cW 1 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cW 1 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r2?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cW 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨t⟩ | cW 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨len(t)⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cW 3 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | (ν s1) (cW 3 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cW 4 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cW 5 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cW 4 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='Vϵ � V � (r4, s1) | cW 5 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � ⟩) | r2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨“Hello”⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c7!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c7?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r3?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c11!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | (ν r5 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str), r6 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩, r7 : M∗) c8?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r4 ◁ l1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c12!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y (r5, r6, r7) | c9?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨“World”⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c11!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c11?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r7 ◁ l2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c12!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c12?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () = D3 The next interesting process emerges once silent actions on r are mimicked by r2 and r3: D3 −→∗(ν c8, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c12) (ν r4 : M∗) (ν s1) Vϵ � V � (r4, s1) | s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � ⟩) | (ν r5 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str), r6 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩, r7 : M∗) c8?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r4 ◁ l1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c12!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y (r5, r6, r7) | c9?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨“World”⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c11!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c11?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r7 ◁ l2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c12!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c12?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () = D4 In D4, name r4 with type M∗, is applied to the abstraction Vϵ � V � , which encapsulates a “new instance” of the recursive branch process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' After application, we obtain the following process: D4 −→∗(ν c8, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c12) (ν r4 : M∗) (ν s1) (ν cV 1 cV 2 ) cV 1 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | cV 1 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='s1?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cV 2 !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨y⟩ | cV 2 ?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r4 ▷ {l1 : r4!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩, l2 : 0} | s1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨Vϵ � V � ⟩) | (ν r5 :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (str), r6 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨int⟩, r7 : M∗) c8?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r4 ◁ l1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c12!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r4?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='y (r5, r6, r7) | c9?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r5!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨“World”⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c10!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c10?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r6?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c11!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c11?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='r7 ◁ l2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='c12!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩ | c12?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' () = D5 Thus, we can see that after few administrative reductions (on cV 1 , s1, and cV 2 ) the process is able to mimic the a next selection on r on name r4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As the process again selects l1, we can see that the next selection will occur on name r7, again typed with M∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ◁ We would like to finish this subsection with the following remark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' So far we have only considered recursive types which did not contain any actions between recursion and branching/selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' However, types with prefixed branching µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='α1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='αn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='&{li : Si}i∈I, where α1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , αn are some session prefixes, can also be accommodated in the same framework, as these types can be written equivalently without prefixed branching: α1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='αn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='&{li : Si{α1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='.αn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t/t}}i∈I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 Adapting Operational Correspondence We briefly remark on how to adapt the operational correspondence result from Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For the operational correspondence result, and the related lemmas, we must enforce additional constraints on the processes that we break down.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' These concerns arise from the following fact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' When a type &{li : Si}i∈I is broken down as G(&{li : Si}i∈I) = &{li :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨G(Si)⊸⋄⟩}i∈I, an additional action gets introduced on the level of MST processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' After performing the branching, an abstraction needs to be sent out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This additional action will be matched by a corresponding 53 abstraction-input action on the side of selection, if present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' However, this abstraction-sending action does not correspond to any action of the source process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Therefore, to show the operational correspondence between the source term and its decomposition, we need to restrict our attention to processes in which branching and selection types are both present in (matching) pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Specifically, we assume the following conditions on the source process P: P is a well-typed, that is Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ ⊢ P ▷ ⋄ with balanced(∆);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' for any name u, u ∈ fn(P) with u : S such that S involves selection or branching constructs if and only if u ∈ fn(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Intuitively, these two conditions ensure that every branching action in P has its complement (and vice-versa).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Note that for closed typeable processes both the balancedness condition and the second condition on names are vacuously true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' With this condition in place, we need to enlarge the relation S in order to account for silent actions that are introduced by the breakdown of selection and branching constructs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' That is, when matching the original silent action involving selection/branching, the corresponding broken down process need to perform several silent actions, in order to be able to mimic the process continuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 7 Related Work We draw inspiration from insights developed by Parrow [21], who showed that every process in the untyped, summation-free π-calculus with replication is weakly bisimilar to its decomposition into trios (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', P ≈ D(P)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As already mentioned, we are concerned with a different technical setting: our decomposition treats processes from a calculus without name-passing but with higher-order concurrency (abstraction-passing), supports recursive types, and can accommodate labeled choices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Our goals are different than those of Parrow [21]: for us, trios processes are a relevant instrument for defining and justifying minimal session types, but they are not an end in themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Still, we retain the definitional style and terminology for trios from [21], which are elegant and clear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Our main results connect the typability and the behaviour of a process with its decomposition, as witnessed by the static and dynamic correctness theorems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Static correctness was not considered by Parrow, as he worked in an untyped setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As for dynamic correctness, a similar result was established in [21], linking the process and its decomposition through weak bisimilarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In our setting we had to use a different, typed notion of bisimilarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' An obstacle here is that known notions of typed bisimilarity for session-typed processes, such as those given by Kouzapas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [18], only relate processes typed under the same typing environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To that extent, our notion of equivalence (MST bisimulations) is more flexible than prior related notions as it (i) relates processes typable under different environments (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', ∆ and G(∆)) and (ii) admits that actions along a name s from P can be matched by D(P) using actions along indexed names sk, for some k (and viceversa).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As mentioned in the introduction, our approach is broadly related to works that relate session types with other type systems for the π-calculus (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [16, 5, 6, 7, 9]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hence, these works target the relative expressiveness of session-typed process languages, by encoding processes between two different systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By contrast, we relate a session types system with its subsystem of minimal types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, by explaining session types in terms of themselves, our work emerges as the first study of absolute expressiveness in the context of session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In this context, works by Kobayashi [16] and Dardha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [5, 6] are worth discussing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Kobayashi [16] encoded a finite session π-calculus into a π-calculus with linear types with usages (without sequenc- ing);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' this encoding uses a continuation-passing style to codify a session name using multiple linear channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Dardha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [5, 6] formalize and extend Kobayashi’s approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' They use two separate encodings, one for processes and one for types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The encoding of processes uses a freshly generated linear name to mimic each session action;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' this fresh name becomes an additional argument in communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The encoding of types codifies sequencing in session types by nesting payload types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In contrast, we “slice” the n actions occurring in a session s : S along indexed names s1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , sn 54 with minimal session types—n slices of S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hence, Dardha et al.’s could be described as codifying sequencing in a “dynamic style”, via the freshly generated names, whereas we follow a “static style” using names that are indexed according to the corresponding session type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Recently, Jacobs [15] developed a small programming calculus with a single fork-like construct and a linear type system, which can be used to encode session-typed communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' His system can be seen as a distillation of Wadler’s GV [23] which is, in essence, a λ-calculus with session-based concurrency;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' in contrast, HO can be seen as a π-calculus in which abstractions can be exchanged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' While similar in spirit, our work and the developments by Jacobs are technically distant;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' we observe that the operational correspondences developed in [15] are strictly simpler than our dynamic correspondence result (Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1) although they are mechanized in the Coq proof assistant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, we elaborate further on our choice of HO as source language for minimal session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' HO is one of the sub-calculi of HOπ, a higher-order process calculus with recursion and both name- and abstraction-passing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The basic theory of HOπ was studied by Kouzapas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [17, 18] as a hierarchy of session-typed calculi based on relative expressiveness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Our results enable us to place HO with minimal session types firmly within this hierarchy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Still, the definition of minimal session types does not rely on having HO as source language, as they can be defined on top of other process languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In fact, in separate work we have defined minimal session types on top of the first-order sub-calculus of HOπ [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This development attests that minimal session types admit meaningful formulations independently from the kind of communicated objects (abstractions or names).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 8 Concluding Remarks We have presented a minimal formulation of session types, one of the most studied classes of behavioral types for message-passing programs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This minimal formulation forgoes sequencing on the level of types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We formally connect standard and minimal session types (MSTs), through a decomposition of session-typed processes, adopting the higher-order process calculus HO as target language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Following Parrow [21], we defined the decomposition of a process P, denoted D(P), as a collection of trio processes (processes with at most three actions) that trigger each other mimicking the sequencing in the original process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We proved that typability of P using standard session types implies the typability of D(P) with minimal session types;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' we also established that P and D(P) are behaviourally equivalent through an MST bisimulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Our results hold for all session types constructs, including labeled choices and recursive types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' From a foundational standpoint, our study of minimal session types is a conceptual contribution to the theory of behavioral types, in that we clarify the status of sequencing in theories of session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As remarked in Section 1, there are many session types variants, and their expressivity often comes at the price of an involved underlying theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Our work contributes in the opposite direction, as we identified a simple yet expressive fragment of an established session-typed framework [17, 18], which allows us to justify session types in terms of themselves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Understanding further the underlying theory of minimal session types (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', notions such as type-based compatibility) is an exciting direction for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As mentioned above, one insight derived from our results is that sequentiality in session types is convenient but not indispensable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Convenience is an important factor in the design of type systems for message-passing programs, because types are abstract specifications of communication structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By identifying sequencing as a source of redundancy, our minimal formulation of session types does not contradict or invalidate the prior work on standard session types and their extensions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' rather, it contributes to our understanding of the sources of convenience of those advanced type systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In formulating minimal session types we have committed to a specific notion of minimality, tied to sequencing constructs in types—arguably the most distinctive feature in session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' There could be other notions of minimality, unrelated to sequencing but worth exploring nevertheless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Consider, for instance, the framework of context-free session types [22], which extend standard session types by allowing sequencing of the form S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This form of sequential composition is quite powerful, and yet it could be seen as achieving a form of minimality different from the one we studied here: 55 as illustrated in [22, Section 5], context-free session types allow to describe the communication of tree-structured data while minimizing the need for channel creation and avoiding channel passing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Our work can be seen as a new twist on Parrow’s decomposition results in the untyped setting [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' While Parrow’s work indeed does not consider types, in fairness we must observe that when Parrow’s work appeared (1996) the study of types (and typed behavioral equivalences) for the π-calculus was rather incipient (for instance, the widely known formulation of binary session types, given in [12], appeared in 1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' That said, we would like to stress that our results are not merely an extension of Parrow’s work with session types, for types in our setting drastically narrow down the range of conceivable decompositions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Additionally, in this work we exploit features not supported in [21], most notably higher-order concurrency (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Section 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, from a practical standpoint, we believe that our approach paves a new avenue to the integration of session types in programming languages whose type systems lack sequencing, such as Go.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' It is natural to envision program analysis tools which, given a message-passing program that should conform to protocols specified as session types, exploit our decomposition as an intermediate step in the verification of communication correctness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Remarkably, our decomposition lends itself naturally to an implementation—in fact, we generated our examples automatically using MISTY, an associated artifact written in Haskell [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Acknowledgments We are grateful to Erik Voogd, who as a BSc student was one of the authors in the conference version of this paper [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' References [1] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Ancona, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Bono, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Bravetti, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Campos, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Castagna, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Deniélou, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Gay, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Gesbert, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Giachino, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hu, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Johnsen, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Martins, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Mascardi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Montesi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Neykova, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Ng, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Padovani, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Vasconcelos, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Yoshida.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Behavioral types in programming languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Foundations and Trends in Programming Languages, 3(2-3):95–230, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [2] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Arslanagic, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Palamariuc, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Pérez.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Minimal session types for the π-calculus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Veltri, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Benton, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Ghilezan, editors, PPDP 2021: 23rd International Symposium on Principles and Practice of Declarative Programming, Tallinn, Estonia, September 6-8, 2021, pages 12:1–12:15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ACM, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [3] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Arslanagić, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Pérez, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Voogd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Minimal Session Types (A Pearl).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In 33rd European Conference on Object-Oriented Programming, ECOOP 2019, July 15-19, 2019, London, UK, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To appear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Arslanagic, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Pérez, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Voogd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Minimal session types (artifact).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Dagstuhl Artifacts Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', 5(2):05:1–05:3, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [5] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Dardha, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Giachino, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Sangiorgi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Session types revisited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' of PPDP 2012, pages 139–150.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ACM, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [6] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Dardha, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Giachino, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Sangiorgi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Session types revisited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', 256:253–286, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [7] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Demangeon and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Honda.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Full abstraction in a subtyped pi-calculus with linear types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' of CONCUR 2011, volume 6901 of LNCS, pages 280–296.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Springer, 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [8] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Dezani-Ciancaglini and U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' de’ Liguoro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Sessions and Session Types: an Overview.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In WS-FM’09, volume 6194 of LNCS, pages 1–28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Springer, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [9] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Gay, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Gesbert, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Ravara.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Session types as generic process types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Borgström and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Crafa, editors, Proceedings Combined 21st International Workshop on Expressiveness in Concurrency and 11th Workshop on Structural Operational Semantics, EXPRESS 2014, and 56 11th Workshop on Structural Operational Semantics, SOS 2014, Rome, Italy, 1st September 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', volume 160 of EPTCS, pages 94–110, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [10] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Gay, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thiemann, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Vasconcelos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Duality of session types: The final cut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Balzer and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Padovani, editors, Proceedings of the 12th International Workshop on Programming Language Approaches to Concurrency- and Communication-cEntric Software, PLACES@ETAPS 2020, Dublin, Ireland, 26th April 2020, volume 314 of EPTCS, pages 23–33, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [11] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Gorla.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Towards a unified approach to encodability and separation results for process calculi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', 208(9):1031–1053, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [12] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Honda, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Vasconcelos, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Kubo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Language primitives and type disciplines for structured communication-based programming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In ESOP’98, volume 1381 of LNCS, pages 22–138.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Springer, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [13] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Honda, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Yoshida, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Carbone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Multiparty Asynchronous Session Types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In POPL’08, pages 273–284.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ACM, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [14] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hüttel, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Lanese, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Vasconcelos, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Caires, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Carbone, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Deniélou, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Mostrous, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Padovani, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Ravara, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Tuosto, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Vieira, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Zavattaro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Foundations of session types and behavioural contracts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ACM Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Surv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', 49(1):3, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [15] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Jacobs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A self-dual distillation of session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Ali and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Vitek, editors, 36th European Conference on Object-Oriented Programming, ECOOP 2022, June 6-10, 2022, Berlin, Germany, volume 222 of LIPIcs, pages 23:1–23:22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [16] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Kobayashi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Type systems for concurrent programs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In Formal Methods at the Crossroads, volume 2757 of LNCS, pages 439–453.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Springer, 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [17] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Kouzapas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Pérez, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Yoshida.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' On the relative expressiveness of higher-order session processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thiemann, editor, Programming Languages and Systems - 25th European Symposium on Programming, ESOP 2016, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2016, Eindhoven, The Netherlands, April 2-8, 2016, Proceedings, volume 9632 of Lecture Notes in Computer Science, pages 446–475.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Springer, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Extended version to appear in Information and Computation (Elsevier).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [18] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Kouzapas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Pérez, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Yoshida.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Characteristic bisimulation for higher-order session processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Acta Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', 54(3):271–341, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [19] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Lange, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Ng, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Toninho, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Yoshida.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' A static verification framework for message passing in go using behavioural types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Chaudron, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Crnkovic, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Chechik, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Harman, editors, Proceedings of the 40th International Conference on Software Engineering, ICSE 2018, Gothenburg, Sweden, May 27 - June 03, 2018, pages 1137–1148.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ACM, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [20] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Ng and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Yoshida.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Static deadlock detection for concurrent go by global session graph synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Zaks and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hermenegildo, editors, Proceedings of the 25th International Conference on Compiler Construction, CC 2016, Barcelona, Spain, March 12-18, 2016, pages 174–184.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ACM, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [21] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Parrow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Trios in concert.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Plotkin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Stirling, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Tofte, editors, Proof, Language, and Interaction, Essays in Honour of Robin Milner, pages 623–638.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The MIT Press, 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Online version, dated July 22, 1996, available at http://user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='uu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='se/~joachim/trios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [22] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thiemann and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Vasconcelos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Context-free session types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Garrigue, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Keller, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Sumii, editors, Proceedings of the 21st ACM SIGPLAN International Conference on 57 Functional Programming, ICFP 2016, Nara, Japan, September 18-22, 2016, pages 462–475.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ACM, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' [23] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Wadler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Propositions as sessions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thiemann and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Findler, editors, ACM SIG- PLAN International Conference on Functional Programming, ICFP’12, Copenhagen, Denmark, September 9-15, 2012, pages 273–286.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ACM, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 58 Contents 1 Introduction 1 2 The Source Language 4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Syntax and Semantics .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 Session Types for HO .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 7 3 Decomposing Session-Typed Processes 11 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Key Ideas .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 12 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 The Decomposition .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 13 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Minimal Session Types and Decomposing Types .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 14 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 Decomposing Processes .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 16 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 The Decomposition by Example .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 21 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Decomposing Processes with Non-Recursive Names .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 21 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 Decomposing Processes with Recursive Names .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 23 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4 Static Correctness .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 25 4 Dynamic Correctness 26 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Behavioral Equivalence in HO and its Limitations .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 27 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 MST Bisimilarity .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 28 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 The Bisimulation Relation .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 30 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 A Motivating Example .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 30 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 The relation S .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 34 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4 Proving Operational Correspondence .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 40 5 Optimizations of the Decomposition 43 6 Extension with Labeled Choice 47 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Breaking Down Selection and Branching .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 48 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 The Interplay of Selection/Branching and Recursion .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 51 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 Adapting Operational Correspondence .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 53 7 Related Work 54 8 Concluding Remarks 55 A Appendix to Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 60 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Auxiliary Results .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 60 B Appendix to Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4 61 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 61 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 74 C Appendix to Section 4 76 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 76 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 78 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='7 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 91 59 A Appendix to Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Auxiliary Results Remark A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We derive polyadic rules for typing HOπ as an expected extension of HO typing rules: PolyVar Γ, �x : �Ux;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �y : �Uy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �x�y : �Ux �Uy PolySess Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �u : �S ⊢ �u ▷ �S Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, u : S ⊢ P ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �x ▷ �U PolyRcv Γ \\ �x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1 \\ Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, u :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S ⊢ u?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ▷ ⋄ u : S ∈ ∆ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �x ▷ �U PolySend Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1, Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (∆ \\ u : S), u :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S ⊢ u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ⇝∈ {⊸, →} Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ V ▷ �C ⇝ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ �u ▷ �C PolyApp Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1, ∆2 ⊢ V �u Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2 ⊢ �x ▷ �C PolyAbs Γ \\ �x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 \\ ∆2 ⊢ λ�x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P ▷ �C ⊸⋄ Γ, �a : � ⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P PolyRes Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ (ν �a) P Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, �s : �S1, �s : �S2 ⊢ P �S1 dual �S2 PolyResS Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ (ν �s) P Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 (Substitution Lemma [17]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, x : S ⊢ P ▷ ⋄ and u /∈ dom(Γ, Λ, ∆) implies Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, u : S ⊢ P{u/x} ▷ ⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 (Shared environment weakening).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' If Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P ▷ ⋄ then Γ, x : C →⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P ▷ ⋄ and Γ, u : ⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P ▷ ⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 (Shared environment strengthening).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' If Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P ▷ ⋄ and x /∈ fv(P) then Γ \\ x;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P ▷ ⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' If Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P ▷ ⋄ and u /∈ fn(P) then Γ \\ u;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P ▷ ⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 60 B Appendix to Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4 We use the following auxiliary lemma: Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let �z be tuple of channel names, U a higher-order type, and S a recursive session type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' If �z : R⋆(!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S) and k = [!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S⟩ then zk : µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨G(U)⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Proof of Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let P be an indexed HO process and V be a value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' If Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ◦ ∆µ ⊢ P ▷ ⋄ then G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆), Θ ⊢ Bk ˜x � P � ▷ ⋄, where: k > 0 �r = dom(∆µ) Φ = � r∈˜r cr : ⟨R⋆(∆µ(r))⊸⋄⟩ �x = fv(P) Γ1 = Γ \\ �x dom(Θ) = {ck, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P�−1} ∪ {ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P�−1} Θ(ck) =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , Un), where (G(Γ), G(Λ))(�x) = (x1 : U1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , xn : Un) balanced(Θ) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' If Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ◦ ∆µ ⊢ V ▷ �T ⊸⋄ then G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆) ⊢ V˜x � V � ▷ G( �T)⊸⋄, where: �x = fv(V ) Φ = � r∈˜r cr : ⟨R⋆(∆µ(r))⊸⋄⟩ Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By mutual induction on the structure of P and V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Here, we analyze only Part (1) of the theorem, as Part (2) and Part (3) are proven similarly: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By assumption Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, ∆µ ⊢ P ▷ ⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' There are four cases, depending on the shape of P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We consider two representative cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We omit other cases as they are similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (a) Case P = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The only rule that can be applied here is Nil.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By inversion of this rule, we have: Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We shall then prove the following judgment: G(Γ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Θ ⊢ Bk ˜x � 0 � ▷ ⋄ (25) where �x = fv(0) = ∅ and Θ = {ck :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (end ⊸ ⋄)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Table 1: Bk ϵ � 0 � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By convention we know that ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 stands for ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 with ck :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(end→⋄).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The following tree proves this case: Nil Γ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 ▷ ⋄ ck /∈ dom(Γ) End Γ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck : end ⊢ 0 ▷ ⋄ LVar G(Γ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' y ▷ end⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ y ▷ end⊸⋄ EProm Γ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ y ▷ end⊸⋄ Prom Γ′;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ y ▷ end→⋄ Rcv G(Γ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Θ ⊢ ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ where Γ′ = G(Γ), y : end → ⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We know ck /∈ dom(Γ) since we use reserved names for propagators channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b) Case P = ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We distinguish three sub-cases: (i) ui ∈ dom(∆) and (ii) ui ∈ dom(Γ), and (iii) ui ∈ dom(∆µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We consider sub-case (i) first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For this case Rule Send can be applied: Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1, ∆µ1 ⊢ P ′ ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2, ∆µ2 ⊢ V ▷ U ui : S ∈ ∆1, ∆2 Send Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1, Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ((∆1, ∆2) \\ {ui : S}), ui :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S, ∆µ1, ∆µ2 ⊢ ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′ ▷ ⋄ (26) 61 Let �w = fv(P ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Also, let Γ′ 1 = Γ \\ �w and Θ1 be a balanced environment such that dom(Θ1) = {ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P ′�} ∪ {ck+2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P ′�} and Θ1(ck+1) =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (� M1) where � M1 = (G(Γ), G(Λ1))( �w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define: Φi = � r∈dom(∆µi) cr : ⟨R⋆(∆µi(r))⊸⋄⟩ for i ∈ {1, 2} (27) Then, by IH on the first assumption of (26) we have: G(Γ′ 1), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1), Θ1 ⊢ Bk+1 ˜z � P ′� ▷ ⋄ (28) Let �y = fv(V ) and Γ′ 2 = Γ \\ �y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, by IH (Part 2) on the second assumption of (26) we have: G(Γ), Φ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2) ⊢ V˜y � V � ▷ G(U) (29) We may notice that if U = C →⋄ then Λ2 = ∅ and ∆2 = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let �x = fv(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define Θ = Θ1, Θ′, where: Θ′ = ck :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (� M), ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M2⟩ with � M = (G(Γ), G(Λ1, Λ2))(�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6, we know �P� = �P ′� + 1, so dom(Θ) = {ck, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P�−1} ∪ {ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P�−1} By construction Θ is balanced since Θ(ck+1) dual Θ(ck+1) and Θ1 is balanced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Table 1, we have: Bk ˜x � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′� = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V˜y � V {ui+1/ui} �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Bk+1 ˜w � P ′{ui+1/ui} � We know fv(P ′) ⊆ fv(P) and fv(V ) ⊆ fv(P) that is �w ⊆ �x and �y ⊆ �x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let Γ1 = Γ \\ �x and Φ = Φ1, Φ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We shall prove the following judgment: G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(((∆1, ∆2) \\ {ui : S}), ui :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S), Θ ⊢ Bk ˜x � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′� ▷ ⋄ (30) Let σ = {ui+1/ui}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To type the left-hand side component of Bk ˜x � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′� we use some auxiliary derivations: Nil G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 ▷ ⋄ End G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 : end ⊢ 0 ▷ ⋄ PolyVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �w ▷ � M2 PolySend G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M2⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ⊢ ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ End G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M2⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, ui : end ⊢ ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (31) (29) (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1) with {˜n/˜u} G(Γ), Φ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2σ) ⊢ V˜y � V σ � ▷ G(U) (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3) with Φ1 G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2σ) ⊢ V˜y � V σ � ▷ G(U) (32) ui :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨G(U)⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ∈ G(∆2σ), ui :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨G(U)⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M2⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end (31) (32) Send G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1, Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2σ), ui :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨G(U)⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M2⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ⊢ ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V˜y � V σ �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ End G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1, Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2σ), ui :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨G(U)⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M2⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, ck : end ⊢ ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V˜y � V σ �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (33) 62 (33) PolyVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �x : � M PolyRcv G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2σ), ui :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨G(U)⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, Θ′ ⊢ ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V˜y � V σ �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (34) The following tree proves this case: (34) (28) (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1) with {˜n/˜u} G(Γ′ 1), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1σ), Θ1 ⊢ Bk+r+1 ˜w � P ′σ � ▷ ⋄ (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3) with ˜x \\ ˜w and Φ2 G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1σ), Θ1 ⊢ Bk+r+1 ˜w � P ′σ � ▷ ⋄ Par G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(((∆1, ∆2) \\ {ui : S}), ui :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S), Θ ⊢ Bk ˜x � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′� ▷ ⋄ (35) where �n = (ui+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ui+|G(S)|) and �u = (ui, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ui+|G(S)|−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes sub-case (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, we consider sub-case (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For this sub-case Rule Req can be applied: Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ u ▷ ⟨U⟩ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1, ∆µ1 ▷ P ′ ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2, ∆µ2 ⊢ V ▷ U Req Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1, ∆2, ∆µ1, ∆µ2 ⊢ u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′ ▷ ⋄ (36) Let �w = fv(P ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, let Γ′ 1 = Γ \\ �w and let Θ1, Φ1, and Φ2 be environments defined as in sub-case (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By IH on the second assumption of (36) we have: G(Γ′ 1), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1), Θ1 ⊢ Bk+1 ˜w � P ′� ▷ ⋄ (37) Let �y = fv(V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By IH on the second assumption of (26) we have: G(Γ), Φ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2) ⊢ V˜y � V � ▷ G(U) (38) Let �x = fv(P) and Γ1 = Γ \\ �x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define Θ = Θ1, Θ′, where: Θ′ = ck :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (� M), ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M2⟩ with � M = (G(Γ), G(Λ))(�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6, we know �P� = �P ′� + 1, so dom(Θ) = (ck, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P�−1) ∪ (ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P�−1) By construction Θ is balanced since Θ(ck+1) dual Θ(ck+1) and Θ1 is balanced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Table 1, we have: Bk ˜x � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′� = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V˜y � V �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Bk+1 ˜w � P ′� We know fv(P ′) ⊆ fv(P) and fv(V ) ⊆ fv(P) that is �w ⊆ �x and �y ⊆ �x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To prove G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1, ∆2), Θ ⊢ Bk ˜x � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′� we use some auxiliary derivations: Nil G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 ▷ ⋄ End G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 : end ⊢ 0 ▷ ⋄ PolyVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �w : � M2 PolySend G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M2⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ⊢ ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (39) (39) (38) (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3) with Φ1 G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2) ⊢ V˜y � V � ▷ G(U) Req G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2), ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M2⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ⊢ ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V˜y � V �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (40) 63 (40) PolyVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �x ▷ � M PolyRcv G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2), Θ′ ⊢ ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V˜y � V �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (41) The following tree proves this case: (41) (37) (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3) with ˜x \\ ˜w and Φ2 G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1), Θ1 ⊢ Bk+1 ˜w � P ′� ▷ ⋄ Par G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1, ∆2), Θ ⊢ Bk ˜x � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′� ▷ ⋄ (42) This concludes sub-case (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, we consider sub-case (iii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Here we know P = ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′ and ui : S ∈ ∆µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For this case Rule Send can be applied: Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1, ∆µ1 ⊢ P ′ ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2, ∆µ2 ⊢ V ▷ U ui : S′ ∈ ∆µ1, ∆µ2 Send Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1, Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1, ∆2, ((∆µ1, ∆µ2) \\ {ui : S′}), ui :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S′ ⊢ ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′ ▷ ⋄ (43) Let �w = fv(P ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let Θ1, Θ′, Θ, Φ1, and Φ2 be defined as in the previous sub-case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Also, let Γ′ 1 = Γ \\ �w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, by IH on the first assumption of (43) we have: G(Γ′ 1), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1), Θ1 ⊢ Bk+1 ˜w � P ′� ▷ ⋄ (44) Let Γ′ 2 = Γ \\ �y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, by IH (Part 2) on the second assumption of (43) we have: G(Γ′ 2), Φ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2) ⊢ V˜y � V � ▷ G(U) (45) By Table 1 we have: Bk ˜x � P � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � NV � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Bk+1 ˜w � P ′� where NV = λ�z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z[S⟩!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V˜y � V � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z � We notice that ui ∈ rn(V ), rn(P) since ui has tail-recursive type S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hence, by (27) we know (Φ1, Φ2)(cu) = ⟨R⋆(S) ⊸ ⋄⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, we know that S =!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨U⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S′ and by Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3, R⋆(S) = R⋆(S′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' So we define Φ = Φ1, Φ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let Γ1 = Γ \\ �x where �x = fv(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We shall prove the following judgment: G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1, ∆2), Θ ⊢ Bk ˜x � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′� ▷ ⋄ We use auxiliary derivations: LVar G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' x : R⋆(S)⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ x ▷ R⋆(S)⊸⋄ PolySess G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �z : R⋆(S) ⊢ �z ▷ R⋆(S) PolyApp G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' x : R⋆(S)⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �z : R⋆(S) ⊢ x �z ▷ ⋄ (46) (46) Sh G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ cu ▷ ⟨R⋆(S)⊸⋄⟩ LVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' x : R⋆(S)⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ x ▷ R⋆(S)⊸⋄ Acc G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Θ′, �z : R⋆(S) ⊢ cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z ▷ ⋄ (47) Nil G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 ▷ ⋄ ck+1 ̸∈ dom(Γ, Φ) End G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 : end ⊢ 0 ▷ ⋄ (48) 64 ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M2⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ∈ Θ′ (48) PolyVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �w ▷ � M2 PolySend G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M2⟩ ⊢ ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ ▷ ⋄ (49) (49) (47) Par G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M2⟩, �z : R⋆(S) ⊢ ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z ▷ ⋄ (50) (50) (44) (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2) with Φ1 G(Γ′ 2), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢V˜y � V � ▷ G(U) (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2) with ˜z G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ V˜y � V � ▷ G(U) Send G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1, Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2), �z : R⋆(S), ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M2⟩ ⊢ z[S⟩!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V˜y � V � ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z � (51) By Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 we know that if �z : R⋆(S) then z[S⟩ : µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨G(U)⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (51) PolySess G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �z : R⋆(S) ⊢ �z ▷ R⋆(S) PolyAbs G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1, Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2), ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M2⟩ ⊢ NV ▷ R⋆(S)⊸⋄ (52) LVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ cu ▷ ⟨R⋆(S)⊸⋄⟩) Nil G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 ▷ ⋄ (52) Req G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1, Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2), ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M2⟩ ⊢ cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � NV � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (53) (53) PolyVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1, Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �x ▷ � M PolyRcv G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2), Θ′ ⊢ ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � NV � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (54) The following tree proves this case: (54) (44) (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2) with Φ2 G(Γ′ 1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1), Θ1 ⊢ Bk+1 ˜w � P ′� ▷ ⋄ (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3) with ˜y G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1), Θ1 ⊢ Bk+1 ˜w � P ′� ▷ ⋄ Par G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1, ∆2), Θ ⊢ Bk ˜x � r!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′� ▷ ⋄ (55) This concludes the analysis for the output case P = ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We remark that the proof for the case when V = y is specialization of above the proof where ˜y = fv(y) = y, V˜y � y � = y and it holds that yσ = y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (c) Case P = ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We distinguish two sub-cases: (i) ui ∈ dom(∆), (ii) ui ∈ dom(Γ), and (iii) ui ∈ dom(∆µ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We consider sub-cases (i) and (ii);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' we omit sub-case (iii) as it follows the same reasoning as the corresponding sub-case of the previous (Send) case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We consider sub-case (i) first.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For this case Rule Rcv can be applied: Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′, ui : S, ∆µ ⊢ P ′ ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ y ▷ U Rcv Γ \\ y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1 \\ Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′, ui :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S, ∆µ ⊢ ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′ ▷ ⋄ (56) Let �x = fv(P) and �w = fv(P ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Also, let Γ′ 1 = Γ \\ �w and Θ1 be a balanced environment such that dom(Θ1) = {ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P ′�} ∪ {ck+2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P ′�} 65 and Θ1(ck+1) =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (� M′) where � M′ = (G(Γ), G(Λ1))( �w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define: Φ = � r∈dom(∆µ) cr : ⟨R⋆(∆µi(r))⊸⋄⟩ (57) Then, by IH on the first assumption of (56) we know: G(Γ′ 1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆′, ui : S), Θ1 ⊢ Bk+1 ˜w � P ′� ▷ ⋄ (58) By Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 and Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 and the second assumption of (56) we have: G(Γ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ y ▷ G(U) (59) We define Θ = Θ1, Θ′, where Θ′ = ck :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (� M), ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M′⟩ with � M = (G(Γ), G(Λ1 \\ Λ2))(�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='6, �P� = �P ′� + 1 so dom(Θ) = {ck, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P�−1} ∪ {ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P�−1} and Θ is balanced since Θ(ck+1) dual Θ(ck+1) and Θ1 is balanced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Table 1: Bk ˜x � ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′� = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Bk+1 ˜w � P ′{ui+1/ui} � Let Γ1 = Γ \\ �x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We shall prove the following judgment: G(Γ1 \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆′, ui :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S), Θ ⊢ Bk ˜x � ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′� The left-hand side component of Bk ˜x � ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′� is typed using some auxiliary derivations: Nil G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 ▷ ⋄ End G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 : end ⊢ 0 ▷ ⋄ PolyVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �w ▷ � M′ PolySend G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1), G(Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M′⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ⊢ ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ End G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1), G(Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M′⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, ui : end ⊢ ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (60) (60) (59) Rcv G(Γ \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1 \\ Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ui :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (G(U));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M′⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ⊢ ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ End G(Γ \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1 \\ Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ui :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (G(U));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M′⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, ck : end ⊢ ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (61) (61) PolyVar G(Γ \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �x ▷ � M PolyRcv G(Γ1 \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ui :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (G(U));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, Θ′ ⊢ ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (62) The following tree proves this case: (62) (58) (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1) with {˜n/˜u} G(Γ1 \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆′, ui+1 : S), Θ1 ⊢ Bk+1 ˜w � P ′{ui+1/ui} � ▷ ⋄ Par G(Γ1\\y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆′, ui :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S), Θ ⊢ ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Bk+1 ˜w � P ′{ui+1/ui} � ▷ ⋄ (63) 66 where �n = (ui+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ui+|G(S)|) and �u = (ui, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ui+|G(S)|−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We may notice that if y ∈ fv(P ′) then Γ′ 1 = Γ1 \\ y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' On the other hand, when y /∈ fv(P ′) then Γ′ 1 = Γ1 so we need to apply Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 with y after Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 to (58) in (63).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Note that we have used the following for the right assumption of (63): G(∆′, ui : S){˜n/˜u} = G(∆′, ui+1 : S) Bk+1 ˜w � P ′� {˜n/˜u} = Bk+1 ˜w � P ′{ui+1/ui} � This concludes sub-case (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We now consider sub-case (ii), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', ui ∈ dom(Γ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Here Rule Acc can be applied: Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ ui ▷ ⟨U⟩ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, ∆µ ⊢ P ′ ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ y ▷ U Acc Γ \\ y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1 \\ Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, ∆µ ⊢ ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′ ▷ ⋄ (64) Let �x = fv(P) and �w = fv(P ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Furthermore, let Θ1, Θ, Γ1, Γ′ 1, and Φ be defined as in sub-case (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By IH on the second assumption of (64) we have: G(Γ′ 1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆), Θ1 ⊢ Bk+1 ˜w � P ′� ▷ ⋄ (65) By Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 and Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 and the first assumption of (64) we have: G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ ui ▷ ⟨G(U)⟩ (66) By Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3, Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10, and the third assumption of (64) we have: G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ y ▷ G(U) (67) By Table 1, we have: Bk ˜x � ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′� = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Bk+1 ˜w � P ′{ui+1/ui} � (68) We shall prove the following judgment: G(Γ1 \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆), Θ ⊢ Bk ˜x � ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′� ▷ ⋄ (69) To this end, we use some auxiliary derivations: Nil G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 ▷ ⋄ End G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 : end ⊢ 0 ▷ ⋄ PolyVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �w ▷ � M′ PolySend G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M′⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ⊢ ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (70) (66) (70) (67) Acc G(Γ \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M′⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ⊢ ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ End G(Γ \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1 \\ Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M′⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end, ck : end ⊢ ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (71) (71) PolyVar G(Γ \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1 \\ Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �x ▷ � M PolyRcv G(Γ1 \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Θ′ ⊢ ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (72) The following tree proves this sub-case: (72) (65) Par G(Γ1 \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆), Θ ⊢ ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Bk+1 ˜w � P ′� ▷ ⋄ (73) 67 As in sub-case (i), we may notice that if y ∈ fv(P ′) then Γ′ 1 = Γ1 \\ y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' On the other hand, if y /∈ fv(P ′) then Γ′ 1 = Γ1 so we need to apply Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 with y to (65) in (73).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes the analysis for the input case P = ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes sub-case (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, we consider sub-case (iii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Here we know P = ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′ and ui : S ∈ ∆µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′, ∆µ, ui : S′ ⊢ P ′ ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ y ▷ U Rcv Γ \\ y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1 \\ Λ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆′, ∆µ, ui :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S′ ⊢ ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P ′ ▷ ⋄ (74) Let �w = fv(P ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let Θ1,Θ2, Θ′, and Φ be defined as in the sub-case (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Also, let Γ′ 1 = Γ \\ �w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, by IH on the first assumption of (74) we have: G(Γ′ 1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆′), Θ1 ⊢ Bk+1 ˜w � P ′� ▷ ⋄ (75) Further, by IH on the second assumption of (74) we have: G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ y ▷ G(U) (76) By Table 1 we have: Bk ˜x � P � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � Ny � | Bk+1 ˜w � P ′� where Ny = λ�z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z[S⟩?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z � Notice that ui ∈ rn(P) as tr(ui).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hence, by (57) we know Φ(cu) = ⟨R⋆(S)⊸⋄⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, we know that S =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (U);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='S′ and by Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3, R⋆(S) = R⋆(S′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let Γ1 = Γ \\ �x where �x = fv(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, we shall prove the following judgment: G(Γ1 \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆′), Θ ⊢ Bk ˜x � ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y)P ′� ▷ ⋄ We use auxiliary derivations: LVar G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' x : R⋆(S)⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ x ▷ R⋆(S)⊸⋄ PolySess G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �z : R⋆(S) ⊢ �z ▷ R⋆(S) PolyApp G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' x : R⋆(S)⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �z : R⋆(S) ⊢ x �z ▷ ⋄ (77) (77) Sh G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ cu ▷ ⟨R⋆(S)⊸⋄⟩ LVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' x : R⋆(S)⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ x ▷ R⋆(S)⊸⋄ Acc G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �z : R⋆(S) ⊢ cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z ▷ ⋄ (78) Nil G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 ▷ ⋄ ck+1 ̸∈ dom(Γ, Φ) End G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 : end ⊢ 0 ▷ ⋄ (79) ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M′⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ∈ Θ′ (79) PolyVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �w ▷ � M′ PolySend G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M′⟩ ⊢ ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ ▷ ⋄ (80) (80) (78) Par G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Θ′, �z : R⋆(S) ⊢ ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z ▷ ⋄ (81) 68 (81) (76) Rcv G(Γ \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1 \\ Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M′⟩, �z : R⋆(S) ⊢ z[S⟩?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �w⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z � (82) By Lemma B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 we know that if �z : R⋆(S) then z[S⟩ : µt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (G(U));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (51) PolySess G(Γ \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �z : R⋆(S) ⊢ �z ▷ R⋆(S) PolyAbs G(Γ \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1 \\ Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M′⟩ ⊢ Ny ▷ R⋆(S)⊸⋄ (83) LVar G(Γ \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ cu ▷ ⟨R⋆(S)⊸⋄⟩ Nil G(Γ \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 ▷ ⋄ (83) Req G(Γ \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ1 \\ Λ2);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck+1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M′⟩ ⊢ cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � Ny � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (84) (84) PolyVar G(Γ \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �x ▷ � M PolyRcv G(Γ1 \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Θ′ ⊢ ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � Ny � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (85) The following tree proves this case: (85) (75) (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3) with ˜y G(Γ1 \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆′), Θ1 ⊢ Bk+1 ˜w � P ′� ▷ ⋄ Par G(Γ1 \\ y), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆′), Θ ⊢ Bk ˜x � ui?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y)P ′� ▷ ⋄ (86) This concludes sub-case (iii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (d) Case P = V (�r, ui).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We assume a certain order in the tuple (�r, ui): names in �r have recursive session types �r = (r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , rn) : (S1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , Sn), and ui has non-recursive session type ui : C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We distinguish two sub-cases: (i) V : �SC ⊸⋄ and (ii) V : �SC →⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We will consider only sub-case (i) since the other is similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For this case Rule PolyApp can be applied: Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1, ∆µ1 ⊢ V ▷ �SC ⊸⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2, ∆µ2 ⊢ (�r, ui) ▷ �SC PolyApp Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1, ∆2, ∆µ1, ∆µ2 ⊢ V (�r, ui) (87) Let �x = fv(V ) and Γ1 \\ �x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let �x = fv(V ) and let Θ1 be a balanced environment such that dom(Θ1) = {ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�V �} ∪ {ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�V �} and Θ1(ck+1) =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (� M) and Θ1(ck+1) =!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M⟩ where � M = (G(Γ), G(Λ))(�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define: Φ1 = � r∈dom(∆µ1) cr : ⟨R⋆(∆µ1(r))⊸⋄⟩ (88) Then, by IH (Part 2) on the first assumption of (87) we have: G(Γ1), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1), Θ1 ⊢ V˜x � V � ▷ G(�SC)⊸⋄ (89) By Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 and Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 and the second assumption of (87) we have: G(Γ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2), G(∆µ2) ⊢ (�r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �rn, �m) : G(�SC) (90) 69 where �ri = (ri i, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ri i+|G(Si)|−1) for i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , n} and �m = (ui, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ui+|G(C)|−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define Φ = Φ1, Φ2 where: Φ2 = � r∈dom(∆µ2) cr : ⟨R⋆(∆µ2(r))⊸⋄⟩ We define Θ = Θ1, ck :?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (� M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We will first consider the case where n = 3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' the proof is then generalized for any n ≥ 1: If n = 3 then P = V (r1, r2, r3, ui).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Table 1 we have: Bk ˜x � V (r1, r2, r3, ui) � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(˜x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cr1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�z1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cr2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�z2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cr3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�z3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 where Q = V˜x � V � (�z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �zn, �m);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �zi = (zi 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , zi |G(Si)|) for i = {1, 2, 3};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �m = (ui, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ui+|G(C)|−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We shall prove the following judgment: G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1∆2), Θ ⊢ Bk ˜x � V (�r, ui) � ▷ ⋄ (91) We use auxiliary derivations: (89) (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2) with Φ2 G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1), Θ1 ⊢ V˜x � V � ▷ G(�SC)⊸⋄ (92) (90) (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1) with σ G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2), G(∆µ2) ⊢ (�z1, �z2, �z3, �m) ▷ G(�SC) (93) (92) (93) PolyApp G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1, ∆2), Θ1, G(∆µ2) ⊢ V˜x � V � (�z1, �z2, �z3, �m) (94) where σ = {�n1/�z1} · {�n2/�z2} · {�n3/�z3} with �ni = (ri i, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ri i+|G(Si)|−1) for i = {1, 2, 3}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (94) PolySess G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �z3 : G(S3) ⊢ �z3 ▷ G(S3) PolyAbs G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1∆2), Θ1 ⊢ λ�z3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q ▷ G(S3)⊸⋄ (95) (95) Nil G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 LVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ cr3 ▷ ⟨G(S3)⊸⋄⟩ Req G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1∆2), Θ1, �z1 : G(S1), �z2 : G(S2) ⊢ cr3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�z3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (96) (96) PolySess G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �z2 : G(S2) ⊢ �z2 ▷ G(S2) PolyAbs G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1∆2), Θ1, �z1 : G(S1) ⊢ λ�z2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cr3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�z3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ G(S2)⊸⋄ (97) (97) Nil G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 LVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ cr2 ▷ ⟨G(S2)⊸⋄⟩ Req G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1∆2), Θ1, �z1 : G(S1) ⊢ cr2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�z2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cr3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�z3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (98) (98) PolySess G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �z1 : G(S1) ⊢ �z1 ▷ G(S1) PolyAbs G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1∆2), Θ1 ⊢ λ�z1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cr2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�z2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cr3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�z3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ G(S1)⊸⋄ (99) 70 (99) Nil G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 LVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ cr1 ▷ ⟨G(S1)⊸⋄⟩ Req G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1∆2), Θ1 ⊢ cr1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�z1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cr2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�z2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' cr3!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�z3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 (100) The following tree proves this case: (100) PolyVar G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �x ▷ � M PolyRcv G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1, ∆2), Θ ⊢ Bk ˜x � V (�r, ui) � ▷ ⋄ Now we consider the general case for any n ≥ 1: By Table 1 we have: Bk ˜x � V �r � = ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' n=|�r| cr1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�z1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' crn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟩ where Q = V˜x � V � (�r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �rn, �m) with: �zi = (zi 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , zi |G(Si)|) for i = {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , n};' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' and �m = (ui, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ui+|G(C)|−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We shall prove the following judgment: G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1∆2), Θ ⊢ Bk ˜x � V (�r, ui) � ▷ ⋄ (101) We construct auxiliary derivations parametrized by k and denoted by d(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' If k = n, derivation d(n) is defined as: (89) (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2) with Φ2 G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1), Θ1 ⊢ V˜x � V � ▷ G(�SC)→⋄ (102) (102) (90) (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1) with σ G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆µ2) ⊢ (�r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �rn, �m) ▷ G(�SC) PolyAbs G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1, ∆2), Θ1, G(∆µ2) ⊢ λ�zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q ▷ G(Sn)⊸⋄ (103) where σ = � i∈{1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=',n}{�ni/�zi} with �ni = (ri i, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ri i+|G(Si)|−1) for i = {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (103) Nil G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 LVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ crn ▷ ⟨G(Sn)⊸⋄⟩ Req G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1, ∆2), Θ1, G(∆µ2) ⊢ crn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 (104) Otherwise, if k ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=', n − 1}, derivation d(k) is as follows: d(k + 1) PolyVar G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �zk : G(Sk) ⊢ �zk ▷ G(Sk) PolyAbs G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1, ∆2), Θ1, (�z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �zk−1) : (G(S1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , G(Sk−1)) ⊢ λ�zk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' n−k crk+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zk+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' crn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q n−k ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷G(S1)⊸⋄ (105) (105) G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ cr1 ▷ ⟨G(S1)⊸⋄⟩ Acc G(Γ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1, ∆2), Θ1, (�z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �zk−1) : (G(S1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , G(Sk−1)) ⊢ n−k+1 crk!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' crn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q n−k+1 ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 (106) The following tree proves this case: d(1) PolyVar G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �x ▷ � M PolyRcv G(Γ1), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1, ∆2), Θ ⊢ Bk ˜x � V (�r, ui) � ▷ ⋄ 71 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This part concerns values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Without a los of generality we assume �T = �S, C with �S = (S1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , Sn) such that tr(Si) for i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We can distinguish two sub-cases: (i) V = y and (ii) V = λ�y, z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We first consider sub-case (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By assumption Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ y ▷ C ⇝ ⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, we can distinguish two sub-sub-cases (a) ⇝=⊸ and (b) ⇝=→.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In sub-sub-case (a), when ⇝=⊸, only Rule LVar can be applied and by inversion Λ = {y : �T ⊸ ⋄} and ∆ = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Table 1 we have V˜x � y � = y and by Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 and Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 we have G(∆) = {G( �T ⊸⋄)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hence, we prove the following judgment by applying Rule LVar: G(Γ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ V˜x � y � ▷ G( �T ⊸⋄) In sub-sub-case (b) only Rule Sh can be applied and by inversion we have Γ = {y : �T →⋄}, Λ = ∅, and ∆ = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Similarly to (a), by Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 and Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 we have G(Γ) = {G( �T →⋄)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hence, we prove the following judgment by applying Rule SH: G(Γ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ V˜x � y � ▷ G( �T →⋄) This concludes sub-case (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, we consider sub-case (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This is the second sub-case concerning values when V = λ�y, z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P where �y = y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , yn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By assumption we have Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, ∆µ ⊢ V ▷ �S, C ⇝ ⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Here we distinguish two sub-sub-cases (a) ⇝=⊸ and (b) ⇝=→: ⇝=⊸.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By assumption, Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆, ∆µ ⊢ V ▷ �S, C ⊸⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In this case Rule Abs can be applied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Firstly, we α-convert value V as follows: V ≡α λ�y, z1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P{z1/z} (107) For this case only Rule Abs can be applied: Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1, ∆µ1 ⊢ P{z1/z} ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆2, ∆µ2 ⊢ �y, z1 ▷ �S, C Abs Γ \\ z1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 \\ ∆2, ∆µ1 \\ ∆µ2 ⊢ λ�y, z1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P{z1/z} ▷ �S, C ⊸⋄ (108) Let �x = fv(P) and Γ1 = Γ \\ �x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Also, let Θ1 be a balanced environment such that dom(Θ1) = {c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c�P�} ∪ {c2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c�P�} and Θ1(c1) =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (� M);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end with � M = (G(Γ \\ y1), G(Λ))(�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define: Φi = � r∈dom(∆µi) cr : ⟨R⋆(∆µi(r))⊸⋄⟩ for i ∈ {1, 2} Then, by IH (Part 1) on the first assumption of (108) we have: G(Γ1), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1), Θ1 ⊢ B1 ˜x � P{y1/y} � ▷ ⋄ (109) Let �T = G(S1), .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , G(Sn), G(C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 and Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 and the second assumption of (108) we have: G(Γ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆2) ⊢ �y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �yn, �z ▷ �T (110) where �z = (z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , z|G(C)|) and �yi = (yi 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , yi |G(Si)|)) for i ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define Θ = Θ1, ck :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Table 1, we have: V˜x � λy1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , yn, z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P � = λ( �y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , � yn, �z) : ( �T) ⇝.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' N 72 where N = (ν �c) (ν �cr) � i∈|�y| (cyi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �yi) | c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�x⟩ | B1 ˜x � P{z1/z} � with �c = (c1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , c�P�) and �cr = � r∈˜y cr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We use an auxiliary derivation: Nil G(Γ), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ 0 ▷ ⋄ End G(Γ), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck : end ⊢ 0 ▷ ⋄ PolyVar G(Γ), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ �x ▷ � M Send G(Γ), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' c1 :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨� M⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ⊢ c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�x⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 ▷ ⋄ (111) LVar G(Γ), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' x : R⋆(∆µ2(yi))⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ x ▷ R⋆(∆µ2(yi))⊸⋄ (112) (112) PolySess G(Γ), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �yi : R⋆(∆µ2(yi)) ⊢ �yi ▷ R⋆(∆µ2(yi)) PolyApp G(Γ), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' x : R⋆(∆µ2(yi))⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �yi : R⋆(∆µ2(yi)) ⊢ (b �yi) (113) (113) Sh G(Γ), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ cyi▷ ⟨R⋆(∆µ(yi))⊸⋄⟩ LVar G(Γ), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' x : R⋆(∆µ(yi))⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ x ▷ R⋆(∆µ(yi))⊸⋄ Acc G(Γσ), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �yi : R⋆(∆µ1(yi)) ⊢ cyi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �yi (114) for yi ∈ �y (114) Par (|�y| − 1 times) G(Γ), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1), G(∆µ2) ⊢ � i∈|�y|(cyi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �yi) ▷ ⋄ (115) (115) (111) (109) (Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2) with ˜x G(Γ), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1), Θ1 ⊢ B1 ˜x � P{z1/z} � ▷ ⋄ Par G(Γ), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1), Θ ⊢ c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�x⟩ | B1 ˜x � P{z1/z} � ▷ ⋄ G(Γ), Φ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1), G(∆µ2), Θ ⊢ � i∈|�y|(cyi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �yi) | c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�x⟩ | B1 ˜x � P{z1/z} � ▷ ⋄ PolyRes G(Γ), Φ1 \\ Φ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1), G(∆µ2), Θ ⊢ (ν �cr) � i∈|�y|(cyi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �yi) | c1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨�x⟩ | B1 ˜x � P{z1/z} � ▷ ⋄ PolyResS G(Γ), Φ1 \\ Φ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1), G(∆µ2) ⊢ N ▷ ⋄ (116) The following tree proves this part: (116) (110) Abs G(Γ \\ z1), Φ1 \\ Φ2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(Λ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆1 \\ ∆2) ⊢ λ( �y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , � yn, �z) : ( �T)⊸.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' N ▷ ⋄ (117) ⇝=→.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By assumption, Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ V ▷ C →⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In this case Rule Prom can be applied: Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ P{y1/y} ▷ ⋄ Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ⊢ y1 ▷ C Abs Γ \\ z1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ λ�y, z1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P{z1/z} ▷ C ⊸⋄ Prom Γ \\ z1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ λ�y, z1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P{z1/z} ▷ C →⋄ (118) 73 Now, we can see that we can specialize previous sub-case by taking ∆1 \\ ∆2 = ∅ (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆µ1 \\ ∆µ2 = ∅), that is ∆1 = ∆2 (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆µ1 = ∆µ2) and Λ = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Subsequently, we have Φ1 \\ Φ2 = ∅, G(Λ) = ∅, and G(∆1 \\ ∆2) = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, we can apply Rule Prom to (117) to prove this sub-case as follows: (117) Prom G(Γ \\ z1);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ λ( �y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , � yn, �z) : ( �T)→.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' N ▷ ⋄ This concludes this part (and the proof).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 Proof of Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 (Static Correctness).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let P be a closed HO process (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' fv(P) = ∅) with �u = fn(P).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' If Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ◦ ∆µ ⊢ P ▷ ⋄, then G(Γσ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆σ), G(∆µσ) ⊢ D(P) ▷ ⋄, where σ = {init(�u)/�u}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By assumption Γ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆ ◦ ∆µ ⊢ P ▷ ⋄.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, by applying Lemma A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 we have: Γσ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆σ ◦ ∆µσ ⊢ Pσ ▷ ⋄ (119) By Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 on (119) we have: G(Γ1σ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆σ), Θ ⊢ Bk ϵ � Pσ � ▷ ⋄ (120) where Θ is balanced with dom(Θ) = {ck, ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P�−1}∪{ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P�−1}, and Θ(ck) =?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (·), and Φ = � r∈dom(∆µ) cr : ⟨R⋆(∆µ(r))⊸⋄⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By assumption, fv(P) = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='9, we shall prove the following judgment: G(Γσ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆σ) ◦ G(∆µσ) ⊢ (ν �c) (ν �cr) � � r∈˜v cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �r | ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Bk ϵ � Pσ �� where: k > 0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �v = rn(P);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �r = (r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , r|G(S)|) for each r ∈ �v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We know dom(∆µ) = �v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We assume that recursive session types are unfolded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 and Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3, for r ∈ dom(∆µ) we have: G(∆µ)(r) = R(∆µ(r)) = R⋆(∆µ(r)) We use a family of auxiliary derivations parametrized by r ∈ �v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' LVar G(Γσ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' x : R⋆(∆µ(r))⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ x ▷ R⋆(∆µ(r))⊸⋄ PolySess G(Γσ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �r : R⋆(∆µ(r)) ⊢ �r ▷ R⋆(∆µ(r)) PolyApp G(Γσ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' x : R⋆(∆µ(r))⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �r : R⋆(∆µ(r)) ⊢ (x �r) (121) (121) Sh G(Γσ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ cr▷ ⟨R⋆(∆µ(r))⊸⋄⟩ LVar G(Γσ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' x : R⋆(∆µ(r))⊸⋄;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅ ⊢ x ▷ R⋆(∆µ(r))⊸⋄ Acc G(Γσ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �r : R⋆(∆µ(r)) ⊢ cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �r (122) We will then use: for r ∈ �v (122) Par (|�v| − 1 times) G(Γσ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆µσ) ⊢ � r∈˜v cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �r (123) 74 where we apply Rule Par |�v| − 1 times and for every r ∈ �v we apply derivation (122).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Notice that by Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 and Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 we have G(∆µσ) = � r∈˜v �r : R⋆(∆µ(r)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Sess G(Γσ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ck :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨·⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ⊢ ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 (120) Par G(Γσ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆σ), Θ, ck :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨·⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ⊢ ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Bk ϵ � Pσ � (124) The following tree proves this case: (123) (124) Par G(Γσ), Φ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆σ), Θ, ck :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨·⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ◦ G(∆µσ) ⊢ � r∈˜v(cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �r) | ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Bk ϵ � Pσ � PolyRes G(Γσ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆σ), Θ, ck :!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨·⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='end ◦ G(∆µσ) ⊢ (ν �cr) (� r∈˜v(cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z) | ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Bk ϵ � Pσ � ) PolyResS G(Γσ);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∅;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' G(∆σ) ◦ G(∆µσ) ⊢ (ν �c) (ν �cr) (� r∈˜v(cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �r) | ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 | Bk ϵ � Pσ � ) (125) 75 C Appendix to Section 4 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Given an indexed process P1{ ˜W/˜x}, the set C ˜ W ˜x � P1 � is closed under τ-transitions on non-essential prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' That is, if R1 ∈ C ˜ W ˜x � P1 � and R1 τ−→ R2 is inferred from the actions on non-essential prefixes, then R2 ∈ C ˜ W ˜x � P1 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By the induction on the structure of P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We consider two base cases: Case P1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let �B such that � W⊠ �B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, the elements of C ˜ W ˜x � 0 � are R1 = (ν ck) ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | ck?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (�x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='0 and R2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Clearly, R1 τ−→ R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Case P1 = V1 (�r, u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let n = |�r|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, we have C ˜ W ˜x � P1 � = N1 ∪ N4 ∪ � ∪1≤l≤n Nl 2 � ∪ � ∪1≤l≤n−1 Nl 3 � where N1 = {R˜v,˜r | ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk ˜x � P1 � : � W ⊠ �B} Nl 2 = {R˜v,rl,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=',rn | |˜r|−l+1 crl!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � λ�zl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='crl+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zl+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='crn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' QV2 l ⟩ ⟩ � : V1{ ˜W/˜x} ⊠ V2} Nl 3 = {R˜v,rl+1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=',rn | λ�zl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' |˜r|−l crl+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zl+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='crn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' QV2 l ⟩ � �rl : V1{ ˜W/˜x} ⊠ V2} N4 = {R˜v | V2 (�r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �rn, �m) : V1{ ˜W/˜x} ⊠ V2} with QV2 l = V2 (�r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �rl−1, �zl, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �zn, �m) We can see that for R1 ∈ N1 there exist R0 2 ∈ N0 2 such that R1 τ−→ R0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, we could see that for Rl 2 ∈ Nl 2 there is Rl 3 ∈ Nl 3 such that Rl 2 τ−→ Rl 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, we can see that for Rl 3 ∈ Nl 3 there is Rl+1 2 ∈ Nl+1 2 such that Rl 3 τ−→ Rl+1 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, we have for Rn 3 ∈ Nn 3 = {R˜v | λ�zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' QV2 n �rn : V1{ ˜W/˜x} ⊠ V2} there is R4 ∈ N4 such that Rn 3 τ−→ R4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We consider two inductive cases as remaining cases are similar: Case P1 = ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We distinguish two sub-case: (i) ¬tr(ui) and (ii) tr(ui).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In both sub- cases, we distinguish two kinds of an object value V1: (a) V1 ≡ x, such that {Vx/x} ∈ { ˜W/˜x} and (b) V1 = λy : C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P ′, that is V1 is a pure abstraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, we consider sub-case (i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let �y = fv(V1), �w = fv(P2), � W1, and � W2 such that {� W/�x} = {� W1/�y} · {� W2/ �w}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, let �v = rn(P1{ ˜W/˜x}) and σ = {ui+1/ui}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, by the definition of C− − � − � (Table 3), we have that C ˜ W ˜x � ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P2 � = N1 ∪ N2 where: N1 = {R˜v | ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk ˜x � P1 � : � W ⊠ �B} N2 = {R˜v | ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk2 ˜w � P2σ � : V1σ{� W1/�y} ⊠ V2, � W2 ⊠ �B2} We can see that in both cases of V1, a variable or a pure abstraction, we have that for R1 ∈ N1 there is R2 ∈ N2 such that R1 τ−→ R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the sub-case (a) by {Vx/x} ∈ { ˜W/˜x} we have V2 ∈ �B, 76 such that Vx ⊠ V2, that by τ-move substitutes x in Bk ˜x � P1 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, by xσ{ ˜W1/˜y} = Vx we have V1σ{ ˜W1/˜y} ⊠ V2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the sub-case (b), by definition of B− − � − � we have that by τ-move �B1 ⊆ �B substitute �y in V˜y � V1σ � so we have R1 τ−→ R2 where V2 = V˜y � V1σ � { ˜B1/˜y} Now, we may notice that by Table 3 we have V2 ∈ C ˜ W1 ˜y � V1σ � Hence, by Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='11 and Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='13 we have V1σ{ ˜W1/˜y} ⊠ V2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, we may notice that there is no τ-transition involving non-essential prefixes in R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes this sub-case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, we consider sub-case (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let �y = fv(V1), �w = fv(P2), � W1, and � W2 such that {� W/�x} = {� W1/�y} · {� W2/ �w}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, we have C ˜ W ˜x � P1 � = N1 ∪ N2 ∪ N3 ∪ N4 where N1 = {R˜v | ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk ˜x � P1 � : � W ⊠ �B} N2 = {R˜v | cu!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � M ˜B2 V2 � | Bk ˜w � P2 � : V1{ ˜W1/˜y} ⊠ V2, � W2 ⊠ �B2} N3 = {R˜v\\u | M ˜B2 V2 �u | Bk ˜w � Q � : V1{ ˜W1/˜y} ⊠ V2, � W2 ⊠ �B2} N4 = {R˜v\\u | u[S⟩!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b �u) | Bk ˜w � P2 � : V1{ ˜W1/˜y} ⊠ V2, � W2 ⊠ �B2} where M ˜B2 V2 = λ�z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z[S⟩!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | cu?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b �z) As in the previous sub-case, we can see that in both cases of V1, a variable or a pure abstraction, we have that for R1 ∈ N1 there is R2 ∈ N2 such that R1 τ−→ R2, for appropriate choice of �B, �B2, and k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Similarly, by the communication on shared name cu for R2 ∈ N2 there is R3 ∈ N3 such that R2 τ−→ R3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, for R3 ∈ N3 there is R4 ∈ N4 such that R3 τ−→ R4 by the application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes output case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Case P1 = Q1 | Q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let �y = fv(Q1), �w = fv(Q2), � W1, and � W2 such that {� W/�x} = { ˜W1/˜y} · { ˜W2/ ˜w}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, by the definition of C− − � − � (Table 3), we have that C ˜ W ˜x � Q1 | Q2 � = N1∪N2∪N3 where: N1 = {ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk ˜x � Q1 | Q2 � : � W ⊠ �B} N2 = {ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+l!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk ˜y � Q1 � | Bk+l ˜w � Q2 � : � W1 ⊠ �B1, � W2 ⊠ �B2} N3 = {R1 | R2 : R1 ∈ C ˜ W1 ˜y � Q1 � , R2 ∈ C ˜ W2 ˜w � Q2 � } with l = �Q1�.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We show that the thesis holds for processes in each of these three sets: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Clearly, by picking appropriate �B, �B1, and �B2, for any R1 1 ∈ N1 there is R1 2 such that R1 1 τ−→ R1 2 and R1 2 ∈ N2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, we consider set N3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let us pick R3 = R1 | R2 ∈ N3, for some R1 ∈ C ˜ W1 ˜y � Q1 � and R2 ∈ C ˜ W2 ˜w � Q2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By the definition of C− − � − � (Table 3) we know all propagator names are restricted element-wise in R3, and so there is no communication between R1 and R2 on propagator prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This ensures that any τ-actions emanating from R3 arise from R1 or R2 separately, not from their interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The thesis then follows by IH, for we know that if R1 τ−→ R′ 1 then R′ 1 ∈ C ˜ W1 ˜y � Q1 � ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' similarly, if R2 τ−→ R′ 2 then R′ 2 ∈ C ˜ W2 ˜w � Q2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, by the definition R′ 1 | R′ 2 ∈ N3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 77 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, we show that for any R2 ∈ N2 if R2 τ−→ R′ 2 then R′ 2 ∈ C ˜ W ˜x � Q1 | Q2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We know that R2 = ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+l!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk ˜y � Q1 � | Bk+l ˜w � Q2 � , where �Bi are such that � Wi ⊠ �Bi for i ∈ {1, 2}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Clearly, by a synchronization on ck, we have R2 τ−→ ck+l!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | BQ1 | Bk+l ˜w � Q2 � = R′ 2 where BQ1 stands for the derivative of Bk ˜y � Q1 � after the synchronization (and substitution of �B1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' To show that R′ 2 is already in C ˜ W ˜x � Q1 | Q2 � , we consider an R3 ∈ N3 such that R3 = ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B1⟩ | Bk ˜y � Q1 � | ck+l!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk+l ˜w � Q2 � Note that there is a τ-transition on ck such that R3 τ−→ R′ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Because processes in N3 satisfy the thesis (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' the previous sub-sub-case), we have that R′ 2 ∈ N3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Therefore, R′ 2 ∈ C ˜ W ˜x � Q1 | Q2 � , as desired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes parallel composition case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4 For the proof we will use the following syntactic sugar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Definition C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='1 (Function �C− − � − � ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let P be a HO process, ρ be a values substitution, and σ be an indexed name substitution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We define �Cρ σ � P � as follows: �Cρ σ � P1 � = C ˜ Wσ ˜x � P1σ � with ρ = { ˜W/˜x} Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Assume P1{ ˜W/˜x} is a process such that Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1{ ˜W/˜x} ▷ ⋄ with balanced(∆1) and P1{ ˜W/˜x} S Q1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever P1{ ˜W/˜x} (ν �m1) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩ −−−−−−−−→P2 , such that n ̸∈ fn(P1{ ˜W/˜x}), then there exist Q2 and V2 such that Q1 (ν �m2) ˘n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ ========⇒Q2 and, for a fresh t, (ν �m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν �m2)(Q2 ∥ t1 ←�H V2) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever P1{ ˜W/˜x} n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V1) −−−−→P2 , such that n ̸∈ fn(P1{ ˜W/˜x}), then there exist Q2, V2, and σ such that Q1 ˘n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) ====⇒Q2 where V1σ ⊠ V2 and P2 S Q2, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever P1 τ−→P2 then there exists Q2 such that Q1 τ=⇒Q2 and P2 S Q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By transition induction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let ρ1 = { ˜W/˜x}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By inversion of P1ρ1 S Q1 we know there is σ1 ∈ index(fn(Pρ1)) such that Q1 ∈ �Cρ1 σ1 � P1 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, we need the following assertion on the index substitution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' If P1ρ1 ℓ−→ P2ρ2 and subj(ℓ) = n such that ¬tr(n) then there exists Q2 such that Q1 ˘ℓ=⇒ Q2 with subj(˘ℓ) = ni and Q2 ∈ �Cρ2 σ2 � P2 � such that σ2 ∈ index(P2ρ2) and next(ni) ∈ σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, we consider three base cases: Rules Snd, Rv, and App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, we distinguish five inductive cases and analyze three cases (as cases ParR and ParL, and New and Res are similar).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, in total we consider six cases: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Case ⟨Snd⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then P1 = n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We first consider the case when P1 is not a trigger collection, and then briefly discuss the case when it is a trigger collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We distinguish two sub-cases: (i) ¬tr(n) and (ii) tr(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In both sub-cases, we distinguish two kinds of an object value V1: (a) V1 ≡ x, such that {Vx/x} ∈ { ˜W/˜x} and (b) V1 = λy : C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P ′, that is V1 is a pure abstraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Next, we consider two sub-cases: 78 i) Sub-case ¬tr(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let � W1, � W2, �y, and �w such that P1{ ˜W/˜x} = n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1{ ˜W1/˜y}⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P2{ ˜W2/ ˜w} We have the following transition: ⟨Snd⟩ P1{ ˜W/˜x} n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1{ ˜W1/˜y}⟩ −−−−−−−−−→ P2{ ˜W2/ ˜w} Let σ1 ∈ index(�u) where �u = fn(P1{ ˜W/˜x}) such that {ni/n} ∈ σ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Also, let σ2 = σ1 · next(ni).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, let �v = rn(P1{ ˜W/˜x}), �cr = ∪r∈˜vcr, �ck = (ck, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P1�−1), and �ck+1 = (ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P1�−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' When P1 is not a trigger, by the definition of S (Table 3), for both sub-cases, we have Q1 ∈ N1 ∪ N2 where: N1 = � (ν �cr) (ν �ck) R˜v | ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk ˜x � P1σ1 � : � W ⊠ �B � N2 = � (ν �cr) (ν �ck+1) R˜v | ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk+1 ˜w � P2σ2 � : V1σ{� W1/�y} ⊠ V2, � W2 ⊠ �B2 � If Q1 ∈ N1, then there is some Q2 ∈ N2 such that Q1 reduces to Q2 through communication on non-essential prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 it is then sufficient to consider the situation when Q2 ∈ N2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let �v1 = rn(P2{ ˜W2/˜z}), �v2 = rn(V2{ ˜W1/˜y}), �cr1 = ∪r∈˜v1cr, and �cr2 = ∪r∈˜v2cr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='16 and the assumption that P1{ ˜W/˜x} is well-typed we have �cr = �cr1 · �cr2 and �cr1 ∩ �cr2 = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In that case we have the following transition: ⟨Snd⟩ ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−→ ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ ⟨ParL⟩ ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk+1 ˜w � P2σ2 � ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−→ R1 ⟨ParR⟩ R˜v | ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk+1 ˜w � P2σ2 � ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−→ R1 �cr · �ck+1 ∩ fn(ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩) = ∅ ⟨New⟩ (ν �cr) (ν �ck+1) (R˜v | ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk+1 ˜z � P2σ2 � ) (ν �cr2) ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−−−−−→ Q′ 2 (126) where Q′ 2 = (ν �cr1) (ν �ck+1) R˜v | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk+1 ˜w � P2σ2 � with V1{ ˜W1/˜y}σ2 ⊠ V2 and � W2σ1 ⊠ �B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, we shall show the following: (P2 ∥ t ←�H V1){ ˜W/˜x} S (ν �cr2) (Q′ 2 ∥ t1 ←�H V2) (127) By assumption that P1{ ˜W/˜x} is well-typed, we know �v = �v1 · �v2 and �v1 ∩ �v2 = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, by Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='16 we know R˜v = R˜v1 | R˜v2, that is (ν �cr2) (Q′ 2 ∥ t1 ←�H V2) ≡ (ν �cr1) (ν �cr2) (ν �ck+1)(R˜v1 | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk+1 ˜w � P2σ1 � | R˜v2 ∥ t1 ←�H V2) ≡ (ν �cr) (ν �ck+1)(R˜v1 | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk+1 ˜w � P2σ1 � | R˜v2 ∥ t1 ←�H V2) = (ν �cr) (ν �ck+1) R From the definition of S (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='17) we have that n ̸∈ fn(� W2) and thus � W2σ1 = � W2σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, by the definition of �B2 (� W2σ2 ⊠ �B2) we can see that R˜v1 | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk+1 ˜w � P2σ1 � | R˜v2 ∈ C ˜ W2σ2 ˜w � P2σ2 � (128) 79 Now, we can see that assertion next(ni) ∈ σ2 holds, as by definition σ2 = σ1 · next(ni).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let σ′ 2 = σ2 · {t1/t}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' we have C ˜ W1σ′ 2 ˜y � t1 ←�H V1σ2 � = {P ′ : (t1 ←�H V1){ ˜W1/˜y}σ2 ⋄ P ′} As (t1 ←�H V1){ ˜W1/˜y}σ2 = t1 ←�H V1{ ˜W1/˜y}σ2 and V1{ ˜W1/˜y}σ2 ⊠ V2 we have (t1 ←�H V1){ ˜W1/˜y}σ2 ⋄ (t1 ←�H V2) (129) that is R˜v2 ∥ t1 ←�H V2 ∈ C ˜ W1σ′ 2 ˜y � t1 ←�H V1σ2 � Finally,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' by Table 3 we have C ˜ Wσ′ 2 ˜x � P2σ2 ∥ t1 ←�H V1σ2 � = � R1 ∥ R2 : R1 ∈ C ˜ W2σ′ 2 ˜w � P2σ2 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' R2 ∈ C ˜ W1σ′ 2 ˜y � t1 ←�H V1σ2 �� So,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' by this,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (128),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' and (129) we have: R ∈ C ˜ Wσ′ 2 ˜x � P2σ′ 2 ∥ t1 ←�H V1σ2 � Further,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' by σ′ 2 = σ1 · next(ni) · {tj/t} and Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10, we have σ′ 2 ∈ index(fn((P2 ∥ t ←�H V1){ ˜W/˜x})) Hence, the goal (127) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes sub-case ¬tr(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ii) Sub-case tr(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let � W1, � W2, �y, and �w be such that P1{ ˜W/˜x} = n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1{ ˜W1/˜y}⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P2{ ˜W2/ ˜w} The transition inference tree is as follows: ⟨Snd⟩ P1{ ˜W/˜x} n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1{ ˜W1/˜y}⟩ −−−−−−−−−→ P2{ ˜W2/ ˜w} Let σ1 ∈ index(�u) where �u = fn(P1{ ˜W/˜x}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Also, let �v = rn(P1), �cr = ∪r∈˜vcr, �ck = (ck, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P1�−1), �ck+1 = (ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P1�−1), and let S be such that n : S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, by the definition of S (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='17) we have Q1 ∈ N1 ∪ N2 ∪ N3 ∪ N4 where N1 = {(ν �cr) (ν �ck) R˜v | ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk ˜x � P1σ1 � : � Wσ1 ⊠ �B} N2 = {(ν �cr) (ν �ck+1) R˜v | cn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � M ˜B2 V2 � | Bk+1 ˜w � P2σ1 � : � W2σ1 ⊠ �B2} N3 = {(ν �cr) (ν �ck+1) R˜v | M ˜B2 V2 �n | Bk+1 ˜w � P2σ1 � : V1{ ˜W1/˜y}σ1 ⊠ V2, � W2σ1 ⊠ �B2} N4 = � (ν �cr) (ν �ck+1) R˜v\\n | n[S⟩!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | cn?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z | Bk+1 ˜w � P2σ1 � : V1{ ˜W1/˜y}σ1 ⊠ V2, � W2σ1 ⊠ �B2 � with M ˜B2 V2 = λ�z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z[S⟩!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � V2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | cn?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z � If Q1 ∈ N1 ∪ N2 ∪ N3, then Q1 reduces to some Q4 ∈ N4 through communication on non-essential prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 it suffices to consider the case when Q4 ∈ N4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let �v1 = rn(P2), �v2 = rn(V2), �cr1 = ∪r∈˜v1cr, and �cr2 = ∪r∈˜v2cr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='16 and the 80 assumption that P1{ ˜W/˜x} is well-typed we have �cr = �cr1 · �cr2 and �cr1 ∩ �cr2 = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We then infer the following transition: Q4 (ν �cr2) n[S⟩!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−−−−−−−→ Q′ 4 where Q′ 4 = (ν �cr1) (ν �ck+1) R˜v\\n | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | cn?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b �n) | Bk+1 ˜w � P2σ1 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, we shall show the following (P2 ∥ t ←�H V1){ ˜W/˜x} S (ν �cr2) � Q′ 4 ∥ t1 ←�H V2 � (130) By assumption that P1{ ˜W/˜x} is well-typed, we know �v = �v1 · �v2 and �v1 ∩ �v2 = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hence, by Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='16 we know R˜v = R˜v1 | R˜v2, that is Q′ 4 ≡ (ν �cr1) (ν �ck+1) R˜v\\n | cn?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �n | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk+1 ˜w � P2σ1 � = (ν �cr1) (ν �ck+1) R˜v | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk+1 ˜w � P2σ1 � = (ν �cr1) (ν �ck+1) R˜v1 | R˜v2 | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk+1 ˜w � P2σ1 � That is, we have (ν �cr2) � Q′ 4 ∥ t1 ←�H V2 � ≡ (ν �cr2) � (ν �cr1) (ν �ck+1) R˜v1 | R˜v2 | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk+1 ˜w � P2σ1 � ∥ t1 ←�H V2 � ≡ (ν �cr1) (ν �cr2) (ν �ck+1)(R˜v1 | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk+1 ˜w � P2σ1 � | R˜v2 ∥ t1 ←�H V2) ≡ (ν �cr) (ν �ck+1)(R˜v1 | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk+1 ˜w � P2σ1 � | R˜v2 ∥ t1 ←�H V2) = (ν �cr) (ν �ck+1) R Now, by Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='8 we may notice that �v2 = rn(t ←�H V2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let σ′ 1 = σ1 · {t1/t}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' So, by Table 3 we have R˜v1 | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk+1 ˜w � P2σ1 � ∈ C ˜ W2σ1 ˜w � P2σ1 � and R˜v2 ∥ t1 ←�H V2 ∈ C ˜ W1σ1 ˜y � t1 ←�H V1σ′ 1 � (131) Thus, by the definition of the parallel composition case of C− − � − � (Table 3) we have R ∈ C ˜ Wσ′ 1 ˜x � (P2 ∥ t ←�H V1)σ′ 1 � Now, we can notice that �cr = cr(R) and �ck+1 = fpn(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, we have σ′ 1 ∈ index(fn((P2 ∥ t ←�H V1){ ˜W/˜x})) Thus, (130) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes sub-case tr(n) of case ⟨Snd⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Finally, we briefly analyze the case when P1 is a trigger collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let σ1 be defined as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let H′ 1 be such that P1{ ˜W/˜x}σ1 ⋄ H′ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, by Table 3, Q1 is as follows: Q1 = R˜v ∥ H′ 1 where �v = rn(P1{ ˜W/˜x}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, by Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='15 we know H′ 1 = ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='H′ 2 such that V1{ ˜W1/˜y}σ2 ⊠ V2 and P2{ ˜W2/ ˜w}σ2 ⋄ H′ 2 with σ2 = σ1 · next(ni).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We can see that H′ 1 ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−→ H′ 2 81 So, we should show (P2 ∥ t ←�H V1){ ˜W/˜x} S (R˜v ∥ H′ 2 | t1 ←�H V2) (132) Similarly to previous sub-cases, we have R˜v ∥ H′ 2 | t1 ←�H V2 ≡ R˜v1 ∥ H′ 2 ∥ R˜v2 ∥ t1 ←�H V2 By P2{ ˜W2/ ˜w}σ2 ⋄ H′ 2 and �v1 = rn(P2{ ˜W2/ ˜w}) we have R˜v1 ∥ H′ 2 ∈ C ˜ W2σ2 ˜w � P2σ2 � (133) Let σ′ 2 = σ2 · {t1/t}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By (133), (131), and definition of C− − � − � (Table 3) for the parallel composition case we have R˜v1 ∥ H′ 2 ∥ R˜v2 ∥ t1 ←�H V2 ∈ C ˜ Wσ′ 2 ˜x � P2 ∥ t ←�H V1 � Thus, we reach goal (132).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes case ⟨Snd⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Case ⟨Rv⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In this case we know P1 = n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We first consider cases when P1 is not a trigger collection, and then briefly discuss the case when it is a trigger collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As in the previous case, we distinguish two sub-cases: (i) ¬tr(n) and (ii) tr(n): i) Sub-case ¬tr(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We have the following transition: ⟨Rv⟩ (ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P2){ ˜W/˜x} n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V1) −−−−→ P2{ ˜W/˜x}{V1/y} Here we assume y ∈ fv(P2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let σ1 ∈ index(�u) with �u = fn(P1{ ˜W/˜x}) such that {ni/n} ∈ σ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Also, let σ2 = σ1 · next(ni).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, let �v = rn(P1{ ˜W/˜x}), �cr = ∪r∈˜vcr, �ck = (ck, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P1�−1), and �ck+1 = (ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P1�−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By the definition of S (Table 3) we have Q1 ∈ N1 ∪ N2 where N1 = � (ν �cr) (ν �ck) R˜v | ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk ˜x � P1σ1 � : � Wσ1 ⊠ �B � N2 = � (ν �cr) (ν �ck+1) R˜v | ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �By⟩ | Bk+1 ˜xy � P2σ2 � : � Wσ1 ⊠ �B � Similar to the other cases, if Q1 ∈ N1, then Q1 reduces to some Q′ 1 ∈ N2 through communication on non-essential prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, we pick V2 such that V1σv · σ2 ⊠ V2 where σv ∈ index(fn(V ) \\ �u) such that σv · σ2 ∈ index(fn(P2{ ˜WV1/˜xy})) (134) By Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 it suffices to consider the case when Q′ 1 ∈ N2, under which we have the following transition: ⟨Rv⟩ ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �By⟩ ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) −−−−→ ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �BV2⟩ (135) (135) bn(ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2)) ∩ fn(Bk+1 ˜xy � P2σ � ) = ∅ ⟨ParL⟩ ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �By⟩ | Bk+1 ˜xy � P2σ2 � ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) −−−−→ ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �BV2⟩ | Bk+1 ˜xy � P2σ2 � (136) (136) �cr · �ck+1 ∩ fn(ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2)) = ∅ ⟨Res⟩ (ν �cr) (ν �ck+1) R˜v | ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �By⟩ | Bk+1 ˜xy � P2σ2 � ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) −−−−→ R 82 where R = (ν �cr) (ν �ck+1) ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �BV2⟩ | Bk+1 ˜xy � P2σ2 � with � Wσ1 ⊠ �B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We can see that assertion next(ni) ∈ σ2 holds by the definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We should show that P2{ ˜WV1/˜xy} S R (137) We know n ̸∈ fn(� W) and n ̸∈ fn(V1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, � WV1σv · σ1 = � WV1σv · σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' That is, we may notice that � WV1σv · σ2 ⊠ �BV2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, by the definition of σv, we have P2σ2 = P2σv · σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, we have R ∈ C ˜ WV1σv·σ2 ˜xy � P2σv · σ2 � Finally, by this and (134) the goal (137) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes sub-case ¬tr(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ii) Sub-case tr(n).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The transition inference tree is as follows: ⟨Rv⟩ (n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P2){ ˜W/˜x} n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V1) −−−−→ P2{ ˜W/˜x}{V1/y} Let σ1 = index(�u) where �u = fn(P1{ ˜W/˜x}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Also, let �v = rn(P1), �cr = ∪r∈˜vcr, �ck = (ck, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P1�−1), �ck+1 = (ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P1�−1), and let S be such that n : S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, by the definition of S (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='17) we have Q1 ∈ N1 ∪ N2 ∪ N3 ∪ N4 where N1 = {(ν �cr) (ν �ck) R˜v | ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk ˜x � P1σ1 � : � Wσ1 ⊠ �B} N2 = {(ν �cr) (ν �ck) R˜v | cn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � M ˜B V � | Bk+1 ˜xy � P2σ1 � : � Wσ1 ⊠ �B} N3 = {(ν �cr) (ν �ck) R˜v\\n | M ˜B V �n | Bk+1 ˜xy � P2σ1 � : � Wσ1 ⊠ �B} N4 = {(ν �cr) (ν �ck+1) R˜v\\n | n[S⟩?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �By⟩ | cn?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �n | Bk+1 ˜xy � P2σ1 � : � Wσ1 ⊠ �B} with M ˜B V = λ�z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' z[S⟩?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �By⟩ | cn?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �z � Similar to the other cases, if Q1 ∈ N1 ∪ N2 ∪ N3, then there exists some Q′ 1 ∈ N4 such that Q1 reduces to Q′ 1 through communication on non-essential prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 it suffice to consider the case when Q1 ∈ N4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We infer the following transition: Q1 n[S⟩?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) −−−−−−→ (ν �cr) (ν �ck+1) R where R = R˜v\\n | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �BV2⟩ | cn?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b �n) | Bk+1 ˜xy � P2σ1 � and V1σ ⊠ V2 for some σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We should show that P2{ ˜WV1/˜xy} S (ν �cr) (ν �ck+1) R (138) We may notice that we have �v = rn(P1) = rn(P2) and as tr(n) we have n ∈ �v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, we have the following structural equivalence R ≡ R˜v | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �BV2⟩ | Bk+1 ˜xy � P2σ1 � Further, we have V1σ ⊠ V2, � Wσ1 ⊠ �B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus by the definition of C− − � − � (Table 3) the goal (138) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes sub-case tr(n) of case ⟨Rv⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, we briefly consider the case when P1 is a trigger collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let σ1 be defined as above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let H′ 1 be such that P1{ ˜W/˜x}σ1 ⋄ H′ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, by definition of S , we know Q1 has the following shape: Q1 = R˜v ∥ H1 83 where �v = rn(P1{ ˜W/˜x}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, by Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='15 we know H′ 1 = ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='H′ 2 such that P2{ ˜W/˜x}σ2 ⋄ H′ 2, where σ2 = σ1 · next(ni).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, let V2 be such that V1σ ⊠ V2, for some σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We could see that H′ 1 ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) −−−−→ H′ 2{V2/y} We should show that P2{ ˜W/˜x}{V1/y} S R˜v ∥ H2{V2/y} (139) By P2{ ˜W/˜x}σ2 ⋄ H′ 2 and noticing that ⋄ is closed under the substitution of ⊠-related values we have P2{ ˜W/˜x}{V1/y}σ2 ⋄ H′ 2{V2/y} Thus, goal (139) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes case ⟨Rv⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Case ⟨App⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Here we know P1 = V1 (�r, u) where �r = (r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , rn).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We distinguish two sub-cases: (i) V1 = x where {Vx/x} ∈ { ˜W/˜x} and (ii) V1 is an abstraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let V1{ ˜W/˜x} = λ(�y, z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P2 where �y = �y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �yn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The inference tree is as follows ⟨App⟩ (V1 (�r, u)){ ˜W/˜x} τ−→ P2{˜r, u/˜y, z} Let σ1 = index(fn(P1ρ1)) such that {ui/u} ∈ σ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, let �v = rn(V1), �cvr = � r∈˜v,˜r cr, �ck = (ck, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P1�−1), and �ck+1 = (ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P1�−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Also, let �m = (ui, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ui+|G(C)|−1) with ui : C and �ri = (ri 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ri |R⋆(Si)|)) with ri : Si for i = {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , n}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, by the definition of S we have Q1 ∈ N where N is defined as follows: N = N1 ∪ N4 ∪ � ∪1≤l≤n Nl 2 � ∪ � ∪1≤l≤n−1 Nl 3 � where N1 = {(ν �ck) (ν �cvr) R˜v,˜r | ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk ˜x � P1σ1 � : � Wσ1 ⊠ �B} Nl 2 = {(ν �ck+1) (ν �cvr) R˜v,rl,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=',rn | |˜r|−l+1 crl!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' � λ�zl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='crl+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zl+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='crn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' QV2 l ⟩ ⟩ � : V1{ ˜W/˜x}σ1 ⊠ V2} Nl 3 = {(ν �ck+1) (ν �cvr) R˜v,rl+1,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=',rn | λ�zl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' |˜r|−l crl+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zl+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' · · · .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='crn!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨λ�zn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' QV2 l ⟩ � �rl : V1{ ˜W/˜x}σ1 ⊠ V2} N4 = {(ν �ck+1) (ν �cvr) R˜v | V2 (�r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �rn, �m) : V1{ ˜W/˜x}σ1 ⊠ V2} where QV2 l = V2 (�r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �rl−1, �zl, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �zn, �m) Note that for any Q1 ∈ N1 ∪ N4 ∪ � ∪1≤l≤n Nl 2 � ∪ � ∪1≤l≤n−1 Nl 3 � there exist Q′ 1 ∈ N5 such that Q1 reduces to Q′ 1 through communication on non-essential prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 it then suffices to consider the case Q′ 1 ∈ N5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let V2 = λ�y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , �yn, �z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q2 where �z = (z1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , z|G(C)|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Then, we have the following transition: Q′ 1 τ−→ (ν �ck+1) (ν �cr) R 84 where R = R˜v | Q2{˜r1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ˜rn, ˜m/˜y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ˜yn, ˜z}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We should show that P2{˜r, u/˜y, z} S (ν �ck+1) (ν �cvr) R (140) By V1ρ1σ1 ⊠ V2 (with ρ1 = { ˜W/˜x}) and Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='13 either V2 ∈ C � V1ρ1σ1 � or V1ρ1 ▷◁ V2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the former case, we know V2 ∈ �Cρ′ 1 σ′ 1 � V ′ 1 � where ρ′ 1 = { ˜W ′/˜x′} is such that V ′ 1ρ′ 1σ′ 1 = V1ρ1σ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let �B′ be such that � W ′σ′ 1 ⊠ �B′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Table 3 we have V2 = V˜x′ � λ(�y, z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P ′ 2 � { ˜B′/˜x′} = λ( �y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , � yn, �z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Q2{ ˜B′/˜x′} where Q2 = (ν �cy) � i∈|�y| (cyi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b �yi)) | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B′⟩ | Bk+1 ˜x′ � P ′ 2{z1/z} � with �cy = � i∈|˜y| cyi and P ′ 2 is such that P ′ 2{ ˜W ′/˜x′} = P2 Thus, we know R ≡ R˜v | (ν �cy) � i∈|�y| (cyi?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b �ri)) | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B′⟩ | Bk+1 ˜x′ � P ′ 2{z1/z} � Now, we know (ν �cvr) R ≡ (ν �cv) R where �cv = � r∈˜v cr since �cvr \\ �cv ̸⊆ fn(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, by renaming bound names we have R ≡ R˜v | (ν �cr) � r∈�r (cr?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (b �r)) | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B′⟩ | Bk+1 ˜x′ � P ′ 2{z1/z} � {˜cr/˜cy} where �cr = � r∈˜r cr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, by the definition of R˜v (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='16) we know R˜v,˜r = R˜v | � r∈�r (cn?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='x �r) Thus, we have R ≡ (ν �cr) R˜v,˜r | ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B′⟩ | Bk+1 ˜x′ � P ′ 2{z1/z} � {˜cr/˜cy} = (ν �cr) R′ and by the definition we have R′ ∈ C ˜ W ′ ˜x′ � P ′ 2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We may notice that �v, �r = rn(P ′ 2) and (ν cvr) R ≡ (ν cv) (ν cr) R′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The later case, when V1ρ1 ▷◁ V2, follows by the fact that bodies of characteristic and triggers values are ⋄-related to their minimal counterparts as shown in Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='2 and that relation ⋄ is closed under names substitutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' So, the goal (140) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes case ⟨App⟩ (and base cases).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Next, we consider inductive cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Case ⟨ParL⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In this case we distinguish two sub-cases: (i) P1ρ = P ′ 1ρ′ 1 | P ′′ 1 ρ′′ 1 and (ii) P1ρ = P ′ 1ρ′ 1 ∥ P ′′ 1 ρ′′ 1 where P ′ 1 is a triggers collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The final rule in the inference tree is: P ′ 1ρ′ 1 ℓ−→ P ′ 2ρ′ 2 bn(ℓ) ∩ fn(P ′′ 1 ) = ∅ ⟨ParL⟩ P ′ 1ρ′ 1 | P ′′ 1 ρ′′ 1 ℓ−→ P ′ 2ρ′ 2 | P ′′ 1 ρ′′ 1 85 Let σ1 ∈ index(�u) where �u = fn(P1{ ˜W/˜x}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, we know ρ′ 1 = { ˜W1/˜y} and ρ′′ 1 = { ˜W2/˜z}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, let σ′ 1 and σ′′ 1 such that P1ρ1σ1 = P ′ 1ρ′ 1σ′ 1 | P ′′ 1 ρ′′ 1σ′′ 1 In sub-case (i), by the definition of S (Table 3) we have Q1 ∈ N1 ∪ N2 ∪ N3 where N1 ={(ν �ck) (ν �cr) (ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk ˜x � P ′ 1σ′ 1 | P ′′ 1 σ′′ 1 � ) : � Wσ1 ⊠ �B} N2 ={(ν �ck+1) (ν �cr) (ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+2!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk+1 ˜y � P ′ 1σ′ 1 � | Bk+2 ˜z � P ′′ 1 σ′′ 1 � ) : � Wiσ1 ⊠ �Bi, i ∈ {1, 2}} N3 ={(ν �c) (ν �cr) R′ 1 | R′′ 1 : R′ 1 ∈ C ˜ W1 ˜y � P ′ 1σ′ 1 � , R′′ 1 ∈ C ˜ W2 ˜z � P ′′ 1 σ′′ 1 � } where �ck = (ck, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P1�−1), �ck+1 = (ck+1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , ck+�P1�−1), and �c = fpn(R′ 1 | R′′ 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Note that for Q1 ∈ N1 ∪ N2 there exists some Q′ 1 and Q′′ 1 such that Q1 reduces to Q′ 1 | Q′′ 1 ∈ N3 through communication on non-essential prefixes, with Q′ 1 ∈ �Cρ′ 1 σ′ 1 � P ′ 1 � (141) Q′′ 1 ∈ �Cρ′′ 1 σ′′ 1 � P ′′ 1 � (142) Then, by Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 it suffices to consider the case of Q′ 1 | Q′′ 1 ∈ N3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By the definition of S we have P ′ 1ρ′ 1 S Q′ 1 (143) P ′′ 1 ρ′′ 1 S Q′′ 1 (144) To apply IH we do the case analysis on the action ℓ: Sub-case ℓ ̸≡ (ν �m1) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By (143) and IH we know there is Q′ 2 such that Q′ 1 ℓ=⇒ Q′ 2 and P ′ 2ρ′ 2 S Q′ 2 (145) We should show that P ′ 2ρ′ 2 | P ′′ 1 ρ′′ 1 S Q′ 2 | Q′′ 1 (146) We know that there is R′ such that Q′ 1 τ=⇒ R′ ˘ℓ−→ Q′ 2 (147) Thus, by Rule ⟨ParL⟩ we can infer the following: Q′ 1 | Q′′ 1 τ=⇒ R′ | Q′′ 1 Further, we can infer R′ ˘ℓ−→ Q′ 2 ⟨ParL⟩ R′ | Q′′ 1 ˘ℓ−→ Q′ 2 | Q′′ 1 Then, by the IH (145) and the definition of S (Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='17) we know Q′ 2 ∈ �Cρ′ 2 σ′ 1·σ′ 2 � P ′ 2 � 86 So, we may notice that Cρ′′ 1 σ′′ 1 ·σ′ 2 � P ′′ 1 � = Cρ′′ 1 σ′′ 1 � P ′′ 1 � So, by (142) and definition of C− − � − � we have Q′ 2 | Q′′ 1 ∈ �Cρ′ 2·ρ′′ 1 σ′ 2·σ′′ 1 � P ′ 2 | P ′′ 1 � By IH and assertion, we know that if ℓ = n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩ then next(ni) ∈ σ′ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' So, assertion next(ni) ∈ σ′ 2 · σ′′ 1 holds in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, by (143) we have σ′′ 1 ∈ index(fn(P ′′ 1 ρ′′ 1)) and by (145) we have σ′ 2 ∈ index(fn(P ′ 2ρ′ 2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We may notice that if ℓ = n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩, by transition rule ⟨SRv⟩ we have ¯n ̸∈ fn(P ′ 2ρ′ 2 | P ′′ 1 ρ′′ 1) so by 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 we have {nj/n} ̸∈ σ′′ 1 for any j > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' So, we have σ′ 2 · σ′′ 1 ∈ index(fn(P ′ 2ρ′ 2 | P ′′ 1 ρ′′ 1)) Thus, the goal (146) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes this sub-case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Sub-case ℓ ≡ (ν �m1) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This sub-case follows the essential steps of the previous sub-case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By (143) and IH we know there is Q′ 2 such that Q′ 1 (ν ˜m2) ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ =========⇒ Q′ 2 and (ν �m1) (P ′ 2 ∥ t ←�H V1)ρ′ 1 S (ν �m2) (Q′ 2 ∥ t ←�H V2) (148) We should show that (ν �m1) (P ′ 2 | P ′′ 1 ∥ t ←�H V1)ρ1 S (ν �m2) (Q′ 2 | Q′′ 1 ∥ t ←�H V2) (149) We pick R′ as in the previous sub-case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' So, we can infer the following transition: R′ (ν ˜m2) ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−−−−−→ Q′ 2 ⟨ParL⟩ R′ | Q′′ 1 (ν ˜m2) ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−−−−−→ Q′ 2 | Q′′ 1 Next, by Table 3 we can infer the following.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, by (148) we know Q′ 2 ∥ t ←�H V2 ∈ �Cρ′ 1 σ′ 2 � P ′ 2 ∥ t ←�H V1 � By IH and assertion, we know next(ni) ∈ σ′ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' So, assertion next(ni) ∈ σ′ 2 · σ′′ 1 holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Similarly to the previous sub-case, we have �Cρ′′ 1 σ′′ 1 ·σ′ 2 � P ′′ 1 � = Cρ′′ 1 σ′′ 1 � P ′′ 1 � Thus, we have (ν �m2) (Q′ 2 | Q′′ 1 ∥ t ←�H V2) ∈ �Cρ1 σ′′ 1 ·σ′ 2 � (ν �m1) (P ′ 2 | P ′′ 1 ∥ t ←�H V1) � Now, by (143) we have σ′′ 1 ∈ index(fn(P ′′ 1 ρ′′ 1)) and by (148) we have σ′ 2 ∈ index(P ′ 2ρ′ 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We may notice that if ℓ = n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩, by transition rule SSnd we have ¯n ̸∈ fn(P ′ 2ρ′ 2 | P ′′ 1 ρ′′ 1) so by Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 we have {nj/n} ̸∈ σ′′ 1 for any j > 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' So, we have σ′ 2 · σ′′ 1 ∈ index(fn(P ′ 2ρ′ 2 | P ′′ 1 ρ′′ 1)) Thus, (149) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes case ⟨ParL⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 87 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Case ⟨Tau⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We distinguish two sub-cases: (i) P1ρ1 = P ′ 1ρ′ 1 | P ′′ 1 ρ′′ 1 and (ii) P1ρ1 = P ′ 1ρ′ 1 ∥ P ′′ 1 ρ′′ 1 where one of parallel components is a trigger collection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Without loss of generality, we assume ℓ1 = (ν �m1) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩ and ℓ2 = n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(V1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The final rule in the inference tree is then as follows: P ′ 1ρ′ 1 ℓ1 −→ P ′ 2ρ′ 2 P ′′ 1 ρ′′ 1 ℓ2 −→ P ′′ 2 ρ′′ 2 ℓ1 ≍ ℓ2 ⟨Tau⟩ P ′ 1ρ′ 1 | P ′′ 1 ρ′′ 1 τ−→ (ν �m1) (P ′ 2ρ′ 2 | P ′′ 2 ρ′′ 2) Let σ1 = index(�u) where �u = fn(P1{ ˜W/˜x}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, let σ′ 1 and σ′′ 1 such that P1ρ1σ1 = P ′ 1ρ′ 1σ′ 1 | P ′′ 1 ρ′′ 1σ′′ 1 We know ρ′ 1 = { ˜W1/˜y} and ρ′′ 1 = { ˜W2/ ˜w}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By the definition of S (Table 3) we have Q1 ∈ N1 ∪ N2 ∪ N3 where N1 = {(ν �ck) (ck!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B⟩ | Bk ˜x � P ′ 1σ′ 1 | P ′′ 1 σ′′ 1 � ) : � Wσ1 ⊠ �B} N2 = {(ν �ck+1) (ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+l+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk+1 ˜y � P ′ 1σ′ 1 � | Bk+l+1 ˜w � P ′′ 1 σ′′ 1 � ) : � Wiσ1 ⊠ �Bi, i ∈ {1, 2}} N3 = {R′ 1 | R′′ 1 : R′ 1 ∈ C ˜ W1 ˜y � P ′ 1σ′ 1 � , R′′ 1 ∈ C ˜ W2 ˜w � P ′′ 1 σ′′ 1 � } By Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3, for Q1 1 ∈ N1 there exists Q2 1 ∈ N2 such that Q1 1 τ=⇒ Q2 1 τ=⇒ Q′ 1 | Q′′ 1 where Q′ 1 | Q′′ 1 ∈ N3, that is Q′ 1 ∈ �Cρ′ 1 σ′ 1 � P ′ 1 � (150) Q′′ 1 ∈ �Cρ′′ 1 σ′′ 1 � P ′′ 1 � (151) Thus, in both cases we only consider how Q′ 1 | Q′′ 1 evolves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By the definition of S we have P ′ 1ρ′ 1 S Q′ 1 (152) P ′′ 1 ρ′′ 1 S Q′′ 1 (153) We have the following IH: (a) By (152) and IH there is Q′ 2 such that Q′ 1 (ν �m1) ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ =========⇒ Q′ 2 and (ν �m1) (P ′ 2 ∥ t ←�H V1)ρ′ 1 S (ν �m2) (Q′ 2 ∥ t1 ←�H V2) (154) By Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='17 we know there is σv · σ′ 2 ∈ index(fn((P ′ 2 ∥ t ←�H V1)ρ′ 1)) such that σv ∈ index(fn(t ←�H V1ρ′ 1)) and σ′ 2 ∈ index(fn(P ′ 2ρ′ 2)) and Q′ 2 ∥ t1 ←�H V2 ∈ �Cρ′ 1 σv·σ′ 2 � P ′ 2 ∥ t1 ←�H V1 � So, we can infer Q′ 2 ∈ �Cρ′ 2 σ′ 2 � P ′ 2 � (155) 88 (b) By (153) and IH there is Q′′ 2 such that Q′′ 1 nj?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) =====⇒ Q′′ 2 and P ′′ 2 ρ′′ 2 S Q′′ 2 (156) By 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='17 and (156) we know there is σ′′ 2 ∈ index(fn(P ′′ 2 ρ′′ 2)) such that Q′′ 2 ∈ Cρ′′ 2 σ′′ 2 � P ′′ 2 � (157) Similarly to the ParL case, we know there is R′ such that Q′ 1 τ=⇒ R′ (ν �m2) ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−−−−−→ Q′ 2 where ˘ℓ1 = (ν �m2) ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, there is R′′ such that Q′′ 1 τ=⇒ R′′ nj?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) −−−−−→ Q′′ 2 where ˘ℓ2 = nj?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='(V2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Rule ParL and Rule ParR we can infer the following: Q′ 1 | Q′′ 1 τ=⇒ R′ | R′′ Now, to proceed we must show ˘ℓ1 ≍ ˘ℓ2, which boils down to showing that indices of ni and nj match.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' For this, we distinguish two sub-cases: (i) ¬tr(ni) and ¬tr(nj) and (ii) tr(ni) and tr(nj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In the former sub-case, we have {ni/n} ∈ σ1 and {nj/n} ∈ σ1, where σ1 = index(�u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, by this and and Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 we know that i = j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, we consider the later case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By assumption that P1{ ˜W/˜x} is well-typed, we know there Γ1, Λ1, and ∆1 such that Γ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Λ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' ∆1 ⊢ P1{ ˜W/˜x} ▷ ⋄ with balanced(∆1), Thus, we have n : S ∈ ∆1 and n : T ∈ ∆1 such that S dual T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hence, by the definition of [−⟩ (Definition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='5) we have i = [S⟩ = [T⟩ = j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Hence, we can infer the following transition: R′ (ν �m2) ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−−−−−→ Q′ 2 R′′ ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) −−−−→ Q′′ 2 ˘ℓ1 ≍ ˘ℓ2 ⟨Tau⟩ (R′ | R′′) τ−→ (ν �m2) (Q′ 2 | Q′′ 2) Now, we should show that (ν �m1) (P ′ 2ρ′ 2 | P ′′ 2 ρ′′ 2) S (ν �m2) (Q′ 2 | Q′′ 2) (158) Further, we have (P ′ 2 | P ′′ 2 )ρ′ 2 · ρ′′ 2 = P ′ 2ρ′ 2 | P ′ 2ρ′′ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' So, by (155) and (157) we have (ν �m2) (Q′ 2 | Q′′ 2) ∈ �Cρ′ 2·ρ′′ 2 σ′ 2·σ′′ 2 � (ν �m1) (P ′ 2ρ′ 2σ′ 2 | P ′′ 2 ρ′′ 2σ′′ 2) � Finally, we need to show σ′ 2 · σ′′ 2 ∈ index(�u), where �u = fn(P ′ 2ρ′ 2 | P ′′ 2 ρ′′ 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By IH we have σ′ 2 ∈ index(fn(P ′ 2ρ′ 2)) and σ′′ 2 ∈ index(fn(P ′′ 2 ρ′′ 2)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Further, as P is well-typed, we have n ∈ fn(P ′ 2ρ′ 2), n ̸∈ fn(P ′ 2ρ′ 2), n ∈ fn(fn(P ′′ 2 ρ′′ 2)), and n ̸∈ fn(P ′′ 2 ρ′′ 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, by Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 in sub-case ¬tr(n) we only need to show that for some k > 0 we have {nk/n} ∈ σ′ 2 and {nk/n} ∈ σ′′ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This follows by the assertion as we know next(ni) = {ni+1/ni} ∈ σ′ 2 and next(ni) = {ni+1/ni} ∈ σ′′ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The sub-case tr(n) follows directly by the Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='10 as we have {n1/n} ∈ σ′ 2 and {n1/n} ∈ σ′′ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' So, we have σ′ 2 ·σ′′ 2 ∈ index(�u).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Thus, the goal (158) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes case ⟨Tau⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 89 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Case ⟨New⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In this case we know P1 = (ν m : C) P ′ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' The final rule in the transition inference tree is as follows: P ′ 1ρ1 (ν �n1) u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩ −−−−−−−→ P2ρ2 m ∈ fn(V1) ⟨New⟩ (ν m) P ′ 1ρ1 (ν m·�n1) u!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩ −−−−−−−−−→ P2ρ1 (159) Let σ1 = index(fn(P1ρ1)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By the definition of S (Table 3) we have Q1 ∈ N1 where N1 ={(ν �cr) (ν �c) (ν �m2) (ν ˜cm) R : R ∈ C ˜ Wσ1 ˜x � P ′ 1σ1 · {m1m1/mm} � } where �cr = cr(R), �m2 = (m1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' , m|G(C)|), and ˜cm = cm · cm if tr(C), otherwise ˜cm = ϵ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By IH, if P ′ 1ρ1 S Q′ 1 there are Q2 and V2 such that Q′ 1 (ν �n2) ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ ========⇒ Q2 and (ν �n1) (P2 ∥ t ←�H V1)ρ1 S (ν �n2) (Q2 ∥ t ←�H V2) (160) For Q1 ∈ N1 we should show that Q1 (ν �m2·�n2) ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ ===========⇒ Q2 (161) such that (ν m · �n1) (P2 ∥ t ←�H V1)ρ1 S (ν �c′ r · �m2 · �n2) (Q2 ∥ t ←�H V2) (162) where �c′ r = cr(V2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Note that by the definition we have fpn(V2) = ∅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3, we know there is R such that P ′ 1ρ1 S R and Q′ 1 τ=⇒ R (ν ˜n2) ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−−−−−→ Q2 (163) Now, by rule ⟨New⟩ we have Q1 τ=⇒ (ν �c′ r) (ν �m2) R Now, we need to apply Rule ⟨New⟩ | �m2| times to (163) to infer the following: R′ (ν �n2) ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−−−−−→ Q2 �m2 ⊆ fn(V2) ⟨New⟩ (ν �m2) R (ν �m2·�n2) ui!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−−−−−−−→ Q2 Therefore, the sub-goal (161) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, by (160) and by Definition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='17 we can infer the following: (ν �n2) (Q2 ∥ t ←�H V2) ≡ (ν �c′ r) (ν �n) (R˜v | R2 | R ˜w ∥ t ←�H V2) where �v = rn(R2),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �w = rn(V2),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' �c′ r = cr(V2),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' and (ν �n) (R˜v | R2 | R ˜w ∥ t ←�H V2) ∈ �Cρ1 σ1 � (ν �n1) (P2 ∥ t ←�H V1) � By this and the definition of C− − � − � (Table 3) we have (ν �m) (ν ˜cm) (ν �n) (R˜v | R2 | R ˜w ∥ t ←�H V2) ∈ �Cρ1 σ1 � (ν m) (ν �n1) (P2 ∥ t ←�H V1) � Further,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' we may notice (ν �m2 · �n2) (Q2 ∥ t ←�H V2) ≡ (ν �cr) (ν �m2) (ν �n) (R˜v | R2 | R ˜w ∥ t ←�H V2) Therefore,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' the sub-goal (162) follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes case ⟨New⟩ and the proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 90 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3 Proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='7 Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Assume P1{ ˜W/˜x} is a process and P1{ ˜W/˜x} S Q1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Q1 (ν � m2) ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−−−−−→Q2 , such that ni ̸∈ fn(Q1), then there exist P2 and V2 such that P1{ ˜W/˜x} (ν � m2) n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩ −−−−−−−−→P2 and, for a fresh t, (ν � m1)(P2 ∥ t ←�H V1){ ˜W/˜x} S (ν � m2)(Q2 ∥ t1 ←�H V2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Q1 ni?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V2) −−−−→Q2 , such that ni ̸∈ fn(Q1), there exist P2, V2, and σ such that P1{ ˜W/˜x} n?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' (V1) −−−−→P2 where V1σ ⊠ V2 and P2 S Q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Whenever Q1 τ−→ Q2 either (i) P1{ ˜W/˜x} S Q2 or (ii) there exists P2 such that P1 τ−→P2 and P2 S Q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Proof (Sketch).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' By transition induction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' First, we analyze the case of non-essential prefixes, which induce τ-actions that do not correspond to actions in P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concerns the sub-case (i) of Part 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This directly follows by Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='3, that is by the fact that C ˜ W ˜x � P1 � is closed under transitions on non-essential prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Now, assume Q1 ℓ−→ Q2 when ℓ is an essential prefix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This is mainly the converse of the proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4 noting that there are no essential actions in C ˜ W ˜x � P1 � not matched in P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We consider only one case: Case ⟨Snd⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In this case we know P1 = n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We distinguish two sub-cases: (i) ¬tr(ui) and (ii) tr(ui).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' In both sub-cases, we distinguish two kinds of an object value V1: (a) V1 ≡ x, such that {Vx/x} ∈ { ˜W/˜x} and (b) V1 = λy : C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' P ′, that is V1 is a pure abstraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We only consider sub-case (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Let � W1, � W2, �y, and �w such that P1{ ˜W/˜x} = n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1{ ˜W1/˜y}⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='P2{ ˜W2/ ˜w} Let σ1 ∈ index(�u) where �u = fn(P1{ ˜W/˜x}) such that {ni/n} ∈ σ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Also, let σ2 = σ1 · next(ni).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' When P1 is not a trigger, by the definition of S (Table 3), for both sub-cases, we have Q1 ∈ N1 where: N1 = � (ν �cr) (ν �ck+1) R˜v | ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk+1 ˜w � P2σ2 � : V1σ{� W1/�y} ⊠ V2, � W2 ⊠ �B2 � For Q1 ∈ N1 we have the following transition inference tree: ⟨Snd⟩ Q1 ni!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1⟩ −−−−→ Q2 where Q2 = (ν �cr) (ν �ck+1) ck+1!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨ �B2⟩ | Bk ˜w � P2σ2 � We have ⟨Snd⟩ P1{ ˜W/˜x} n!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='⟨V1{ ˜W1/˜y}⟩ −−−−−−−−−→ P2{ ˜W2/ ˜w} We should show that (ν � m1)(P2 ∥ t ←�H V1) S (ν � m2)(Q2 ∥ t1 ←�H V2) This immediately follows by the definition of S and Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This concludes Snd case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' As can be seen the proof of this part is essentially the inverse of the proof of Lemma 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' We just need to show that C ˜ Wσ ˜x � P1σ � does not introduce extra actions on essential prefixes not present in P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' This is evident by the inspection of the definition of C− − � − � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Briefly, only in the case of the input and the output prefix J − − � − � introduce actions that mimic those prefixes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' Remaining cases only introduce actions on non-essential prefixes (τ-actions on propagator names).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} +page_content=' 91' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/8dE4T4oBgHgl3EQf2w3D/content/2301.05301v1.pdf'} diff --git a/9tFST4oBgHgl3EQfbTje/content/2301.13799v1.pdf b/9tFST4oBgHgl3EQfbTje/content/2301.13799v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..987915ba56e389f96240c0bd64c0e8ba2883ae34 --- /dev/null +++ b/9tFST4oBgHgl3EQfbTje/content/2301.13799v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:644d141d5b3acd5c2852ea64358bf39a0eee085f65bc0741345df20296ae3d39 +size 2718188 diff --git a/9tFST4oBgHgl3EQfbTje/vector_store/index.pkl b/9tFST4oBgHgl3EQfbTje/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..c962f790cea9cbf38bfc8f1d7e0da2462f8afe39 --- /dev/null +++ b/9tFST4oBgHgl3EQfbTje/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a94d68383bdbd8509ec52b2a6d372735d54f0c66130f6f6f7fee1074c8aaa777 +size 359326 diff --git a/ANE3T4oBgHgl3EQfsQvt/content/2301.04667v1.pdf b/ANE3T4oBgHgl3EQfsQvt/content/2301.04667v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b19493a6124cb10d25bd387b8ce5f2b53d2596f7 --- /dev/null +++ b/ANE3T4oBgHgl3EQfsQvt/content/2301.04667v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e6cc4617012e3211e49d27f4e261ba079f22bbf77e1d461cd8328900efd3436d +size 982606 diff --git a/ANE3T4oBgHgl3EQfsQvt/vector_store/index.pkl b/ANE3T4oBgHgl3EQfsQvt/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..48f8310014c359505cf4a55cb3e34bb725873c00 --- /dev/null +++ b/ANE3T4oBgHgl3EQfsQvt/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:914baa87c8adaec3aad4a441588575a154850734047a622a949fc0dbe172c34f +size 178201 diff --git a/B9AzT4oBgHgl3EQfTfz1/vector_store/index.faiss b/B9AzT4oBgHgl3EQfTfz1/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..b89d831dbc61554b2067779e371128d245e4d579 --- /dev/null +++ b/B9AzT4oBgHgl3EQfTfz1/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9080ac2ce98f53aaf04ac9992d68389a761049a14a3ebf70935c23d7603eb6bd +size 6553645 diff --git a/B9FJT4oBgHgl3EQfsy1U/content/tmp_files/2301.11614v1.pdf.txt b/B9FJT4oBgHgl3EQfsy1U/content/tmp_files/2301.11614v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..0b81a78c3cc5558cba2b043fd146fa41ca628cb5 --- /dev/null +++ b/B9FJT4oBgHgl3EQfsy1U/content/tmp_files/2301.11614v1.pdf.txt @@ -0,0 +1,5162 @@ +Non-Abelian Anyons and Non-Abelian Vortices in Topological +Superconductors +Yusuke Masakia,b, Takeshi Mizushimac,∗ and Muneto Nittab,d,∗ +aDepartment of Physics, Tohoku University, Sendai, Miyagi 980-8578, Japan +bResearch and Education Center for Natural Sciences, Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521, Japan +cDepartment of Materials Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan +dDepartment of Physics, Keio University, Hiyoshi 4-1-1, Japan +A R T I C L E I N F O +Keywords: +Non-Abelian +vortices, +non-Abelian +anyons, +non-Abelian +statistics, +topological +quantum +computation, +topological +materials, +topological +superconductors, +topological +su- +perfluids, +superfluid +3He, +spinor +Bose-Einstein condensates, +nematic +liquid crystals, chiral liquid crystals, +quark matter, nuclear matter, nuclear +superfluids +A B S T R A C T +Anyons are particles obeying statistics of neither bosons nor fermions. Non-Abelian anyons, whose +exchanges are described by a non-Abelian group acting on a set of wave functions, are attracting a +great attention because of possible applications to topological quantum computations. Braiding of +non-Abelian anyons corresponds to quantum computations. The simplest non-Abelian anyons are +Ising anyons which can be realized by Majorana fermions hosted by vortices or edges of topological +superconductors, 휈 = 5∕2 quantum Hall states, spin liquids, and dense quark matter. While Ising +anyons are insufficient for universal quantum computations, Fibonacci anyons present in 휈 = 12∕5 +quantum Hall states can be used for universal quantum computations. Yang-Lee anyons are non- +unitary counterparts of Fibonacci anyons. Another possibility of non-Abelian anyons (of bosonic +origin) is given by vortex anyons, which are constructed from non-Abelian vortices supported by a +non-Abelian first homotopy group, relevant for certain nematic liquid crystals, superfluid 3He, spinor +Bose-Einstein condensates, and high density quark matter. Finally, there is a unique system admitting +two types of non-Abelian anyons, Majorana fermions (Ising anyons) and non-Abelian vortex anyons. +That is 3푃2 superfluids (spin-triplet, 푝-wave paring of neutrons), expected to exist in neutron star +interiors as the largest topological quantum matter in our universe. +1. Introduction +In three spatial dimensions, all particles are either bosons +or fermions in quantum physics, that is, a wave function +of multi-particle states is symmetric (antisymmetric) under +the exchanges of two bosons (fermions). On contrary, in +two spatial dimensions, there exist exotic particles classi- +fied to neither bosons nor fermions, anyons. A wave func- +tion of two anyons receives a nontrivial phase factor un- +der their exchanges Leinaas & Myrheim (1977), Wilczek +(1982). Such exotic particles play essential roles in frac- +tional quantum Hall states Halperin (1984), Arovas et al. +(1984), and have been experimentally observed for 휈 = 1∕3 +fractional quantum Hall states Nakamura et al. (2020). +Recently, yet exotic particles attracted great attention, +that is, non-Abelian anyons. +Non-Abelian anyons are +described by a set of multiple wave functions, and the +exchanges of two non-Abelian anyons lead to unitary +matrix operations on a set of wave functions. They have +been theoretically predicted to exist in 휈 = 5∕2 fractional +quantum Hall states Moore & Read (1991), Nayak & +Wilczek (1996), topological superconductors (SCs) and +superfluids (SFs) Read & Green (2000), Ivanov (2001), +Kitaev (2001), and spin liquids Kitaev (2006), Motome +& Nasu (2020), and experimental observation is pursued. +Non-Abelian anyons are attracting significant interests +owing to the possibility to offer a platform of topologically +∗Corresponding author +mizushima@mp.es.osaka-u.ac.jps (T. Mizushima); +nitta@phys-h.keio.ac.jp (M. Nitta) +ORCID(s): 0000-0001-6891-7008 (Y. Masaki); 0000-0002-7313-6094 (T. +Mizushima) +protected quantum computations realized by braiding of +non-Abelian anyons Kitaev (2003), Kitaev, Alexei and +Laumann, Christopher (2008), Nayak et al. (2008), Pachos +(2012), Sarma et al. (2015), Field & Simula (2018). Since +the Hilbert space and braiding operations are topologically +protected, they are robust against noises in contrast to the +conventional quantum computation methods. Recently, it +has been reported that non-Abelian braiding and fusions +has been experimentally realised in a superconducting +quantum processor, where the fusion and braiding protocols +are implemented using a quantum circuit on a supercon- +ducting quantum processor Andersen et al. (2022), thereby +opening a significant step to realize topological quantum +computations. +One of the main routes to realize non-Abelian anyons +is based on Majorana fermions in topological SCs Ivanov +(2001), Kitaev (2001), Alicea (2012), Leijnse & Flensberg +(2012), Beenakker (2013), Silaev & Volovik (2014), Elliott +& Franz (2015), Sato & Fujimoto (2016), Mizushima et al. +(2016), Sato & Ando (2017), Beenakker (2020). Majorana +fermions were originally proposed in high energy physics to +explain neutrinos; they are particles that coincide with their +own anti-particles Majorana (1937). In condensed matter +physics, Majorana fermions are localized at vortices or edge +of materials for which several protocols of non-Abelian +braiding were proposed. Non-Abelian anyons constructed +from Majorana fermions are so-called Ising anyons. They +are not enough for universal quantum computations, and +thus some non-topological process should be included +Nayak et al. (2008). +In contrast, another type of anyons +called Fibonacci anyons Trebst et al. (2008) can offer a +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 1 of 34 +arXiv:2301.11614v1 [cond-mat.supr-con] 27 Jan 2023 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +promising platform for universal topological quantum com- +putation that all quantum gates are implemented by braiding +manipulation in a topologically protected way Preskill +(2004), Bonesteel et al. (2005), Hormozi et al. (2007). +Such Fibonacci anyons are proposed to exist in 휈 = 12∕5 +quantum Hall states, a junction made of a conventional +SC and a 휈 = 2∕3 fractional quantum Hall state Mong +et al. (2014), interacting Majorana fermions realized in +a septuple-layer structure of topological SCs Hu & Kane +(2018), and Rydberg atoms in a lattice Lesanovsky & +Katsura (2012). +Yang-Lee anyons are also proposed as +non-unitary counterparts of Fibonacci anyons, obeying +nonunitary non-Abelian statistics Ardonne et al. (2011), +Freedman et al. (2012), Sanno et al. (2022). +The aforementioned anyons are all quasiparticle excita- +tions composed of fermions. On the other hand, a different +type of non-Abelian anyons can be composed of bosons +in certain ordered states accompanied with symmetry +breakings 퐺 → 퐻. They are called non-Abelian vortex +anyons, whose exchange statistics are non-Abelian due to +non-Abelian vortices, that is quantum vortices supported +by a non-Abelian first homotopy (fundamental) group of +order parameter manifolds, 휋1(퐺∕퐻) Bais (1980), Wilczek +& Wu (1990), Bucher (1991), Brekke et al. (1993), Lo & +Preskill (1993), Lee (1994), Brekke et al. (1997).1 +Such +non-Abelian vortices exist in liquid crystals Poenaru & +Toulouse (1977), Mermin (1979), Lavrentovich & Kleman +(2001), 3He SFs Balachandran et al. (1984), Salomaa & +Volovik (1987), Volovik (2003), spinor Bose-Einstein +condensates (BECs) Semenoff & Zhou (2007), Kobayashi +et al. (2009, 2012), Borgh & Ruostekoski (2016), and high +density quark (QCD) matter Fujimoto & Nitta (2021a,b,c), +Eto & Nitta (2021). Non-Abelian braiding of vortex anyons +in spinor BECs and its application to quantum computations +were proposed Mawson et al. (2019). +In addition to these systems admitting one type of non- +Abelian anyons, there is the unique system simultaneously +admitting two kinds of non-Abelian anyons, Ising anyons +based on Majorana fermions and non-Abelian vortex anyons. +It is a 3푃2 SF, spin-triplet and 푝-wave paring with the total +angular momentum two Hoffberg et al. (1970), Tamagaki +(1970), Takatsuka & Tamagaki (1971), Takatsuka (1972), +Richardson (1972). Such 3푃2 SFs are expected to be realized +by neutrons, relevant for neutron star interiors Sedrakian & +Clark (2018). +3푃2 SFs are the largest topological SFs in +our universe Mizushima et al. (2017) and admit non-Abelian +vortices Masuda & Nitta (2020). Non-Abelian vortices host +Majorana fermions in their cores Masaki et al. (2022), thus +behaving as non-Abelian anyons. +1The term “non-Abelian” on vortices depends on the context. In the +other contexts (in particular in high energy physics), vortices in a symme- +try breaking 퐺 → 퐻 with non-Abelian magnetic fluxes are often called +non-Abelian even though 휋1(퐺∕퐻) the first homotopy group is Abelian +Hanany & Tong (2003), Auzzi et al. (2003), Eto et al. (2006), Shifman & +Yung (2007), Eto et al. (2014). In condensed matter physics, vortices with +Majorana fermions in their cores are also sometimes called non-Abelian +vortices (because they are non-Abelian anyons). In this article, the term +“non-Abelian” on vortices is used only for vortices with non-Abelian first +homotopy group 휋1. +Figure 1: Schematic of the braid relations in Eqs. (1) and +(2): 푇푖푇푗 = 푇푗푇푖 for |푖 − 푗| ≥ 2 (left) and 푇푖푇푗푇푖 = 푇푗푇푖푇푗 for +|푖 − 푗| = 1 (right). +The purpose of this article is to summarise these non- +Abelian anyons of various types. After introducing basics +of non-Abelian anyons in Sec. 2, we describe non-Abelian +anyons in fermionic and bosonic systems, based on Ma- +jorana fermions and non-Abelian first homotopy group in +Secs.3 and 4, respectively. In Sec. 5, we introduce 3푃2 SFs +as the unique system simultaneously admitting two kinds of +non-Abelian anyons. We summarize this article in Sec. 6 +2. Non-Abelian anyons +2.1. Braid group and quantum statistics +Here we consider pointlike topological defects (e.g., +vortices in two-dimensional spinless SCs) which behave +as identical particles in a two-dimensional plane. +The +exchange of 푛 particles in three or higher dimension is +described by the symmetric group 푆푛 Leinaas & Myrheim +(1977). +There are two one-dimensional representations +of 푆푛, ±1, due to even/odd permutation and +1 (−1) +corresponds the Bose (Fermi) statistics. Two dimension is +special and the exchange of particles is given by the braid +group 퐵푛 Wu (1984). The braid of particles is expressed +as a set of operators 푇푘 (1 ≤ 푘 ≤ 푛 − 1) that exchange the +neighboring 푘th and (푘 + 1)th particles in an anticlockwise +direction. The operators obey the relations (see Fig. 1) +푇푖푇푗푇푖 = 푇푗푇푖푇푗, +for |푖 − 푗| = 1, +(1) +푇푖푇푗 = 푇푗푇푖, +for |푖 − 푗| ≥ 2. +(2) +The exotic statistics of particles represented by the braid +group stems from the relation 푇 −1 +푖 +≠ 푇푖. In the one dimen- +sional representation, the generator of 푇푖 is given by a phase +factor that a wave function under the exchange of particles +acquires, 휏푗 ≡ 휏(푇푗) = 푒푖휃푗 (0 ≤ 휃푗 < 2휋). The relation in +Eq. (1) implies that the exchange operation of any two par- +ticles induces the same phase factor 휏1 = 휏2 = ⋯ = 휏푛−1 = +푒푖휃. The phase factor characterizes the quantum statistics of +particles Wu (1984), and the absence of the relation 푇 2 +푖 = 1 +allows for the fractional (anyon) statistics with neither 휃 = 0 +(bosons) nor 휃 = 휋 (fermions). In addition to the one- +dimensional representation, the braid group has non-Abelian +representations. In Sec. 3, we will show that the generators +of the braid of Majorana zero modes are noncommutative as +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 2 of 34 + +Time +2 +i+1 +¥+1 +2 +T;T;+1 +¥+1 +2 +2+1i+ +T,T +T:T:1T2 ++12+2 +Ti+1 +TTi+1Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +[휏푖, 휏푗] ≠ 0 for |푖 − 푗| = 1 and the pointlike defects hosting +Majorana modes behave as non-Abelian anyons. +Although the braid group is trivial in three dimensions, a +three-dimensional model with pointlike topological defects +which host Majorana modes and obey the non-Abelian +statistics has been proposed Teo & Kane (2010a). +The +non-Abelian statistics of the defects, which behave as +hedgehogs, can be interpreted as the projective ribbon +permutation statistics Freedman, Hastings, Nayak, Qi, +Walker & Wang (2011), Freedman, Hastings, Nayak & Qi +(2011). +Such non-Abelian statistics enables to construct +three-dimensional networks of topological superconducting +wires supporting Majorana modes. +2.2. Non-Abelian anyons +In three spatial dimensions, the statistics of particles is +determined by their intrinsic spins. According to the spin +statistics theorem, all particles with integer (half-integer) +spin are bosons (fermions). A pair formed by two fermions +with the spin 1∕2 behaves as a boson, and the spin of the +composite particle obeys the “fusion rule” 1 +2 ⊗ 1 +2 = 0 ⊕ 1, +where 0 and 1 denote the spin singlet and triplet states, +respectively. When particles are trapped in a two dimen- +sional plane, however, there is another possibility that is +neither fermions nor bosons, i.e., anyons. In general, anyons +can be characterized by the topological charge, the fusion +rule (푁푐 +푎푏), the associative law (the 퐹-matrix), and the +braiding operation (the 푅-matrix) Preskill (2004), Nayak +et al. (2008), Pachos (2012). +Let ퟏ and {푎, 푏, ⋯} be the vacuum and the different +species of particles, respectively. Consider the anyon model +spanned by 푀 = {ퟏ, 푎, 푏, ⋯} and bring two anyons 푎 and 푏 +together. The fused particle also belongs to 푀. The fusion +rule is represented by +푎 ⊗ 푏 = +∑ +푐∈푀 +푁푐 +푎푏푐, +(3) +where fusion coefficients 푁푐 +푎푏 are non-negative integers. +Figure 2(a) shows the diagrammatic expression of the fusion +of two anyons with topological charges 푎 and 푏 to an anyon +with charge 푐. When 푁푐 +푎푏 is not zero for only one value of 푐, +the fusion of paired 푎 and 푏 anyons is uniquely determined +and the anyon is called the Abelian anyon. The non-Abelian +anyons are characterized by two or more coefficients that +satisfy 푁푐 +푎푏 ≠ 0. In the context of quantum computation, +the fusion rule determines the Hilbert space that encodes +quantum information, and quantum computation is im- +plemented by the braiding manipulation of non-Abelian +anyons in a topologically protected way. Figure 2(b) shows +the diagrammatic expression of the 푅-matrix. When one +anyon moves around the other, the pairwise anyons acquire +a phase. +As mentioned below, the 푅-matrix describes +a phase resulting from the exchange of anyons 푎 and 푏 +which fuse to a anyon 푐. Let us also consider the fusion +of three anyons 푎, 푏, and 푐 into an anyon 푑. The outcome +of the fusion process is independent of order in which the +anyons are to be fused. This implies that the fusion process +(c) +(b) +(a) +Figure 2: (a) Diagram of the fusion of two anyons 푎 and 푏 +to an anyon 푐. Diagrammatic expressions of the 푅-matrix (b) +and the 퐹-matrix (c). +obeys the associative law, (푎 ⊗ 푏) ⊗ 푐 = 푎 ⊗ (푏 ⊗ 푐), +which is characterized by the 퐹-matrix. +The 퐹 matrix +represents the transformation between different fusion bases +or the choice of order of fusion, which is expressed as +shown in Fig. 2(c). The 푅-matrix and the 퐹-matrix are the +building-blocks for constructing the braid group in multiple +anyon systems Preskill (2004). +Ising anyons. An example of the non-Abelian anyons is +the Ising anyon Kitaev (2006), Nayak et al. (2008), Pachos +(2012). The Ising anyon model consists of the vacuum ퟏ, +Ising anyons 휎, and Dirac (complex) fermions 휓, which obey +the fusion rules +휎 ⊗ 휎 = ퟏ ⊕ 휓, 휎 ⊗ 휓 = 휎, 휓 ⊗ 휓 = ퟏ, ퟏ ⊗ 푥 = 푥, +(4) +where 푥 ∈ {ퟏ, 휎, 휓}. Consider three Ising anyons, where the +two left-most anyons fusing into either ퟏ or 휓 (see Fig. 2(c) +with (푎, 푏, 푐) → 휎 and 푖, 푗 = {ퟏ, 휓}). The 푅-matrix and the +퐹-matrix are given, respectively, by +푅 = +(푅휎휎 +ퟏ +0 +0 +푅휎휎 +휓 +) += 푒−푖휋∕8 +( +1 +0 +0 +푖 +) +, +(5) +퐹 휎 +휎휎휎 = +1 +√ +2 +( +1 +1 +1 +−1 +) +. +(6) +The diagonal components of the 푅-matrix are the phases re- +sulting from the counterclockwise exchange of two left-most +Ising anyons (휎) fusing to ퟏ or 휓, while the twice exchange +operation of two right-most Ising anyons is represented by +the unitary matrix, 퐹 −1푅2퐹 = 푒−푖휋∕4휎푥. Hence, braiding +two anyons corresponds to the implementation of the quan- +tum gates acting on the quantum states spanned by ퟏ and 휓. +In general, the anyons are described by conformal field +theory, corresponding to gapless edge states residing in the +boundary of two-dimensional gapped topological phases. +For Ising anyons, the theory is the conformal field theory +with the central charge 푐 = 1∕2, which describes critical +Ising models such as the two-dimensional Ising model at +the point of second-order phase transition Di Francesco +et al. (1997). +The Moore-Read state in the fractional quantum Hall +state at the filling factor 휈 = 5∕2 supports this type of non- +Abelian anyons Nayak et al. (2008). The Ising anyons can +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 3 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +also be realized in the Kitaev’s honeycomb model, which is +an exactly solvable model of quantum spin liquid states Ki- +taev (2006). In this model, the spins are fractionalized to +Majorana fermions coupled to ℤ2 gauge fields. The Ising +anyons appear as Majorana zero modes bound to the ℤ2 flux. +Materials including 4푑 or 5푑 atoms with a strong spin-orbit +coupling have been proposed as candidates of Kitaev mag- +nets, and the half-integer thermal Hall effect was reported +in 훼-RuCl3 Kasahara et al. (2018), Yamashita et al. (2020), +Yokoi et al. (2021), Bruin et al. (2022), which is a signa- +ture of Majorana fermions in the chiral quantum spin liq- +uid phase Vinkler-Aviv & Rosch (2018), Ye et al. (2018). +Apart from materials, Google team reported the demonstra- +tion of fusion and braiding rules of non-Abelian Ising anyons +on a superconducting quantum processor, where the fusion +and braiding protocols are implemented using a quantum +circuit on a superconducting quantum processor Andersen +et al. (2022). Another platform to realize Ising anyons is a +topological SC. In the context of topological SCs, the Ising +anyons (휎) appear as Majorana zero modes bound at their +boundaries or topological defects, such as the surface, in- +terface, and vortices Read & Green (2000), Kitaev (2001), +Nayak et al. (2008), Alicea (2012), Sato & Fujimoto (2016), +Mizushima et al. (2016). Pairwise Majorana zero modes +form a complex fermion that can define either the unoccu- +pied state (ퟏ) or the occupied state (휓) of the zero energy +eigenstate, implying 휎 ⊗ 휎 = ퟏ ⊕ 휓. The vacuum ퟏ corre- +sponds to a condensate of Cooper pairs, while 휓 represents a +Bogoliubov quasiparticle which can pair into a condensate, +i.e., 휓 ⊗ 휓 = ퟏ. The detailed properties and realization +of Majorana zero modes in topological SCs are described in +Secs. 3.1 and 3.2. +Fibonacci anyons. Another example is the Fibonacci +anyons Trebst et al. (2008). The Fibonacci anyon model con- +sists of the vacuum ퟏ and the non-trivial anyon 휏, which obey +the fusion rules +휏 ⊗ 휏 = ퟏ ⊕ 휏, +ퟏ ⊗ 푥 = 푥, +(7) +where 푥 = ퟏ, 휏. The first rule implies that the fusion of +two anyons may result in either annihilation or creation of +a new anyon, and thus the Fibonacci anyon may be its own +anti-particle. Repeated fusions of the 푛 + 1 휏-anyons result +in either the vacuum or the 휏 anyon as 휏 ⊗ 휏 ⊗ ⋯ ⊗ 휏 = +푎푛 ⋅ ퟏ ⊕ 푏푛휏, where 푎푛 = 1 for 푛 = 2 and 푎푛 = 푛 − 2 for +푛 ≥ 3. The coefficient 푏푛 grows as the Fibonacci series, +and the first few values in the sequence are 푏2 = 1, 푏3 = 2, +푏4 = 3, 푏5 = 5, ⋯. The 푅-matrix and the 퐹-matrix are +given, respectively, by +푅 = +(푅휏휏 +ퟏ +0 +0 +푅휏휏 +휏 +) += +( +푒푖4휋∕5 +0 +0 +−푒푖2휋∕5 +) +, +(8) +퐹 휏 +휏휏휏 = +( +휙−1 +휙−1∕2 +휙−1∕2 +−휙−1, +) +, +(9) +where 휙 = (1 + +√ +5)∕2 is the golden ratio. The Fibonacci +anyons are described by the level-1 퐺2 Wess-Zumino-Witten +theory with the central charge 푐 = 14∕5 Mong et al. (2014), +where 퐺2 is the simplest exceptional Lie group. While Ising +anyons are not sufficient for universal quantum computation, +the Fibonacci anyon systems can offer a promissing platform +for universal topological quantum computation that all quan- +tum gates are implemented by braiding manipulation in a +topologically protected way Preskill (2004), Bonesteel et al. +(2005), Hormozi et al. (2007). +The existence of the Fibonacci anyons is predicted in +the 휈 = 12∕5 fractional quantum Hall state that is described +by the Read-Rezayi state Read & Rezayi (1999). It is also +proposed that a junction made of a conventional SC and +the 휈 = 2∕3 fractional quantum Hall state supports the +Fibonacci anyons Mong et al. (2014). Fibonacci anyons can +also be made from interacting Majorana fermions realized +in a septuple-layer structure of topological SCs Hu & Kane +(2018) and from Rydberg atoms in a lattice Lesanovsky & +Katsura (2012). +Yang-Lee anyons. There are nonunitary counterparts +of Fibonacci anyons, which are referred to as Yang-Lee +anyons. +The conformal field theory corresponding to +Yang-Lee anyons is nonunitary and Galois conjugate to the +Fibonacci conformal field theory Ardonne et al. (2011), +Freedman et al. (2012). Because of nonunitarity, the central +charge and the scaling dimension for the one nontrivial +primary field are negative, 푐 = −22∕5 and Δ = −2∕5, re- +spectively. As shown in Eq. (9), the 퐹-matrix for Fibonacci +anyons is given by the golden ratio 휙, i.e., one solution of +the equation 푥2 = 1 + 푥, which is an algebraic analogue +of the fusion rule. The 퐹-matrix for Yang-Lee anyons is +obtained from Eq. (9) by replacing 휙 → −1∕휙 as +퐹 휏 +휏휏휏 = +( +−휙 +푖 +√ +휙 +푖 +√ +휙 +휙 +) +, +(10) +as −1∕휙 is the other solution of the equation 푥2 = 1 + 푥. +In Eq. (10), the bases of the 퐹-matrix are spanned by the +vacuum state ퟏ and a Yang-Lee anyon 휏. The 푅-matrix are +given by +푅 = +(푅휏휏 +ퟏ +0 +0 +푅휏휏 +휏 +) += +( +푒푖2휋∕5 +0 +0 +푒푖휋∕5 +) +. +(11) +Unlike the Fibonicci anyons, braiding two Yang-Lee anyons +is represented by a combination of the 푅-matrix and the +nonunitary matrix, 퐹 −1푅퐹. While Yang-Lee anyons obey +the same fusion rule as that of Fibonacci anyons given by +Eq. (7), the 퐹-matrix in Eq. (10) is the nonunitary and +the Yang-Lee anyons obey the nonunitary non-Abelian +statistics. +The nonunitary conformal field theory with 푐 = −22∕5 +describes the nonunitary critical phenomenon known as the +Yang-Lee edge singularity Cardy (1985). Let us consider the +Ising model with an imaginary magnetic field 푖ℎ (ℎ ∈ ℝ). +For temperatures above the critical temperature, the zeros of +the partition function in the thermodynamic limit, which are +referred to as the Lee-Yang zeros, accumulate on the line +ℎ > ℎc and the edge of the Lee-Yang zeros corresponds +to the critical point ℎ푐 Lee & Yang (1952). As ℎ (> ℎc) +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 4 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +approaches the edge, the density of zeros has a power-law +behavior as |ℎ − ℎc|휎, which characterizes the critical phe- +nomenon Kortman & Griffiths (1971), Fisher (1978). For +instance, the magnetization exhibits singular behavior with +the same critical exponent 휎. The Yang-Lee edge singular- +ity is also realized by the quantum Ising model with a real +transverse field and a pure-imaginary longitudinal field von +Gehlen (1991). +The quantum Ising model with an imaginary longitu- +dinal field, which supports the Yang-Lee anyons, can be +constructed from Majorana zero modes in a network of +topological superconducting wires coupled with dissipative +electron baths Sanno et al. (2022). The Majorana modes +bound at the end points of one-dimensional topological +SCs constitute spin 1∕2 operators. A coupling of Majorana +zero modes with electrons in a metallic substrate plays an +role of the pure-imaginarly longitudinal field, while the +tunneling of Majorana zero modes between neighboring +superconducting wires induces a transverse magnetic field. +Schemes for the fusion, measurement, and braiding of +Yang-Lee anyons are also proposed in Ref. Sanno et al. +(2022). As mentioned above, the Yang-Lee anyons obey the +nonunitary non-Abelian statistics. The nonunitary evolution +of quantum states has been discussed in connection with +measurement-based quantum computation Terashima & +Ueda (2005), Usher et al. (2017), Piroli & Cirac (2020), +Zheng (2021). +Although the Yang-Lee anyons with the +nonunitary 퐹-matrix are not suitable for application to +unitary quantum computation, they can be the building- +blocks for the construction of measurement-based quantum +computation. +In addition, as the nonunitary quantum +gates can be implemented by braiding manipulations, the +Yang-Lee anyon systems may offer a quantum simulator for +nonunitary time evolution of open quantum systems in a +controllable way. +Vortex anyons. +In this article, we also discuss non- +Abelian anyons made of bosonic (topological) excitations in +ordered states. The nontrivial structure of the order parame- +ter manifold appears in the liquid crystals, spin-2 BECs, the +A phase of SF 3He, dense QCD matter, and 3푃2 SFs. The +line defects in such ordered systems, such as vortices, are +represented by non-Abelian first homotopy group and their +topological charges are noncommutative. Such topological +defects with noncommutative topological charges behave as +non-Abelian anyons, called the non-Abelian vortex anyons. +In Sec. 4, we demonstrate that order parameter manifolds in +nematic liquid crystals and spin-2 BECs admit the existence +of non-Abelian vortices and show the fusion rules of such +non-Abelian vortex anyons. +3. Non-Abelian anyons in topological SCs +3.1. Majorana zero modes as Ising anyons +Majorana zero modes. An elementary excitation from +superconducting ground states is a Bogoliubov quasiparticle +that is a superposition of the electron and hole. The quasipar- +ticle excitations are described by the Bogoliubov-de Gennes +(BdG) Hamiltonian +퐻 = +∑ +푖푗 +( +흍† +푖 , 흍푖 +) 푖푗 +(흍푗 +흍† +푗 +) +, +(12) +푖푗 = +(ℎ푖푗 +Δ푖푗 +Δ† +푖푗 +−ℎ∗ +푖푗 +) +. +(13) +Here, 흍푗 is the 푁-component vector of the electron field op- +erator and  is the 2푁 × 2푁 hermitian matrix, where 푁 is +the sum of the spin degrees of freedom and the number of +the lattice sites and so on. The 푁 ×푁 hermitian matrix ℎ de- +scribes the normal state Hamiltonian and the superconduct- +ing pair potential Δ obeys Δt = −Δ because of the Fermi +statistics, where 푎t denotes the transpose of a matrix 푎. The +BdG Hamiltonian naturally holds the particle-hole symme- +try +−1 = −, +(14) +where the particle-hole operator  = Θ퐾 is an antiunitary +operator composed of the unitary operator Θ and the +complex conjugation operator 퐾. The self-conjugate Dirac +fermions are called Majorana fermions, where the quantized +field 횿 ≡ (흍, 흍†)t obeys +횿 = 횿, +2 = +1. +(15) +We expand the quantized field 횿 in terms of the energy +eigenstates. The energy eigenstates are obtained from the +BdG equation, +∑ +푗 +푖푗(흋퐸)푗 = 퐸(흋퐸)푖, +(16) +which describes the quasiparticle with the energy 퐸 and +the wave function 흋퐸. Equation (14) guarantees that the +quasiparticle state with 퐸 > 0 and 흋퐸 is accompanied +by the negative energy state with −퐸 and 흋−퐸 = 흋퐸. +Thus, the negative energy states are redundant as long as +the particle-hole symmetry is maintained. Let 휂퐸 be the +quasiparticle operator which satisfies the anticommutation +relations, {휂퐸, 휂† +퐸′} = 훿퐸,퐸′ and {휂퐸, 휂퐸′} = {휂† +퐸, 휂† +퐸′} = 0 +(퐸, 퐸′ > 0). The self-charge conjugation relation (15) then +implies that the quasiparticle annihilation operator with a +positive energy is equivalent to the creation with a negative +energy as 휂퐸 = 휂† +−퐸, and 횿 is expanded only in terms of +positive energy states as 횿(풓) = ∑ +퐸>0[흋퐸휂퐸 + 흋퐸휂† +퐸]. +The condition (15) can be fulfilled by odd-parity SCs. In +the absence of spin-orbit coupling, the spin-singlet pair +potential is always invariant under the spin rotation, and +the particle-hole exchange operator is given by 2 = −1 +in each spin sector. Hence, spin-singlet SCs cannot satisfy +Eq. (15). Spin-orbit coupling, however, enables even spin +singlet SCs to host Majorana fermions Sato & Ando (2017), +Alicea (2012), Sato & Fujimoto (2016). +Now, let us suppose that a single zero-energy state ex- +ists, and 흋0 is its wave function. Then, we can rewrite the +quantized field to +횿 = 흋0훾 + +∑ +퐸>0 +[ +흋퐸휂퐸 + 흋퐸휂† +퐸 +] +. +(17) +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 5 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +Figure 3: Schematic of the quasiparticle states bound at a +single vortex (a) and energy spectrum of many vortices (b) in +a spinless SC, where the level spacing of vortex bound states +is Δ퐸 ∼ Δ2 +0∕휀F and Δ퐸M denotes the band width of Majorana +states bound at each core. (c) Operations of the braiding ma- +trices 푈12 and 푈23 and the 퐹-matrix in four Majorana modes. +We have introduced 훾, instead of 휂퐸=0, to distinguish the +zero mode from other energy eigenstates. Owing to Eq. (14), +the zero-energy quasiparticle is composed of equal contri- +butions from the particle-like and hole-like components of +quasiparticles, i.e., 흋0 = 흋0. The self-conjugate constraint +in Eq. (15) imposes the following relations: +훾† = 훾, +(18) +and (훾)2 = 1 and {훾, 휂퐸>0} = {훾, 휂† +퐸>0} = 0. The quasipar- +ticle obeying this relation is called the Majorana zero mode. +The zero energy states appear in a topological defect of +topological SCs, such as chiral SCs. In Fig. 3(a), we show +the spectrum of Andreev bound states bound at a vortex +in a chiral SC, where the level spacing between the zero +mode and the lowest excitation state is Δ퐸 ∼ Δ2 +0∕휀F Kop- +nin & Salomaa (1991), Volovik (1999), Read & Green +(2000), Matsumoto & Heeb (2001). In many vortices, the +hybridization between neighboring Majorana modes gives +rise to the formation of the band structure with the width +Δ퐸M ∼ 푒−퐷∕휉 Cheng et al. (2009), Mizushima & Machida +(2010), where 퐷 and 휉 is the mean distance of neighboring +vortices and superconducting coherence length, respectively +(see Fig. 3(b)). +The Majorana zero modes exhibit the non-Abelian any- +onic behaviors Ivanov (2001). To clarify this, we start with +two Majorana zero modes residing in a SC. Using two Ma- +jorana operators, 훾1 and 훾2, we define the new fermion op- +erators 푐 and 푐† as +푐 = 1 +2(훾1 + 푖훾2), +푐† = 1 +2(훾1 − 푖훾2), +(19) +which obey the anticommutation relations, {푐, 푐†} = 1 and +{푐, 푐} = {푐†, 푐†} = 0. The two degenerate ground states are +defined as the vacuum |0⟩ and the occupied state of the zero +energy state |1⟩ = 푐† |0⟩, respectively, where the former +(latter) state is the even (odd) fermion parity. We note that as +the BdG Hamiltonian for superconducting states is generally +commutable with the parity operator, the fermion parity +remains as a good quantum number. For the even (odd) +parity sector, the Hilbert space is spanned by using |0⟩ (|1⟩) +and excited states that are constructed as 휂† +퐸휂† +퐸′휂† +퐸′′ ⋯ |0⟩ +(휂† +퐸휂† +퐸′휂† +퐸′′ ⋯ |1⟩). +The Majorana operators, 훾1, 훾2, and +푖훾1훾2, act on the Hilbert space as the Pauli matrices 휎푥, +휎푦, and 휎푧, respectively. The eigenstates of the Majorana +operators 훾1 and 훾2 are given by the superposition of the +degenerate states with different fermion parity, |0⟩ and +|1⟩. Hence, the eigenstate of a single Majorana zero mode +cannot be a physical state. +Consider 2푁 Majorana zero modes denoted by 훾푗 (푗 = +1, ⋯ , 2푁), where 푁 complex fermions are constructed by +the fusion of 푖th and 푗th Majorana zero modes as 푐푖푗 = (훾푖 + +푖훾푗)∕2. We define the occupation number operator of the +complex fermion, +푛푖푗 ≡ 푐† +푖푗푐푖푗 = 1 +2(1 + 푖훾푖훾푗). +(20) +In a basis that diagonalizes paired Majorana modes 푖훾푖훾푗, +two eigenvalues of the complex fermion, 푛푖푗 = 0 and 1, cor- +respond to the fusion channels ퟏ and 휓, respectively. Hence, +the Majorana zero mode is referred to as the Ising anyon. +2푁 degenerate ground states are expressed in terms of the +occupation numbers as |푛12, 푛34, ⋯⟩, which are separated to +the sectors of the even/odd fermion parity. Here we assume +that the temperature of the system is much lower than the +level spacing (Δ퐸) between the Majorana zero mode and +the lowest excitation (non-Majorana) state. Then, the 2푁−1 +degenerate ground states in each fermion parity sector can be +utilized as topological qubits, where quantum information is +stored in a topologically protected way. +Braiding Majorana zero modes. +Here we discuss +the braiding statistics of Majorana zero modes 훾푖 and +훾푗 and show the non-Abelian statistics of Majorana zero +modes Ivanov (2001), Alicea et al. (2011), Clarke et al. +(2011). +While we consider the exchange of Majorana +zero modes residing in vortices, the theory is also appli- +cable to Majorana zero modes bound at the end points of +one-dimensional topological SCs. +Let 푇푖푗 be the braid operators that satisfy Eqs. (1) and +(2) and transform 훾푖 and 훾푗 to 푒휃푖훾푗 and 푒푖휃푗훾푖, respectively. +The unitary time-evolution of Majorana zero modes is gov- +erned by the Heisenberg equation, 푖 푑 +푑푡훾푗(푡) = [훾푗(푡), (푡)]. +The positions of two Majorana modes are adiabatically ex- +changed in the time interval [0, 푇 ]. The adiabatic condition +defines the lower bound for the time scale of the braiding +operation, 푇 , so that 푇 is much longer than the inverse of +the level spacing between the Majorana zero mode and the +lowest excitation (non-Majorana) state, Δ퐸. In addition, the +upper bound is associated with the band width of Majorana +modes Δ퐸M ∼ 푒−퐷∕휉 (see Fig. 3(b)), i.e., Δ퐸−1 ≪ 푇 ≪ +Δ퐸−1 +M . Within the adiabatic condition, the braiding dynam- +ics of Majorana zero modes can be regarded as the unitary +time evolution, 훾푗(푡) = 푈† +푖푗(푡)훾푗(0)푈푖푗(푡). After the braiding +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 6 of 34 + +(a) +E +个 +0V +[△(p)I +△E ～ △/EF +U12 +C12 +F(b) +E +个 +OV +AEM +0 +C13 +C2423 +C34Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +operation, 훾푖 (훾푗) changes to 훾푗 (훾푖) with an additional phase +shift. Then, the braiding operation is represented by +푈† +푖푗훾푖푈푖푗 = 푒푖휃푖훾푗, +푈† +푖푗훾푗푈푖푗 = 푒푖휃푗훾푖, +(21) +where 푈푖푗 ≡ 푈푖푗(푇 ) is the unitary operator which describes +the exchange operation of two Majorana zero modes 훾푖 and +훾푗, i.e., the representation of 푇푖푗. According to the condi- +tions, (푒푖휃푖훾푗)2 = (푈† +푖푗훾푖푈푖푗)2 = 1 and (훾푗)2 = 1, the phase +shifts obey 휃푖 = 푛휋 and 휃푗 = 푚휋, where 푛, 푚 ∈ ℤ. The +braiding operations must not change the parity of the occupa- +tion number defined in Eq. (20) and thus satisfy 푈† +푖푗푛푖푗푈푖푗 = +푛푖푗, which imposes the condition, 휃1 + 휃2 = (2푛 + 1)휋, on +the phase shift. As a result, the exchange operation of two +Majorana zero modes obtains the following braiding rules: +푈† +푖푗훾푖푈푖푗 = 훾푗, +푈† +푖푗훾푗푈푖푗 = −훾푖. +(22) +Consider four Majorana zero modes denoted by 훾1, +훾2, 훾3, and 훾4, which form two complex fermions as +푐12 ≡ (훾1 + 푖훾2)∕ +√ +2 and 푐34 ≡ (훾3 + 푖훾4)∕ +√ +2 (Fig. 3(c)). +When the Majorana mode “3” adiabatically encircles +the Majorana mode “2”, both Majorana modes operators +acquire the 휋 phase shift, 훾2 ↦ −훾2 and 훾3 ↦ −훾3, +corresponding to the twice operation of Eq. (22). Therefore, +the braiding operation changes the occupation numbers of +the complex fermion 푛12 ≡ 푐† +12푐12 and 푛34 ≡ 푐† +34푐34. For +example, the above braiding generates a pair of the complex +fermions |11⟩ from their vacuum |00⟩. +Here these two +states are orthogonal, ⟨11|00⟩ = 0. The braiding rule can +be generalized to 2푁 Majorana modes. The 2푁 Majorana +modes are fused to 푁 complex fermions, leading to the +2푁−1-fold degeneracy of ground states while preserving +fermion parity. As discussed above, when the 푖th and 푗th +Majorana modes are exchanged with each other, their oper- +ators behave as 훾푖 ↦ 훾푗 and 훾푗 ↦ −훾푖. The representation +of the braid operator 푇푖푗 that satisfies Eq. (22) is given in +terms of the zero mode operators as Ivanov (2001) +푈푖푗 = 푒푖휃 exp +(휋 +4 훾푗훾푖 +) += 푒푖휃 1 +√ +2 +(1 + 훾푗훾푖 +) . +(23) +From now on, we omit the overall Abelian phase factor 푒푖휃 as +it is not important for quantum computation. Equation (23) +also holds in the case of the Moore-Read state Nayak & +Wilczek (1996). For 푁 = 1, there is only a single ground +state in each sector with definite fermion parity, and the +exchange of two vortices results in the global phase of the +ground state by 푒푖휋∕4. One can easily find that for 푁 ≥ 2 +the exchange operators 푈푖푗 and 푈푗푘 do not commute to +each other, [푈푖푗, 푈푗푘] ≠ 0, implying the non-Abelian anyon +statistics of the Majorana zero modes. +For four Majorana zero modes (푁 = 2), twofold de- +generate ground states exist in each ferimon-parity sector: +|00⟩ ≡ |vac⟩ and |11⟩ = 푐† +12푐† +34 |vac⟩ in the sector of even +fermion parity, and |10⟩ = 푐† +12 |vac⟩ and |01⟩ = 푐† +34 |vac⟩ +in the sector of odd fermion parity. For the even-parity sec- +tor, the representation matrix for the exchange of 1 ↔ 2 and +3 ↔ 4 [Fig. 3(c)] is given by +푈12 = 푈34 = 푒−푖 휋 +4 |00⟩ ⟨00| + 푒푖 휋 +4 |11⟩ ⟨11| . +(24) +This merely rotates the phase of the ground state as in the +푁 = 1 case. In contrast, the representation matrix for the +intervortex exchange [2 ↔ 3 in Fig. 3(c)] has the mixing +terms of the two degenerate ground states |00⟩ and |11⟩, +푈23 = 1 +√ +2 +[|00⟩ ⟨00| − 푖 |00⟩ ⟨11| ++ |11⟩ ⟨11| − 푖 |11⟩ ⟨00|] . +(25) +We note that the choice of the pairing to form the complex +fermion is arbitrary. +The change of the fused Majorana +modes corresponds to the change of the basis from one +which diagonalizes 푖훾1훾2 and 푖훾3훾4 to another which +diagonalizes 푖훾1훾3 and 푖훾2훾4. The basis transformation is +represented by the 퐹-matrix as +퐹 = +1 +√ +2 +( +1 +1 +1 +−1 +) +. +(26) +The braiding matrix in Eq. (24) implies that the exchange +of two Majorana zero modes fusing to 휓 (|11⟩) acquires an +additional 휋∕2 phase compared to the fusion channel to ퟏ +(|00⟩). Hence, Eq. (24) satisfies the property of the 푅-matrix +in Eq. (5), i.e., 푅휎휎 +ퟏ += −푖푅휎휎 +휓 . +3.2. Platforms for Majorana zero modes +The realization of non-Abelian anyons requires to freeze +out the internal degrees of freedom of Majorana modes. The +simplest example is spinless 푝-wave SCs/SFs, which emerge +from the low-energy part of spinful chiral 푝-wave SCs. To +clarify this, we start with spin-triplet SCs, whose pair poten- +tial is given by a 2 × 2 spin matrix Leggett (1975) +̂Δ(풌) = +(Δ↑↑(풌) +Δ↑↓(풌) +Δ↓↑(풌) +Δ↓↓(풌) +) +=푖휎휇휎푦푑휇(풌) = 푖휎휇휎푦퐴휇푖̂푘푖, +(27) +where ̂푘푖 ≡ 푘푖∕푘F is scaled with the Fermi momentum 푘F, +and the repeated Greek/Roman indices imply the sum over +푥, 푦, 푧. Here we omit the spin-singlet component. Owing to +the Fermi statistics, the spin-triplet order parameter, 풅(풌), +obeys 풅(풌) = −풅(−풌). For spin-triplet 푝-wave pairing, the +most general form of the order parameter is given by a 3 × 3 +complex matrix, 퐴휇푖 ∈ ℂ, where the components are la- +belled by 휇, 푖 ∈ {푥, 푦, 푧}. +HQVs with Majorana zero modes in SF 3He. We con- +sider the Anderson-Brinkman-Morel (ABM) state Anderson +& Morel (1961), Anderson & Brinkman (1973), as a pro- +totypical example of chiral 푝-wave states hosting Majorana +zero modes. The ABM state is realized in the A-phase of the +SF 3He, which appears in high pressures and high temper- +atures Vollhardt & Wölfle (1990), Volovik (2003). At tem- +peratures above the SF transition temperature, 푇 > 푇c ≈ 1– +2 mK, the normal Fermi liquid 3He maintains a high degree +of symmetry +퐺 = 푆푂(3)푳 × 푆푂(3)푺 × 푈(1), +(28) +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 7 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +where 푆푂(3)푳, 푆푂(3)푺, and 푈(1) are the rotation symme- +try in space, the rotational symmetry of the nuclear spin de- +grees of freedom, and the global gauge symmetry, respec- +tively. The tensor 퐴휇푖 transforms as a vector with respect +to index 휇 under spin rotations, and, separately, as a vector +with respect to index 푖 under orbital rotations. The order pa- +rameter of the ABM state is then given by the complex form +퐴휇푗 = Δ푒푖휑 ̂푑휇( ̂푚푗 + 푖̂푛푗). +(29) +The ABM state is the condensation of Cooper pairs with the +“ferromagnetic” orbital, and spontaneously breaks the time- +reversal symmetry. The orbital part of the order parame- +ter is characterized by a set of three unit vectors forming +the triad ( ̂풎, ̂풏, ̂풍), where ̂풍 = ̂풎 × ̂풏 denotes the orientation +of the orbital angular momentum of Cooper pairs. The re- +maining symmetry in the ABM state is 퐻A = 푆푂(2)푆푧 × +푆푂(2)퐿푧−휑 ×ℤ2, where 푆푂(2)푆푧 is the two-dimensional ro- +tation symmetry in the spin space. The ABM state is also +invariant under 푆푂(2)퐿푧−휑 which is the combined gauge- +orbital symmetry, where the 푈(1) phase rotation, 휑 → 휑 + +훿휑, is compensated by the continuous rotation of the orbital +part about ̂풍, ̂푚푗+푖 ̂푛푗 → 푒−푖훿휑( ̂푚′ +푗+푖 ̂푛′ +푗). In addition, ℤ2 is the +mod-2 discrete symmetry ( ̂풅, ̂풎, ̂풏) → (− ̂풅, − ̂풎, −̂풏). The +manifold of the order parameter degeneracy is then given by +푅A ≃ 퐺∕퐻A ≃ 푆2 +푺 × 푆푂(3)퐿푧,휑∕ℤ2. +(30) +The two-sphere, 푆2 +푺, is associated with the variation of ̂풅. +The degeneracy space has an extra ℤ2 symmetry that the +change from ̂풅 to − ̂풅 can be compensated by the phase ro- +tation 휑 → 휑 + 휋. +The topologically stable linear defects in the ABM state +are characterized by the group of the integers modulo 4 Voll- +hardt & Wölfle (1990), Volovik (1992), Salomaa & Volovik +(1987), Volovik (2003), +휋1(푅A) ≃ 휋1(푆푂(3)∕ℤ2) ≃ ℤ4. +(31) +There exist four different classes of topologically protected +linear defects in the dipole-free case. The four linear defects +can be categorized by the fractional topological charge, +푁A = 0, 1 +2, 1, 3 +2, +(32) +where 푁A = 3∕2 is topologically identical to 푁A = −1∕2. +The representatives of 푁A = 0 and 푁A = 1∕2 classes in- +clude continuous vortex such as the Anderson-Toulouse vor- +tex and half quantum vortex (HQV), respectively. Owing to +푁A = 2 = 0, a pure phase vortex with winding number 2 +is continuously deformed into a nonsingular vortex without +a core, that is, the Anderson-Toulouse vortex Anderson & +Toulouse (1977). The 푁A = 1∕2 vortex is a combination of +the half-wound 풅-disgyration with a half-integer value of the +푈(1) phase winding (Fig. 4). The extra ℤ2 symmetry allows +us to take the half-integer value of the topological charge, +because the 휋-phase jump arising from the half-winding of +the 푈(1) phase (휑 = 휃∕2) can be canceled out by the change +in the orientation of ̂풅 ( ̂풅 → − ̂풅). The 푁A = 1 class in- +cludes a pure phase vortex with odd winding number and the +radial/tangential disgyrations without phase winding. The +latter was originally introduced by de Gennes as 풍-textures +with a singularity line De Gennes (1973), Ambegaokar et al. +(1974). +The vortex with the fractional charge 푁A = 1∕2 is a +harbor for spinless Majorana zero modes. We introduce the +center-of-mass coordinate of Cooper pairs, 푹 = (휌, 휃, 푧), as +̂Δ(풌) → ̂Δ(풌, 푹), where 휌 = +√ +푥2 + 푦2. The vortex core is +located at 휌 = 0. The vortex state is subject to the boundary +condition at 휌 → ∞ where the orbital angular momentum +of the Cooper pair is aligned to the 푧-axis (̂풍 ∥ ̂풛) and the +푈(1) phase 휑 continuously changes from 0 to 2휋휅 along the +azimuthal (휃) direction, +퐴휇푖(휌 = ∞, 휃) = Δ푒푖휅휃 ̂푑휇(휃)(̂푥푗 + 푖 ̂푦푗). +(33) +Owing to the spontaneous breaking of the gauge-orbital +symmetry, there are two classes for the vorticity 휅: Integer +quantum vortices with 휅 ∈ ℤ and HQVs with 휅 ∈ ℤ∕2. In +the HQVs, both the 푈(1) phase and ̂풅 rotate by 휋 about the +vortex center (see Fig. 4). In genral, the ̂풅-texture for HQVs +is obtained as +̂풅(휃) = cos(휅sp휃)̂풙 + sin(휅sp휃)̂풚, +(34) +where 휅sp denotes the winding of ̂풅. The HQV is character- +ized by (휅, 휅sp) = (1∕2, ±1∕2), while the integer quantum +vortex has (휅, 휅sp) = (1, 0). It is remarkable to notice that +since the ABM state is the equal spin pairing state, the order +parameter for the HQV is recast into the representation in +the spin basis as +̂Δ = Δ +[ +푒푖(휅−휅sp)휃 |↑↑⟩ + 푒푖(휅+휅sp)휃 |↓↓⟩ +] +. +(35) +For the HQV with (휅, 휅sp) = (1∕2, 1∕2) the |↑↑⟩ Cooper pair +possesses the spatially uniform phase, while the |↓↓⟩ pair has +the phase winding of 2휋 around the vortex as in a conven- +tional singly quantized vortex. Thus, the vortex-free state +in the ↑ spin sector exhibits fully gapped quasiparticle exci- +tations, while the low-lying structures in half quantum vor- +tex are effectively describable with a singly quantized vor- +tex in the ↓ spin sector, i.e., the spin-polarized chiral 푝-wave +SC. An odd-vorticity vortex in the spin-polarized chiral sys- +tem hosts a single spinless Majorana zero mode that obeys +non-Abelian statistics. The existence of non-Abelian any- +onic zero modes in half quantum vortices was first revealed +by Ivanov, who developed the non-Abelian braiding statis- +tics of vortices with spinless Majorana zero modes Ivanov +(2001). +In the bulk A-phase of the SF 3He, the formation of con- +tinuous vortices with the ̂풍-texture, which are characterized +by the topological charge 푁 = 0, is an obstacle to realizing +the HQVs. As the orientation of the ̂풍-vector is associated +with the orbital motion of the Cooper pair, the ̂풍-texture can +be uniformly aligned in a parallel plate geometry with thick- +ness 퐷. The motion of Cooper pairs is confined in the two- +dimensional plane and ̂풍 is locked perpendicular to the plates. +Applying a magnetic field further restricts the orientation of +̂풅 to the two-dimensional plane perpendicular to the applied +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 8 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +Figure 4: Schematic of the HQV realized in the ABM state. +The color map shows the U(1) phase winding from 휑 = 0 (red) +at 휃 to 휋 (blue) at 휃 = 2휋, and the arrows represent the texture +of the ̂풅-vectors shown in Eq. (34) with 휅sp = 1∕2. +field, which is a favorable situation to stabilize the HQVs. In +the parallel plate geometry with 퐷 = 12.5 휇m, the measure- +ments of NMR frequency shift observed that the ̂풅-vectors +are confined to the two-dimensional plane perpendicular to +̂풍 Yamashita et al. (2008). The experiment was performed in +a rotating cryostat at ISSP, University of Tokyo. The parallel +plates are rotated at the angular velocity ≲ 12rad∕s but no +conclusive evidence of HQVs was observed Yamashita et al. +(2008). Although the SF 3He-A thin film provides an ideal +platform for HQVs with Majorana zero modes, the realiza- +tion of HQVs remains as a challenging task. +Another promising route to realize HQVs with Majo- +rana zero modes is to artificially introduce well-controlled +disorders with high-porosity aerogel. +In particular, the +polar phase was observed in anisotropic aerogels consisting +of uniaxially ordered alumina strands, called the nematic +aerogels Dmitriev et al. (2015), Halperin (2019) [See +Fig. 5(a)]. +The order parameter of the polar phase is +given by 퐴휇푖 = Δ푒푖휑 ̂푑휇 ̂푧푖, where the orbital state of the +Cooper pair (̂푧푖) is confined by the uniaxially anisotropic +disorders. As in the ABM state in the bulk 3He, the texture +of the ̂풅-vector concomitant with the half-integer vorticity +can realize HQVs in the polar phase. In the polar phase, +HQVs are energetically preferable to integer quantum +vortices at zero magnetic fields and magnetic fields applied +along the uniaxial anisotropy Nagamura & Ikeda (2018), +Mineev (2014), Regan et al. (2021). +Indeed, the HQVs +were experimentally observed in nematic aerogels under +rotation Autti et al. (2016). The HQVs were also created by +temperature quench via the Kibble-Zurek mechanism Rysti +et al. (2021). As shown in Fig. 5(a), the superfluid phase +diagram in nematic aerogels is drastically changed from that +of the bulk 3He without disorders, where the polar-distorted +A and B (PdA and PdB) phases are stabilized in addition +to the polar phase. The NMR measurements performed in +Ref. Mäkinen et al. (2019) observed that the HQVs survive +across the phase transition to the PdA phase. As shown in +Fig. 4, the HQV is accompanied by the ̂풅-soliton in which +the ̂풅 orientation rotates. Figure 5(b) shows the observed +NMR spectra which have satellite peaks in addition to the +(a) +(b) +Figure 5: (a) The experimental setup and the phase diagram +in the liquid 3He with nematic disorders and (b) NMR spec- +tra at pressure 푃 = 7 bar and 푇 = 0.60푇c in the presence of +a magnetic field perpendicular to the anisotropy direction of +nematic disorders Mäkinen et al. (2019), where 푇c is the crit- +ical temperature of the bulk SF 3He without disorders. The +disorders consist of nearly parallel Al2O3 strands, where the +diameter and mean distance are 푑2 ≈ 8 nm and 푑1 ≈ 50 nm, +respectively. In (b), the main peaks with green and magenta +colors correspond to the signal of the bulk PdA phase, while +the satellite peaks originate from the spin excitation bound to +the ̂풅-solitons connecting pairs of HQVs. The satellite peak +remains unchanged after the thermal cycling illustrated by pur- +ple arrows in (a). Both figures are taken from Ref. Mäkinen +et al. (2019). +main peak around the Larmor frequency. The main peak +is a signal of the bulk PdA phase. The satellite peak orig- +inates from the spin excitation localized at the ̂풅-solitons +connecting pairs of HQVs. The order parameter of the PdA +phase is given by 퐴휇푖 = Δ푒푖휑 ̂푑휇( ̂풎 + 푖휀̂풏)푖, where ̂풎 is +aligned along the axis of nematic aerogels and 휀 ∈ (0, 1) +is the temperature- and pressure-dependent parameter on +the distortion of Eq. (29) by nematic aerogels. Although +the HQVs in the polar phase host no Majorana zero modes, +the low energy structure of the HQVs in the PdA phase is +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 9 of 34 + +a +b +Rotation +NMRpick-up coils +2 +axis + 휇). +In fact, if the proximitized superconducting +gap is taken into account, a combination of spin-orbit +coupling with the superconducting gap induces topological +odd-parity superconductivity. The topological phase with +the spinless Majorana zero mode appears in the higher +magnetic field satisfying 퐵 > 퐵c = +√ +Δ2 + 휇2. +A direct signature of Majorana zero mode is the quanti- +zation of a zero-bias peak in differential conductance, where +the height of the zero-bias peak stemming from the Majo- +rana zero mode is predicted to be quantized to the universal +conductance value of 2푒2∕ℎ at zero temperature Akhmerov +et al. (2011), Fulga et al. (2011). Consider a charge-transfer +process through a normal metal-SC junction. When an elec- +tron with the incident energy 퐸 enters from the normal metal +to the SC, it forms the Cooper pair with an electron in the +Fermi sea at the interface and a hole is created in the nor- +mal side as a consequence of momentum conservation. Such +a process in which electrons are retroreflected as holes is +called Andreev reflection. Let 휙in,out +퐸 += [푢퐸, 푣퐸]t be the two- +component wavefunctions of the incident and reflected par- +ticles, respectively, where 푢퐸 (푣퐸) accounts for the electron +(hole) component. We now consider the scattering prob- +lem 휙out +퐸 (풙) = 푆(퐸)휙in +퐸(풙). The 푆-matrix is defined in the +particle-hole space as +푆(퐸) = +( +푟ee(퐸) +푟eh(퐸) +푟he(퐸) +푟hh(퐸) +) +, +(36) +which is a unitary matrix 푆 ∈ 푈(2). The coefficient 푟ee +(푟eh(퐸)) is the amplitude of the normal (Andreev) reflection, +and the others are the reflection coefficients of incident holes. +The conductance 퐺(퐸) at the normal/SC interface is ob- +tained with the conductance quantum 퐺0 = 푒2∕ℎ per spin +as 퐺(퐸) = 2퐺0|푟eh(퐸)|2. The particle-hole symmetry im- +poses on the 푆 matrix the constraint, 푆(퐸)−1 = 푆(−퐸), +leading to det 푆(0) = |푟ee(0)|2 − |푟eh(0)|2 at 퐸 = 0. Let 푉 +be the unitary matrix defined by 푉 휙0 = (Re푢, Im푢). In this +basis, the scattering matrix 푆(0) is transformed as 푆′(0) = +푉 푆(0)푉 †, where 푆′(0) ∈ 푂(2) is an orthogonal matrix sat- +isfying 푆′† = 푆′−1 = 푆′tr and det 푆(0) = det 푆′(0) = ±1. +Hence, there are two different processes, a perfect normal +reflection process (det 푆(0) = +1) and a perfect Andreev +reflection process (det 푆(0) = −1). +This discrete value, +det 푆(0) = ±1, is a topological invariant representing the +parity of the number of Majorana zero modes residing at the +interface. When det 푆(0) = −1, there exists at least one Ma- +jorana zero mode, which involves the perfect Andreev reflec- +tion process and the quantized conductance, +퐺(0) = 2푒2 +ℎ . +(37) +The conductance has recently been measured in a junc- +tion system of InSb-Al hybrid semiconductor-SC nanowire +devices. The differential conductance yields the plateau be- +havior where the peak height reaches values 2푒3∕ℎ Zhang +et al. (2021). In the device used in the experiment, the tunnel +barrier is controlled by applying a gate voltage to the narrow +region between the electrode and the region where the prox- +imity effect occurs in the semiconductor wire. In the vicin- +ity of the barrier, the unintentionally formed quantum dot or +nonuniform potential formed in the vicinity of the interface +gives rise to the formation of nearly zero-energy Andreev +bound states. Such Andreev bound states mimic the plateau +of 퐺(0) = 2푒2∕ℎ even in the topologically trivial region of +the magnetic field (퐵 < 퐵c) Liu et al. (2017), Prada et al. +(2020), Cayao & Burset (2021), Yu et al. (2021), Valentini +et al. (2021). From the plateau of 퐺(0), it is not possible to +identify whether the observed 퐺(0) ∼ 2푒2∕ℎ is due to Majo- +rana zero mode or the effect of accidentally formed s bound +states. Alternative experimental schemes to distinguish the +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 10 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +trivial and topological bound states have been proposed Liu +et al. (2018), Ricco et al. (2019), Yavilberg et al. (2019), +Awoga et al. (2019), Zhang & Spånslätt (2020), Schulen- +borg & Flensberg (2020), Pan et al. (2021), Liu et al. (2021), +Ricco et al. (2021), Thamm & Rosenow (2021), Chen et al. +(2022), Sugeta et al. (2022). +Vortices in Fe(Se,Te). +The iron-based SC Fe(Se,Te) +is a candidate of topologically nontrivial superconducting +state supporting Majorana zero modes. +In the parent +material FeSe, the 3푑 electrons of Fe near the Fermi +level mainly contribute to superconductivity, and the 푝푧 +orbitals of Se appear on the higher energy. +Substitution +of Se with Te causes a band inversion between the 푝푧 +and 3푑 orbitals. +As a result of the band inversion, the +normal state of FeTe1−푥Se푥 is topologically nontrivial, and +accompanied by the surface Dirac fermions Zhang et al. +(2018). Below the superconducting critical temperature, the +superconducting gap is proximitized to the surface Dirac +states. It was theoretically pointed out that the topological +phase with a spinless Majorana zero mode can be realized +when the superconducting proximity effect occurs in the +Dirac fermion system Sato (2003), Fu & Kane (2008). +Therefore, the surface state of Fe(Se,Te) is a topological +superconucting state. When a magnetic field is applied to +Fe(Se,Te), the vortex lines penetrate to the surface state and +the zero energy state appears. +The wave function of the +zero mode is tightly bound at the intersection of the vortex +line and the surface Hosur et al. (2011), Kawakami & Hu +(2015). +When a magnetic field is applied to a SC, a quantized +vortex penetrates. The magnetic flux is accompanied by the +2휋푚 winding of the 푈(1) phase and the superconducting +gap vanishes. In other words, a quantized vortex can be re- +garded as a quantum well with a radius of 휉 and a height +of Δ. Hence, the Andreev bound states are formed and the +level spacing between them is on the order of Δ2∕휀F, where +the level spacing is about 100–200 휇eV in Fe(Se,Te). In the +topological phase, the lowest level has the exact zero energy, +and the quasiparticle behaves as Majorana fermion. Ultra- +low temperature STM/STS with high energy resolution ob- +served a pronounced zero-bias conductance peak Machida +et al. (2019). If a Majorana zero mode is bound to the vortex, +the conductance should be quantized to the universal value +2푒2∕ℎ independent of tunnel barriers. In the tunneling spec- +troscopy performed while changing the distance between the +sample surface and the STM tip, the height of the zero-bias +conductance peak is approximately 0.6 times as large as the +universal value stemming from the Majorana zero mode Zhu +et al. (2020). Although 2푒2∕ℎ has not been reached, this +plateau structure strongly suggests the existence of Majorana +zero modes because it cannot be explained by non-Majorana +vortex bound states. +3.3. Topological quantum computation +Quantum computation based on the braiding of Majo- +rana zero modes is basically along the two directions: imple- +mentation of quantum gates and measurement-based quan- +tum computation. The unitary evolution of the qubits is con- +trolled by a set of discrete unitary operations, i.e., quantum +gates. The simple example of the quantum gates acting on a +single qubit is the set of the Pauli gates, which are given by +the three Pauli matrices 푋 ≡ 휎푥, 푌 ≡ 휎푦, and 푍 ≡ 휎푧. The +multi-qubit gate operation can be implemented by a com- +bination of a set of single-qubit gates and the controlled- +NOT (CNOT) gate. According to the Solovay-Kitaev theo- +rem Nielsen & Chuang (2010), an arbitrary single-qubit gate +can be approximated by a sequence of the discrete gate op- +erations (퐻, 푆, 푇 ), where 퐻 = (푋 + 푍)∕ +√ +2, 푆 = +√ +푍, +and 푇 = +√ +푆 are the Hadamard gate, the single-qubit 4휋 +rotation, and the 푇 -gate (휋∕8-gate), respectively. Universal +quantum computation can be implemented by a sequence of +the single-qubit gates (퐻, 푆, 푇 ) and the CNOT gate. +In Majorana qubits, the Pauli gates are expressed in +terms of the braiding operations as 푋 = 푖푈2 +23, 푌 = 푖푈2 +31, and +푍 = 푖푈2 +12, and the Hadamard and 푆 gates are implemented +by a combination of such operations as 퐻 = 푖푈12푈23푈12 +and 푆 = 푒푖휋∕4푈12. +In addition, the CNOT gate can be +implemented by a combination of the measurement and +braiding operations in two Majorana qubits (i.e., 8 Majorana +zero modes) with a single ancilla Majorana qubit Bravyi +(2006). All the Clifford gates (퐻, 푆, CNOT) are realized +as a composition of braiding operators in a topologically +protected way. According to the Gottesman-Knill theorem, +however, quantum circuits only using the elements of +Clifford group can be efficiently simulated in polynomial +time on a classical computer Nielsen & Chuang (2010). +Indeed, degenerate quantum states composed of multiple +Ising anyons offer tolerant storage of quantum information +and their braiding operations provide all necessary quantum +gates in a topologically protected way, except for the non- +Clifford 푇 -gate. The 푇 -gate can be implemented only in a +topologically unprotected way. For instance, Karzig et al. +proposed a scheme to implement the 푇 -gate in a Y-shaped +junction accompanied by 4 Majorana zero modes Karzig +et al. (2016). +As mentioned in Sec. 2, Fibonacci anyon systems can +offer a platform for universal topological quantum compu- +tation, where all the single-qubit gates (퐻, 푆, 푇 ) and the +CNOT gate are implemented by the braiding manipulations +of the anyons in a topologically protected way Preskill +(2004), Bonesteel et al. (2005), Hormozi et al. (2007). +Another way to realize universal quantum computation +in Majorana qubits is measurement-based quantum com- +putation. +It was realized that all braiding manipulations +can be implemented in a topologically protected manner +by the measurements of topological charges of pairwise +anyons Bonderson et al. (2008, 2009). The process of the +quantum information encoded to Majorana qubits can take +place by a series of simple projective measurements without +braiding Majorana modes. The building block is a Coulomb +blockaded Majorana box which is made from even numbers +of Majorana modes in a floating topological SC Plugge et al. +(2017), Karzig et al. (2017), Oreg & von Oppen (2020). +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 11 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +3.4. Symmetry-protected non-Abelian anyons +Symmetry-protected non-Abelian anyons in spinful SCs +and SFs were discussed for class D Ueno et al. (2013), Sato +et al. (2014), Fang et al. (2014) and for class DIII Liu et al. +(2014), Gao et al. (2016). In the former (latter) case, mirror +reflection symmetry (time reversal symmetry) plays an es- +sential role on the topological protection of non-Abelian na- +ture. In addition, unitary symmetry-protected non-Abelian +statistics has been theoretically proposed Hong et al. (2022). +The non-Abelian statistics of vortices supporting multiple +Majorana zero modes has also been discussed in Refs. Ya- +sui et al. (2011) and Hirono et al. (2012) in the context of +high-energy physics. +Mirror and unitary symmetries. As the simple ex- +ample of symmetry-protected non-Abelian anyons, we con- +sider integer quantum vortices in chiral 푝-wave SCs and 3He- +A Sato et al. (2014), where each vortex core supports spin- +ful Majorana zero modes. Contrary to the standard wisdom, +a pair of Majorana zero modes in integer quantum vortices +can be protected by the mirror symmetry and obey the non- +Abelian statistics Ueno et al. (2013), Sato et al. (2014). +Let us consider two-dimensional superconducting film +and assume that the normal state holds the mirror symmetry +with respect to the 푥푦-plane, 푀푥푦ℎ(풌)푀† +푥푦 = ℎ(풌), where +풌 = (푘푥, 푘푦) is the two-dimensional momentum and the +mirror operator is defined as 푀푥푦 = 푖휎푧. The nontrivial +topological properties are characterized by the first Chern +number in each mirror subsector. +When Δ(풌) obeys +푀푥푦Δ(풌)푀t +푥푦 = 휂Δ(풌) (휂 = ±), the BdG Hamiltonian +is commutable with the mirror reflection operator in the +particle-hole space, 휂, as +[휂, (풌)] = 0, +휂 = +(푀푥푦 +0 +0 +휂푀∗ +푥푦 +) +. +(38) +Thus, the eigenstates of (풌) are the simultaneous eigen- +states of 휂. Let |푢(휆) +푛 (풌)⟩ and 퐸(휆) +푛 +be the wavefunction +and eigenenergy of the Bogoliubov quasiparticles in each +mirror subsector, where the 휆 = ±푖 are the eigenvalues of +휂. Then, the first Chern number is defined in each mirror +subsector, +Ch(휆) +1 += 푖 +2휋 ∫ (휆) ∈ ℤ, +(39) +where (휆) = 푑(휆) is the Berry curvature in each mirror +subsector and (휆) +휇 (풌) = ∑ +퐸(휆) +푛 <0 ⟨푢(휆) +푛 (풌)|휕푘휇푢(휆) +푛 (풌)⟩. The +nonzero value ensures the existence of the zero energy state +in the 휆 subsector. For the 3He-A thin film and chiral 푝-wave +SCs, |Ch(휆) +1 | = 1 in each mirror subsector, implying that +integer quantum vortices support two Majorana zero modes +per each core. +Multiple Majorana zero modes behave as non-Abelian +anyons only when the mirror subsector holds the particle- +hole symmetry, which are referred to as mirror Majorana +zero modes. +The condition for each mirror subsector to +maintain the particle-hole symmetry is given by Ueno et al. +(2013), Sato et al. (2014) +{, 휂} = 0. +(40) +Figure 6: Complex fermions formed by intervortex pairs (a) and +intravoretx pairs (b), where 훾푖 +푎 denotes a Majorana zero mode +with internal degrees of freedom 푎 (e.g., spin) bound at the +푖th vortex. (c) Schematic of the exchange of two vortices with +multiple Majorana zero modes. (d) When the system holds a +unitary symmetry such as the mirror symmetry in Eq. (38), the +operation (c) is equivalent to the exchange of two Majorana +zero modes in each sector. +For integer quantum vortices, the condition depends on the +orientation of the 풅-vector. For ̂풅 ∥ ̂풛, the mirror subsector +supports its own particle-hole symmetry, but otherwise the +subsector does not maintain the particle-hole symmetry and +belongs to class A. +Now let us clarify the non-Abelian statistics of spin- +degenerate Majorana modes. Consider 2푁 integer quantum +vortices. +Two Majorana zero modes bound at the 푖th +vortex are denoted by 훾푖 +휆 with mirror eigenvalues 휆 = ±푖. +The Majorana zero modes satisfy the self-conjugate +condition 훾푖 +휆 = (훾푖 +휆)† and the anticommutation relation, +{훾푖 +휆, 훾푗 +휆′} = 2훿푖,푗훿휆,휆′. +In contrast to spinless Majorana +zero modes, there are two possibilities to form a complex +fermion: (i) intervortex pairs, 푐휆 +푖푗 ≡ (훾푖 +휆 + 푖훾푗 +휆)∕2 and (ii) +intravortex pairs, 휓푖 ≡ (훾푖 +휆=푖 + 푖훾푖 +휆=−푖)∕2 [See Figs. 6(a,b)]. +In the former case (i), the exchange operators of the 푖th +and 푗th vortices are defined in a manner similar to that for +spinless Majorana zero modes as +푈휆† +푖푗 훾푖 +휆푈휆 +푖푗 = 훾푗 +휆, +푈휆† +푖푗 훾푗 +휆푈휆 +푖푗 = −훾푖 +휆. +(41) +The above transformation is realized by the unitary operator, +푈휆 +푖푗 = exp +(휋 +4 훾푗 +휆훾푖 +휆 +) += +1 +√ +2 +( +1 + 훾푗 +휆훾푖 +휆 +) +, +(42) +Similarly to 푈푖푗 and 푈푗푘 in spinless Majorana zero modes, +the exchange operators 푈휆 +푖푗 and 푈휆 +푗푘 defined in each mirror +subsector do not commute to each other, which implies the +non-Abelian anyon statistics of integer quantum vortices +hosting mirror Majorana zero modes. +In the case (ii) [Fig. 6(b)], +a complex fermion +is formed as a local pair of two mirror Majorana +modes, +which +also +obeys +the +non-Abelian +statis- +tics Yasui et al. (2012), Sato et al. (2014). +The +expression of the exchange operator is obtained as +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 12 of 34 + +(a) +b +(c) +2 +a(b) +a +(d) +YbNon-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +푈푖푗 = 1 + 휓푗휓† +푖 + 휓† +푗 휓푖 − 휓† +푖 휓푖 − 휓† +푗 휓푗 + 2휓† +푗 휓푗휓† +푖 휓푖. In +general, the exchange operators are not commutable with +each other, [푈푖푗, 푈푗푘] ≠ 0. As the operator preserves the +fermion number 푁f += ∑ +푖 휓† +푖 휓푖, the degenerate ground +states are expressed in terms of the occupation number of +the complex fermion in each vortex. For example, let us +consider the four-vortex state |1100⟩ where the first and +second vortices are accompanied by the Dirac zero modes, +while the third and fourth are not. Up to a phase factor, +this state changes under 푈12 and 푈34 as |1100⟩ → |1100⟩ +and |1100⟩ → |1010⟩, respectively. +The complete rep- +resentations of the exchange operators 푈푖푗 are presented +in Ref. Yasui et al. (2012). The extension to non-Abelian +statistics of multiple complex fermions was discussed in +Ref. Yasui et al. (2013). +When the BdG Hamiltonian maintains the mirror +symmetry in Eq. (38), as mentioned above, the braiding +of vortices supporting spinful Majorana modes is decom- +posed into two individual exchanges between Majorana zero +modes 훾푖 +휆 and 훾푗 +휆 in each mirror subsector [see also Figs. 6(c) +and 6(d)] and the exchange matrices are represented by +Eqs. (41) and (42). +This argument is applicable for the +systems hosting multiple Majorana modes protected by +unitary symmetries Hong et al. (2022), where the couplings +between Majorana zero modes in each core are excluded by +the unitary symmetries. The braiding of two vortices with +푛 unitary-symmetry-protected multiple Majorana modes +generically reduces to the 푛 independent braiding operations +in each sector as +푈푖푗 = +∏ +푎 +푈푎 +푖푗, +(43) +where 푎 denotes the internal degrees of freedom of Majo- +rana zero modes. The unitary time evolution representing +the braiding process does not dynamically break the unitary +symmetry, which prohibits the coupling between Majorana +modes in different subsectors labeled by 푎. +The mirror +reflection symmetry in Eq. (38) is an example of such +symmetry-protected non-Abelian anyons. Another example +is the non-Abelian vortices in dense QCD matter which +trap multiple Majorana zero modes in each core Yasui +et al. (2010), Fujiwara et al. (2011). As discussed below, +such vortices with multiple Majorana zero modes obey +the non-Abelian statistics and the braiding matrices are +identical with the elements in the Coxeter group Yasui et al. +(2011), Hirono et al. (2012). +Contrary to unitary symmetries, the braiding process, +characterized as a unitary evolution, may dynamically +break antiunitary symmetry such as the time-reversal +symmetry. We note that in contrast to time-reversal -broken +topological SCs such as superconducting nanowires, topo- +logical superconductors with time-reversal symmetry do +not require an external magnetic field for realizing the +topological phase and can keep the topological gap close to +the proximity-induced superconducting gap Haim & Oreg +(2019), Wong & Law (2012), Zhang et al. (2013). Hence, +the Majorana-Kramers pairs leads to longer decoherence +time of the stored quantum information Liu et al. (2014). +As mentioned above, however, the braiding process of +the Majorana-Kramers pairs may dynamically break the +antiunitary symmetry. Such dynamical symmetry breaking +gives rise to the local mixing of the Majorana-Kramers +pairs Wölms et al. (2014, 2016), Knapp et al. (2020). +Gao et al. +proposed the conditions to protect the non- +Abelian statistics of the Majorana-Kramers pairs Gao et al. +(2016). In addition, Tanaka et al. examined by numerical +simulations the tolerance of non-Abelian braidings of +Majorana-Kramers pairs against two types of perturba- +tions which may cause decoherence of Majorana-Kramers +quits Tanaka et al. (2022): (i) Applied magnetic fields, and +(ii) the effect of a gate-induced inhomogeneous potential at +junctions of superconducting nanowires. The former break +time-reversal symmetry and generate the energy gap of +Majorana states, while the latter gives rise to non-Majorana +low-energy Andreev bound states Kells et al. (2012), Liu +et al. (2017), Moore, Zeng, Stanescu & Tewari (2018), +Moore, Stanescu & Tewari (2018), Pan et al. (2020), Pan & +Das Sarma (2020). The numerical simulation revealed that +the non-Abelian braiding is successful when the direction +of the applied magnetic field preserves the chiral symmetry +in the initial and final states of a braiding process, where the +chiral symmetry is a combination of time-reversal symmetry +and mirror symmetry Tanaka et al. (2022). +Remarkably, +this tolerance is preserved even when the intermediate +states of the braiding process breaks this symmetry. As for +(ii), non-Majorana bound states emergent in gate-induced +inhomogeneous potentials make Majorana-Kramers qubits +vulnerable to quasiparticle poisoning and disturbe the +braiding protocol. However, the influence can be ignored +when the width of the gate-induced potential is sufficiently +smaller than the superconducting coherence length. +Multiple Majorana zero modes and Coxeter group. It +has been demonstrated that the non-Abelian statistics of vor- +tices hosting three Majorana zero modes has a novel struc- +ture, when the Majorana modes have additional 푆푂(3) sym- +metry Yasui et al. (2011), Hirono et al. (2012). The repre- +sentation of braiding operations in four vortices is given by a +tensor product of two matrices, where one is identical to the +matrix for the braiding of spinless Majorana zero modes, and +the other is a generator of the Coxeter group. +Let 훾푖 +푎 (푎 = 1, 2, 3) be the operators of three Majorana +zero modes in the 푖th vortex, belonging to the triplet of +푆푂(3). +Consider four vortices hosting three Majorana +zero modes in each core. The braiding of these vortices is +decomposed into the three individual exchanges between +Majorana zero modes 훾푖 +푎 and 훾푗 +푎 [see Figs. 6(c,d)]. +For +each component 푎, Majorana zero modes 훾푖 +푎 and 훾푗 +푎 under +braiding manipulations transforms in the same way as +Eq. (41) and the exchange matrices, 푈푎 +푖푗, are obtained by +푈휆 +푖푗 → 푈푎 +푖푗 in Eqs. (41) and (42). Then, the representations +of 푈푖푗 for vortices with triplet Majorana zero modes are +obtained by the 64 × 64 matrix, 푈푖푗 = ∏ +푎=1,2,3 푈푎 +푖푗, as in +Eq. (43). +We now introduce the complex fermion operators as the +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 13 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +nonlocal pairs of Majorana zero modes, 푐푎 +푖푗 = (훾푖 +푎 + 푖훾푗 +푎)∕2. +For two vortices (i.e., six Majorana modes), this leads to +the 23-fold degenerate ground states and the Hilbert space +is spanned by the four basis sets: singlet-even |ퟏ0⟩ ≡ |0⟩ +(vacuum) and triplet-even |ퟑ2⟩ ≡ +1 +2!휖푎푏푐푐푏† +푖푗 푐푐† +푖푗 |0⟩ (occu- +pied by two fermions) for even fermion parity and singlet- +odd |ퟏ3⟩ ≡ 1 +3!휖푎푏푐푐푎† +푖푗 푐푏† +푖푗 푐푐† +푖푗 |0⟩ (occupied by three fermions) +and triplet-odd |ퟑ1⟩ ≡ 푐푎† +푖푗 |0⟩ (occupied by single fermion). +In the case of four vortices, the ground state degeneracy is +26 = 64 and the bases of the Hilbert space are singlet (ퟏ), +triplet (ퟑ), and quintet (ퟓ) states, which are further divided +in terms of the fermion parity. The exchange operator is ex- +pressed as a product of two 푆푂(3) invariant unitary opera- +tors, +푈푖푗 = +∏ +푎=1,2,3 +푈푎 +푖푗 = 휎푖푗ℎ푖푗 +(44) +where both matrices are given in terms of 훾푎 +푖 as +휎푖푗 = 1 +2 +( +1 − 훾1 +푗 훾2 +푗 훾1 +푖 훾2 +푖 − 훾2 +푗 훾3 +푗 훾2 +푖 훾3 +푖 − 훾3 +푗 훾1 +푗 훾3 +푖 훾1 +푖 +) +, +(45) +and +ℎ푖푗 = +1 +√ +2 +( +1 − 훾1 +푗 훾2 +푗 훾3 +푗 훾1 +푖 훾2 +푖 훾3 +푖 +) +. +(46) +While the matrices ℎ푖푗 are a natural extension of that origi- +nally introduced in Ref. Ivanov (2001), the matrices 휎푖푗 are +proper to vortices with three or more Majorana zero modes. +It was demonstrated that the matrices 휎푖푗 are identified with +the elements in the Coxeter group which satisfies the rela- +tions +(휎푖푗)2 = 1, (휎푖푗휎푗푘)3 = 1, (휎푖푗휎푘푙)2 = 1. +(47) +The Coxeter group is a symmetry group of polytopes in high +dimensions such as a triangle and a tetrahedron. The ex- +change operators acting on the singlet (ퟏ) and triplet (ퟑ) are +identified with the elements in the Coxeter group, such as +a 2-simplex (triangle) under the reflections for the singlet +and a 3-simplex (tetrahedron) under the reflections for the +triplet Yasui et al. (2011). The decomposition of the braid- +ing operators 푈푖푗 in the 푆푂(3) triplet was generalized to the +Majorana zero modes of arbitrary odd 푛M ≥ 3 with 푆푂(푛M) +symmetry Hirono et al. (2012). +Such multiple Majorana zero modes were first found in +Refs. Yasui et al. (2010), Fujiwara et al. (2011) inside the +cores of color flux tubes (“non-Abelian” vortices) Balachan- +dran et al. (2006), Nakano et al. (2008), Eto & Nitta (2009), +Eto et al. (2014) in high density quark (QCD) matter Alford +et al. (2008). They were also discussed in edges of a topolog- +ical superconducting wire coupled to a normal lead Kashuba +& Timm (2015). +4. Non-Abelian vortex anyons +Here we introduce non-Abelian anyons made of bosonic +excitations, which is, non-Abelian vortices obeying a +non-Abelian statistics Bais (1980), Wilczek & Wu (1990), +Bucher (1991), Brekke et al. (1993), Lo & Preskill (1993), +Lee (1994), Brekke et al. (1997), Mawson et al. (2019). +These non-Abelian vortices are sometime called fluxons.2 +4.1. Non-Abelian vortices +When a symmetry 퐺, that is either global or local, is +spontaneously broken into its subgroup 퐻, there appears an +order parameter space +푀 ≃ 퐺∕퐻 +(48) +parameterized by Nambu-Goldstone modes. The first homo- +topy group of the order parameter space +휋1(퐺∕퐻) ≃ 휋0(퐻) +(49) +is responsible for the existence of quantum vortices, where +we have assumed that 퐺 is semisimple. We further have +휋0(퐻) ≃ 퐻∕퐻0(≃ 퐻 for a discrete group 퐻) +(50) +with a normal subgroup 퐻0 of 퐻. +When 휋1(퐺∕퐻) is +Abelian (and thus 퐻∕퐻0 (for semisimple 퐺) is Abelian), +vortices are Abelian, while when it is non-Abelian, vortices +are non-Abelian Balachandran et al. (1984), Alford et al. +(1990, 1991, 1992). +One of characteristic features of non-Abelian vortices is +that 퐻 is not globally defined (or multi-valued): the unbro- +ken symmetry 퐻휃 depends on the azimuthal angle 휃 around +a non-Abelian vortex as 퐻휃 = 푔(휃)퐻휃=0푔−1(휃) with 푔(휃) ∈ +퐺, 푔(0) = ퟏ and 푔(2휋) taking a disconnected component +of 퐻∕퐻0, see Eq. (50). Then, after an adiabatic transport +along a loop encircling the non-Abelian vortex, the unbroken +symmetry at 휃 = 2휋 does not have to come back: 퐻휃=2휋 ≠ +퐻휃=0. This is called topological obstruction, and the sym- +metry 퐻 is topologically broken down to a subgroup 퐾 ≡ +{ℎ|[ℎ, 푔(2휋)] = 0, ℎ ∈ 퐻} which is single-valued and glob- +ally defined Balachandran et al. (1984), Alford et al. (1990). +This is also called topological symmetry breaking. When 퐺 +and 퐻 are local gauge symmetries, it gives a non-Abelian +Aharonov-Bohm effect Bais (1980), Wilczek & Wu (1990), +Bucher (1991), Alford et al. (1990, 1991, 1992). Another +related feature is the existence of non-local charges, called +Cheshire charges, existing among separated vortices Preskill +& Krauss (1990), Alford et al. (1990), Bucher et al. (1992). +Let 훼, 훽 ∈ 휋1(퐺∕퐻) being closed passes enclosing two +vortices. Then, if one adiabatically transports the vortex 훼 +around the vortex 훽 counterclockwisely, the vortex 훼 trans- +forms as (see Fig. 7(b)) +훼 → 훽훼훽−1. +(51) +Therefore, when one exchanges a pair (훼, 훽) counterclock- +wisely, they transform as +(훼, 훽) → (훽, 훽훼훽−1). +(52) +2Here, the term “flux” originally comes from the fact that they were +proposed in gauge theory where non-Abelian symmetry is gauged in the +context of high energy physics Bais (1980). In this article, we consider +only global non-Abelian symmetry relevant for condensed matter physics +and they do not carry non-Abelian fluxes. +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 14 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +Figure 7: Exchange of two vortices. (a) Two closed paths 훼 +and 훽 encircle two vortices. (b) Exchange them counterclock- +wisely. +The first homotopy group 휋1 is a based fundamental group +for which every loop starts from a fixed point 푂. Instead of +it, the conjugacy classes +[훼] = 훽훼훽−1, ∀훽 ∈ 휋1(퐺∕퐻) +(53) +characterize individual vortices as can be seen from +Eqs. (51) and (52). +Two vortices corresponding to +two different elements in the same conjugacy class are +indistinguishable even though they are not the same. +Non-Abelian first homotopy groups significantly control +the dynamics of vortices. In two spatial dimensions, scatter- +ing of such non-Abelian vortices was discussed in the case +that 퐺 and 퐻 are local gauge symmetries Wilczek & Wu +(1990), Bucher (1991), Lo & Preskill (1993). In three spatial +dimensions, vortices are lines. When two vortex lines collide +in three spatial dimensions, the fate is determined by corre- +sponding elements of the first homotopy group. When these +elements commute, the two vortices pass through or recon- +nect each other if these elements are identical. On the other +hand, when these elements are non-commutative, the third +vortex bridging them must be created Poenaru & Toulouse +(1977), Mermin (1979), Kobayashi et al. (2009). +4.2. Examples of non-Abelian vortices +Nematic liquid crystals. Let us start from nematic liq- +uid crystals focusing on uniaxial nematics (UNs), and 퐷2- +and 퐷4-biaxial nematics (BNs). +UN liquid crystals. The order parameter of UNs is an +unoriented rod. The rotational symmetry 퐺 = 푆푂(3) is +spontaneously broken down to 퐻 ≃ 푂(2), which implies +the order parameter manifold +퐺 +퐻 = 푆푂(3) +푂(2) ≃ 푆푈(2) +푃푖푛(2) ≃ 푆2∕ℤ2 ≃ ℝ푃 2, +(54) +which is a real projective space of two dimensions, where +푆푈(2) and 푃 푖푛(2) are double covering groups of 푆푂(3) +and 푂(2), respectively. +Since the fundamental group +휋1(ℝ푃 2) = ℤ2 is Abelian, this does not admits non-Abelian +vortices. +These vortices are called Alice strings (when +퐺 and 퐻 are local gauge symmetries) Schwarz (1982). +Around the Alice string, 푆푂(2) ⊂ 퐻 is not globally defined +and 퐻 is topologically broken to 퐾 ≃ ℤ2. +퐷2-BN liquid crystals Poenaru & Toulouse (1977), +Mermin (1979), Balachandran et al. (1984). +Cholesteric liquid crystals (chiral nematic liquid crys- +tals) can also have the same order parameter space with 퐷2- +BN liquid crystals Lavrentovich & Kleman (2001) and all +the following discussions hold. The order parameter of BNs +is a set of two unoriented rods of different lengths orthogo- +nal to each other. The (unbroken) symmetry is the dihedral +group 퐷2 keeping a rectangular invariant. Thus, the rota- +tional symmetry 퐺 = 푆푂(3) is spontaneously broken down +to +퐻 ≃ 퐷2 = +⎧ +⎪ +⎨ +⎪⎩ +ퟏ3, 퐼푥 = +⎛ +⎜ +⎜⎝ +−1 +0 +0 +0 +1 +0 +0 +0 +1 +⎞ +⎟ +⎟⎠ +, +퐼푦 = +⎛ +⎜ +⎜⎝ +1 +0 +0 +0 +−1 +0 +0 +0 +1 +⎞ +⎟ +⎟⎠ +, 퐼푧 = +⎛ +⎜ +⎜⎝ +1 +0 +0 +0 +1 +0 +0 +0 +−1 +⎞ +⎟ +⎟⎠ +⎫ +⎪ +⎬ +⎪⎭ +. +(55) +Note that 퐷2 ≃ ℤ2 × ℤ2 is Abelian. +The order parameter +manifold is +퐺∕퐻 = 푆푂(3)∕퐷2 ≃ 푆푈(2)∕ℚ, +(56) +where the quaternion group ℚ are universal (double) cover- +ing group of 퐷2: +ℚ = {±ퟏ2, ±푖휎푥, ±푖휎푦, ±푖휎푧 +} . +(57) +Note that 퐻∗ ≃ ℚ is a non-Abelian group while 퐻 ≃ 퐷2 +is an Abelian group. This breaking can occur for instance +by five real-scalar order-parameters belonging to spin-2 rep- +resentation of 푆푂(3), which is a traceless symmetric 3 × 3 +tensor 퐴 with real components, taking a form of +퐴 = diag(1, 푟, −1 − 푟) +(58) +The first homotopy group is isomorphic to the quaternion +group ℚ in Eq. (57) +휋1(푆푈(2)∕ℚ) ≃ ℚ. +(59) +The elements in Eq. (57) correspond to the ground state (ퟏ), +spin vortices of 2휋 rotation (−ퟏ), and spin vortices of ±휋 ro- +tation about the 푥, 푦, 푧-axes (±푖휎푥,푦,푧). These vortex config- +urations at the large distance can be asymptotically written +as +퐴 ∼ 푂(휃)퐴휃=0푂푇 (휃), +푂(휃) ∈ 푆푂(3) +(60) +with the azimuthal angle 휃. The concrete forms of 푂(휃)’s +are given in Table 1. Corresponding 푆푈(2) elements 푔(휃) +can be defined as a double covering of 푆푂(3) with 푔(2휋) ∈ +휋1(퐺∕퐻). A spin vortex of 2휋 rotation (−ퟏ) and a spin vor- +tex of 휋 rotation (±푖휎푎) (푎 = 푥, 푦, 푧) are given by +푔(휃) = exp(±푖휃휎 ⋅ 퐧) = cos 휃 +2ퟏ2 ± 푖휎 ⋅ 퐧 sin 휃 +2, +푔(휃) = exp +( +±푖휃 +2휎푎 +) += cos 휃 +4ퟏ2 ± 푖휎푎 sin 휃 +4, +(61) +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 15 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +푔(2휋) ∈ 휋1(퐺∕퐻) +ퟏ2 +−ퟏ2 +±푖휎푥 +±푖휎푦 +±푖휎푧 +푔(휃) +ퟏ2 +exp (푖휃퐧 ⋅ 휎) +exp +( +±푖 휃 +2휎푥 +) +exp +( +±푖 휃 +2휎푦 +) +exp +( +±푖 휃 +2휎푧 +) +푂(2휋) +ퟏ3 +ퟏ3 +퐼푥 +퐼푦 +퐼푧 +푂(휃) +ퟏ3 +exp(푖휃퐧 ⋅ 퐋) +exp +( +±푖 휃 +2퐿푥 +) +exp +( +±푖 휃 +2퐿푦 +) +exp +( +±푖 휃 +2퐿푧 +) +Table 1 +Asymptotic configurations of spin vortices in 퐷2-BNs: the fundamental group elements +푔(2휋) ∈ 휋1(퐺∕퐻), the 푆푈(2) elements 푔(휃) ∈ 푆푈(2), 푂(2휋), and the 푆푂(3) group elements +푂(휃) ∈ 푆푂(3), acting on the the order parameter 퐴 as Eq. (60). The group actions 푂(휃) +and 푔(휃) for a spin vortex of 2휋 rotation (−ퟏ2) can be a rotation around any axis along +the unit vector 핟. 퐿푖 are 3 × 3 spin-1 matrices [퐿푖]푗푘 = −푖휖푖푗푘. +respectively, with a unit three-vector 퐧, giving the el- +ements of 휋1(퐺∕퐻) at 휃 += +2휋: +푔(2휋) += +−ퟏ2 and +푔(2휋) = ±푖휎푎, respectively. While the former is Abelian +because [푔(2휋), 퐻∗] = 0 (even though 푔(2휋) ≠ 푔(0)), the +latter is non-Abelian because [푔(2휋), 퐻∗] ≠ 0 with the +universal covering 퐻∗ ≃ 푆푈(2),3 and 퐻∗ is topologically +broken to 퐾∗ +푎 = {±ퟏ2, ±푖휎푎}. +The elements in Eq. (57) are grouped to the conjugacy +classes, Eq. (53), consisting of five elements: +{ퟏ2}, {−ퟏ2}, {±푖휎푥}, {±푖휎푦}, {±푖휎푧}. +(62) +This follows for instance from (푖휎푦)−1(푖휎푥)(푖휎푦) = −푖휎푥, +impling that a vortex corresponding to 푖휎푥 becomes −푖휎푥 +when it travels around a vortex corresponding to 푖휎푦. Thus, +the vortices corresponding to 푖휎푥 and −푖휎푥 are indistinguish- +able although they are not the same. From (푖휎푎)(−푖휎푎) = ퟏ2 +(푎 = 푥, 푦, 푧), vortices belonging to the same conjugacy class +are anti-particles of each other, and thus they are similar to +Majorana fermions discussed in the last section. +In three spatial dimensions, this phenomenon of non- +commutativity appears as follows: when two vortex lines +corresponding to 푖휎푥 and 푖휎푦 collide in three spatial dimen- +sions, the third vortex bridging them is created Poenaru & +Toulouse (1977), Mermin (1979). +퐷4-BN liquid crystals. The order parameter of 퐷4 BNs +is a set of two unoriented indistinguishable rods of the same +lengths orthogonal to each other. In this case, the (unbroken) +symmetry is a dihedral group 퐷4 keeping a square invariant: +퐺∕퐻 = 푆푂(3)∕퐷4 ≃ 푆푈(2)∕퐷∗ +4, +(63) +where 푀∗ denotes a universal covering group of 푀. The +fundamental group is given by +휋1(푆푈(2)∕퐷∗ +4) ≃ 퐷∗ +4 +(64) +with the sixteen elements +{±ퟏ2, ±푖휎푥, ±푖휎푦, ±푖휎푧, ±퐶4, ±퐶−1 +4 , ±푖휎푥퐶4, ±푖휎푥퐶−1 +4 +} (65) +with 퐶4 ≡ 푒푖 휋 +4 휎푧 = (1∕ +√ +2)(ퟏ2 + 푖휎푧). Note (퐶4)2 = 푖휎푧 and +(퐶4)4 = −ퟏ2. The conjugacy classes consist of the following +3Note that [푂(2휋), 퐻] = 0, and thus the criterion of non-Abelian prop- +erty should be considered in the universal covering group 퐻∗ but not in 퐻. +seven elements +{ퟏ2}, {−ퟏ2}, {±푖휎푥, ±푖휎푦}, {±푖휎푧}, +{퐶4, 퐶−1 +4 }, {−퐶4, −퐶−1 +4 }, {±푖휎푥퐶4, ±푖휎푥퐶−1 +4 }. +. +(66) +Since −퐶4 = 퐶3 +4 (−퐶−1 +4 += 퐶−3 +4 ), vortices of these elements +have more energy than those of 퐶4 and 퐶−1 +4 . This symmetry +breaking of 퐷4 nematics can be realized by a higher rank ten- +sor order parameter Mietke & Dunkel (2022), in which more +generally 퐷푛 nematic liquid crystals were also discussed. +Spinor BECs. +Next we provide examples of spinor +BECs Kawaguchi & Ueda (2012). The order parameter of +spin-2 BECs is a traceless symmetric 3 × 3 tensor 퐴 with +complex components transforming under the symmetry +퐺 = 푈(1) × 푆푂(3) as +퐴 → 푒푖휃푔퐴푔푇 , +푒푖휃 ∈ 푈(1), +푔 ∈ 푆푂(3). +(67) +Phases of condensations with total angular momentum two +are classified by Mermin Mermin (1974). They are nematic, +cyclic and ferromagnetic phases. All phases are theoretically +possible in the case of spin-2 BECs. The spin-2 BECs are +experimentally realized by 87Rb atoms for which the phase +is around the boundary between cyclic phase and ferromag- +netic phase, see e.g. Ref. Tojo et al. (2009). Here, we discuss +nematic and cyclic phases which host non-Abelian vortex +anyons. In the next section, we discuss 3푃2 SF which is in +the nematic phase. +BN phases in spin-2 BEC. Song et al. (2007), Uchino +et al. (2010), Kobayashi et al. (2012), Borgh & Ruostekoski +(2016). +The nematic phase consists of three degenerate +phases: +the UN, 퐷2- and 퐷4-BN phases. +The order +parameters of the UN, 퐷2- and 퐷4-BN phases are given by +UN ∶퐴 ∼ diag(1, −1∕2, −1∕2), +퐷2-BN ∶퐴 ∼ diag(1, 푟, −1 − 푟), +퐷4-BN ∶퐴 ∼ diag(1, −1, 0), +(68) +respectively, where 푟 ∈ ℝ and −1 < 푟 < −1∕2. In the +퐷2-BN phase, the limits 푟 → −1∕2, −1 correspond to UN +and 퐷4-BN phases, respectively. The symmetry breaking +patterns and the order parameter manifolds are +UN ∶ 퐺 +퐻 = 푈(1) × 푆푂(3) +푂(2) ≃ 푈(1) × ℝ푃 2, +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 16 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +퐷2-BN ∶ 퐺 +퐻 = 푈(1) × 푆푂(3) +퐷2 +≃ 푈(1) × 푆푈(2) +ℚ +, +퐷4-BN ∶ 퐺 +퐻 = 푈(1) × 푆푂(3) +퐷4 +≃ 푈(1) × 푆푈(2) +퐷∗ +4 +. +(69) +These phases are continuously connected by the parameter 푟 +interpreted as a quasi-Nambu-Goldstone mode. The degen- +eracy is lifted by quantum effects and either of these phases +remains as the ground state Uchino et al. (2010). +The 퐷2-BN and 퐷4-BN admit non-Abelian vortices. +The order parameters of the UN and 퐷2-BN phases of +spin-2 BECs are merely products of the 푈(1) phonon and +the order parameters of the corresponding nematic liquids. +Thus, we concentrate on the 퐷4-BN phase hereafter. The +fundamental group of the 퐷4-BN phase is given by +휋1 +( +푈(1) × 푆푈(2) +퐷∗ +4 +) +≅ ℤ ×ℎ 퐷∗ +4 +(70) +where ×ℎ is defined in Ref. Kobayashi et al. (2012). This +consists of the following sixteen elements +{ +(푁, ±ퟏ2), (푁, ±푖휎푥), (푁, ±푖휎푦), (푁, ±푖휎푧), +( +푁 + 1 +2, ±퐶4 +) +, +( +푁 + 1 +2, ±푖휎푥퐶4 +) +, +( +푁 + 1 +2, ±퐶−1 +4 +) +, +( +푁 + 1 +2, ±푖휎푥퐶−1 +4 +) } +, +(71) +where the first and second elements of a pair (⋅, ⋅) denote the +circulation 휅 (푈(1) winding number) and an 푆푈(2) element, +respectively with 푁 ∈ ℤ. Here 퐶4 ≡ 푒푖 휋 +4 휎푧 = (1∕ +√ +2)(ퟏ2 + +푖휎푧) satisfying 퐶4 +4 = −ퟏ2. The conjugacy classes of Eq. (71) +are composed of seven elements for each 푁: +(I) +{(푁, ퟏ2)}, +(II) +{(푁, −ퟏ2)}, +(III) +{(푁, ±푖휎푥), (푁, ±푖휎푦)}, +(IV) +{(푁, ±푖휎푧)}, +(V) +{( +푁 + 1 +2, 퐶4 +) +, +( +푁 + 1 +2, 퐶−1 +4 +)} +, +(VI) +{( +푁 + 1 +2, −퐶4 +) +, +( +푁 + 1 +2, −퐶−1 +4 +)} +, +(VII) +{( +푁 + 1 +2, ±푖휎푥퐶4 +) +, +( +푁 + 1 +2, ±푖휎푥퐶−1 +4 +)} +. +(72) +They describe (I) integer vortices (푁 = 0 corresponds to +the vacuum), (II) spin vortices of 2휋 rotation, (III),(IV) spin +vortices of 휋 rotation around the 푥, 푦, and 푧 axes, and (V) – +(VII) non-Abelian HQVs. +In Sec. 5, we see that 3푃2 SFs are in the 퐷4-BN phase +in a strong magnetic field. There, a singly quantized vortex +(1, ퟏ) splits into two HQVs (1∕2, 퐶4) and (1∕2, 퐶−1 +4 ) both +in the conjugacy class (V)4. When they fuse, they go back +4Topologically a decay into a pair (1∕2, −퐶4) and (1∕2, −퐶−1 +4 ) in the +conjugacy class (VI) is also possible, but energetically disfavored. +to the singly quantized vortex (1, ퟏ). However, one of them, +e.g., (1∕2, 퐶−1 +4 ) can transform to the other (1∕2, 퐶4) once +some other vortex passes through between them because +they belong to the same conjugacy class. If they fuse after +that, they become (1, 푖휎푧) because 퐶2 +4 = 푖휎푧 which is a +composite belonging to (IV), of a singly quantized vortex +and a spin vortex of 휋 rotation. +Cyclic phase in spin-2 BEC. Semenoff & Zhou (2007), +Kobayashi et al. (2009, 2012). The order parameter of the +cyclic phase is +퐴 ∼ diag(1, 푒2휋푖∕3, 푒4휋푖∕3), +(73) +yielding the symmetry breaking to the tetrahedral group +퐻 ≃ 푇 and the order parameter manifold, given by +퐺 +퐻 = 푈(1) × 푆푂(3) +푇 +≃ 푈(1) × 푆푈(2) +푇 ∗ +(74) +with the universal covering group 푇 ∗ of 푇 . The fundamental +group in the cyclic phase is given by +휋1 +(푈(1) × 푆푈(2) +푇 ∗ +) +≅ ℤ ×ℎ 푇 ∗ +(75) +with the 24 elements +{ +(푁, ±ퟏ2), (푁, ±푖휎푥), (푁, ±푖휎푦), (푁, ±푖휎푧), +( +푁 + 2휋푖 +3 , ±퐶3 +) +, +( +푁 + 2휋푖 +3 , ±푖휎푥퐶3 +) +, +( +푁 + 2휋푖 +3 , ±푖휎푦퐶3 +) +, +( +푁 + 2휋푖 +3 , ±푖휎푧퐶3 +) +, +( +푁 − 2휋푖 +3 , ±퐶2 +3 +) +, +( +푁 − 2휋푖 +3 , ±푖휎푥퐶2 +3 +) +, +( +푁 − 2휋푖 +3 , ±푖휎푦퐶2 +3 +) +, +( +푁 − 2휋푖 +3 , ±푖휎푧퐶2 +3 +) } +(76) +with the same notation with Eq. (71). Here 퐶3 ≡ (1∕2)(ퟏ2 + +푖휎푥 + 푖휎푦 + 푖휎푧) satisfying (퐶3)3 = −ퟏ2. The conjugacy +classes of Eq. (76) are composed of the following seven el- +ements for each 푁 Semenoff & Zhou (2007): +(I) +{(푁, ퟏ2)}, +(II) +{(푁, −ퟏ2)}, +(III) +{(푁, ±푖휎푥), (푁, ±푖휎푦), (푁, ±푖휎푧)}, +(IV) +{ ( +푁 + 2휋푖 +3 , 퐶3 +) +, +( +푁 + 2휋푖 +3 , −푖휎푥퐶3 +) +, +( +푁 + 2휋푖 +3 , −푖휎푦퐶3 +) +, +( +푁 + 2휋푖 +3 , −푖휎푧퐶3 +) } +, +(V) +{ ( +푁 + 2휋푖 +3 , −퐶3 +) +, +( +푁 + 2휋푖 +3 , 푖휎푥퐶3 +) +, +( +푁 + 2휋푖 +3 , 푖휎푦퐶3 +) +, +( +푁 + 2휋푖 +3 , 푖휎푧퐶3 +) } +, +(VI) +{ ( +푁 − 2휋푖 +3 , 퐶2 +3 +) +, +( +푁 − 2휋푖 +3 , 푖휎푥퐶2 +3 +) +, +( +푁 − 2휋푖 +3 , 푖휎푦퐶2 +3 +) +, +( +푁 − 2휋푖 +3 , 푖휎푧퐶2 +3 +) } +, +(VII) +{ ( +푁 − 2휋푖 +3 , −퐶2 +3 +) +, +( +푁 − 2휋푖 +3 , −푖휎푥퐶2 +3 +) +, +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 17 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +I0 +II0 +III0 +IV0 +V0 +VI−1 +VII−1 +ퟏ = I0 +I0 +II0 +III0 +IV0 +V0 +VI−1 +VII−1 +휎 = II0 +II0 +I0 +III0 +V0 +IV0 +VII−1 +VI−1 +휏 = III0 +III0 +III0 +6I0 ⊕ 6II0 ⊕ 4III0 +3IV0 ⊕ 3V0 +3IV0 ⊕ 3V0 +3VI−1 ⊕ 3VII−1 +3VI−1 ⊕ 3VII−1 +IV0 +IV0 +V0 +3IV0 ⊕ 3V0 +3VI0 ⊕ VII0 +VI0 ⊕ 3VII0 +4I0 ⊕ 3III0 +4II0 ⊕ 2III0 +V0 +V0 +IV0 +3IV0 ⊕ 3V0 +VI0 ⊕ 3VII0 +3VI0 ⊕ VII0 +4II0 ⊕ 2III0 +4I0 ⊕ 2III0 +VI−1 +VI−1 +VII−1 +3VI−1 ⊕ 3VII−1 +4I0 ⊕ 2III0 +4II0 ⊕ 2III0 +3IV−1 ⊕ V−1 +IV−1 ⊕ 3V−1 +VII−1 +VII−1 +VI−1 +3IV−1 ⊕ 3VII−1 +4II0 ⊕ 2III0 +4I0 ⊕ 2III0 +IV−1 ⊕ 3V−1 +3IV−1 ⊕ 2V−1 +Table 2 +Fusion rule for vortex anyons in a cyclic spin-2 BEC Mawson et al. (2019). The subscript +on the conjugacy class denotes the 푈(1) winding number 푁. +I0 +II0 +III0 +IV0 +V0 +VI0 +VII0 +ퟏ = I0 +I0 +II0 +III0 +IV0 +V0 +VI0 +VII0 +휎 = II0 +II0 +I0 +III0 +IV0 +VI0 +V0 +VII0 +휏1 = III0 +III0 +III0 +4I0 ⊕ 4II0 ⊕ 4IV0 +2III0 +2VII0 +2VII0 +4V0 ⊕ 4VI0 +휏2 = IV0 +IV0 +IV0 +2III0 +2I0 ⊕ 2II0 +V0 ⊕ VI0 +V0 ⊕ VI0 +2VII0 +V0 +V0 +VI0 +2VII0 +V0 ⊕ VI0 +2I1 ⊕ IV1 +2II1 ⊕ IV1 +2III1 +VI0 +VI0 +V0 +2VII0 +V0 ⊕ VI0 +2II1 ⊕ IV1 +2I1 ⊕ IV1 +2III1 +VII0 +VII0 +VII0 +4IV0 ⊕ 4V0 +2VII0 +2III1 +2III1 +4I1 ⊕ 4II1 ⊕ 4IV1 +Table 3 +Fusion rule for for vortex anyons in a 퐷4-BN spin-2 BEC Mawson et al. (2019). +The +subscript on the conjugacy class denotes the 푈(1) winding number 푁. +( +푁 − 2휋푖 +3 , −푖휎푦퐶2 +3 +) +, +( +푁 − 2휋푖 +3 , −푖휎푧퐶2 +3 +) } +. +(77) +They describe (I) integer vortices (푁 = 0 corresponds to the +vacuum), (II) spin vortices of 2휋 rotation, (III) spin vortices +of 휋 rotation around the 푥, 푦, 푧 axes, and (IV) – (VII) 1/3- +quantum vortices. +Other examples. Another example in condensed mat- +ter physics can be found in vortex lines in the dipole-free +A-phase of SF 3He Balachandran et al. (1984), Salomaa & +Volovik (1987). An example in high energy physics can be +found in color flux tubes (“non-Abelian” vortices) in high +density QCD matter Fujimoto & Nitta (2021a,b,c), Eto & +Nitta (2021). +4.3. Fusion rules for non-Abelian vortex anyons +Two non-Abelian vortices belonging to the same conju- +gacy class are indistinguishable even if they are not iden- +tical. For instance, a vortex 푎 ∈ 휋1(퐺∕퐻) and a vortex +푏 = 푐푎푐−1 with 푐 ∈ 휋1(퐺∕퐻) are not the same and thus +푎 and anti-vortex of 푏 cannot pair annihilate. Nevertheless +they are indistinguishable with a help of 푐. This leads a class +of non-Abelian statistics Brekke et al. (1993), Lo & Preskill +(1993), Lee (1994), Brekke et al. (1997). Such non-Abelian +anyons are called non-Abelian vortex anyons. +In order to discuss non-Abelian vortex anyons, first we +define anyons {ퟏ, 휎, 휏} appropriately by conjugacy classes +of non-Abelian vortices. +Then, the fusion rule (3) for +non-Abelian vortex anyons can be written as Mawson et al. +(2019) +휏 ⊗ 휏 = 푁ퟏ +휏휏ퟏ ⊕ 푁휎 +휏휏휎 ⊕ 푁휏 +휏휏휏, +휏 ⊗ 휎 = 휏, +휎 ⊗ 휎 = ퟏ, +푥 ⊗ ퟏ = 푥, +(78) +with 푥 ∈ {ퟏ, 휎, 휏}. +Non-Abelian vortex anyons in 퐷2-BN. Let us discuss +the simplest case. +For 퐷2-BN liquid crystals or 퐷2-BN +phases of spin-2 BECs, the conjugacy class is given in +Eq. (62). We then define +ퟏ = {+ퟏ2}, +휎 = {−ퟏ2}, +휏 = {±푖휎푎} +(79) +with 푎 being either 푥, 푦, or 푧. The coefficient 푁푐 +푎푏 counts how +many ways anyons 푎 and 푏 fuse to an anyon 푐. The relations +(−푖휎푎)(+푖휎푎) = (+푖휎푎)(−푖휎푎) = +ퟏ2 and (−푖휎푎)(−푖휎푎) = +(+푖휎푎)(+푖휎푎) = −ퟏ2 lead 푁ퟏ +휏휏 = 2 and 푁휎 +휏휏 = 2, respec- +tively. Furthermore, 휏 anyons do not fuse to 휏 in this case +and then 푁휏 +휏휏 = 0. We thus reach +휏 ⊗ 휏 = 2ퟏ2 ⊕ 2휎, +휏 ⊗ 휎 = 휏, +휎 ⊗ 휎 = ퟏ, +푥 ⊗ ퟏ = 푥, +(80) +with 푥 ∈ {ퟏ, 휎, 휏}. Since two 휏-anyons fuse to two different +anyons ퟏ and 휎, 휏 anyons are non-Abelian anyons Compar- +ing this fusion rule with that of the Ising anyons in Eq. (4), +we find that these non-Abelian vortex anyons are similar to +the Ising anyons. In fact, a 휏 aynon coincide with its anti- +particle, and so similar to a Majorana fermion. +Gathering all 휏푎 = {±휎푎} (푎 = 푥, 푦, 푧) together, we +obtain the following fusion formula from the relation +(푖휎푎)(푖휎푏) = −훿푎푏 + 휖푎푏푐(−푖휎푐): +휏푎 ⊗ 휏푏 = 2훿푎푏ퟏ ⊕ 2훿푎푏휎 ⊕ 2휖푎푏푐휏푐 +휏푎 ⊗ 휎 = 휏푎, +휎 ⊗ 휎 = ퟏ, +푥 ⊗ ퟏ = 푥, +(81) +with 푥 ∈ {ퟏ, 휎, 휏푥, 휏푦, 휏푧}. In this case, there are the three +non-Abelian anyons 휏푎 coupled to each other. +Non-Abelian vortex anyons in spin-2 BECs. +Non-Abelian vortex anyons in spin-2 BECs were studied +in Mawson et al. (2019). For the cyclic phase in a spin-2 +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 18 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +BEC, {ퟏ, 휎, 휏} are defined by the conjugacy classes (I), (II) +and (III) with 푁 = 0 in Eq. (77). Then, we have (see Table 2) +푁ퟏ +휏휏 = 6, 푁휎 +휏휏 = 6, 푁휏 +휏휏 = 4: +휏 ⊗ 휏 = 6ퟏ ⊕ 6휎 ⊕ 4휏, +휏 ⊗ 휎 = 휏, +휎 ⊗ 휎 = ퟏ, +푥 ⊗ ퟏ = 푥, +(82) +with 푥 ∈ {ퟏ, 휎, 휏}. The non-Abelian 1/3-quantum vortices +in (IV)–(VII) are also non-Abelian anyons but one cannot +restrict to the 푁 = 0 sector, and needs infinite numbers of +anyons for a closed algebra. +The fusion rule for vortex anyons in the 퐷4-BN phase of +a spin-2 BEC was also obtained by the conjugacy classes (I)– +(IV) in Eq. (72) Mawson et al. (2019). In this case, 휏 in the +cyclic phase is split into 휏1 = III0 and 휏2 = IV0. Then, we +have 푁ퟏ +휏1휏1 = 4, 푁휎 +휏1휏1 = 4, 푁휏1 +휏1휏1 = 4, 푁ퟏ +휏2휏2 = 2, 푁휎 +휏2휏2 = +2 with the other components zero: +휏1 ⊗ 휏1 = 4ퟏ ⊕ 4휎 ⊕ 4휏1, +휏2 ⊗ 휏2 = 2ퟏ ⊕ 2휎, +휏푖 ⊗ 휎 = 휏푖, +휎 ⊗ 휎 = ퟏ, +푥 ⊗ ퟏ = 푥, +(83) +with 푖 = 1, 2 and 푥 ∈ {ퟏ, 휎, 휏푖}. See Table 3. The non- +Abelian HQVs in (V)–(VII) are also non-Abelian anyons, +but again infinite numbers of anyons are necessary for a +closed algebra. The same fusion rule in Eq. (83) should +hold for a 퐷4-BN liquid crystal, as seen in Eq. (66). +Including Bogoliubov modes, the algebra of vortex +anyons is extended to a quantum double Koornwinder et al. +(1999), Mawson et al. (2019). An application to quantum +computation was also proposed in Ref. Génetay Johansen +& Simula (2022). +5. 3푃2 topological SFs +Finally we discuss the two-fold non-Abelian object in +a novel topological SF called a 3푃2 SF: The two-fold non- +Abelian nature is attributed to the fermionic part (Sec. 3) +and the vortex part (Sec. 4). The 3푃2 SF is a condensate of +spin-triplet (푆 = 1) 푝-wave (퐿 = 2) Cooper pairs with total +angular momentum 퐽 = 2. In the following, we briefly re- +view 3푃2 SFs in Sec. 5.1. In Sec. 5.2, the stability of a pair of +HQVs compared with a singly quantized vortex is discussed. +In Sec. 5.3, we show that a Majorana fermion, a non-Abelian +Ising anyon, exists in the core of each HQV. +5.1. Overview of 3푃2 topological SFs +Study of 3푃2 SFs was initiated since 1970s Hoffberg et al. +(1970), Tamagaki (1970), Takatsuka & Tamagaki (1971), +Takatsuka (1972), Richardson (1972), Sedrakian & Clark +(2018). On the basis of the analysis of the phase-shifts from +nucleon-nucleon scattering in a free space, spin-singlet 푠- +wave 1푆0 symmetry is a dominant attractive channel in the +inner crust region (휌 ≲ 0.5휌0, where 휌0 = 0.17fm−3 is called +the nuclear density) Tamagaki (1970). The critical temper- +ature was estimated as 108 − 1010 K, which is two orders +of magnitude smaller than the Fermi energy. For further in- +crease in density 0.7휌0 ≲ 휌 ≲ 3휌0 in the inner core region, +0 +1 +2 +1 +2 +Ferro.: Weyl +Cyclic: Weyl +UN/BN +weak coupling limit + 0 + 0.2 + 0.4 + 0.6 + 0.8 + 1.0 + 0 + 0.02 + 0.04 + 0.06 + 0.08 + 0.10 + 0.12 + 0 +1.0 + 0 +1.0 +0.8 +0.4 +0.6 +0.2 +0.8 +0.4 +0.6 +0.2 +1.0 +-1.0 +-0.9 +-0.8 +-0.7 +-0.6 +-0.5 +(a) +(b) +(c) +(d) +topo. UN +topo. +BN +topo. +BN +Figure 8: (a) Phase diagram without magnetic field based on +the GL theory. (b) Gap structure of the nematic state. (c) +Phase diagram with magnetic field in the weak coupling limit. +(d) The momentum resolved local density state at the surface +perpendicular to the ̂푧 axis. +The magnetic field is applied +parallel (perpendicular) to the surface [top (bottom) panel]. +Figures are adapted from Ref. Mizushima et al. (2017) ©2022 +American Physical Society. +the 1푆0 superfluidity is suppressed, and instead the attrac- +tive channel of the 3푃2 grows. Because of the attractively +strong spin-orbit force, the 3푃2 Cooper pair channels with +high angular momentum become more attractive than other +3푃 pairing symmetry in contrast to the atomic physics where +the lower total angular momentum state is favored as in the +SF 3He-B phase. The anisotropic form of the Cooper pair is +thought to affect the Cooling rate of nuetron stars. Extreme +conditions of neutron stars are not only high density, but also +rapid rotation, and a strong magnetic field. Especially, neu- +tron stars accompanied by magnetic field ranging from 1015 +– 1018 G are called magnetars. Rich structures of exotic con- +densates and vortices explained below may be the origin of +the observed pulser glitches, that is, the sudden increase of +the angular momentum of neutron stars. Among them, the +existence of non-Abelian HQVs in high magnetic fields is +responsible for the scaling law of the glitches without any +fitting parameters Marmorini et al. (2020). +In terms of the symmetry point of view, 3푃2 SFs spon- +taneously break the global gauge symmetry 푈(1)휑 and the +simultaneous rotational symmetry in the spin-momentum +space 푆푂(3)퐽 which originally exist in the normal state +inside neutron stars. +The order parameter of 3푃2 SFs is +spanned by 3 by 3 traceless symmetric tensor 퐴휇푖, where +the 2 by 2 gap function in momentum space can be given by +̂Δ(풌) = 퐴휇푖̄푘푖 ̂휎휇푖̂휎푦. For later convenience, we introduce a +representation based on the total angular momentum along +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 19 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +the quantization axis, 푀 = −2, ⋯ , 2: +퐴휇푖 = +2 +∑ +푀=−2 +훾푀[Γ푀]휇푖, +(84) +where 훾푀 is a complex wave function of the Cooper pair in +the angular momentum sector 푀. A basis set Γ푀 is given +for the quantization axis ̂푤 by +[Γ±2]휇푖 = +(̂푢 ± 푖 ̂푣)휇(̂푢 ± 푖 ̂푣)푖 +2 +, +(85) +[Γ±1]휇푖 = ∓ +(̂푢 ± 푖 ̂푣)휇 ̂푤푖 + ̂푤휇(̂푢 ± 푖 ̂푣)푖 +2 +, +(86) +[Γ0]휇푖 = +−̂푢휇 ̂푢푖 − ̂푣휇 ̂푣푖 + 2 ̂푤휇 ̂푤푖 +√ +6 +, +(87) +where ̂푢, ̂푣, and ̂푤 constitute the orthonormal triad. +From a phenomenological aspect, the Ginzburg-Landau +(GL) energy functional invariant under the 푆푂(3)퐽 and +푈(1)휑 symmetry was obtained for 3푃2 SFs as Richardson +(1972), Fujita & Tsuneto (1972), Sauls & Serene (1978), +Muzikar et al. (1980), Sauls et al. (1982) + = 훼tr[퐴퐴∗] + 훽1|tr퐴2|2 ++ 훽2(tr[퐴퐴∗])2 + 훽3tr[퐴2퐴∗2]. +(88) +It should be remarked that spin-2 spinor BECs (퐿 = 0, 푆 = +2) and 푑-wave superconductivty (퐿 = 2, 푆 = 0) have +similar order parameter structures. The GL functional for +the 3푃2 Cooper pairs was minimized by Sauls and Serene +by using the correspondence to the 퐿 = 2 GL functional +which was solved by Mermin Sauls & Serene (1978), +Mermin (1974). The ground state solutions are classified +into three types of phases determined by 훽푖=1,2,3, as shown +in Fig. 8(a): nematic phases with time reversal symmetry +and the cyclic and ferromagnetic phases as non-unitary +state. +The microscopic derivation of the GL parameters +clarifies that the ground state is the nematic phases in the +weak coupling limit Sauls & Serene (1978), Sauls (1980). +The order parameter tensor of a nematic phase is given by +퐴휇푖 = Δ[̂푢휇 ̂푢푖 + 푟 ̂푣휇 ̂푣푖 − (1 + 푟) ̂푤휇 ̂푤푖] with a real number +푟 ∈ [−1, −1∕2] [see also Eq. (68)]. The nematic phase +has a continuous degeneracy which is lifted by either a +magnetic field or sixth-order terms in the GL free energy. +For the GL parameters derived from the microscopic model, +the UN phase for 푟 = −1∕2 is favored at zero magnetic +field while 퐷2-BN (−1 < 푟 < −1∕2) and 퐷4-BN 푟 = −1 +phases are favored for moderate and strong magnetic fields, +respectively Masuda & Nitta (2016), relevant for magnetars. +The schematic images of the gap structures for the UN and +퐷4-BN states are shown in Fig. 8(b), where the arrows +account for the momentum-dependent direction of the +푑-vector, defined by 푑휇(풌) = ∑ +푖 퐴휇푖푘푖. We will discuss +other possible states later in the context of the fermionic +topology. +The microscopic model of 3푃2 SFs in terms of the +fermion degrees of freedom was constructed by Richard- +son Richardson (1972) and Tamagaki and Takatsuka Tam- +agaki (1970), Takatsuka & Tamagaki (1971), Takatsuka +(1972): The starting microscopic Hamiltonian is composed +of the one-body term 퐻1 and the interaction term 퐻2 given, +respectively, in the following forms: +퐻1 = ∫ d풓 ⃗휓†(풓)[̂ℎ푁(−푖훁)] ⃗휓(풓), +(89) +퐻2 = − ∫ d풓 +∑ +훼훽=푥,푦,푧 +푔 +2푇 † +훼훽(풓)푇훼훽(풓). +(90) +In the first line, [ ⃗휓(풓)]휎 = 휓휎(풓) and [̂ℎ푁(−푖훁)]휎,휎′ is the +sum of the kinetic energy ℎ0(−푖훁)훿휎,휎′ = (−∇2∕2푚−휇)훿휎,휎′ +measured from the chemical potential 휇, and the Zeeman +energy −푩 ⋅ ̂흈 for a magnetic field 푩 = 퐵풏. +The 3푃2 +force with coupling strength 푔 > 0 is represented by 퐻2 +with the pair-annihilation operator 푇 defined by 푇훼훽(풓) = +∑ +휎휎′[푡훼훽,휎휎′(−푖 ̄훁)휓휎′(풓)]휓휎(풓), where ̄훁 ≡ 푘−1 +F 훁. We have +introduced a spin-momentum coupling in the pair force via +the 2 × 2 matrix in spin space ̂푡훼훽 defined by ̂푡훼훽(−푖 ̄훁) = +푖̂휎푦 +{[̂휎훼(−푖 ̄∇훽) + ̂휎훽(−푖 ̄∇훼)] ∕2 +√ +2 − 훿훼훽 ̂흈 ⋅ (−푖 ̄훁)∕3 +√ +2 +} +. +Within the mean field approximation, the BdG equation is +derived as, +̌(−푖훁, 푹)⃗푢휈(푹) = 휖휈⃗푢휈(푹), +(91) +̌(−푖훁, 푹) = +( +̂ℎ푁(−푖훁) +̂Δ(−푖훁, 푹) +−[ ̂Δ(−푖훁, 푹)]∗ +−[̂ℎ푁(−푖훁)]∗ +) +, +(92) +where +the +gap +matrix +is +given +by +̂Δ(−푖훁, 푹) += +∑ +훼,훽 +푖̂휎훼 ̂휎푦 +2푘F {2퐴훼훽(푹)(−푖∇훽) + [(−푖∇훽)퐴훼훽(푹)]}. +This +model was also used to determine the aforementioned GL +parameters in the weak coupling limit and was directly +investigated within a quasiclassical approximation recently +in Ref. Mizushima et al. (2017). +Even in the presence +of the magnetic field, the quasiclassical approximation +where the size of the Fermi surface is treated as an infinite +one, predicts that a nematic state is the most stable with +parameter 푟 determined by the strength of the magnetic +field as in the GL theory. The 푇 -퐵 phase diagram is shown +in Fig. 8(c). +As explained later, the ferromagnetic state +appears near 푇푐 when the finite-size correction of the Fermi +surface is taken into account. +The microscopic analysis +reveals the existence of the tricritical point on the phase +boundary between the 퐷4-BN and 퐷2-BN states in the +푇 -퐵 phase diagram shown in Fig. 8(c): at temperatures +below the tricritical point, the phase transition becomes +discontinuous Mizushima et al. (2017). The existence of +the tricritical point was later confirmed in Ref. Mizushima +et al. (2020) also in the GL theory with higher order terms +(up to the eighth order Yasui, Chatterjee, Kobayashi & +Nitta (2019)). In addition to such drastic change in critical +phenomena, the advantage of the microscopic model lies +in studies of the fermionic topology of the superfluidity. +In the following, we explain the fermionic topology of the +possible phases of the 3푃2 SFs. +Nematic state. In the weak coupling limit without a +magnetic field, the UN state is the ground state. The order +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 20 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +parameter tensors of the UN state and the BN state under +a magnetic field are already explained above. On the basis +of the symmetry of the BdG Hamiltonian, the nematic state +is revealed as a topological SF with time reversal symmetry +(a class DIII in the classification of topological insulators +and SCs). The analysis of the BdG equation in the pres- +ence of the boundary clarifies the existence of the gapless +surface bound Majorana fermion, the hallmark character of +the topological states. The surface Majorana fermion has an +Ising spin character Chung & Zhang (2009), Nagato et al. +(2009), Volovik (2010), Mizushima & Machida (2011), that +is, the only external field coupled to the Ising spin gives a +mass gap to the Majorana fermion as shown in Fig. 8(d). +The magnetic field direction giving the gap to the Majorana +fermion is the direction perpendicular to the surface, denoted +by 풏⟂. This is because the surface Majorana fermion is pro- +tected not only by the time reversal symmetry but also an- +other key symmetry, which is the magnetic 휋-rotation sym- +metry about 풏⟂. The magnetic 휋-rotation symmetry is also +called the ̄푃3 symmetry5. The magnetic 휋-rotation is the +combined operation of the time-reversal and the 휋 rotation. +The chiral operator, defined by the combination of particle- +hole operation  and the magnetic 휋-rotation ̄푃3 as Γ =  ̄푃3, +commutes with the Hamiltonian (풌⟂) with magnetic field +푩 ⋅풏⟂ = 0 and the chiral symmetric momentum 풌⟂ = 푘⟂풏⟂ +such that Γ ∶ 풌⟂ → 풌⟂. Using this commutation rela- +tion, a one-dimensional winding number can be introduced +as 푤1d = − 1 +4휋푖 ∫ 푑푘⟂Tr[Γ(풌⟂)휕푘⟂(풌⟂)] = 2, which is +unchanged unless the symmetry is broken or the bulk gap is +closed. The 푃3 symmetry and thus the chiral symmetry is +broken by the magnetic filed 푩 ⋅ 풏⟂ ≠ 0 which gives a mass +gap to the Majorana fermion (the bottom panel of Fig. 8(d), +where 풏⟂ ∥ ̂푧). +Cyclic state. For −6훽1 < 훽3 < 0 based on the basis +of 푆푂(3)퐽 invariant GL functional, the cyclic state is the +ground state. +The order parameter tensor has a form of +퐴휇푖 = Δ[̂푢휇 ̂푢푖 + 휔 ̂푣휇 ̂푣푖 + 휔2 ̂푤휇 ̂푤푖] with 휔 = 푒2휋푖∕3 [see +also Eq. (73)], which is unique except for trivial 푆푂(3)퐽 +and 푈(1)휑 rotations. In the absence of magnetic field, the +quasiparticle excitation energy consists of two branches +퐸±(풌) = [ℎ0(풌)2 + |풅(풌)|2 ± |풅(풌) × 풅∗(풌)|]1∕2, where +퐸+(풌) is full gap and 퐸−(풌) has 8 nodal points ±풌훼=1,⋯,4, +each of which is a Weyl point. The subscript 훼 denotes the +4 vertices of a tetrahedron, and ± represents the monopole +charge of the Weyl point. Because of the topological nature +of Weyl SCs/SFs, there exist surface zero energy states +which connect two oppositely charged Weyls points on the +projected momentum space normal to the surface direction. +Ferromagnetic state. For |훽1| − 훽1 < 훽3, the ferro- +magnetic state described by 퐴휇푖 = Δ(̂푢휇 + 푖 ̂푣휇)(̂푢푖 + 푖 ̂푣푖) +minimizes the GL functional. This non-unitary state is also +unique except for trivial 푆푂(3)퐽 and 푈(1)휑 rotations. The +order parameter is equivalent to the 퐴1 state of the SF 3He. +The bulk quasiparticle spectrum consists of two parts: one +is a normal fluid, and the other is a Weyl SF with a pair of +5Here we use the bar to distinguish the magnetic 휋-rotation about the +푥-axis introduced later. +oppositely charged Weyl fermions. The ferromagnetic state +is also realized in the limit of a strong magnetic field or the +vicinity of the critical temperature even in the weak coupling +limit owing to the finite-size correction of the Fermi surface. +Magnetized nematic state. Recently, even in the weak +coupling limit, non-unitary states are predicted in a magnetic +field Mizushima et al. (2021). As mentioned above, quasi- +classical approximation, which treats the size of the Fermi +surface as infinity, allows only the nematic states, which is +unitary. By contrast, in the presence of the finite-size cor- +rection of the Fermi surface, a magnetic field along the ̂푤- +direction induces the non-unitary component into the ne- +matic state with 푟 ∈ (−1, −1∕2) as 퐴휇푖 = Δ[̂푢휇 ̂푢푖 + 푟 ̂푣휇 ̂푣푖 + +푖휅(̂푢휇 ̂푣푖 + ̂푣휇 ̂푢푖) − (1 + 푟) ̂푤휇 ̂푤푖] or equivalently +퐴휇푖 = Δ +⎛ +⎜ +⎜⎝ +1 +푖휅 +0 +푖휅 +푟 +0 +0 +0 +−(1 + 푟) +⎞ +⎟ +⎟⎠ +. +(93) +For simplicity, Ref. Mizushima et al. (2021) studies the case +of 푟 = −1, i.e., in a strong magnetic field. In the quasi- +classical limit, 휅 = 0 and the 퐷4-BN state is realized. The +order parameter tensor in the angular momentum represen- +tation is reduced to 퐴휇푖 = Δ[Γ2 + Γ−2]휇푖, which shows the +same gap amplitudes for 푀 = ±2. The finite size correction +of the Fermi surface induces a finite 휅. In the angular mo- +mentum representation, the order parameter tensor becomes +퐴휇푖 = Δ[(1 + 휅)Γ2 + (1 − 휅)Γ−2]휇푖. Thus, 휅 represents the +imbalance between the 푀 = ±2 sectors. In terms of the gap +matrix in the spin basis, the Cooper pairs are decomposed +into two spin polarized sectors |↑↑⟩ and |↓↓⟩ with different +gap amplitudes. Each spin sector has a polarized orbital an- +gular momentum state, and thus, a pair of the Weyl fermions +appears at the north pole and the south pole in each spin sec- +tor. The orbital angular momentum between these two spin +states are opposite, which means that two Weyl fermions +with opposite helicity at each pole. This is in contrast to +the 퐴2 phase proposed for the SF 3He. In the limit of a +strong magnetic field or the vicinity of the critical temper- +ature, 휅 → 1, the ferromagnetic state is realized. However, +we note that this imbalance originates from the finite size +effect of the Fermi surface. The effect is parametrized by +Δ∕휀F, which is usually small for conventional neutron stars, +and thus the imbalance 휅 is also expected to be small. +Vortices in 3푃2 SFs. +The vortices admitted in 3푃2 +SFs are basically the same as those in spin-2 BECs, which +are discussed in Sec. 4.2. Table 4 summarizes remaining +symmetry, order parameter manifold, and fundamental +group of the topological defects of the above-discussed +possible phases. Non-Abelian vortex anyons are included in +the 퐷2- and 퐷4-BN states and the cyclic state as discussed +in Sec. 4.3. Non-Abelian vortex anyons in the 퐷2-BN states +are spin vortices of 휋 rotation, as shown in Eq. (81). The +퐷4-BN states admit HQVs (V)–(VII) in Eq. (72) in addition +to spin vortices (III) and (IV) in Eq. (72) as non-Abelian +vortex anyons (see also Table 3). +The cyclic states admit +1/3-quantum vortices (IV)–(VII) in Eq. (77) as well as spin +vortices (III) in Eq. (77) as non-Abelian vortex anyons (see +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 21 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +Table 4 +Summary of order parameters (푟, 휅 in Eq. (93)), remaining symmetry (퐻), (푅 ≃ 퐺∕퐻), +and topological vortices 휋1(푅) in possible phases, taken from Ref. Mizushima et al. (2021). +See also the references therein. +phase +푟 & 휅 in Eq. (93) +퐻 +푅 ≃ 퐺∕퐻 +휋1(푅) +UN +푟 = −1∕2 & 휅 = 0 +퐷∞ ≃ 푂(2) +푈(1) × ℝ푃 2 +ℤ ⊕ ℤ2 +퐷2-BN +푟 ∈ (−1, −1∕2) & 휅 = 0 +퐷2 +[푈(1) × 푆푂(3)]∕퐷4 +ℤ ⊕ ℚ +퐷4-BN +푟 = −1 & 휅 = 0 +퐷4 +[푈(1) × 푆푂(3)]∕퐷4 +ℤ ×ℎ 퐷∗ +4 +Cyclic +푟 = 푒푖2휋∕3 & 휅 = 0 +푇 +[푈(1) × 푆푂(3)]∕푇 +ℤ ×ℎ 푇 ∗ +Mag. 퐷2-BN +푟 ∈ (−1, −1∕2) & 휅 ∈ (0, 1) +0 +푈(1) × 푆푂(3) +ℤ ⊕ ℤ2 +Mag. 퐷4-BN +푟 = −1 & 휅 = −1 +퐶4 +[푈(1) × 푆푂(3)]∕ℤ4 +ℤ ×ℎ 퐶∗ +4 +FM +푟 = −1 & 휅 = 1 +푈(1)퐽푧+2Φ +푆푂(3)퐽푧−2Φ∕ℤ2 +ℤ4 +5 +0 +5 +y/ 0 +2 +(a) +M= +2 +2 +(b) +M=2 +5 +0 +5 +y/ 0 +2 +2 +4 +(c) +M= +1 +(d) +M=1 +5 +0 +5 +x/ 0 +5 +0 +5 +y/ 0 +2 +(e) +M=0 +5 +0 +5 +x/ 0 +(f) +total +0.0 +0.5 +1.0 +1.5 +2.0 +0.0 +0.5 +1.0 +1.5 +2.0 +0.0 +0.5 +1.0 +0.0 +0.5 +1.0 +1.5 +2.0 +0.0 +0.5 +1.0 +1.5 +2.0 +1.8 +2.0 +2.2 +2.4 +2.6 +2.8 +Figure 9: +Gap structure of the 푑 vortex in the 퐷4-BN state +(푇 = 0.4푇푐 and 퐵 = 0.5푇푐). (a)-(e) Amplitude of each angular +momentum sector. +Red arrows indicate the phase winding +structures. (f) Total amplitude of the order parameter defined +by [ 3 +2Tr ⟨ ̂Δ† ̂Δ⟩F]1∕2. +also Table 2). +Especially, the non-Abelian vortex in the 퐷4-BN state is +the main target in the remaining part. We explain the vortices +in the 퐷4-BN state in the beginning of the next subsection. +5.2. Half quantum vortex in 퐷4-BN state +Vortices in 퐷4-BN state. The 퐷4-BN state, which can +be thermodynamically stabilized by a large magnetic field, +has a pair of point nodes at the north and south poles along +the direction of the magnetic field Masuda & Nitta (2016), +Mizushima et al. (2017), Yasui, Chatterjee & Nitta (2019), +Mizushima et al. (2020). Hereafter, we focus on the 퐷4-BN +state with a pair of point node along ̂푤 = ̂푧. The homoge- +neous order parameter tensor has a diagonal form Sauls & +Serene (1978): 퐴 = Δdiag(1, −1, 0) [Eq. (68)], which is in- +variant under a 퐷4 group. (A similar order parameter form +is taken in the planar state of SF 3He Makhlin et al. (2014), +Silaev & Volovik (2014), but different topological defects +are resulted from different order parameter manifolds.) +As already discussed in Sec. 4, the order parameter man- +ifold in the 퐷4-BN state is then characterized by the broken +symmetry, 푅 ≃ [푈(1)×푆푂(3)]∕퐷4, see Eq. (69). The topo- +logical charges of line defects are characterized by the first +homotopy group, Eq. (75) +휋1(푅) ≃ ℤ ×ℎ 퐷∗ +4 +(94) +where ×ℎ denotes a product defined in Ref. Kobayashi et al. +(2012). This ensures two different classes of topological +line defects: Vortices with commutative topological charges +and vortices with non-commutative topological charges. +The former includes integer vortices (I) in Eq. (72) with +or without internal structures, while an example of the +latter is the non-Abelian HQV, (V)–(VII) in Eq. (72). +Integer vortices are characterized by vorticity quantized +to an integer number because of the singlevaluedness of +the order parameter. Fractionally quantized case such as a +HQV usually has a phase jump (휋-phase jump for a HQV) +along the contour surrounding the vortex. In the 퐷4-BN +state, however, the phase discontinuity is compensated by +the phase originating from the discrete rotation of the 퐷4 +symmetry. Thereby HQVs are topologically allowed. Here, +we particularly focus on the case where the vorticity is +along the ̂푧-direction accompanying the 휋-phase jump com- +pensated by the 퐶4 rotation about the ̂푧-axis, as indicated +in Figs. 8(b), 10(a), 10(f), and 11(a). Such HQVs belong to +the group (V) or (VI) in Eq. (72). +Hereafter, we review possible vortices when the vortic- +ity and the point nodes of the 퐷4-BN state are along the +̂푧-direction. As a basis set of the order parameter tensor +퐴휇푖, the eigenstates of the 푧 component of the total angu- +lar momentum, denoted by 퐽푧Γ푀 = 푀Γ푀, are convenient: +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 22 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +퐴휇푖(휌, 휃) = ∑2 +푀=−2 훾푀(휌, 휃)[Γ푀]휇푖, where the cylindrical +coordinate system 푹 = (휌, 휃) is introduced with assump- +tion of uniformity along the 푧-direction. In the region far +from the vortex core 휌 → ∞, there is no radial dependence, +and the order parameter modulation is described by the 푈(1) +phase rotation characterized by vorticity 휅 and the simulta- +neous rotation in the spin-orbit space of Cooper pairs. For +the latter rotation by angle 휑 about the ̂푧-axis, the other com- +ponents of the triad, ̂푥, and ̂푦, are transformed as +푅(휑) ∶ ̂푥 → cos 휑̂푥 + sin 휑 ̂푦, +(95) +푅(휑) ∶ ̂푦 → − sin 휑̂푥 + cos 휑 ̂푦. +(96) +Using Γ푀, the 푈(1) phase winding and the spin-orbit rota- +tion for non-zero bulk components are expressed as +퐴휇푖(휃) = +2 +∑ +푀=−2 +훾푀,∞푒푖휅휃−푀휑[Γ푀]휇푖 (휌 → ∞) +≡ +2 +∑ +푀=−2 +훾푀,∞푒푖(휅−푛푀)휃[Γ푀]휇푖. +(97) +Especially, in the 퐷4-BN state with the point nodes along +the ̂푧-axis, |훾2,∞| = |훾−2,∞| and 훾±1,∞ = 훾0.∞ = 0. Here in +the second line, we parametrize 휑 = 푛휃 along the contour +surrounding the vortex, where the spin-orbit rotation can be +regarded as the 푛-fold 퐽-disgyration6. Note that 푛 is not nec- +essarily an integer. The boundary condition of a vortex char- +acterized by (휅, 푛) is given by Eq. (97). +Axisymmetric singly quantized vortex. The integer +vortices belong to a class 휅 ∈ ℤ. +Even in the singly +quantized case 휅 = ±1, however, there are many pos- +sibilities because of differences in the internal structure +and the disgyration in the spin-orbit space. +As a sim- +ple case, the axisymmetic vortex can be described as +퐴휇푖(휌, 휃) += +∑2 +푀=−2 훾푀(휌)푒푖(휅−푀)휃[Γ푀]휇푖 in a whole +region, which includes complex radial functions 훾푀(휌) +to be determined. +The disgyration of the axisymmetric +vortex is 1-fold (푛 = 1 in Eq. (97)), that is, the 2휋 rotation +of the triad around the vortex. +Thus, the axisymmetric +vortex belongs to the conjugacy class (II) in Eq. (72)7. +Although the loss in the kinetic energy becomes large +because of the 퐽-disgyration, there is a nice analogy with +vortices in SF 3He-B phase. As in the SF 3He-B phase, +the symmetry of the vortices can be characterized by three +discrete symmetries called 푃1,2,3 symmetries Salomaa & +Volovik (1985b, 1987), which are discussed in the next +subsection8. The internal structures 훾−1,0,1(휌) characterize +a classification based on these discrete symmetries, which +allows several vortices as summarized in Table 5.2. Within +an axisymmetric condition, only 표 vortex or 푣 vortex is +realized as a self-consistent solution. +The 표 vortex has +6The term “퐽-disgyration" accounts for a singularity in the spin-orbit +space, i.e., the total angular momentum (퐽) space. Spin disgyrations and +orbital disgyrations are introduced after Eq. (32). +7In Sec. 4.2, we discuss the spin vortex of 2휋 rotation in spin-2 BECs. +8The 푃3 symmetry is already introduced when defining the one- +dimensional winding number in the bulk nematic state. +vortex +훾푀=0(휌) +훾푀=±1(휌) +core +symmetry +표 vortex +real +zero +singular +푃1, 푃2, 푃3 +푢 vortex +complex +zero +singular +푃1 +푣 vortex +real +real +coreless +푃2 +푤 vortex +real +imaginary +coreless +푃3 +푢푣푤 vortex +complex +complex +coreless +- +Table 5 +Internal structures of axisymmetric vortices. The second and +third columns show order parameters of the core structure. +The fourth column is coreless (singular) whether the vortex +core is occupied (unoccupied) by some SF components. The +last column accounts for the preserved symmetry. +a singular core and is the most symmetric one so that it +meets all the discrete symmetries. By contrast, the core of +the axisymmetric 푣 vortex is occupied by the SF compo- +nent 훾±1 for 휅 = ±1, and it has the 푃2 (magnetic mirror +reflection) symmetry, but does not have the 푃1 (inversion) +or 푃3 (magnetic 휋-rotation about the 푥 axis) symmetries. +Energetically, the 푣 vortex is more stable than the 표 vortex +because of a gain in the condensation energy in the core +region. However, the induced component of the 푣 vortex +which occupies the core is suppressed by a magnetic field . +Non-axisymmetric singly quantized vortex. Without +the axisymmetric condition, the lower energy condition for +a singly quantized vortex is given by (휅, 푛) = (±1, 0) to re- +duce the loss of the gradient energy. Such a vortex belongs +to the conjugacy class (I) in Eq. (72). In this case, so called +double-core vortex (푑 vortex) can be a self-consistent solu- +tion Masaki et al. (2022) as in the SF 3He-B phase Thuneberg +(1986), Salomaa & Volovik (1986). The 푑 vortex is also +called the non-axisymmetric 푣 vortex because it has the 푃2 +symmetry but does not have the 푃1 and 푃3 symmetries Tsut- +sumi et al. (2015). Note that the axial symmetry is spon- +taneously broken for the 푑 vortex in the SF 3He-B phase, +while the symmetry is broken by the boundary condition for +the 푑 vortex in a 3푃2 SF. Figure 9 shows the order param- +eter structure of the 푑 vortex in the 퐷4-BN state for 푇 = +0.4푇푐 and 퐵 = 0.5푇푐 with critical temperature 푇푐. In the +panels, the unit of length is the coherence length defined +by 휉0 = 푣F∕2휋푇푐 with Fermi velocity 푣F, where ⟨⋯⟩F ac- +counts for the Fermi surface average. The bulk components +훾±2 have a conventional vortex structure with a single phase +winding [see panels (a) and (b)]. The double core struc- +ture can be clearly observed in the total amplitude defined +by [ 3 +2Tr ⟨ ̂Δ† ̂Δ⟩F]1∕2 in panel (f). Such a structure is due to +the occupations of the core by 훾푀=±1 as shown in panels (c) +and (d). As can be seen below, the 푑 vortex is not the lowest +energy state among the vortex states with (휅, 푛) = (±1, 0) in +the 퐷4-BN state and it splits into two HQVs. The 푑 vortex +in the SF 3He-B phase is the most stable vortex solution in +the low pressure region Kasamatsu et al. (2019), Regan et al. +(2019). A 푑 vortex is realized as the lowest energy state in +the UN and the 퐷2-BN states. +HQVs. The HQVs can be characterized by 휅 = ±1∕2. +The possibility of the half-quantized vortex in the 퐷4-BN +state was pointed out long back in 1980 Sauls (1980) on the +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 23 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +θ1 +θ2 +(a) (κ, n) = (1/2, +1/4) +−10 +−5 +0 +5 +10 +y/ξ0 +M = −2 +(b) |γ−2| +(c) arg(γ−2) +M = 0 +(d) |γ0| +(e) arg(γ0) +θ1 +θ2 +(f) (κ, n) = (1/2, −1/4) +−10 −5 +0 +5 +10 +x/ξ0 +−10 +−5 +0 +5 +10 +y/ξ0 +M = +2 +(g) |γ+2| +−10 −5 +0 +5 +10 +x/ξ0 +(h) arg(γ+2) +−10 −5 +0 +5 +10 +x/ξ0 +M = 0 +(i) |γ0| +−10 −5 +0 +5 +10 +x/ξ0 +(j) arg(γ0) +0.0 +0.5 +1.0 +1.5 +2.0 +−π +−π/2 +0 +π/2 +π +0.0 +0.2 +0.4 +0.6 +−π +−π/2 +0 +π/2 +π +0.0 +0.5 +1.0 +1.5 +2.0 +−π +−π/2 +0 +π/2 +π +0.0 +0.1 +0.2 +−π +−π/2 +0 +π/2 +π +Figure 10: HQV with (휅, 푛) = (1∕2, +1∕4) [(a) - (e)] and (휅, 푛) = (1∕2, −1∕4) [(f) - (j)]. The boundary conditions are sketched in +(a) and (f). The amplitudes of 훾푀 for 푀 = −2 and 0 (+2 and 0) are shown in (b) and (d) [(g) and (i)], respectively. The phases +of 훾푀 for 푀 = −2 and 0 (+2 and 0) are shown in (c) and (e) [(h) and (j)], respectively. Figures are adapted from Ref. Masaki +et al. (2022) ©2022 American Physical Society. +basis of the topological consideration of the form of 퐴휇푖. +Since 휅 is a half odd integer, the 푈(1) phase part gives the +minus sign under the spatial rotation 휃 → 휃 + 2휋. By rotat- +ing the triad by angle ±휋∕2 while going around the vortex, +which is denoted by 푛 = ±1∕4 in Eq. (97), the above minus +sign can be compensated by the other minus sign stemming +from the disgyration. This topological consideration is rep- +resented by the boundary condition Eq. (97) with (휅, 푛) = +(±1∕2, ±1∕4), which belongs to the conjugacy class (V) or +(VI) in Eq. (72). The gradient energy of an isolated HQV +far from the core is a half of that of an singly quantized vor- +tex described by (휅, 푛) = (±1, 0), namely, the energy of two +HQVs is the same as that of the singly quantized vortex ex- +cept for contributions from the vortex cores. In other words, +whether the singly quantized vortex can split into two HQVs +depends on the energy of their internal structures and the in- +teraction energy between two HQVs. +Although the above topological consideration does +not take into account the core structure, recently, the +whole structures of isolated HQVs were studied using the +phenomenological GL theory Masuda & Nitta (2020), +Kobayashi & Nitta (2022a,b), and the microscopic quasi- +classical theory Masaki et al. (2022). It is proposed that +an integer vortex with 휅 = 1 can split into two HQVs with +(휅, 푛) = (1∕2, 1∕4) and (휅, 푛) = (1∕2, −1∕4) Masuda & +Nitta (2020). Here we assume that 휅 > 0 without loss of +generality. +The configuration of the two HQVs given as +one for 푛1 = +1∕4 with its core at 푹1 and the other for +푛2 = −1∕4 with its core at 푹2 has the following boundary +condition at 푹: +퐴(푹) ∼ +∑ +푀=±2 +푒푖(휅−푛1푀)휃1+푖(휅−푛2푀)휃2훾푀Γ푀, +(98) +where 휃1 (휃2) is the angle of 푹 − 푹1 (푹 − 푹2). Since the +difference between 휃1 and 휃2 is negligible for |푹| → ∞, the +phase part behaves as exp(2푖휅휃) [휃 ≃ (휃1 + 휃2)∕2], which +means the boundary conditions for the two HQVs and the +singly quantized vortex are equivalent in the limit 휌 → ∞. In +the following, we explain the internal structure of each HQV, +and the interaction energy of the two HQV vortex through +the comparison of the singly quantized vortex Masaki et al. +(2022). Particularly, the non-axisymmetric internal struc- +ture of each HQV is important to the interaction energy. +Isolated HQV (휅, 푛) = (1∕2, +1∕4). The two disgy- +rations of the triads, given by 푛 = ±1∕4, are inequivalent +because one is parallel to the vorticity, while the other is an- +tiparallel. Here we first explain the antiparallel case (푛, 휅) = +(1∕2, 1∕4). In the above notation, by setting 푹1 = (0, 0) and +푹2 = (−∞, 0), and thus setting 휃2 → 0, the boundary con- +dition is obtained from Eq. (98). In this case, the relative +phase of 훾±2 is zero, and the schematic image of the disgy- +ration is drawn in Fig. 10(a). Each circular object shows the +directions of 푑-vectors by colored arrows, whose color bar +is the same as in panel (c). There are also the cyan and ma- +genta lines, which represent the directions of the eigenval- +ues +1 and −1 of the order parameter 퐴, respectively. This +HQV is (1∕2, 퐶4) in the conjugacy class (V) in Eq. (72). The +self-consistent solutions of the non-trivial components are +shown in panels (b)–(e). Here 훾2, not shown, is almost uni- +form without phase winding, as expected from the bound- +ary condition 휅 − 푛1푀 = 1∕2 − 1∕4 ∗ 2 = 0. The other +bulk component 훾−2 is a conventional singular vortex with +the single phase winding shown in panel (c). The ampli- +tude and the phase of the internal structure of 훾0 are, respec- +tively, shown in panels (d) and (e). The phase of the internal +structure is oppositely winding against 훾−2, which can be +understood by analogy with a vortex in a spinless chiral 푝- +wave SC. We assume, for simplicity, ̄푘푧 = 0, and then write +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 24 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +̄푘휒 = (푘푥 + 푖휒푘푦)∕푘F = 푒푖휒훼 with the sign of the angular +momentum 휒 = ±. With this notation, the gap function is +written as +̂Δ(풌F, 푹) = [−훾2(푹)̄푘+ + 훾0(푹)∕ +√ +6̄푘−] |↑↑⟩ ++ [훾−2(푹)̄푘− − 훾0(푹)∕ +√ +6̄푘+] |↓↓⟩ . +(99) +In each spin sector, two opposite orbital-angular-momenta, +̄푘±, are mixed owing to the induced component 훾0. In a spin- +less chiral 푝-wave SC, the induced component has the op- +posite angular momentum relative to the component which +has a non-zero order parameter far from the vortex core, i.e., +휒푖 = −휒푏 Heeb & Agterberg (1999), Matsumoto & Heeb +(2001). Here we call the latter component the bulk com- +ponent, and 휒푏 (휒푖) represents the sign of the angular mo- +mentum for the bulk (induced) component. The vorticity of +the induced component, 휅푖, is given by 휅푖 = 휅푏 + 휒푏 − 휒푖, +where 휅푏 is the vorticity of the bulk component. Here the +휒푏 − 휒푖 accounts for the angular momentum difference be- +tween the bulk and induced components, and is reduced to +2휒푏. For the (1∕2, +1∕4)-HQV, the bulk component 훾−2 has +the vorticity 휅푏 = 휅 − 푛(−2) = 1, and 휒푏 = −1. Thereby +휅푖 = 휅푏 + 2휒푏 = −1 successfully explains the vorticity of +the induced component shown in panel (e). More striking +feature is the three-fold symmetry in the amplitude of the +induced component |훾0|. Reflecting this discrete symmetry, +the phase evolution of the induced component surrounding +the vortex is non-linear. As seen from Eq. (99), the main +structure of this HQV is in the spin-down sector. +Isolated HQV (휅, 푛) = (1∕2, −1∕4). The other HQV, +characterized by (1∕2, −1∕4), at 푹2 = (0, 0), is obtained by +푹1 → (+∞, 0), i.e., 휃 → 휋 in Eq. (98), in which the rel- +ative phase of 훾±2 is opposite because of the phase factor +exp[푖(1∕2+푀∕4)휋] from the (1∕2, +1∕4) HQV. This HQV +is (1∕2, 퐶−1 +4 ) in the conjugacy class (V) in Eq. (72), and its +disgyration is schematically drawn in Fig. 10(f). In contrast +to the previous case, a conventional vortex structure appears +in the 푀 = +2 sector shown in panels (g) and (h), while +an almost uniform structure without phase winding is in the +푀 = −2 sector. In panel (j) the phase winding of the in- +duced component is +3, which can be understood as in the +previous case: 휅푖 = 휅푏 + 2휒푏 = 3 for 휅푏 = 휅 + 푀∕4 = 1 +and 휒푏 = +1. The phase evolution surrounding the vortex +is again non-linear reflecting the discrete symmetry of the +amplitude |훾0|, which is five-fold as shown in panel (h). The +major vortex structure of this HQV is in the spin-up sector. +Molecule of HQVs (stability). The two types of internal +structures in the 푀 = 0 component induced for the HQVs +with 푛 = ±1∕4 are modulated by the connection of these two +HQVs. This modulation causes an interaction between the +two HQVs. The interaction energy of the two HQVs are de- +fined by Δsn(푑v) = sn(푹1, 푹2)− + +sn(푹1)− − +sn(푹2) based +on the Luttinger–Ward energy functional sn Vorontsov & +Sauls (2003). Here the two HQVs are at 푹1 = (푑v∕2, 0) and +푹2 = (−푑v∕2, 0), schematically shown in Fig. 11(a), whose +energy is denoted by sn(푹1, 푹2). The energies of the iso- +lated HQVs (휅, 푛) = (1∕2, +1∕4) at 푹1 and (1∕2, −1∕4) at +푹2 are denoted by  + +sn(푹1) and  − +sn(푹2), respectively. +Figure 11(b) shows the interaction energies of the two +HQVs as a function of intervortex distance 푑v. When 푑v = +0, the 푑 vortex (the singly quantized vortex with double core +structure) is realized. The gap structure is show in Fig. 9. +Importantly, the positive energy of the 푑 vortex means that +two isolated HQVs (푑v → ∞) are more stable than the 푑 +vortex. The actual interaction energy takes the minimum +at finite 푑v, indicating the instability of the 푑 vortex into +a bound state of the two HQVs like a molecule. As dis- +cussed in Sec. 4.2, a singly quantized vortex (휅, 푛) = (1, 0) +in the conjugacy class (I) in Eq. (72) splits into two HQVs +(1∕2, +1∕4) and (1∕2, −1∕4) in the class (V). +The stabilization mechanism in this molecule state is a +deformation in the non-axisymmetric induced component +훾0, as shown in Figs. 11(c-1) and 11(c-2), realized in the +strongly spin-orbit coupled Cooper pairs Masaki et al. +(2022). +This mechanism is purely intrinsic and possible +even in the weak coupling limit, different from those in +other systems such as the SF 3He Salomaa & Volovik +(1985a) and unconventional SCs Chung et al. (2007): In the +SF 3He-A phase, Volovik and Salomaa phenomenologically +introduced some corrections in spin mass to stabilize the +HQV Salomaa & Volovik (1985a); This correction might +be regarded as a kind of strong coupling effect through +the Fermi liquid correction, but another strong coupling +effect is known to destabilize the HQV Kawakami et al. +(2009, 2010, 2011), Mizushima et al. (2016). Vakaryuk and +Leggett unveiled that the HQVs in equal spin pairing states, +such as 3He-A and 퐷4-BN, are accompanied by a nonzero +spin polarization even in the absence of external Zeeman +coupling Vakaryuk & Leggett (2009). +The coupling of +such spin polarization to external magnetic fields may +affect the stability of HQVs. +Another example of the +stabilization mechanism is an extrinsic one in the polar and +polar distorted phases of the SF 3He because of strongly +anisotropic impurities, as discussed in Sec. 3.2. +5.3. Non-Abelian anyon in non-Abelian vortex +In this section, first the zero energy bound states in +above-discussed HQVs are demonstrated. +Second we +summarize the discrete symmetries in the presence of +vortices, and finally discuss the topological protection of +the zero energy states and their non-Abelian nature. +Existence of zero energy states. +To investigate +fermionic bound states at discrete energy levels, it is +necessary to solve the BdG equation (92). +By assuming +the spatial uniformity along the 푧-direction, the quantum +number is labeled as 휈 = (훼, 푘푧), and only the 푘푧 = 0 sector +is focused on to seek for zero energy bound states. The +direct numerical calculation gives us a spectral function +including the discrete bound states around the HQV-cores, +as shown in Fig. 12(a). There are two zero energy states +localized in both of the cores. +Here, the molecule state +of the two HQVs with 푑v +≃ 10.7휉0 is used for a gap +function in the BdG equation, and the spectral function, +also known as the local density of state, is defined as +휈푘푧=0(푹; 휔) = ∑ +훼,휎 |푢훼,푘푧=0,휎(푹)|2훿(휔 − 휖훼,푘푧=0) along +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 25 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +0 +20 +40 +60 +dv/⇠0 +�0.25 +0.00 +0.25 +0.50 +0.75 +1.00 +� ¯Jsn(dv) +d vortex +�15 �10 �5 +0 +5 +10 +15 +x/⇠0 +�10 +�5 +0 +5 +10 +y/⇠0 +h3 +2Trhˆ�† ˆ�iF +i1/2 +2.0 +2.2 +2.4 +2.6 +2.8 +(a) +(b) +(c-1) Amplitude +(c-2) Phase +�15 +�10 +�5 +0 +5 +10 +15 +x/⇠0 +�10 +�5 +0 +5 +10 +y/⇠0 +�15 +�10 +�5 +0 +5 +10 +15 +x/⇠0 +M = 0 +0.0 +0.2 +0.4 +0.6 +0.8 +�⇡ +�⇡/2 +0 +⇡/2 +⇡ +Figure 11: +(a) Schematic image of a molecule of non-Abelian HQVs in a 퐷4-BN state at a cross section perpendicular to the +two parallel vortex lines, characterized by (휅, 푛) = (1∕2, +1∕4) at 푥 = 푑v∕2 and (1∕2, −1∕4) at 푥 = −푑v∕2. Its spin-momentum +structure is shown by objects with color arrows representing 푑 vectors. The color map on the surface shows the 푈(1) phase, and +the bottom plot shows the induced component also shown in panel (c-1). (b) Interaction energy of two HQVs as a function of +their separation 푑v. The inset shows the total amplitude of the order parameter for the HQV molecule whose intervortex distance +is indicated by the arrow. The free energy is scaled as +̄sn = sn∕(휈n푇 2 +c 휉2 +0Ω푧), where Ω푧 is the length of the system in the 푧 +direction, and 휈n is the density of states at the Fermi energy in the normal state. The energy at 푑v = 0 is the free energy of the +푑 vortex shown in Fig. 9. (c-1) and (c-2) The amplitude and the phase of the induced component 훾0. The intervortex distance +푑v is the same as that in the inset of panel (b). Figures are adapted from Ref. Masaki et al. (2022) ©2022 American Physical +Society. +푹 = (푥, 0), where 푢훼,푘푧,휎(푹) is the particle component with +spin 휎 of the eigenfunction ⃗푢훼,푘푧(푹). +In the calculation, +the parameter 푘F휉0, characterizing the discreteness of +the bound states, is set to 5. +The Majorana condition, +푢훼,푘푧=0,휎(푹) = [푣훼,푘푧=0,휎(푹)]∗, for the wave functions of +the zero energy state can be confirmed Masaki et al. (2022). +−20 +−10 +0 +10 +20 +x/ξ0 +0.0 +0.5 +1.0 +1.5 +2.0 +2.5 +ω/Tc +0.0 +0.1 +0.2 +Figure 12: +Local density of states 휈푘푧=0(푹; 휔) at 푘푧 = 0 and +푦 = 0 for a pair of HQVs located at (푥, 푦) = (±푑v∕2, 0) with +푑v ≃ 10.7휉0. The spatial distributions of the two zero energy +states are different. +Figures are adapted from Ref. Masaki +et al. (2022) ©2022 American Physical Society. +Discrete symmetry of vortices. We utilize the semiclas- +sical approximation to clarify the symmetry and topology of +vortices, following Refs. Tsutsumi et al. (2015), Mizushima +et al. (2016), Shiozaki & Sato (2014). In the semiclassical +approximation, the spatial modulation due to a vortex line is +treated as adiabatic changes as a function of the real-space +coordinate surrounding the defect with the angle 휃. Then, +the BdG Hamiltonian in the base space, (풌, 휃), is obtained +from Eq. (92) as +̌(풌, 휃) = +( ̂ℎ푁(풌) +̂Δ(풌, 휃) +̂Δ†(풌, 휃) +−̂ℎ∗ +푁(풌) +) +, +(100) +where the 3푃2 pair potential within a semiclassical approxi- +mation is given by +̂Δ(풌, 휃) = 푖̂휎휇퐴휇푖(휃)푘푖∕푘F ̂휎푦. +(101) +Let us now summarize the discrete symmetries of the +BdG Hamiltonian in Eq. (100). In the presence of vortex, the +BdG Hamiltonian breaks the time-reversal symmetry ̂ = +−푖̂휎푦퐾, but holds the particle-hole symmetry +̌ ̌(풌, 휃) ̌−1 = − ̌(−풌, 휃), +(102) +where ̌ = ̌휏푥퐾 and 퐾 is the complex conjugation oper- +ator. In addition to the particle-hole symmetry, three dis- +crete symmetries, the {푃1, 푃2, 푃3}, are pointed out to be rel- +evant to vortices of the SF 3He-B phase Salomaa & Volovik +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 26 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +(1985b, 1987). Their representations are given by +̂푃1 = 푃 푈휋 ̂1, ̂푃3 = ̂ ̂퐶2,푥, +(103) +and ̂푃2 = ̂푃1 ̂푃3. Here, 푃 , 푈휋 = 푒푖(휅+1)휋, ̂퐶2.푥 = 푒−푖 ̂퐽푥휋 are +the spatial inversion, the discrete phase rotation, and the 휋- +rotation in the spin-orbit space about the 푥-axis. The physi- +cal meanings of 푃1, 푃2, and 푃3 symmetries are, the inversion, +magnetic reflection, and magnetic 휋-rotation symmetries re- +spectively. From the definition, 푃1푃2푃3 = 1. Under these +symmetry operations, a momentum 풌 and a spin 흈 are trans- +formed as +푃1 ∶ 풌 → (−푘푥, −푘푦, −푘푧), 흈 → (휎푥, 휎푦, 휎푧), +(104) +푃2 ∶ 풌 → (푘푥, −푘푦, −푘푧), 흈 → (−휎푥, 휎푦, 휎푧), +(105) +푃3 ∶ 풌 → (−푘푥, 푘푦, 푘푧), 흈 → (−휎푥, 휎푦, 휎푧). +(106) +Under these transformation, the order parameters are trans- +formed as +푃1 ∶ 훾푀(휌, 휃) → −훾푀(휌, 휃 + 휋), +(107) +푃2 ∶ 훾푀(휌, 휃) → (−1)휅+푀[훾푀(휌, 휋 − 휃)]∗, +(108) +푃3 ∶ 훾푀(휌, 휃) → (−1)푀[훾푀(휌, −휃)]∗. +(109) +For axisymmetric vortices, +we confirm the non-zero +components of 훾푀(휌) summarized in Table. 5.2 by using +the relation 훾푀(휌, 휃) += +훾푀(휌)푒푖(휅−푀)휃. +For example, +푃2 ∶ 훾푀(휌)푒푖(휅−푀)휃 → 훾∗ +푀(휌)푒푖(휅−푀)휃, and when the 푃2 +symmetry is preserved, 훾푀(휌) = 훾∗ +푀(휌) can be obtained. In +the case of the 푑 vortex, the 푃3 symmetry is broken because +of the non-zero 훾±1 components, and the 푃2 symmetry is +the only preserved symmetry among these three. +In the +case of isolated HQVs, even though 훾±1 = 0, because of +the three-fold, and five-fold symmetry in the gap amplitude +of 훾0, the 푃1 and 푃2 symmetries are broken, but the 푃3 +symmetry is preserved. +Another discrete symmetry is the mirror reflection sym- +metry about the plane perpendicular to the vortex line, that +is, the 푥푦-plane, which is already discussed in Sec. 3.4. The +mirror refection symmetry 푀푥푦 transforms the momentum +and the spin as +푀푥푦 ∶ 풌 → (푘푥, 푘푦, −푘푧), 흈 → (−휎푥, −휎푦, 휎푧), +(110) +and thus the order parameter is transformed as +푀푥푦 ∶ 훾푀(휌, 휃) → (−1)푀+1훾푀(휌, 휃). +(111) +Therefore, in the presence of 푀푥푦, even 푀 and odd 푀 can- +not be mixed. In the case of the 퐷4-BN state with the point +nodes along the 푧-direction, 훾푀=±2 ≠ 0, and the only pos- +sible mirror operation that commutes with the BdG Hamil- +tonian at the mirror invariant momentum 풌푀 = (푘푥, 푘푦, 0) +is 휂 = − in Eq. (38) when 훾±1 = 0. The above-discussed +vortices of a 3푃2 SF which preserve the 푀푥푦 symmetry are +the axisymmetric 표 and 푢 vortices, and the HQVs. +Topology of the vortex bound states. On the basis of +the above-discussed discrete symmetries, the zero energy +state of each HQV is shown to be protected by two topolog- +ical number: one based on the chiral symmetry, a combined +symmetry between the particle-hole symmetry and the 푃3 +symmetry, and the other based on the mirror reflection sym- +metry. +When the 푃3 symmetry is preserved, the semiclassical +BdG Hamiltonian is transformed under the combined sym- +metry operation Γ = 푃3 with Γ2 = +1 as +̌Γ ̌(풌, 휃)̌Γ−1 = − ̌(푘푥, −푘푦, −푘푧, −휃). +(112) +Particularly, for 푘푦 = 푘푧 = 0 and 휃 = 0 or 휋, the BdG +Hamiltonian anticommutes with Γ, which can be regarded as +chiral symmetry Sato et al. (2011), Mizushima et al. (2012), +Tsutsumi et al. (2013), Shiozaki & Sato (2014), Tsutsumi +et al. (2015), Masaki et al. (2020), Mizushima et al. (2016). +As in the bulk nematic state, as long as the chiral symmetry +is preserved, one can define the one-dimensional winding +number for 풌푥 = (푘푥, 0, 0) and 휃 = 0 or 휋 as +푤1d(휃) = − 1 +4휋푖 ∫ 푑푘푥tr +[ +̌Γ ̌−1(풌푥, 휃)휕푘푥 ̌(풌푥, 휃) +] +. +(113) +The vortices which preserve the 푃3 symmetry are 표, +and 푤 vortices and the non-Abelian HQVs. +Among +them, the winding numbers (푤1d(0), 푤1d(휋)) of 표 and 푤 +vortices are (2, −2), and thus the topological invariant +푤1d = (푤1d(0) − 푤1d(휋))∕2 = 2 ensures the existence of +two zero energy states. In the case of non-Abelian HQVs, +(푤1d(0), 푤1d(휋)) is (2, 0) for (휅, 푛) += +(1∕2, +1∕4) and +(0, −2) for (1∕2, −1∕4)9. +In both cases, the topological +invariant 푤1d becomes 1, which ensures the existence of +one zero energy state in each HQV core. +Next we explain the topological invariant based on the +mirror reflection symmetry 푀푥푦. As discussed above, the +BdG Hamiltonian ̌(풌푀, 휃) for the mirror invariant momen- +tum 풌푀 commutes with the mirror operator +̌ +휂 for 휂 = − +in Eq. (38). Thus, ̌(풌M, 휃) can be block diagonalized with +respect to the mirror eigenstates with eigenvalues 휆 = ±푖 as +̌(풌M, 휃) = +⨁ +휆 +̃휆(풌M, 휃). +(114) +Significantly, even for the BdG Hamiltonian in each mirror +subsector, ̃휆, the reduced particle-hole symmetry ̃ is pre- +served, though it is not for the other mirror symmetry op- +erator +̌ +휂=+. Therefore, ̃퐻휆 belongs to the class D as well +as spinless chiral SCs Schnyder et al. (2008), and the ℤ2 in- +variant, 휈휆 can be constructed in each mirror subsector Teo +& Kane (2010b), Qi et al. (2008). Non-trivial (odd) value of +휈휆 ensures that the vortex has a single Majorana zero mode +which behaves as a non-Abelian (Ising) anyon Ueno et al. +(2013), Sato et al. (2014), Tsutsumi et al. (2013). +9The choice of the relative phase between 훾±2 as 휋 by 휃1 → 휋 leads +to (푤1d(0), 푤1d(휋)) = (0, −2) rather than (2, 0) for the HQV of (휅, 푛) = +(1∕2, −1∕4). +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 27 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +The ℤ2 invariant 휈휆 is defined on the base space (푆2×푆) +composed of the two dimensional mirror invariant momen- +tum space 풌M and the angle in the real space surrounding +the vortex 휃, and constructed by the dimensional reduction +of the second Chern number defined in the four dimensional +base space (푆3 × 푆) composed of 풌 and 휃. The ℤ2 invari- +ant in each mirror subsector is given by the integral of the +Chern-Simons form: +휈휆 = +( 푖 +휋 +)2 +∫푆2×푆1 +̃푄3,휆 +mod 2, +(115) +̃푄3,휆 = tr[ ̃ +휆 ∧ 푑 ̃ +휆 + 2 +3 +̃ +휆 ∧ ̃ +휆 ∧ ̃ +휆]. +(116) +A non-Abelian Berry connection ̃ +휆 is given by +푖[ ̃ +휆]푛푚 = +∑ +훼 +⟨̃푢휆,푛(풌M, 휃)|휕훼 ̃푢휆,푚(풌M, 휃)⟩ 푑훼, (117) +where 훼 denotes (푘푥, 푘푦, 휃), and |̃푢휆,푚(풌M, 휃)⟩ is the 푚th +eigenstate of ̃휆(풌, 휃). Within the semiclassical approxi- +mation in the 퐷4-BN state, the ℤ2 invariant is calculated +as +휈휆 = 퓁휆휅휆 +mod 2, +(118) +where 퓁휆 and 휅휆 are the first Chern number and the vorticity +in the mirror subsector 휆. The former characterizes the bulk +topology and 퓁휆=±푖 = ±1. The latter is given by 휅휆 = 휅 − +푛푀 for the bulk component 푀 in the 휆 subsector. In the +case of the isolated HQVs, (휈+푖, 휈−푖) = (0, −1) [(+1, 0)] for +(휅, 푛) = (1∕2, +1∕4) [(1∕2, −1∕4)]. The two HQVs host +Majorana fermions in different mirror sectors, and thus the +ℤ2 invariant of the molecule state is given by (휈+푖, 휈−푖) = +(+1, −1). The ℤ2 invariant of the 표 vortex has the same one, +and the pairwise Majorana fermions are localized at the same +core Masaki et al. (2020). +The zero energy state bound in each HQV core is pro- +tected by the two topological invariants based on the mirror +reflection symmetry and the chiral symmetry, and it is identi- +fied as non-Abelian (Ising) anyon of the Majorana fermion. +Therefore, the HQV in the 퐷4-BN state has two fold non- +Abelian nature: one from the non-Abelian Ising anyon, and +the other from non-Abelian first homotopy group. +6. Summary +We have presented various types of non-Abelian anyons +in topological SCs/SFs and other systems. +Non-Abelian +anyons are attracting a great attention because of possible +applications to topological quantum computations, where +quantum computations are realized by braiding of non- +Abelian anyons. The simplest non-Abelian anyons are Ising +anyons realized by Majorana fermions hosted by vortices (or +edges) of topological superconductors, 휈 = 5∕2 quantum +Hall states, spin liquids, and high density quark matter. +These are, however, insufficient for universal quantum +computations. The other anyons which can be used for uni- +versal quantum computations is given by Fibonacci anyons +which exist in 휈 = 12∕5 quantum Hall states. There are +also Yang-Lee anyons which are non-unitary counterparts +of Fibonacci anyons. Another class of non-Abelian anyons +of the bosonic origin can be given by non-Abelian vortex +anyons realized by non-Abelian vortices supported by a +non-Abelian first homotopy group. +These vortex anyons +exist in BN liquid crystals, cholesteric liquid crystals, +spin-2 spinor BECs, and high density quark matter. There +is a unique system simultaneously admitting two kinds of +non-Abelian anyons, which is the Majorana fermions (Ising +anyons) and non-Abelian vortex anyons. That is 3푃2 SFs, +spin-triplet, 푝-wave paring of neutrons, expected to exist +in neutron star interiors as the largest topological quantum +matter in universe. +Acknowledgements +This work was supported by a Grant-in-Aid for Scien- +tific Research on Innovative Areas “Quantum Liquid Crys- +tals” (Grant No. JP22H04480) from JSPS of Japan and JSPS +KAKENHI (Grants No. JP18H01217, No. JP19K14662, +No. JP20K03860, No. JP20H01857, No. JP21H01039, and +No. JP22H01221). +References +Akhmerov, A. R., Dahlhaus, J. P., Hassler, F., Wimmer, M. & Beenakker, C. +W. J. (2011), ‘Quantized Conductance at the Majorana Phase Transition +in a Disordered Superconducting Wire’, Phys. Rev. Lett. 106, 057001. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.106.057001 +Alford, M. G., Benson, K., Coleman, S. R., March-Russell, J. & Wilczek, F. +(1990), ‘The Interactions and Excitations of Nonabelian Vortices’, Phys. +Rev. Lett. 64, 1632. [Erratum: Phys.Rev.Lett. 65, 668 (1990)]. +Alford, M. G., Benson, K., Coleman, S. R., March-Russell, J. & Wilczek, +F. (1991), ‘Zero modes of nonabelian vortices’, Nucl. Phys. B 349, 414– +438. +Alford, M. G., Lee, K.-M., March-Russell, J. & Preskill, J. (1992), ‘Quan- +tum field theory of non-abelian strings and vortices’, Nucl. Phys. B +384, 251–317. +Alford, M. G., Schmitt, A., Rajagopal, K. & Schäfer, T. (2008), ‘Color su- +perconductivity in dense quark matter’, Rev. Mod. Phys. 80, 1455–1515. +Alicea, J. (2012), ‘New directions in the pursuit of Majorana fermions in +solid state systems’, Rep. Prog. Phys. 75(7), 76501. +Alicea, J., Oreg, Y., Refael, G., von Oppen, F. & Fisher, M. P. A. (2011), +‘Non-Abelian statistics and topological quantum information processing +in 1D wire networks’, Nat. Phys. 7, 412. +URL: https://doi.org/10.1038/nphys1915 +Ambegaokar, V., deGennes, P. G. & Rainer, D. (1974), ‘Landau-Ginsburg +equations for an anisotropic superfluid’, Phys. Rev. A 9, 2676–2685. +URL: https://link.aps.org/doi/10.1103/PhysRevA.9.2676 +Andersen, T. I. et al. (2022), ‘Observation of non-Abelian exchange statis- +tics on a superconducting processor’, arXiv:2210.10255 . +Anderson, P. W. & Brinkman, W. F. (1973), ‘Anisotropic superfluidity in +3He: A possible interpretation of its stability as a spin-fluctuation effect’, +Phys. Rev. Lett. 30, 1108–1111. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.30.1108 +Anderson, P. W. & Morel, P. (1961), ‘Generalized bardeen-cooper- +schrieffer states and the proposed low-temperature phase of liquid he3’, +Phys. Rev. 123, 1911–1934. +URL: https://link.aps.org/doi/10.1103/PhysRev.123.1911 +Anderson, P. W. & Toulouse, G. (1977), ‘Phase slippage without vortex +cores: Vortex textures in superfluid 3He’, Phys. Rev. Lett. 38, 508–511. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.38.508 +Ardonne, E., Gukelberger, J., Ludwig, A. W. W., Trebst, S. & Troyer, M. +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 28 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +(2011), ‘Microscopic models of interacting Yang-Lee anyons’, New J. +Phys. 13(4), 045006. +URL: https://dx.doi.org/10.1088/1367-2630/13/4/045006 +Arovas, D., Schrieffer, J. R. & Wilczek, F. (1984), ‘Fractional Statistics and +the Quantum Hall Effect’, Phys. Rev. Lett. 53, 722–723. +Autti, S., Dmitriev, V. V., Mäkinen, J. T., Soldatov, A. A., Volovik, G. E., +Yudin, A. N., Zavjalov, V. V. & Eltsov, V. B. (2016), ‘Observation of +Half-Quantum Vortices in Topological Superfluid 3He’, Phys. Rev. Lett. +117(25), 255301. +Auzzi, R., Bolognesi, S., Evslin, J., Konishi, K. & Yung, A. (2003), ‘Non- +Abelian superconductors: Vortices and confinement in N=2 SQCD’, +Nucl. Phys. B 673, 187–216. +Awoga, O. A., Cayao, J. & Black-Schaffer, A. M. (2019), ‘Supercurrent De- +tection of Topologically Trivial Zero-Energy States in Nanowire Junc- +tions’, Phys. Rev. Lett. 123, 117001. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.123.117001 +Bais, F. A. (1980), ‘Flux Metamorphosis’, Nucl. Phys. B 170, 32–43. +Balachandran, A. P., Digal, S. & Matsuura, T. (2006), ‘Semi-superfluid +strings in high density QCD’, Phys. Rev. D 73, 074009. +Balachandran, A. P., Lizzi, F. & Rodgers, V. G. J. (1984), ‘Topological +Symmetry Breakdown in Cholesterics, Nematics, and 3He’, Phys. Rev. +Lett. 52, 1818–1821. +Beenakker, C. (2013), ‘Search for Majorana Fermions in Superconductors’, +Annu. Rev. Condens. Matter Phys. 4(1), 113–136. +URL: http://dx.doi.org/10.1146/annurev-conmatphys-030212-184337 +Beenakker, C. W. J. (2020), ‘Search for non-Abelian Majorana braiding +statistics in superconductors’, SciPost Phys. Lect. Notes 15, 15. +URL: https://scipost.org/10.21468/SciPostPhysLectNotes.15 +Bonderson, P., Freedman, M. & Nayak, C. (2008), ‘Measurement-Only +Topological Quantum Computation’, Phys. Rev. Lett. 101, 010501. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.101.010501 +Bonderson, P., Freedman, M. & Nayak, C. (2009), ‘Measurement-only +topological quantum computation via anyonic interferometry’, Annals +of Physics 324(4), 787–826. +Bonesteel, N. E., Hormozi, L., Zikos, G. & Simon, S. H. (2005), ‘Braid +topologies for quantum computation’, Phys. Rev. Lett. 95, 140503. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.95.140503 +Borgh, M. O. & Ruostekoski, J. (2016), ‘Core Structure and Non-Abelian +Reconnection of Defects in a Biaxial Nematic Spin-2 Bose-Einstein +Condensate’, Phys. Rev. Lett. 117(27), 275302. [Erratum: Phys. Rev. +Lett. 118, 129901 (2017)]. +Bravyi, S. (2006), ‘Universal quantum computation with the 휈 = 5∕2 frac- +tional quantum Hall state’, Phys. Rev. A 73, 042313. +URL: https://link.aps.org/doi/10.1103/PhysRevA.73.042313 +Brekke, L., Collins, S. J. & Imbo, T. D. (1997), ‘Non-abelian vortices on +surfaces and their statistics’, Nucl. Phys. B 500, 465–485. +Brekke, L., Imbo, T. D., Dykstra, H. & Falk, A. F. (1993), ‘Novel spin and +statistical properties of nonabelian vortices’, Phys. Lett. B 304, 127–133. +Bruin, J. A. N., Claus, R. R., Matsumoto, Y., Kurita, N., Tanaka, H. & +Takagi, H. (2022), ‘Robustness of the thermal Hall effect close to half- +quantization in 훼-RuCl3’, Nat. Phys. 18, 401. +URL: https://doi.org/10.1038/s41567-021-01501-y +Bucher, M. (1991), ‘The Aharonov-Bohm effect and exotic statistics for +nonabelian vortices’, Nucl. Phys. B 350, 163–178. +Bucher, M., Lee, K.-M. & Preskill, J. (1992), ‘On detecting discrete +Cheshire charge’, Nucl. Phys. B 386, 27–42. +Cardy, J. L. (1985), ‘Conformal Invariance and the Yang-Lee Edge Singu- +larity in Two Dimensions’, Phys. Rev. Lett. 54, 1354–1356. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.54.1354 +Cayao, J. & Burset, P. (2021), ‘Confinement-induced zero-bias peaks in +conventional superconductor hybrids’, Phys. Rev. B 104, 134507. +URL: https://link.aps.org/doi/10.1103/PhysRevB.104.134507 +Chen, W., Wang, J., Wu, Y., Qi, J., Liu, J. & Xie, X. C. (2022), ‘Non- +Abelian statistics of Majorana zero modes in the presence of an Andreev +bound state’, Phys. Rev. B 105, 054507. +URL: https://link.aps.org/doi/10.1103/PhysRevB.105.054507 +Cheng, M., Lutchyn, R. M., Galitski, V. & Das Sarma, S. (2009), ‘Splitting +of majorana-fermion modes due to intervortex tunneling in a 푝푥 + 푖푝푦 +superconductor’, Phys. Rev. Lett. 103, 107001. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.103.107001 +Chung, S. B., Bluhm, H. & Kim, E.-A. (2007), ‘Stability of Half-quantum +Vorticies in 푝푥 + 푖푝푦 Superconductors’, Phys. Rev. Lett. 99, 197002. +Chung, S. B. & Kivelson, S. A. (2010), ‘Entropy-driven formation of a half- +quantum vortex lattice’, Phys. Rev. B 82, 214512. +URL: https://link.aps.org/doi/10.1103/PhysRevB.82.214512 +Chung, S. B. & Zhang, S.-C. (2009), ‘Detecting the Majorana Fermion +Surface State of 3He−퐵 through Spin Relaxation’, Phys. Rev. Lett. +103(23), 235301. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.103.235301 +Clarke, D. J., Sau, J. D. & Tewari, S. (2011), ‘Majorana fermion exchange +in quasi-one-dimensional networks’, Phys. Rev. B 84, 035120. +URL: https://link.aps.org/doi/10.1103/PhysRevB.84.035120 +De Gennes, P. (1973), ‘Long range distortions in an anisotropic superfluid’, +Phys. Lett. A 44(4), 271–272. +Di Francesco, P. D., Mathieu, P. & Sénéchal (1997), Conformal Field The- +ory, Spinger-Verlag, New York. +Dmitriev, V. V., Senin, A. A., Soldatov, A. A. & Yudin, A. N. (2015), +‘Polar phase of superfluid 3He in anisotropic aerogel’, Phys. Rev. Lett. +115, 165304. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.115.165304 +Elliott, S. R. & Franz, M. (2015), ‘Colloquium : Majorana fermions in nu- +clear, particle, and solid-state physics’, Rev. Mod. Phys. 87(1), 137–163. +URL: https://link.aps.org/doi/10.1103/RevModPhys.87.137 +Eto, M., Hirono, Y., Nitta, M. & Yasui, S. (2014), ‘Vortices and Other Topo- +logical Solitons in Dense Quark Matter’, PTEP 2014(1), 012D01. +URL: https://doi.org/10.1093/ptep/ptt095 +Eto, M., Isozumi, Y., Nitta, M., Ohashi, K. & Sakai, N. (2006), ‘Solitons +in the Higgs phase: The Moduli matrix approach’, J. Phys. A 39, R315– +R392. +Eto, M. & Nitta, M. (2009), ‘Color Magnetic Flux Tubes in Dense QCD’, +Phys. Rev. D 80, 125007. +Eto, M. & Nitta, M. (2021), ‘Chiral non-Abelian vortices and their confine- +ment in three flavor dense QCD’, Phys. Rev. D 104(9), 094052. +Fang, C., Gilbert, M. J. & Bernevig, B. A. (2014), ‘New class of topological +superconductors protected by magnetic group symmetries’, Phys. Rev. +Lett. 112, 106401. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.112.106401 +Field, B. & Simula, T. (2018), ‘Introduction to topological quantum com- +putation with non-Abelian anyons’, Quantum Sci. Technol. 3, 045004. +Fisher, M. E. (1978), ‘Yang-Lee Edge Singularity and 휙3 Field Theory’, +Phys. Rev. Lett. 40, 1610–1613. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.40.1610 +Freedman, M. H., Gukelberger, J., Hastings, M. B., Trebst, S., Troyer, M. & +Wang, Z. (2012), ‘Galois conjugates of topological phases’, Phys. Rev. +B 85, 045414. +URL: https://link.aps.org/doi/10.1103/PhysRevB.85.045414 +Freedman, M., Hastings, M. B., Nayak, C. & Qi, X.-L. (2011), ‘Weakly cou- +pled non-abelian anyons in three dimensions’, Phys. Rev. B 84, 245119. +URL: https://link.aps.org/doi/10.1103/PhysRevB.84.245119 +Freedman, M., Hastings, M. B., Nayak, C., Qi, X.-L., Walker, K. & Wang, +Z. (2011), ‘Projective ribbon permutation statistics: A remnant of non- +abelian braiding in higher dimensions’, Phys. Rev. B 83, 115132. +URL: https://link.aps.org/doi/10.1103/PhysRevB.83.115132 +Fu, L. & Kane, C. L. (2008), ‘Superconducting proximity effect and majo- +rana fermions at the surface of a topological insulator’, Phys. Rev. Lett. +100, 096407. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.100.096407 +Fujimoto, Y. & Nitta, M. (2021a), ‘Non-Abelian Alice strings in two-flavor +dense QCD’, Phys. Rev. D 103, 054002. +Fujimoto, Y. & Nitta, M. (2021b), ‘Topological confinement of vortices in +two-flavor dense QCD’, JHEP 09, 192. +Fujimoto, Y. & Nitta, M. (2021c), ‘Vortices penetrating two-flavor quark- +hadron continuity’, Phys. Rev. D 103(11), 114003. +Fujita, T. & Tsuneto, T. (1972), ‘The ginzburg-landau equation for 3p2 pair- +ingsuperfluidity in neutron stars’, Prog. Theor. Phys. 48(3), 766–782. +URL: http://dx.doi.org/10.1143/PTP.48.766 +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 29 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +Fujiwara, T., Fukui, T., Nitta, M. & Yasui, S. (2011), ‘Index theorem and +Majorana zero modes along a non-Abelian vortex in a color supercon- +ductor’, Phys. Rev. D 84, 076002. +Fulga, I. C., Hassler, F., Akhmerov, A. R. & Beenakker, C. W. J. (2011), +‘Scattering formula for the topological quantum number of a disordered +multimode wire’, Phys. Rev. B 83, 155429. +URL: https://link.aps.org/doi/10.1103/PhysRevB.83.155429 +Gao, P., He, Y.-P. & Liu, X.-J. (2016), ‘Symmetry-protected non-abelian +braiding of majorana kramers pairs’, Phys. Rev. B 94, 224509. +URL: https://link.aps.org/doi/10.1103/PhysRevB.94.224509 +Génetay Johansen, E. & Simula, T. (2022), ‘Prime number factorization +using a spinor Bose–Einstein condensate-inspired topological quantum +computer’, Quant. Inf. Proc. 21(1), 31. +Haim, A. & Oreg, Y. (2019), ‘Time-reversal-invariant topological super- +conductivity in one and two dimensions’, Physics Reports 825, 1–48. +Time-reversal-invariant topological superconductivity in one and two di- +mensions. +Halperin, B. I. (1984), ‘Statistics of quasiparticles and the hierarchy of frac- +tional quantized Hall states’, Phys. Rev. Lett. 52, 1583–1586. [Erratum: +Phys.Rev.Lett. 52, 2390 (1984)]. +Halperin, W. (2019), ‘Superfluid 3he in aerogel’, Annual Review of Con- +densed Matter Physics 10(1), 155–170. +URL: https://doi.org/10.1146/annurev-conmatphys-031218-013134 +Hanany, A. & Tong, D. (2003), ‘Vortices, instantons and branes’, JHEP +07, 037. +Heeb, R. & Agterberg, D. F. (1999), ‘Ginzburg-Landau theory for a 푝-wave +Sr2RuO4 superconductor: Vortex core structure and extended London +theory’, Phys. Rev. B 59(10), 7076–7082. +URL: +http://arxiv.org/abs/cond-mat/9811190 +https://link.aps.org/doi/10.1103/PhysRevB.59.7076 +Hirono, Y., Yasui, S., Itakura, K. & Nitta, M. (2012), ‘Non-Abelian +statistics of vortices with multiple Majorana fermions’, Phys. Rev. B +86, 014508. +Hoffberg, M., Glassgold, A. E., Richardson, R. W. & Ruderman, M. (1970), +‘Anisotropic Superfluidity in Neutron Star Matter’, Phys. Rev. Lett. +24(14), 775. +Hong, J.-S., Poon, T.-F. J., Zhang, L. & Liu, X.-J. (2022), ‘Unitary +symmetry-protected non-abelian statistics of majorana modes’, Phys. +Rev. B 105, 024503. +URL: https://link.aps.org/doi/10.1103/PhysRevB.105.024503 +Hormozi, L., Zikos, G., Bonesteel, N. E. & Simon, S. H. (2007), ‘Topolog- +ical quantum compiling’, Phys. Rev. B 75, 165310. +URL: https://link.aps.org/doi/10.1103/PhysRevB.75.165310 +Hosur, P., Ghaemi, P., Mong, R. S. K. & Vishwanath, A. (2011), ‘Majorana +modes at the ends of superconductor vortices in doped topological insu- +lators’, Phys. Rev. Lett. 107, 097001. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.107.097001 +Hu, Y. & Kane, C. L. (2018), ‘Fibonacci topological superconductor’, Phys. +Rev. Lett. 120, 066801. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.120.066801 +Ivanov, D. A. (2001), ‘Non-abelian statistics of half-quantum vortices in +p-wave superconductors’, Phys. Rev. Lett. 86(2), 268. +Karzig, T., Knapp, C., Lutchyn, R. M., Bonderson, P., Hastings, M. B., +Nayak, C., Alicea, J., Flensberg, K., Plugge, S., Oreg, Y., Marcus, +C. M. & Freedman, M. H. (2017), ‘Scalable designs for quasiparticle- +poisoning-protected topological quantum computation with majorana +zero modes’, Phys. Rev. B 95, 235305. +URL: https://link.aps.org/doi/10.1103/PhysRevB.95.235305 +Karzig, T., Oreg, Y., Refael, G. & Freedman, M. H. (2016), ‘Universal +geometric path to a robust majorana magic gate’, Phys. Rev. X 6, 031019. +URL: https://link.aps.org/doi/10.1103/PhysRevX.6.031019 +Kasahara, Y., Ohnishi, T., Mizukami, Y., Tanaka, O., Ma, S., Sugii, K., Ku- +rita, N., Tanaka, H., Nasu, J., Motome, Y., Shibauchi, T. & Matsuda, Y. +(2018), ‘Majorana quantization and half-integer thermal quantum Hall +effect in a Kitaev spin liquid’, Nature 559, 227. +URL: https://doi.org/10.1038/s41586-018-0274-0 +Kasamatsu, K., Mizuno, R., Ohmi, T. & Nakahara, M. (2019), ‘Effects +of a magnetic field on vortex states in superfluid 3He−푏’, Phys. Rev. B +99, 104513. +URL: https://link.aps.org/doi/10.1103/PhysRevB.99.104513 +Kashuba, O. & Timm, C. (2015), ‘Topological Kondo Effect in Transport +through a Superconducting Wire with Multiple Majorana End States’, +Phys. Rev. Lett. 114, 116801. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.114.116801 +Kawaguchi, Y. & Ueda, M. (2012), ‘Spinor Bose-Einstein condensates’, +Phys. Rept. 520, 253–381. +Kawakami, T. & Hu, X. (2015), ‘Evolution of density of states and a spin- +resolved checkerboard-type pattern associated with the majorana bound +state’, Phys. Rev. Lett. 115, 177001. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.115.177001 +Kawakami, T., Mizushima, T. & Machida, K. (2011), ‘Zero Energy Modes +and Statistics of Vortices in Spinful Chiral p -Wave Superfluids’, J. Phys. +Soc. Jpn. 80(4), 044603. +URL: http://journals.jps.jp/doi/10.1143/JPSJ.80.044603 +Kawakami, T., Tsutsumi, Y. & Machida, K. (2009), ‘Stability of a half- +quantum vortex in rotating superfluid 3He−퐴 between parallel plates’, +Phys. Rev. B 79(9), 092506. +URL: https://link.aps.org/doi/10.1103/PhysRevB.79.092506 +Kawakami, T., Tsutsumi, Y. & Machida, K. (2010), ‘Singular and Half- +Quantum Vortices and Associated Majorana Particles in Superfluid 3 +He-A between Parallel Plates’, J. Phys. Soc. Jpn. 79(4), 044607. +URL: http://journals.jps.jp/doi/abs/10.1143/JPSJ.79.044607 +Kells, G., Meidan, D. & Brouwer, P. W. (2012), ‘Near-zero-energy +end states in topologically trivial spin-orbit coupled superconducting +nanowires with a smooth confinement’, Phys. Rev. B 86, 100503. +URL: https://link.aps.org/doi/10.1103/PhysRevB.86.100503 +Kitaev, A. (2006), ‘Anyons in an exactly solved model and beyond’, Ann. +Phys. (N. Y). 321(1), 2–111. +URL: https://linkinghub.elsevier.com/retrieve/pii/S0003491605002381 +Kitaev, A. Y. (2001), ‘Unpaired Majorana fermions in quantum wires’, +Phys. Usp. 44(10S), 131–136. +Kitaev, A. Y. (2003), ‘Fault tolerant quantum computation by anyons’, An- +nals Phys. 303, 2–30. +Kitaev, Alexei and Laumann, Christopher (2008), Topological phases and +quantum computation, Lecture Notes of the Les Houches Summer +School. No.89., Oxford University Press. +Knapp, C., Chew, A. & Alicea, J. (2020), ‘Fragility of the fractional joseph- +son effect in time-reversal-invariant topological superconductors’, Phys. +Rev. Lett. 125, 207002. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.125.207002 +Kobayashi, M., Kawaguchi, Y., Nitta, M. & Ueda, M. (2009), ‘Collision +Dynamics and Rung Formation of Non-Abelian Vortices’, Phys. Rev. +Lett. 103, 115301. +Kobayashi, M. & Nitta, M. (2022a), ‘Core structures of vortices in +Ginzburg-Landau theory for neutron 3푃2 superfluids’, Phys. Rev. C +105(3), 035807. +Kobayashi, M. & Nitta, M. (2022b), ‘Proximity effects of vortices in neu- +tron 3푃2 superfluids in neutron stars: Vortex core transitions and cova- +lent bonding of vortex molecules’. +Kobayashi, S., Kobayashi, M., Kawaguchi, Y., Nitta, M. & Ueda, M. +(2012), ‘Abe homotopy classification of topological excitations under +the topological influence of vortices’, Nucl. Phys. B 856, 577–606. +Koornwinder, T. H., Schroers, B. J., Slingerland, J. K. & Bais, F. A. (1999), +‘Fourier transform and the Verlinde formula for the quantum double of +a finite group’, J. Phys. A 32, 8539–8549. +Kopnin, N. B. & Salomaa, M. M. (1991), ‘Mutual friction in superfluid 3He: +Effects of bound states in the vortex core’, Phys. Rev. B 44, 9667–9677. +URL: https://link.aps.org/doi/10.1103/PhysRevB.44.9667 +Kortman, P. J. & Griffiths, R. B. (1971), ‘Density of Zeros on the Lee-Yang +Circle for Two Ising Ferromagnets’, Phys. Rev. Lett. 27, 1439–1442. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.27.1439 +Lavrentovich, O. D. & Kleman, M. (2001), Cholesteric Liquid Crystals: +Defects and Topology, in H.-S. Kitzerow & C. Bahr, eds, ‘Chirality in +Liquid Crystals’, Springer New York, New York, NY, pp. 115–158. +Lee, K.-M. (1994), ‘Vortices on higher genus surfaces’, Phys. Rev. D +49, 2030–2040. +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 30 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +Lee, T. D. & Yang, C. N. (1952), ‘Statistical Theory of Equations of State +and Phase Transitions. II. Lattice Gas and Ising Model’, Phys. Rev. +87, 410–419. +URL: https://link.aps.org/doi/10.1103/PhysRev.87.410 +Leggett, A. J. (1975), ‘A theoretical description of the new phases of liquid +3He’, Rev. Mod. Phys. 47, 331–414. +URL: https://link.aps.org/doi/10.1103/RevModPhys.47.331 +Leijnse, M. & Flensberg, K. (2012), ‘Introduction to topological su- +perconductivity and Majorana fermions’, Semicond. Sci. Technol. +27(12), 124003. +URL: http://stacks.iop.org/0268-1242/27/i=12/a=124003 +Leinaas, J. M. & Myrheim, J. (1977), ‘On the theory of identical particles’, +Nuovo Cim. B 37, 1–23. +Lesanovsky, I. & Katsura, H. (2012), ‘Interacting fibonacci anyons in a ry- +dberg gas’, Phys. Rev. A 86, 041601. +URL: https://link.aps.org/doi/10.1103/PhysRevA.86.041601 +Liu, C.-X., Sau, J. D. & Das Sarma, S. (2018), ‘Distinguishing topological +Majorana bound states from trivial Andreev bound states: Proposed tests +through differential tunneling conductance spectroscopy’, Phys. Rev. B +97, 214502. +Liu, C.-X., Sau, J. D., Stanescu, T. D. & Das Sarma, S. (2017), ‘Andreev +bound states versus majorana bound states in quantum dot-nanowire- +superconductor hybrid structures: Trivial versus topological zero-bias +conductance peaks’, Phys. Rev. B 96, 075161. +URL: https://link.aps.org/doi/10.1103/PhysRevB.96.075161 +Liu, D., Cao, Z., Liu, X., Zhang, H. & Liu, D. E. (2021), ‘Topological +Kondo device for distinguishing quasi-Majorana and Majorana signa- +tures’, Phys. Rev. B 104, 205125. +URL: https://link.aps.org/doi/10.1103/PhysRevB.104.205125 +Liu, X.-J., Wong, C. L. M. & Law, K. T. (2014), ‘Non-Abelian Ma- +jorana Doublets in Time-Reversal-Invariant Topological Superconduc- +tors’, Phys. Rev. X 4, 021018. +URL: https://link.aps.org/doi/10.1103/PhysRevX.4.021018 +Lo, H.-K. & Preskill, J. (1993), ‘Non-Abelian vortices and non-Abelian +statistics’, Phys. Rev. D 48, 4821–4834. +Machida, T., Sun, Y., Pyon, S., Takeda, S., Kohsaka, Y., Hanaguri, T., +Sasagawa, T. & Tamegai, T. (2019), ‘Zero-energy vortex bound state in +the superconducting topological surface state of Fe(Se,Te)’, Nat. Mater +18, 811. +URL: https://doi.org/10.1038/s41563-019-0397-1 +Majorana, E. (1937), ‘Teoria simmetrica dell’elettrone e del positrone’, +Nuovo Cim. 14, 171–184. +Makhlin, Y., Silaev, M. & Volovik, G. E. (2014), ‘Topology of the planar +phase of superfluid 3He and bulk-boundary correspondence for three- +dimensional topological superconductors’, Phys. Rev. B 89, 174502. +URL: https://link.aps.org/doi/10.1103/PhysRevB.89.174502 +Mäkinen, J. T., Dmitriev, V. V., Nissinen, J., Rysti, J., Volovik, G. E., Yudin, +A. N., Zhang, K. & Eltsov, V. B. (2019), ‘Half-quantum vortices and +walls bounded by strings in the polar-distorted phases of topological +superfluid3He’, Nature Commun. 10(1), 237. +Mäkinen, J. T., Zhang, K. & Eltsov, V. B. (2022), ‘Vortex-bound solitons +in topological superfluid 3He’, arXiv:2211.17117 . +Marmorini, G., Yasui, S. & Nitta, M. (2020), ‘Pulsar glitches from quantum +vortex networks’, arXiv:2010.09032 . +Masaki, Y., Mizushima, T. & Nitta, M. (2020), ‘Microscopic description of +axisymmetric vortices in 3푃2 superfluids’, Phys. Rev. Res. 2(1), 013193. +Masaki, Y., Mizushima, T. & Nitta, M. (2022), ‘Non-Abelian half-quantum +vortices in 3푃2 topological superfluids’, Phys. Rev. B 105(22), L220503. +URL: https://link.aps.org/doi/10.1103/PhysRevB.105.L220503 +Masuda, K. & Nitta, M. (2016), ‘Magnetic Properties of Quantized Vor- +tices in Neutron 3푃2 Superfluids in Neutron Stars’, Phys. Rev. C +93(3), 035804. +Masuda, K. & Nitta, M. (2020), ‘Half-quantized non-Abelian vortices in +neutron 3푃2 superfluids inside magnetars’, PTEP 2020(1), 013D01. +Matsumoto, M. & Heeb, R. (2001), ‘Vortex charging effect in a chiral 푝푥 ± +푖푝푦-wave superconductor’, Phys. Rev. B 65(1), 014504. +URL: https://link.aps.org/doi/10.1103/PhysRevB.65.014504 +Mawson, T., Petersen, T. C., Slingerland, J. K. & Simula, T. P. (2019), +‘Braiding and Fusion of Non-Abelian Vortex Anyons’, Phys. Rev. Lett. +123, 140404. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.123.140404 +Mermin, N. D. (1974), ‘d-wave pairing near the transition temperature’, +Phys. Rev. A 9, 868–872. +Mermin, N. D. (1979), ‘The topological theory of defects in ordered media’, +Rev. Mod. Phys. 51, 591–648. +Mietke, A. & Dunkel, J. (2022), ‘Anyonic Defect Braiding and Spontaneous +Chiral Symmetry Breaking in Dihedral Liquid Crystals’, Phys. Rev. X +12(1), 011027. +Mineev, V. P. (2014), ‘Half-Quantum Vortices in Polar Phase of Superfluid +3He’, J. Low Temp. Phys. 177, 48. +URL: https://doi.org/10.1007/s10909-014-1189-2 +Mizushima, T. & Machida, K. (2010), ‘Splitting and oscillation of majorana +zero modes in the 푝-wave bcs-bec evolution with plural vortices’, Phys. +Rev. A 82, 023624. +URL: https://link.aps.org/doi/10.1103/PhysRevA.82.023624 +Mizushima, T. & Machida, K. (2011), ‘Effects of Majorana edge fermions +on dynamical spin susceptibility in topological superfluid 3He-B’, J. +Low Temp. Phys. 162(3-4), 204–211. +Mizushima, T., Masuda, K. & Nitta, M. (2017), ‘3푃2 superfluids are topo- +logical’, Phys. Rev. B 95(14), 140503. +Mizushima, T., Sato, M. & Machida, K. (2012), ‘Symmetry Protected +Topological Order and Spin Susceptibility in Superfluid 3He−퐵’, Phys. +Rev. Lett. 109, 165301. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.109.165301 +Mizushima, T., Tsutsumi, Y., Kawakami, T., Sato, M., Ichioka, M. +& Machida, K. (2016), ‘Symmetry-protected topological superfluids +and superconductors–from the basics to 3He–’, J. Phys. Soc. Jpn. +85(2), 022001. +Mizushima, T., Yasui, S., Inotani, D. & Nitta, M. (2021), ‘Spin-polarized +phases of 3푃2 superfluids in neutron stars’, Phys. Rev. C 104(4), 045803. +URL: https://link.aps.org/doi/10.1103/PhysRevC.104.045803 +Mizushima, T., Yasui, S. & Nitta, M. (2020), ‘Critical endpoint and univer- +sality class of neutron 3푃2 superfluids in neutron stars’, Phys. Rev. Res. +2, 013194. +URL: https://link.aps.org/doi/10.1103/PhysRevResearch.2.013194 +Mong, R. S. K., Clarke, D. J., Alicea, J., Lindner, N. H., Fendley, P., Nayak, +C., Oreg, Y., Stern, A., Berg, E., Shtengel, K. & Fisher, M. P. A. (2014), +‘Universal Topological Quantum Computation from a Superconductor- +Abelian Quantum Hall Heterostructure’, Phys. Rev. X 4, 011036. +URL: https://link.aps.org/doi/10.1103/PhysRevX.4.011036 +Moore, C., Stanescu, T. D. & Tewari, S. (2018), ‘Two-terminal charge tun- +neling: Disentangling majorana zero modes from partially separated an- +dreev bound states in semiconductor-superconductor heterostructures’, +Phys. Rev. B 97, 165302. +URL: https://link.aps.org/doi/10.1103/PhysRevB.97.165302 +Moore, C., Zeng, C., Stanescu, T. D. & Tewari, S. (2018), ‘Quantized +zero-bias conductance plateau in semiconductor-superconductor het- +erostructures without topological majorana zero modes’, Phys. Rev. B +98, 155314. +URL: https://link.aps.org/doi/10.1103/PhysRevB.98.155314 +Moore, G. W. & Read, N. (1991), ‘Nonabelions in the fractional quantum +Hall effect’, Nucl. Phys. B 360, 362–396. +Motome, Y. & Nasu, J. (2020), ‘Hunting Majorana Fermions in Kitaev +Magnets’, J. Phys. Soc. Jpn 89(1), 012002. +URL: https://journals.jps.jp/doi/10.7566/JPSJ.89.012002 +Muzikar, P., Sauls, J. A. & Serene, J. W. (1980), ‘3푃2 pairing in neutron star +matter: magnetic field effects and vortices’, Phys. Rev. D 21, 1494–1502. +Nagamura, N. & Ikeda, R. (2018), ‘Stability of half-quantum vortices in +equal-spin pairing states of 3He’, Phys. Rev. B 98(9), 094524. +URL: https://link.aps.org/doi/10.1103/PhysRevB.98.094524 +Nagato, Y., Higashitani, S. & Nagai, K. (2009), ‘Strong Anisotropy in +Spin Susceptibility of Superfluid 3 He-B Film Caused by Surface Bound +States’, J. Phys. Soc. Jpn. 78(12), 123603. +URL: http://journals.jps.jp/doi/10.1143/JPSJ.78.123603 +Nakamura, J., Liang, S., Gardner, G. C. & Manfra, M. J. (2020), ‘Direct +observation of anyonic braiding statistics’, Nat. Phys. 16, 931–936. +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 31 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +URL: http://dx.doi.org/10.1038/s41567-020-1019-1 +Nakano, E., Nitta, M. & Matsuura, T. (2008), ‘Non-Abelian strings in high +density QCD: Zero modes and interactions’, Phys. Rev. D 78, 045002. +Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Das Sarma, S. (2008), +‘Non-Abelian anyons and topological quantum computation’, Rev. Mod. +Phys. 80, 1083–1159. +Nayak, C. & Wilczek, F. (1996), ‘2푛-quasihole states realize 2푛−1- +dimensional spinor braiding statistics in paired quantum Hall states’, +Nucl. Phys. B 479(3), 529–553. +Nielsen, M. & Chuang, I. (2010), Quantum computation and quantum in- +formation, Cambridge University Press. +Oreg, Y. & von Oppen, F. (2020), ‘Majorana Zero Modes in Networks +of Cooper-Pair Boxes: Topologically Ordered States and Topological +Quantum Computation’, Annu. Rev. Condens. Matter Phys. 11(1), 397– +420. +URL: https://doi.org/10.1146/annurev-conmatphys-031218-013618 +Pachos, J. K. (2012), Introduction to Topological Quantum Computation, +Cambridge University Press. +Pan, H., Cole, W. S., Sau, J. D. & Das Sarma, S. (2020), ‘Generic quantized +zero-bias conductance peaks in superconductor-semiconductor hybrid +structures’, Phys. Rev. B 101, 024506. +URL: https://link.aps.org/doi/10.1103/PhysRevB.101.024506 +Pan, H. & Das Sarma, S. (2020), ‘Physical mechanisms for zero-bias con- +ductance peaks in majorana nanowires’, Phys. Rev. Res. 2, 013377. +URL: https://link.aps.org/doi/10.1103/PhysRevResearch.2.013377 +Pan, H., Sau, J. D. & Das Sarma, S. (2021), ‘Three-terminal nonlocal con- +ductance in Majorana nanowires: Distinguishing topological and trivial +in realistic systems with disorder and inhomogeneous potential’, Phys. +Rev. B 103, 014513. +URL: https://link.aps.org/doi/10.1103/PhysRevB.103.014513 +Piroli, L. & Cirac, J. I. (2020), ‘Quantum cellular automata, tensor net- +works, and area laws’, Phys. Rev. Lett. 125, 190402. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.125.190402 +Plugge, S., Rasmussen, A., Egger, R. & Flensberg, K. (2017), ‘Majorana +box qubits’, New J. Phys. 19, 012001. +URL: https://iopscience.iop.org/article/10.1088/1367-2630/aa54e1 +Poenaru, V. & Toulouse, G. (1977), ‘The crossing of defects in ordered +media and the topology of 3-manifolds’, J. Phys. (Paris) 38, 887. +Prada, E., San-Jose, P., de Moor, M. W. A., Geresdi, A., Lee, E. J. H., +Klinovaja, J., Loss, D., Nygård, J., Aguado, R. & Kouwenhoven, L. P. +(2020), ‘From Andreev to Majorana bound states in hybrid supercon- +ductor–semiconductor nanowires’, Nat. Rev. Phys. 2, 575. +URL: https://doi.org/10.1038/s42254-020-0228-y +Preskill, J. (2004), Lecture notes for physics 219: Quantum computation. +URL: +http://www.theory.caltech.edu/~preskill/ph219/ph219_2004. +html +Preskill, J. & Krauss, L. M. (1990), ‘Local Discrete Symmetry and Quan- +tum Mechanical Hair’, Nucl. Phys. B 341, 50–100. +Qi, X.-L., Hughes, T. L. & Zhang, S.-C. (2008), ‘Topological field theory +of time-reversal invariant insulators’, Phys. Rev. B 78, 195424. +URL: https://link.aps.org/doi/10.1103/PhysRevB.78.195424 +Read, N. & Green, D. (2000), ‘Paired states of fermions in two-dimensions +with breaking of parity and time reversal symmetries, and the fractional +quantum Hall effect’, Phys. Rev. B 61, 10267. +Read, N. & Rezayi, E. (1999), ‘Beyond paired quantum Hall states: +Parafermions and incompressible states in the first excited Landau level’, +Phys. Rev. B 59, 8084–8092. +URL: https://link.aps.org/doi/10.1103/PhysRevB.59.8084 +Regan, R. C., Wiman, J. J. & Sauls, J. A. (2019), ‘The Vortex Phase Dia- +gram of Rotating Superfluid 3He-B’, Phys. Rev. B 101(2), 024517. +Regan, R. C., Wiman, J. J. & Sauls, J. A. (2021), ‘Half-quantum vortices in +nematic and chiral phases of 3He’, Phys. Rev. B 104, 024513. +URL: https://link.aps.org/doi/10.1103/PhysRevB.104.024513 +Ricco, L. S., de Souza, M., Figueira, M. S., Shelykh, I. A. & Seridonio, +A. C. (2019), ‘Spin-dependent zero-bias peak in a hybrid nanowire- +quantum dot system: Distinguishing isolated Majorana fermions from +Andreev bound states’, Phys. Rev. B 99, 155159. +Ricco, L. S., Sanches, J. E., Marques, Y., de Souza, M., Figueira, M. S., +Shelykh, I. A. & Seridonio, A. C. (2021), ‘Topological isoconductance +signatures in Majorana nanowires’, Sci. Rep. 11, 17310. +URL: https://doi.org/10.1038/s41598-021-96415-3 +Richardson, R. W. (1972), ‘Ginzburg-landau theory of anisotropic super- +fluid neutron-star matter’, Phys. Rev. D 5, 1883–1896. +Rysti, J., Mäkinen, J. T., Autti, S., Kamppinen, T., Volovik, G. E. & +Eltsov, V. B. (2021), ‘Suppressing the Kibble-Zurek Mechanism by a +Symmetry-Violating Bias’, Phys. Rev. Lett. 127, 115702. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.127.115702 +Salomaa, M. M. & Volovik, G. E. (1985a), ‘Half-quantum vortices in su- +perfluid 3He-푎’, Phys. Rev. Lett. 55, 1184–1187. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.55.1184 +Salomaa, M. M. & Volovik, G. E. (1985b), ‘Symmetry and structure of +quantized vortices in superfluid 3퐵’, Phys. Rev. B 31, 203–227. +URL: https://link.aps.org/doi/10.1103/PhysRevB.31.203 +Salomaa, M. M. & Volovik, G. E. (1986), ‘Vortices with spontaneously +broken axisymmetry in 3퐵’, Phys. Rev. Lett. 56(4), 363–366. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.56.363 +Salomaa, M. M. & Volovik, G. E. (1987), ‘Quantized vortices in superfluid +3He’, Rev. Mod. Phys. 59, 533–613. +URL: https://link.aps.org/doi/10.1103/RevModPhys.59.533 +Sanno, T., Yamada, M. G., Mizushima, T. & Fujimoto, S. (2022), ‘En- +gineering Yang-Lee anyons via Majorana bound states’, Phys. Rev. B +106, 174517. +URL: https://link.aps.org/doi/10.1103/PhysRevB.106.174517 +Sarma, S. D., Freedman, M. & Nayak, C. (2015), ‘Majorana zero modes +and topological quantum computation’, npj Quantum Inf. 1(1), 15001. +URL: http://www.nature.com/articles/npjqi20151 +Sato, M. (2003), ‘Non-Abelian statistics of axion strings’, Physics Letters +B 575(1), 126–130. +Sato, M. & Ando, Y. (2017), ‘Topological superconductors: a review’, Re- +ports on Progress in Physics 80(7), 076501. +URL: https://iopscience.iop.org/article/10.1088/1361-6633/aa6ac7 +Sato, M. & Fujimoto, S. (2016), ‘Majorana Fermions and Topology in Su- +perconductors’, J. Phys. Soc. Jpn 85(7), 072001. +URL: http://journals.jps.jp/doi/10.7566/JPSJ.85.072001 +Sato, M., Takahashi, Y. & Fujimoto, S. (2009), ‘Non-Abelian Topological +Order in 푠-Wave Superfluids of Ultracold Fermionic Atoms’, Phys. Rev. +Lett. 103, 020401. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.103.020401 +Sato, M., Takahashi, Y. & Fujimoto, S. (2010), ‘Non-Abelian topological +orders and Majorana fermions in spin-singlet superconductors’, Phys. +Rev. B 82, 134521. +URL: https://link.aps.org/doi/10.1103/PhysRevB.82.134521 +Sato, M., Tanaka, Y., Yada, K. & Yokoyama, T. (2011), ‘Topology of an- +dreev bound states with flat dispersion’, Phys. Rev. B 83, 224511. +URL: https://link.aps.org/doi/10.1103/PhysRevB.83.224511 +Sato, M., Yamakage, A. & Mizushima, T. (2014), ‘Mirror Majorana zero +modes in spinful superconductors/superfluids non-Abelian anyons in in- +teger quantum vortices’, Physica E 55, 20. +Sauls, J. A. (1980), Anisotropic superfluidity in neutron stars and strong +coupling effect in superfluid 3He, Ph.D Thesis, SUNY Stony Brook. +Sauls, J. A. & Serene, J. W. (1978), ‘3푃2 pairing near the transition temper- +ature in neutron-star matter’, Phys. Rev. D 17(6), 1524–1528. +Sauls, J. A., Stein, D. L. & Serene, J. W. (1982), ‘Magnetic vortices in a +rotating 3푃2 neutron superfluid’, Phys. Rev. D 25, 967–975. +URL: https://link.aps.org/doi/10.1103/PhysRevD.25.967 +Schnyder, A. P., Ryu, S., Furusaki, A. & Ludwig, A. W. W. (2008), ‘Clas- +sification of topological insulators and superconductors in three spatial +dimensions’, Phys. Rev. B 78(19), 195125. +Schulenborg, J. & Flensberg, K. (2020), ‘Absence of supercurrent sign +reversal in a topological junction with a quantum dot’, Phys. Rev. B +101, 014512. +URL: https://link.aps.org/doi/10.1103/PhysRevB.101.014512 +Schwarz, A. S. (1982), ‘Field theories with no local conservation of the +electric charge’, Nucl. Phys. B 208, 141–158. +Sedrakian, A. & Clark, J. W. (2018), ‘Superfluidity in nuclear systems and +neutron stars’. +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 32 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +Semenoff, G. W. & Zhou, F. (2007), ‘Discrete symmetries and 1/3-quantum +vortices in condensates of F=2 cold atoms’, Phys. Rev. Lett. 98, 100401. +Shifman, M. & Yung, A. (2007), ‘Supersymmetric Solitons and How They +Help Us Understand Non-Abelian Gauge Theories’, Rev. Mod. Phys. +79, 1139. +Shiozaki, K. & Sato, M. (2014), ‘Topology of crystalline insulators and +superconductors’, Phys. Rev. B 90, 165114. +URL: https://link.aps.org/doi/10.1103/PhysRevB.90.165114 +Silaev, M. A. & Volovik, G. E. (2014), ‘Andreev-Majorana bound states in +superfluids’, J. Exp. Theor. Phys. 119(6), 1042–1057. +URL: http://link.springer.com/10.1134/S1063776114120097 +Song, J. L., Semenoff, G. W. & Zhou, F. (2007), ‘Quantum fluctuation- +induced uniaxial and biaxial spin nematics’, Phys. Rev. Lett. 98, 160408. +Sugeta, M., Mizushima, T. & Fujimoto, S. (2022), ‘Enhanced 2휋-periodic +aharonov-bohm effect as a signature of majorana bound states probed by +nonlocal measurements’. +URL: https://arxiv.org/abs/2205.07506 +Takatsuka, T. (1972), ‘Superfluid State in Neutron Star Matter. III Tensor +Coupling Effect in 3P2 Energy Gap’, Prog. Theor. Phys. 47(3), 1062– +1064. +URL: http://dx.doi.org/10.1143/PTP.47.1062 +Takatsuka, T. & Tamagaki, R. (1971), ‘Superfluid State in Neutron Star +Matter. II Properties of Anisotropic Energy Gap of 3P2 Pairing’, Prog. +Theor. Phys. 46(1), 114–134. +URL: http://dx.doi.org/10.1143/PTP.46.114 +Tamagaki, R. (1970), ‘Superfluid State in Neutron Star Matter. IGeneralized +Bogoliubov Transformation and Existence of 3P2 Gap at High Density’, +Prog. Theor. Phys. 44(4), 905–928. +URL: http://dx.doi.org/10.1143/PTP.44.905 +Tanaka, Y., Sanno, T., Mizushima, T. & Fujimoto, S. (2022), ‘Manipulation +of Majorana-Kramers qubit and its tolerance in time-reversal invariant +topological superconductor’, Phys. Rev. B 106, 014522. +URL: https://link.aps.org/doi/10.1103/PhysRevB.106.014522 +Teo, J. C. Y. & Kane, C. L. (2010a), ‘Majorana fermions and non-abelian +statistics in three dimensions’, Phys. Rev. Lett. 104, 046401. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.104.046401 +Teo, J. C. Y. & Kane, C. L. (2010b), ‘Topological defects and gapless modes +in insulators and superconductors’, Phys. Rev. B 82, 115120. +URL: https://link.aps.org/doi/10.1103/PhysRevB.82.115120 +Terashima, H. & Ueda, M. (2005), ‘Nonunitary quantum circuit’, Int. J. +Quantum Inf. 03(04), 633. +URL: https://doi.org/10.1142/S0219749905001456 +Thamm, M. & Rosenow, B. (2021), ‘Transmission amplitude through a +Coulomb blockaded Majorana wire’, Phys. Rev. Res. 3, 023221. +URL: https://link.aps.org/doi/10.1103/PhysRevResearch.3.023221 +Thuneberg, E. V. (1986), ‘Identification of vortices in superfluid 3He퐵’, +Phys. Rev. Lett. 56, 359–362. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.56.359 +Tojo, S., Hayashi, T., Tanabe, T., Hirano, T., Kawaguchi, Y., Saito, H. & +Ueda, M. (2009), ‘Spin-dependent inelastic collisions in spin-2 Bose- +Einstein condensates’, Phys. Rev. A 80, 042704. +URL: https://link.aps.org/doi/10.1103/PhysRevA.80.042704 +Trebst, S., Troyer, M., Wang, Z. & Ludwig, A. W. W. (2008), ‘A Short In- +troduction to Fibonacci Anyon Models’, Progress of Theoretical Physics +Supplement 176, 384–407. +URL: https://doi.org/10.1143/PTPS.176.384 +Tsutsumi, Y., Ishikawa, M., Kawakami, T., Mizushima, T., Sato, M., +Ichioka, M. & Machida, K. (2013), ‘Upt3 as a topological crystalline +superconductor’, J. Phys. Soc. Jpn. 82(11), 113707. +URL: http://dx.doi.org/10.7566/JPSJ.82.113707 +Tsutsumi, Y., Kawakami, T., Shiozaki, K., Sato, M. & Machida, K. (2015), +‘Symmetry-protected vortex bound state in superfluid 3He−퐵 phase’, +Phys. Rev. B 91, 144504. +URL: https://link.aps.org/doi/10.1103/PhysRevB.91.144504 +Uchino, S., Kobayashi, M., Nitta, M. & Ueda, M. (2010), ‘Quasi- +Nambu-Goldstone Modes in Bose-Einstein Condensates’, Phys. Rev. +Lett. 105, 230406. +Ueno, Y., Yamakage, A., Tanaka, Y. & Sato, M. (2013), ‘Symmetry- +Protected Majorana Fermions in Topological Crystalline Superconduc- +tors: Theory and Application to Sr2RuO4’, Phys. Rev. Lett. 111, 087002. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.111.087002 +Usher, N., Hoban, M. J. & Browne, D. E. (2017), ‘Nonunitary quantum +computation in the ground space of local hamiltonians’, Phys. Rev. A +96, 032321. +URL: https://link.aps.org/doi/10.1103/PhysRevA.96.032321 +Vakaryuk, V. & Leggett, A. J. (2009), ‘Spin polarization of half-quantum +vortex in systems with equal spin pairing’, Phys. Rev. Lett. 103, 057003. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.103.057003 +Valentini, M., Peñaranda, F., Hofmann, A., Brauns, M., Hauschild, R., +Krogstrup, P., San-Jose, P., Prada, E., Aguado, R. & Katsaros, G. (2021), +‘Nontopological zero-bias peaks in full-shell nanowires induced by flux- +tunable Andreev states’, Science 373(6550), 82–88. +Vinkler-Aviv, Y. & Rosch, A. (2018), ‘Approximately Quantized Ther- +mal Hall Effect of Chiral Liquids Coupled to Phonons’, Phys. Rev. X +8, 031032. +URL: https://link.aps.org/doi/10.1103/PhysRevX.8.031032 +Vollhardt, D. & Wölfle, P. (1990), The Superfluid Phases of Helium 3, Tay- +lor & Francis, London. +URL: https://books.google.co.jp/books?id=t0Rw75gMuwIC +Volovik, G. E. (1992), Exotic Properties of Superfluid 3He, World Scien- +tific, Singapre. +Volovik, G. E. (1999), ‘Fermion zero modes on vortices in chiral supercon- +ductors’, JETP Lett. 70, 609. +URL: https://doi.org/10.1134/1.568223 +Volovik, G. E. (2003), The Universe in a Helium Droplet, Clarendon, Ox- +ford, U.K. +Volovik, G. E. (2010), ‘Topological superfluid 3He-B in magnetic field and +ising variable’, JETP Lett. 91(4), 201–205. +URL: http://link.springer.com/10.1134/S0021364010040090 +von Gehlen, G. (1991), ‘Critical and off-critical conformal analysis of the +Ising quantum chain in an imaginary field’, J. Phys. A: Math. Gen. +24(22), 5371. +URL: https://dx.doi.org/10.1088/0305-4470/24/22/021 +Vorontsov, A. B. & Sauls, J. A. (2003), ‘Thermodynamic properties of thin +films of superfluid 3He-A’, Phys. Rev. B 68, 064508. +URL: https://link.aps.org/doi/10.1103/PhysRevB.68.064508 +Wilczek, F. (1982), ‘Quantum Mechanics of Fractional Spin Particles’, +Phys. Rev. Lett. 49, 957–959. +Wilczek, F. & Wu, Y.-S. (1990), ‘Space-Time Approach To Holonomy +Scattering’, Phys. Rev. Lett. 65, 13–16. +Wölms, K., Stern, A. & Flensberg, K. (2014), ‘Local adiabatic mixing of +kramers pairs of majorana bound states’, Phys. Rev. Lett. 113, 246401. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.113.246401 +Wölms, K., Stern, A. & Flensberg, K. (2016), ‘Braiding properties of ma- +jorana kramers pairs’, Phys. Rev. B 93, 045417. +URL: https://link.aps.org/doi/10.1103/PhysRevB.93.045417 +Wong, C. L. M. & Law, K. T. (2012), ‘Majorana Kramers doublets in +푑푥2−푦2-wave superconductors with Rashba spin-orbit coupling’, Phys. +Rev. B 86, 184516. +URL: https://link.aps.org/doi/10.1103/PhysRevB.86.184516 +Wu, Y.-S. (1984), ‘General theory for quantum statistics in two dimensions’, +Phys. Rev. Lett. 52, 2103–2106. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.52.2103 +Yamashita, M., Gouchi, J., Uwatoko, Y., Kurita, N. & Tanaka, H. (2020), +‘Sample dependence of half-integer quantized thermal Hall effect in the +Kitaev spin-liquid candidate 훼−RuCl3’, Phys. Rev. B 102, 220404. +Yamashita, M., Izumina, K., Matsubara, A., Sasaki, Y., Ishikawa, O., Tak- +agi, T., Kubota, M. & Mizusaki, T. (2008), ‘Spin Wave and Vortex Exci- +tations of Superfluid 3He-A in Parallel-Plate Geometry’, Phys. Rev. Lett. +101, 025302. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.101.025302 +Yasui, S., Chatterjee, C., Kobayashi, M. & Nitta, M. (2019), ‘Reexamining +Ginzburg-Landau theory for neutron 3푃2 superfluidity in neutron stars’, +Phys. Rev. C 100(2), 025204. +Yasui, S., Chatterjee, C. & Nitta, M. (2019), ‘Phase structure of neutron +3푃2 superfluids in strong magnetic fields in neutron stars’, Phys. Rev. C +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 33 of 34 + +Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors +99(3), 035213. +Yasui, S., Hirono, Y., Itakura, K. & Nitta, M. (2013), ‘Non-Abelian +statistics of vortices with non-Abelian Dirac fermions’, Phys. Rev. E +87(5), 052142. +Yasui, S., Itakura, K. & Nitta, M. (2010), ‘Fermion structure of non-Abelian +vortices in high density QCD’, Phys. Rev. D 81, 105003. +Yasui, S., Itakura, K. & Nitta, M. (2011), ‘Majorana meets Coxeter: Non- +Abelian Majorana Fermions and Non-Abelian Statistics’, Phys. Rev. B +83, 134518. +Yasui, S., Itakura, K. & Nitta, M. (2012), ‘Dirac returns: Non-abelian statis- +tics of vortices with dirac fermions’, Nucl. Phys. B 859, 261. +Yavilberg, K., Ginossar, E. & Grosfeld, E. (2019), ‘Differentiating Majo- +rana from Andreev bound states in a superconducting circuit’, Phys. Rev. +B 100, 241408. +Ye, M., Halász, G. B., Savary, L. & Balents, L. (2018), ‘Quantization of +the Thermal Hall Conductivity at Small Hall Angles’, Phys. Rev. Lett. +121, 147201. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.121.147201 +Yokoi, T., Ma, S., Kasahara, Y., Kasahara, S., Shibauchi, T., Kurita, N., +Tanaka, H., Nasu, J., Motome, Y., Hickey, C., Trebst, S. & Matsuda, +Y. (2021), ‘Half-integer quantized anomalous thermal Hall effect in the +Kitaev material candidate 훼-RuCl3’, Science 373(6554), 568–572. +URL: https://www.science.org/doi/abs/10.1126/science.aay5551 +Yu, P., Chen, J., Gomanko, M., Badawy, G., Bakkers, E. P. A. M., Zuo, K., +Mourik, V. & Frolov, S. M. (2021), ‘Non-Majorana states yield nearly +quantized conductance in proximatized nanowires’, Nat. Phys. 17, 482. +Zhang, F., Kane, C. L. & Mele, E. J. (2013), ‘Time-reversal-invariant topo- +logical superconductivity and majorana kramers pairs’, Phys. Rev. Lett. +111, 056402. +URL: https://link.aps.org/doi/10.1103/PhysRevLett.111.056402 +Zhang, G. & Spånslätt, C. (2020), ‘Distinguishing between topological and +quasi Majorana zero modes with a dissipative resonant level’, Phys. Rev. +B 102, 045111. +URL: https://link.aps.org/doi/10.1103/PhysRevB.102.045111 +Zhang, H., de Moor, M. W. A., Bommer, J. D. S., Xu, D., Wang, G., van +Loo, N., Liu, C.-X., Gazibegovic, S., Logan, J. A., Car, D., het Veld, +R. L. M. O., van Veldhoven, P. J., Koelling, S., Verheijen, M. A., Pend- +harkar, M., Pennachio, D. J., Shojaei, B., Lee, J. S., Palmstrøm, C. J., +Bakkers, E. P. A. M., Das Sarma, S. & Kouwenhoven, L. P. (2021), +‘Large zero-bias peaks in insb-al hybrid semiconductor-superconductor +nanowire devices’, arXiv:2101.11456 . +Zhang, P., Yaji, K., Hashimoto, T., Ota, Y., Kondo, T., Okazaki, K., Wang, +Z., Wen, J., Gu, G. D., Ding, H. & Shin, S. (2018), ‘Observation of +topological superconductivity on the surface of an iron-based supercon- +ductor’, Science 360(6385), 182. +URL: https://www.science.org/doi/abs/10.1126/science.aan4596 +Zheng, C. (2021), ‘Universal quantum simulation of single-qubit nonuni- +tary operators using duality quantum algorithm’, Sci. Rep. 2021, 3960. +URL: https://doi.org/10.1038/s41598-021-83521-5 +Zhu, S., Kong, L., Cao, L., Chen, H., Papaj, M., Du, S., Xing, Y., Liu, W., +Wang, D., Shen, C., Yang, F., Schneeloch, J., Zhong, R., Gu, G., Fu, +L., Zhang, Y.-Y., Ding, H. & Gao, H.-J. (2020), ‘Nearly quantized con- +ductance plateau of vortex zero mode in an iron-based superconductor’, +Science 367(6474), 189. +URL: https://www.science.org/doi/abs/10.1126/science.aax0274 +Y. Masaki, T. Mizushima and M. Nitta: Preprint submitted to Elsevier +Page 34 of 34 + diff --git a/B9FJT4oBgHgl3EQfsy1U/content/tmp_files/load_file.txt b/B9FJT4oBgHgl3EQfsy1U/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..33c988afe867e096f2c8c154f59ec0031caef03a --- /dev/null +++ b/B9FJT4oBgHgl3EQfsy1U/content/tmp_files/load_file.txt @@ -0,0 +1,4279 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf,len=4278 +page_content='Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors Yusuke Masakia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='b,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Takeshi Mizushimac,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='∗ and Muneto Nittab,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='d,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='∗ aDepartment of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Tohoku University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Sendai,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Miyagi 980-8578,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Japan bResearch and Education Center for Natural Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Keio University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Hiyoshi 4-1-1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Yokohama,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Kanagawa 223-8521,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Japan cDepartment of Materials Engineering Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Osaka University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Toyonaka,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Osaka 560-8531,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Japan dDepartment of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Keio University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Hiyoshi 4-1-1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Japan A R T I C L E I N F O Keywords: Non-Abelian vortices,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' non-Abelian anyons,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' non-Abelian statistics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' topological quantum computation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' topological materials,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' topological superconductors,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' topological su- perfluids,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' superfluid 3He,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' spinor Bose-Einstein condensates,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' nematic liquid crystals,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' chiral liquid crystals,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' quark matter,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' nuclear matter,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' nuclear superfluids A B S T R A C T Anyons are particles obeying statistics of neither bosons nor fermions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Non-Abelian anyons, whose exchanges are described by a non-Abelian group acting on a set of wave functions, are attracting a great attention because of possible applications to topological quantum computations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Braiding of non-Abelian anyons corresponds to quantum computations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The simplest non-Abelian anyons are Ising anyons which can be realized by Majorana fermions hosted by vortices or edges of topological superconductors, 휈 = 5∕2 quantum Hall states, spin liquids, and dense quark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' While Ising anyons are insufficient for universal quantum computations, Fibonacci anyons present in 휈 = 12∕5 quantum Hall states can be used for universal quantum computations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Yang-Lee anyons are non- unitary counterparts of Fibonacci anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Another possibility of non-Abelian anyons (of bosonic origin) is given by vortex anyons, which are constructed from non-Abelian vortices supported by a non-Abelian first homotopy group, relevant for certain nematic liquid crystals, superfluid 3He, spinor Bose-Einstein condensates, and high density quark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Finally, there is a unique system admitting two types of non-Abelian anyons, Majorana fermions (Ising anyons) and non-Abelian vortex anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' That is 3푃2 superfluids (spin-triplet, 푝-wave paring of neutrons), expected to exist in neutron star interiors as the largest topological quantum matter in our universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Introduction In three spatial dimensions, all particles are either bosons or fermions in quantum physics, that is, a wave function of multi-particle states is symmetric (antisymmetric) under the exchanges of two bosons (fermions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' On contrary, in two spatial dimensions, there exist exotic particles classi- fied to neither bosons nor fermions, anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' A wave func- tion of two anyons receives a nontrivial phase factor un- der their exchanges Leinaas & Myrheim (1977), Wilczek (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Such exotic particles play essential roles in frac- tional quantum Hall states Halperin (1984), Arovas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (1984), and have been experimentally observed for 휈 = 1∕3 fractional quantum Hall states Nakamura et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Recently, yet exotic particles attracted great attention, that is, non-Abelian anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Non-Abelian anyons are described by a set of multiple wave functions, and the exchanges of two non-Abelian anyons lead to unitary matrix operations on a set of wave functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' They have been theoretically predicted to exist in 휈 = 5∕2 fractional quantum Hall states Moore & Read (1991), Nayak & Wilczek (1996), topological superconductors (SCs) and superfluids (SFs) Read & Green (2000), Ivanov (2001), Kitaev (2001), and spin liquids Kitaev (2006), Motome & Nasu (2020), and experimental observation is pursued.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Non-Abelian anyons are attracting significant interests owing to the possibility to offer a platform of topologically ∗Corresponding author mizushima@mp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='es.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='osaka-u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='jps (T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Mizushima);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' nitta@phys-h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='keio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='jp (M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Nitta) ORCID(s): 0000-0001-6891-7008 (Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Masaki);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 0000-0002-7313-6094 (T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Mizushima) protected quantum computations realized by braiding of non-Abelian anyons Kitaev (2003), Kitaev, Alexei and Laumann, Christopher (2008), Nayak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2008), Pachos (2012), Sarma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2015), Field & Simula (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Since the Hilbert space and braiding operations are topologically protected, they are robust against noises in contrast to the conventional quantum computation methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Recently, it has been reported that non-Abelian braiding and fusions has been experimentally realised in a superconducting quantum processor, where the fusion and braiding protocols are implemented using a quantum circuit on a supercon- ducting quantum processor Andersen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2022), thereby opening a significant step to realize topological quantum computations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' One of the main routes to realize non-Abelian anyons is based on Majorana fermions in topological SCs Ivanov (2001), Kitaev (2001), Alicea (2012), Leijnse & Flensberg (2012), Beenakker (2013), Silaev & Volovik (2014), Elliott & Franz (2015), Sato & Fujimoto (2016), Mizushima et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2016), Sato & Ando (2017), Beenakker (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Majorana fermions were originally proposed in high energy physics to explain neutrinos;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' they are particles that coincide with their own anti-particles Majorana (1937).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In condensed matter physics, Majorana fermions are localized at vortices or edge of materials for which several protocols of non-Abelian braiding were proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Non-Abelian anyons constructed from Majorana fermions are so-called Ising anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' They are not enough for universal quantum computations, and thus some non-topological process should be included Nayak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In contrast, another type of anyons called Fibonacci anyons Trebst et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2008) can offer a Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Masaki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Mizushima and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Nitta: Preprint submitted to Elsevier Page 1 of 34 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='11614v1 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='supr-con] 27 Jan 2023 Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors promising platform for universal topological quantum com- putation that all quantum gates are implemented by braiding manipulation in a topologically protected way Preskill (2004), Bonesteel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2005), Hormozi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Such Fibonacci anyons are proposed to exist in 휈 = 12∕5 quantum Hall states, a junction made of a conventional SC and a 휈 = 2∕3 fractional quantum Hall state Mong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2014), interacting Majorana fermions realized in a septuple-layer structure of topological SCs Hu & Kane (2018), and Rydberg atoms in a lattice Lesanovsky & Katsura (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Yang-Lee anyons are also proposed as non-unitary counterparts of Fibonacci anyons, obeying nonunitary non-Abelian statistics Ardonne et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2011), Freedman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2012), Sanno et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The aforementioned anyons are all quasiparticle excita- tions composed of fermions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' On the other hand, a different type of non-Abelian anyons can be composed of bosons in certain ordered states accompanied with symmetry breakings 퐺 → 퐻.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' They are called non-Abelian vortex anyons, whose exchange statistics are non-Abelian due to non-Abelian vortices, that is quantum vortices supported by a non-Abelian first homotopy (fundamental) group of order parameter manifolds, 휋1(퐺∕퐻) Bais (1980), Wilczek & Wu (1990), Bucher (1991), Brekke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (1993), Lo & Preskill (1993), Lee (1994), Brekke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='1 Such non-Abelian vortices exist in liquid crystals Poenaru & Toulouse (1977), Mermin (1979), Lavrentovich & Kleman (2001), 3He SFs Balachandran et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (1984), Salomaa & Volovik (1987), Volovik (2003), spinor Bose-Einstein condensates (BECs) Semenoff & Zhou (2007), Kobayashi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2009, 2012), Borgh & Ruostekoski (2016), and high density quark (QCD) matter Fujimoto & Nitta (2021a,b,c), Eto & Nitta (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Non-Abelian braiding of vortex anyons in spinor BECs and its application to quantum computations were proposed Mawson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In addition to these systems admitting one type of non- Abelian anyons, there is the unique system simultaneously admitting two kinds of non-Abelian anyons, Ising anyons based on Majorana fermions and non-Abelian vortex anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' It is a 3푃2 SF, spin-triplet and 푝-wave paring with the total angular momentum two Hoffberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (1970), Tamagaki (1970), Takatsuka & Tamagaki (1971), Takatsuka (1972), Richardson (1972).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Such 3푃2 SFs are expected to be realized by neutrons, relevant for neutron star interiors Sedrakian & Clark (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 3푃2 SFs are the largest topological SFs in our universe Mizushima et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2017) and admit non-Abelian vortices Masuda & Nitta (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Non-Abelian vortices host Majorana fermions in their cores Masaki et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2022), thus behaving as non-Abelian anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 1The term “non-Abelian” on vortices depends on the context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In the other contexts (in particular in high energy physics), vortices in a symme- try breaking 퐺 → 퐻 with non-Abelian magnetic fluxes are often called non-Abelian even though 휋1(퐺∕퐻) the first homotopy group is Abelian Hanany & Tong (2003), Auzzi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2003), Eto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2006), Shifman & Yung (2007), Eto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In condensed matter physics, vortices with Majorana fermions in their cores are also sometimes called non-Abelian vortices (because they are non-Abelian anyons).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In this article, the term “non-Abelian” on vortices is used only for vortices with non-Abelian first homotopy group 휋1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Figure 1: Schematic of the braid relations in Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (1) and (2): 푇푖푇푗 = 푇푗푇푖 for |푖 − 푗| ≥ 2 (left) and 푇푖푇푗푇푖 = 푇푗푇푖푇푗 for |푖 − 푗| = 1 (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The purpose of this article is to summarise these non- Abelian anyons of various types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' After introducing basics of non-Abelian anyons in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 2, we describe non-Abelian anyons in fermionic and bosonic systems, based on Ma- jorana fermions and non-Abelian first homotopy group in Secs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='3 and 4, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 5, we introduce 3푃2 SFs as the unique system simultaneously admitting two kinds of non-Abelian anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' We summarize this article in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Non-Abelian anyons 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Braid group and quantum statistics Here we consider pointlike topological defects (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=', vortices in two-dimensional spinless SCs) which behave as identical particles in a two-dimensional plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The exchange of 푛 particles in three or higher dimension is described by the symmetric group 푆푛 Leinaas & Myrheim (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' There are two one-dimensional representations of 푆푛, ±1, due to even/odd permutation and +1 (−1) corresponds the Bose (Fermi) statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Two dimension is special and the exchange of particles is given by the braid group 퐵푛 Wu (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The braid of particles is expressed as a set of operators 푇푘 (1 ≤ 푘 ≤ 푛 − 1) that exchange the neighboring 푘th and (푘 + 1)th particles in an anticlockwise direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The operators obey the relations (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 1) 푇푖푇푗푇푖 = 푇푗푇푖푇푗, for |푖 − 푗| = 1, (1) 푇푖푇푗 = 푇푗푇푖, for |푖 − 푗| ≥ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2) The exotic statistics of particles represented by the braid group stems from the relation 푇 −1 푖 ≠ 푇푖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In the one dimen- sional representation, the generator of 푇푖 is given by a phase factor that a wave function under the exchange of particles acquires, 휏푗 ≡ 휏(푇푗) = 푒푖휃푗 (0 ≤ 휃푗 < 2휋).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The relation in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (1) implies that the exchange operation of any two par- ticles induces the same phase factor 휏1 = 휏2 = ⋯ = 휏푛−1 = 푒푖휃.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The phase factor characterizes the quantum statistics of particles Wu (1984), and the absence of the relation 푇 2 푖 = 1 allows for the fractional (anyon) statistics with neither 휃 = 0 (bosons) nor 휃 = 휋 (fermions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In addition to the one- dimensional representation, the braid group has non-Abelian representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 3, we will show that the generators of the braid of Majorana zero modes are noncommutative as Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Masaki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Mizushima and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Nitta: Preprint submitted to Elsevier Page 2 of 34 Time 2 i+1 ¥+1 2 T;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='T;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='+1 ¥+1 2 2+1i+ T,T T:T:1T2 +12+2 Ti+1 TTi+1Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors [휏푖, 휏푗] ≠ 0 for |푖 − 푗| = 1 and the pointlike defects hosting Majorana modes behave as non-Abelian anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Although the braid group is trivial in three dimensions, a three-dimensional model with pointlike topological defects which host Majorana modes and obey the non-Abelian statistics has been proposed Teo & Kane (2010a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The non-Abelian statistics of the defects, which behave as hedgehogs, can be interpreted as the projective ribbon permutation statistics Freedman, Hastings, Nayak, Qi, Walker & Wang (2011), Freedman, Hastings, Nayak & Qi (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Such non-Abelian statistics enables to construct three-dimensional networks of topological superconducting wires supporting Majorana modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Non-Abelian anyons In three spatial dimensions, the statistics of particles is determined by their intrinsic spins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' According to the spin statistics theorem, all particles with integer (half-integer) spin are bosons (fermions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' A pair formed by two fermions with the spin 1∕2 behaves as a boson, and the spin of the composite particle obeys the “fusion rule” 1 2 ⊗ 1 2 = 0 ⊕ 1, where 0 and 1 denote the spin singlet and triplet states, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' When particles are trapped in a two dimen- sional plane, however, there is another possibility that is neither fermions nor bosons, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=', anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In general, anyons can be characterized by the topological charge, the fusion rule (푁푐 푎푏), the associative law (the 퐹-matrix), and the braiding operation (the 푅-matrix) Preskill (2004), Nayak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2008), Pachos (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Let ퟏ and {푎, 푏, ⋯} be the vacuum and the different species of particles, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Consider the anyon model spanned by 푀 = {ퟏ, 푎, 푏, ⋯} and bring two anyons 푎 and 푏 together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The fused particle also belongs to 푀.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The fusion rule is represented by 푎 ⊗ 푏 = ∑ 푐∈푀 푁푐 푎푏푐, (3) where fusion coefficients 푁푐 푎푏 are non-negative integers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Figure 2(a) shows the diagrammatic expression of the fusion of two anyons with topological charges 푎 and 푏 to an anyon with charge 푐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' When 푁푐 푎푏 is not zero for only one value of 푐, the fusion of paired 푎 and 푏 anyons is uniquely determined and the anyon is called the Abelian anyon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The non-Abelian anyons are characterized by two or more coefficients that satisfy 푁푐 푎푏 ≠ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In the context of quantum computation, the fusion rule determines the Hilbert space that encodes quantum information, and quantum computation is im- plemented by the braiding manipulation of non-Abelian anyons in a topologically protected way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Figure 2(b) shows the diagrammatic expression of the 푅-matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' When one anyon moves around the other, the pairwise anyons acquire a phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' As mentioned below, the 푅-matrix describes a phase resulting from the exchange of anyons 푎 and 푏 which fuse to a anyon 푐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Let us also consider the fusion of three anyons 푎, 푏, and 푐 into an anyon 푑.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The outcome of the fusion process is independent of order in which the anyons are to be fused.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' This implies that the fusion process (c) (b) (a) Figure 2: (a) Diagram of the fusion of two anyons 푎 and 푏 to an anyon 푐.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Diagrammatic expressions of the 푅-matrix (b) and the 퐹-matrix (c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' obeys the associative law, (푎 ⊗ 푏) ⊗ 푐 = 푎 ⊗ (푏 ⊗ 푐), which is characterized by the 퐹-matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The 퐹 matrix represents the transformation between different fusion bases or the choice of order of fusion, which is expressed as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 2(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The 푅-matrix and the 퐹-matrix are the building-blocks for constructing the braid group in multiple anyon systems Preskill (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Ising anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' An example of the non-Abelian anyons is the Ising anyon Kitaev (2006), Nayak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2008), Pachos (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The Ising anyon model consists of the vacuum ퟏ, Ising anyons 휎, and Dirac (complex) fermions 휓, which obey the fusion rules 휎 ⊗ 휎 = ퟏ ⊕ 휓, 휎 ⊗ 휓 = 휎, 휓 ⊗ 휓 = ퟏ, ퟏ ⊗ 푥 = 푥, (4) where 푥 ∈ {ퟏ, 휎, 휓}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Consider three Ising anyons, where the two left-most anyons fusing into either ퟏ or 휓 (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 2(c) with (푎, 푏, 푐) → 휎 and 푖, 푗 = {ퟏ, 휓}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The 푅-matrix and the 퐹-matrix are given, respectively, by 푅 = (푅휎휎 ퟏ 0 0 푅휎휎 휓 ) = 푒−푖휋∕8 ( 1 0 0 푖 ) , (5) 퐹 휎 휎휎휎 = 1 √ 2 ( 1 1 1 −1 ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (6) The diagonal components of the 푅-matrix are the phases re- sulting from the counterclockwise exchange of two left-most Ising anyons (휎) fusing to ퟏ or 휓, while the twice exchange operation of two right-most Ising anyons is represented by the unitary matrix, 퐹 −1푅2퐹 = 푒−푖휋∕4휎푥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Hence, braiding two anyons corresponds to the implementation of the quan- tum gates acting on the quantum states spanned by ퟏ and 휓.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In general, the anyons are described by conformal field theory, corresponding to gapless edge states residing in the boundary of two-dimensional gapped topological phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' For Ising anyons, the theory is the conformal field theory with the central charge 푐 = 1∕2, which describes critical Ising models such as the two-dimensional Ising model at the point of second-order phase transition Di Francesco et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The Moore-Read state in the fractional quantum Hall state at the filling factor 휈 = 5∕2 supports this type of non- Abelian anyons Nayak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The Ising anyons can Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Masaki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Mizushima and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Nitta: Preprint submitted to Elsevier Page 3 of 34 Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors also be realized in the Kitaev’s honeycomb model, which is an exactly solvable model of quantum spin liquid states Ki- taev (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In this model, the spins are fractionalized to Majorana fermions coupled to ℤ2 gauge fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The Ising anyons appear as Majorana zero modes bound to the ℤ2 flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Materials including 4푑 or 5푑 atoms with a strong spin-orbit coupling have been proposed as candidates of Kitaev mag- nets, and the half-integer thermal Hall effect was reported in 훼-RuCl3 Kasahara et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2018), Yamashita et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2020), Yokoi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2021), Bruin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2022), which is a signa- ture of Majorana fermions in the chiral quantum spin liq- uid phase Vinkler-Aviv & Rosch (2018), Ye et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Apart from materials, Google team reported the demonstra- tion of fusion and braiding rules of non-Abelian Ising anyons on a superconducting quantum processor, where the fusion and braiding protocols are implemented using a quantum circuit on a superconducting quantum processor Andersen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Another platform to realize Ising anyons is a topological SC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In the context of topological SCs, the Ising anyons (휎) appear as Majorana zero modes bound at their boundaries or topological defects, such as the surface, in- terface, and vortices Read & Green (2000), Kitaev (2001), Nayak et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2008), Alicea (2012), Sato & Fujimoto (2016), Mizushima et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Pairwise Majorana zero modes form a complex fermion that can define either the unoccu- pied state (ퟏ) or the occupied state (휓) of the zero energy eigenstate, implying 휎 ⊗ 휎 = ퟏ ⊕ 휓.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The vacuum ퟏ corre- sponds to a condensate of Cooper pairs, while 휓 represents a Bogoliubov quasiparticle which can pair into a condensate, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=', 휓 ⊗ 휓 = ퟏ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The detailed properties and realization of Majorana zero modes in topological SCs are described in Secs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Fibonacci anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Another example is the Fibonacci anyons Trebst et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The Fibonacci anyon model con- sists of the vacuum ퟏ and the non-trivial anyon 휏, which obey the fusion rules 휏 ⊗ 휏 = ퟏ ⊕ 휏, ퟏ ⊗ 푥 = 푥, (7) where 푥 = ퟏ, 휏.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The first rule implies that the fusion of two anyons may result in either annihilation or creation of a new anyon, and thus the Fibonacci anyon may be its own anti-particle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Repeated fusions of the 푛 + 1 휏-anyons result in either the vacuum or the 휏 anyon as 휏 ⊗ 휏 ⊗ ⋯ ⊗ 휏 = 푎푛 ⋅ ퟏ ⊕ 푏푛휏, where 푎푛 = 1 for 푛 = 2 and 푎푛 = 푛 − 2 for 푛 ≥ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The coefficient 푏푛 grows as the Fibonacci series, and the first few values in the sequence are 푏2 = 1, 푏3 = 2, 푏4 = 3, 푏5 = 5, ⋯.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The 푅-matrix and the 퐹-matrix are given, respectively, by 푅 = (푅휏휏 ퟏ 0 0 푅휏휏 휏 ) = ( 푒푖4휋∕5 0 0 −푒푖2휋∕5 ) , (8) 퐹 휏 휏휏휏 = ( 휙−1 휙−1∕2 휙−1∕2 −휙−1, ) , (9) where 휙 = (1 + √ 5)∕2 is the golden ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The Fibonacci anyons are described by the level-1 퐺2 Wess-Zumino-Witten theory with the central charge 푐 = 14∕5 Mong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2014), where 퐺2 is the simplest exceptional Lie group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' While Ising anyons are not sufficient for universal quantum computation, the Fibonacci anyon systems can offer a promissing platform for universal topological quantum computation that all quan- tum gates are implemented by braiding manipulation in a topologically protected way Preskill (2004), Bonesteel et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2005), Hormozi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The existence of the Fibonacci anyons is predicted in the 휈 = 12∕5 fractional quantum Hall state that is described by the Read-Rezayi state Read & Rezayi (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' It is also proposed that a junction made of a conventional SC and the 휈 = 2∕3 fractional quantum Hall state supports the Fibonacci anyons Mong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Fibonacci anyons can also be made from interacting Majorana fermions realized in a septuple-layer structure of topological SCs Hu & Kane (2018) and from Rydberg atoms in a lattice Lesanovsky & Katsura (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Yang-Lee anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' There are nonunitary counterparts of Fibonacci anyons, which are referred to as Yang-Lee anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The conformal field theory corresponding to Yang-Lee anyons is nonunitary and Galois conjugate to the Fibonacci conformal field theory Ardonne et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2011), Freedman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Because of nonunitarity, the central charge and the scaling dimension for the one nontrivial primary field are negative, 푐 = −22∕5 and Δ = −2∕5, re- spectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' As shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (9), the 퐹-matrix for Fibonacci anyons is given by the golden ratio 휙, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=', one solution of the equation 푥2 = 1 + 푥, which is an algebraic analogue of the fusion rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The 퐹-matrix for Yang-Lee anyons is obtained from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (9) by replacing 휙 → −1∕휙 as 퐹 휏 휏휏휏 = ( −휙 푖 √ 휙 푖 √ 휙 휙 ) , (10) as −1∕휙 is the other solution of the equation 푥2 = 1 + 푥.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (10), the bases of the 퐹-matrix are spanned by the vacuum state ퟏ and a Yang-Lee anyon 휏.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The 푅-matrix are given by 푅 = (푅휏휏 ퟏ 0 0 푅휏휏 휏 ) = ( 푒푖2휋∕5 0 0 푒푖휋∕5 ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (11) Unlike the Fibonicci anyons, braiding two Yang-Lee anyons is represented by a combination of the 푅-matrix and the nonunitary matrix, 퐹 −1푅퐹.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' While Yang-Lee anyons obey the same fusion rule as that of Fibonacci anyons given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (7), the 퐹-matrix in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (10) is the nonunitary and the Yang-Lee anyons obey the nonunitary non-Abelian statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The nonunitary conformal field theory with 푐 = −22∕5 describes the nonunitary critical phenomenon known as the Yang-Lee edge singularity Cardy (1985).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Let us consider the Ising model with an imaginary magnetic field 푖ℎ (ℎ ∈ ℝ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' For temperatures above the critical temperature, the zeros of the partition function in the thermodynamic limit, which are referred to as the Lee-Yang zeros, accumulate on the line ℎ > ℎc and the edge of the Lee-Yang zeros corresponds to the critical point ℎ푐 Lee & Yang (1952).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' As ℎ (> ℎc) Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Masaki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Mizushima and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Nitta: Preprint submitted to Elsevier Page 4 of 34 Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors approaches the edge, the density of zeros has a power-law behavior as |ℎ − ℎc|휎, which characterizes the critical phe- nomenon Kortman & Griffiths (1971), Fisher (1978).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' For instance, the magnetization exhibits singular behavior with the same critical exponent 휎.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The Yang-Lee edge singular- ity is also realized by the quantum Ising model with a real transverse field and a pure-imaginary longitudinal field von Gehlen (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The quantum Ising model with an imaginary longitu- dinal field, which supports the Yang-Lee anyons, can be constructed from Majorana zero modes in a network of topological superconducting wires coupled with dissipative electron baths Sanno et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The Majorana modes bound at the end points of one-dimensional topological SCs constitute spin 1∕2 operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' A coupling of Majorana zero modes with electrons in a metallic substrate plays an role of the pure-imaginarly longitudinal field, while the tunneling of Majorana zero modes between neighboring superconducting wires induces a transverse magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Schemes for the fusion, measurement, and braiding of Yang-Lee anyons are also proposed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Sanno et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' As mentioned above, the Yang-Lee anyons obey the nonunitary non-Abelian statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The nonunitary evolution of quantum states has been discussed in connection with measurement-based quantum computation Terashima & Ueda (2005), Usher et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2017), Piroli & Cirac (2020), Zheng (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Although the Yang-Lee anyons with the nonunitary 퐹-matrix are not suitable for application to unitary quantum computation, they can be the building- blocks for the construction of measurement-based quantum computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In addition, as the nonunitary quantum gates can be implemented by braiding manipulations, the Yang-Lee anyon systems may offer a quantum simulator for nonunitary time evolution of open quantum systems in a controllable way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Vortex anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In this article, we also discuss non- Abelian anyons made of bosonic (topological) excitations in ordered states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The nontrivial structure of the order parame- ter manifold appears in the liquid crystals, spin-2 BECs, the A phase of SF 3He, dense QCD matter, and 3푃2 SFs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The line defects in such ordered systems, such as vortices, are represented by non-Abelian first homotopy group and their topological charges are noncommutative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Such topological defects with noncommutative topological charges behave as non-Abelian anyons, called the non-Abelian vortex anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 4, we demonstrate that order parameter manifolds in nematic liquid crystals and spin-2 BECs admit the existence of non-Abelian vortices and show the fusion rules of such non-Abelian vortex anyons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Non-Abelian anyons in topological SCs 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Majorana zero modes as Ising anyons Majorana zero modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' An elementary excitation from superconducting ground states is a Bogoliubov quasiparticle that is a superposition of the electron and hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The quasipar- ticle excitations are described by the Bogoliubov-de Gennes (BdG) Hamiltonian 퐻 = ∑ 푖푗 ( 흍† 푖 , 흍푖 ) \ue234푖푗 (흍푗 흍† 푗 ) , (12) \ue234푖푗 = (ℎ푖푗 Δ푖푗 Δ† 푖푗 −ℎ∗ 푖푗 ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (13) Here, 흍푗 is the 푁-component vector of the electron field op- erator and \ue234 is the 2푁 × 2푁 hermitian matrix, where 푁 is the sum of the spin degrees of freedom and the number of the lattice sites and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The 푁 ×푁 hermitian matrix ℎ de- scribes the normal state Hamiltonian and the superconduct- ing pair potential Δ obeys Δt = −Δ because of the Fermi statistics, where 푎t denotes the transpose of a matrix 푎.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The BdG Hamiltonian naturally holds the particle-hole symme- try \ue22f\ue234\ue22f−1 = −\ue234, (14) where the particle-hole operator \ue22f = Θ퐾 is an antiunitary operator composed of the unitary operator Θ and the complex conjugation operator 퐾.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The self-conjugate Dirac fermions are called Majorana fermions, where the quantized field 횿 ≡ (흍, 흍†)t obeys 횿 = \ue22f횿, \ue22f2 = +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (15) We expand the quantized field 횿 in terms of the energy eigenstates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The energy eigenstates are obtained from the BdG equation, ∑ 푗 \ue234푖푗(흋퐸)푗 = 퐸(흋퐸)푖, (16) which describes the quasiparticle with the energy 퐸 and the wave function 흋퐸.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Equation (14) guarantees that the quasiparticle state with 퐸 > 0 and 흋퐸 is accompanied by the negative energy state with −퐸 and 흋−퐸 = \ue22f흋퐸.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Thus, the negative energy states are redundant as long as the particle-hole symmetry is maintained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Let 휂퐸 be the quasiparticle operator which satisfies the anticommutation relations, {휂퐸, 휂† 퐸′} = 훿퐸,퐸′ and {휂퐸, 휂퐸′} = {휂† 퐸, 휂† 퐸′} = 0 (퐸, 퐸′ > 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The self-charge conjugation relation (15) then implies that the quasiparticle annihilation operator with a positive energy is equivalent to the creation with a negative energy as 휂퐸 = 휂† −퐸, and 횿 is expanded only in terms of positive energy states as 횿(풓) = ∑ 퐸>0[흋퐸휂퐸 + \ue22f흋퐸휂† 퐸].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The condition (15) can be fulfilled by odd-parity SCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In the absence of spin-orbit coupling, the spin-singlet pair potential is always invariant under the spin rotation, and the particle-hole exchange operator is given by \ue22f2 = −1 in each spin sector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Hence, spin-singlet SCs cannot satisfy Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Spin-orbit coupling, however, enables even spin singlet SCs to host Majorana fermions Sato & Ando (2017), Alicea (2012), Sato & Fujimoto (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Now, let us suppose that a single zero-energy state ex- ists, and 흋0 is its wave function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Then, we can rewrite the quantized field to 횿 = 흋0훾 + ∑ 퐸>0 [ 흋퐸휂퐸 + \ue22f흋퐸휂† 퐸 ] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (17) Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Masaki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Mizushima and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Nitta: Preprint submitted to Elsevier Page 5 of 34 Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors Figure 3: Schematic of the quasiparticle states bound at a single vortex (a) and energy spectrum of many vortices (b) in a spinless SC, where the level spacing of vortex bound states is Δ퐸 ∼ Δ2 0∕휀F and Δ퐸M denotes the band width of Majorana states bound at each core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (c) Operations of the braiding ma- trices 푈12 and 푈23 and the 퐹-matrix in four Majorana modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' We have introduced 훾, instead of 휂퐸=0, to distinguish the zero mode from other energy eigenstates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Owing to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (14), the zero-energy quasiparticle is composed of equal contri- butions from the particle-like and hole-like components of quasiparticles, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=', \ue22f흋0 = 흋0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The self-conjugate constraint in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (15) imposes the following relations: 훾† = 훾, (18) and (훾)2 = 1 and {훾, 휂퐸>0} = {훾, 휂† 퐸>0} = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The quasipar- ticle obeying this relation is called the Majorana zero mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The zero energy states appear in a topological defect of topological SCs, such as chiral SCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 3(a), we show the spectrum of Andreev bound states bound at a vortex in a chiral SC, where the level spacing between the zero mode and the lowest excitation state is Δ퐸 ∼ Δ2 0∕휀F Kop- nin & Salomaa (1991), Volovik (1999), Read & Green (2000), Matsumoto & Heeb (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In many vortices, the hybridization between neighboring Majorana modes gives rise to the formation of the band structure with the width Δ퐸M ∼ 푒−퐷∕휉 Cheng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2009), Mizushima & Machida (2010), where 퐷 and 휉 is the mean distance of neighboring vortices and superconducting coherence length, respectively (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 3(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The Majorana zero modes exhibit the non-Abelian any- onic behaviors Ivanov (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' To clarify this, we start with two Majorana zero modes residing in a SC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Using two Ma- jorana operators, 훾1 and 훾2, we define the new fermion op- erators 푐 and 푐† as 푐 = 1 2(훾1 + 푖훾2), 푐† = 1 2(훾1 − 푖훾2), (19) which obey the anticommutation relations, {푐, 푐†} = 1 and {푐, 푐} = {푐†, 푐†} = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The two degenerate ground states are defined as the vacuum |0⟩ and the occupied state of the zero energy state |1⟩ = 푐† |0⟩, respectively, where the former (latter) state is the even (odd) fermion parity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' We note that as the BdG Hamiltonian for superconducting states is generally commutable with the parity operator, the fermion parity remains as a good quantum number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' For the even (odd) parity sector, the Hilbert space is spanned by using |0⟩ (|1⟩) and excited states that are constructed as 휂† 퐸휂† 퐸′휂† 퐸′′ ⋯ |0⟩ (휂† 퐸휂† 퐸′휂† 퐸′′ ⋯ |1⟩).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The Majorana operators, 훾1, 훾2, and 푖훾1훾2, act on the Hilbert space as the Pauli matrices 휎푥, 휎푦, and 휎푧, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The eigenstates of the Majorana operators 훾1 and 훾2 are given by the superposition of the degenerate states with different fermion parity, |0⟩ and |1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Hence, the eigenstate of a single Majorana zero mode cannot be a physical state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Consider 2푁 Majorana zero modes denoted by 훾푗 (푗 = 1, ⋯ , 2푁), where 푁 complex fermions are constructed by the fusion of 푖th and 푗th Majorana zero modes as 푐푖푗 = (훾푖 + 푖훾푗)∕2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' We define the occupation number operator of the complex fermion, 푛푖푗 ≡ 푐† 푖푗푐푖푗 = 1 2(1 + 푖훾푖훾푗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (20) In a basis that diagonalizes paired Majorana modes 푖훾푖훾푗, two eigenvalues of the complex fermion, 푛푖푗 = 0 and 1, cor- respond to the fusion channels ퟏ and 휓, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Hence, the Majorana zero mode is referred to as the Ising anyon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 2푁 degenerate ground states are expressed in terms of the occupation numbers as |푛12, 푛34, ⋯⟩, which are separated to the sectors of the even/odd fermion parity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Here we assume that the temperature of the system is much lower than the level spacing (Δ퐸) between the Majorana zero mode and the lowest excitation (non-Majorana) state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Then, the 2푁−1 degenerate ground states in each fermion parity sector can be utilized as topological qubits, where quantum information is stored in a topologically protected way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Braiding Majorana zero modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Here we discuss the braiding statistics of Majorana zero modes 훾푖 and 훾푗 and show the non-Abelian statistics of Majorana zero modes Ivanov (2001), Alicea et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2011), Clarke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' While we consider the exchange of Majorana zero modes residing in vortices, the theory is also appli- cable to Majorana zero modes bound at the end points of one-dimensional topological SCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Let 푇푖푗 be the braid operators that satisfy Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (1) and (2) and transform 훾푖 and 훾푗 to 푒휃푖훾푗 and 푒푖휃푗훾푖, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The unitary time-evolution of Majorana zero modes is gov- erned by the Heisenberg equation, 푖 푑 푑푡훾푗(푡) = [훾푗(푡), \ue234(푡)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The positions of two Majorana modes are adiabatically ex- changed in the time interval [0, 푇 ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The adiabatic condition defines the lower bound for the time scale of the braiding operation, 푇 , so that 푇 is much longer than the inverse of the level spacing between the Majorana zero mode and the lowest excitation (non-Majorana) state, Δ퐸.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In addition, the upper bound is associated with the band width of Majorana modes Δ퐸M ∼ 푒−퐷∕휉 (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 3(b)), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=', Δ퐸−1 ≪ 푇 ≪ Δ퐸−1 M .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Within the adiabatic condition, the braiding dynam- ics of Majorana zero modes can be regarded as the unitary time evolution, 훾푗(푡) = 푈† 푖푗(푡)훾푗(0)푈푖푗(푡).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' After the braiding Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Masaki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Mizushima and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Nitta: Preprint submitted to Elsevier Page 6 of 34 (a) E 个 0V [△(p)I △E ～ △/EF U12 C12 F(b) E 个 OV AEM 0 C13 C2423 C34Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors operation, 훾푖 (훾푗) changes to 훾푗 (훾푖) with an additional phase shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Then, the braiding operation is represented by 푈† 푖푗훾푖푈푖푗 = 푒푖휃푖훾푗, 푈† 푖푗훾푗푈푖푗 = 푒푖휃푗훾푖, (21) where 푈푖푗 ≡ 푈푖푗(푇 ) is the unitary operator which describes the exchange operation of two Majorana zero modes 훾푖 and 훾푗, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=', the representation of 푇푖푗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' According to the condi- tions, (푒푖휃푖훾푗)2 = (푈† 푖푗훾푖푈푖푗)2 = 1 and (훾푗)2 = 1, the phase shifts obey 휃푖 = 푛휋 and 휃푗 = 푚휋, where 푛, 푚 ∈ ℤ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The braiding operations must not change the parity of the occupa- tion number defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (20) and thus satisfy 푈† 푖푗푛푖푗푈푖푗 = 푛푖푗, which imposes the condition, 휃1 + 휃2 = (2푛 + 1)휋, on the phase shift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' As a result, the exchange operation of two Majorana zero modes obtains the following braiding rules: 푈† 푖푗훾푖푈푖푗 = 훾푗, 푈† 푖푗훾푗푈푖푗 = −훾푖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (22) Consider four Majorana zero modes denoted by 훾1, 훾2, 훾3, and 훾4, which form two complex fermions as 푐12 ≡ (훾1 + 푖훾2)∕ √ 2 and 푐34 ≡ (훾3 + 푖훾4)∕ √ 2 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 3(c)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' When the Majorana mode “3” adiabatically encircles the Majorana mode “2”, both Majorana modes operators acquire the 휋 phase shift, 훾2 ↦ −훾2 and 훾3 ↦ −훾3, corresponding to the twice operation of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Therefore, the braiding operation changes the occupation numbers of the complex fermion 푛12 ≡ 푐† 12푐12 and 푛34 ≡ 푐† 34푐34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' For example, the above braiding generates a pair of the complex fermions |11⟩ from their vacuum |00⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Here these two states are orthogonal, ⟨11|00⟩ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The braiding rule can be generalized to 2푁 Majorana modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The 2푁 Majorana modes are fused to 푁 complex fermions, leading to the 2푁−1-fold degeneracy of ground states while preserving fermion parity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' As discussed above, when the 푖th and 푗th Majorana modes are exchanged with each other, their oper- ators behave as 훾푖 ↦ 훾푗 and 훾푗 ↦ −훾푖.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The representation of the braid operator 푇푖푗 that satisfies Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (22) is given in terms of the zero mode operators as Ivanov (2001) 푈푖푗 = 푒푖휃 exp (휋 4 훾푗훾푖 ) = 푒푖휃 1 √ 2 (1 + 훾푗훾푖 ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (23) From now on, we omit the overall Abelian phase factor 푒푖휃 as it is not important for quantum computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Equation (23) also holds in the case of the Moore-Read state Nayak & Wilczek (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' For 푁 = 1, there is only a single ground state in each sector with definite fermion parity, and the exchange of two vortices results in the global phase of the ground state by 푒푖휋∕4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' One can easily find that for 푁 ≥ 2 the exchange operators 푈푖푗 and 푈푗푘 do not commute to each other, [푈푖푗, 푈푗푘] ≠ 0, implying the non-Abelian anyon statistics of the Majorana zero modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' For four Majorana zero modes (푁 = 2), twofold de- generate ground states exist in each ferimon-parity sector: |00⟩ ≡ |vac⟩ and |11⟩ = 푐† 12푐† 34 |vac⟩ in the sector of even fermion parity, and |10⟩ = 푐† 12 |vac⟩ and |01⟩ = 푐† 34 |vac⟩ in the sector of odd fermion parity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' For the even-parity sec- tor, the representation matrix for the exchange of 1 ↔ 2 and 3 ↔ 4 [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 3(c)] is given by 푈12 = 푈34 = 푒−푖 휋 4 |00⟩ ⟨00| + 푒푖 휋 4 |11⟩ ⟨11| .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (24) This merely rotates the phase of the ground state as in the 푁 = 1 case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In contrast, the representation matrix for the intervortex exchange [2 ↔ 3 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 3(c)] has the mixing terms of the two degenerate ground states |00⟩ and |11⟩, 푈23 = 1 √ 2 [|00⟩ ⟨00| − 푖 |00⟩ ⟨11| + |11⟩ ⟨11| − 푖 |11⟩ ⟨00|] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (25) We note that the choice of the pairing to form the complex fermion is arbitrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The change of the fused Majorana modes corresponds to the change of the basis from one which diagonalizes 푖훾1훾2 and 푖훾3훾4 to another which diagonalizes 푖훾1훾3 and 푖훾2훾4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The basis transformation is represented by the 퐹-matrix as 퐹 = 1 √ 2 ( 1 1 1 −1 ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (26) The braiding matrix in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (24) implies that the exchange of two Majorana zero modes fusing to 휓 (|11⟩) acquires an additional 휋∕2 phase compared to the fusion channel to ퟏ (|00⟩).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Hence, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (24) satisfies the property of the 푅-matrix in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (5), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=', 푅휎휎 ퟏ = −푖푅휎휎 휓 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Platforms for Majorana zero modes The realization of non-Abelian anyons requires to freeze out the internal degrees of freedom of Majorana modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The simplest example is spinless 푝-wave SCs/SFs, which emerge from the low-energy part of spinful chiral 푝-wave SCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' To clarify this, we start with spin-triplet SCs, whose pair poten- tial is given by a 2 × 2 spin matrix Leggett (1975) ̂Δ(풌) = (Δ↑↑(풌) Δ↑↓(풌) Δ↓↑(풌) Δ↓↓(풌) ) =푖휎휇휎푦푑휇(풌) = 푖휎휇휎푦퐴휇푖̂푘푖, (27) where ̂푘푖 ≡ 푘푖∕푘F is scaled with the Fermi momentum 푘F, and the repeated Greek/Roman indices imply the sum over 푥, 푦, 푧.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Here we omit the spin-singlet component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Owing to the Fermi statistics, the spin-triplet order parameter, 풅(풌), obeys 풅(풌) = −풅(−풌).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' For spin-triplet 푝-wave pairing, the most general form of the order parameter is given by a 3 × 3 complex matrix, 퐴휇푖 ∈ ℂ, where the components are la- belled by 휇, 푖 ∈ {푥, 푦, 푧}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' HQVs with Majorana zero modes in SF 3He.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' We con- sider the Anderson-Brinkman-Morel (ABM) state Anderson & Morel (1961), Anderson & Brinkman (1973), as a pro- totypical example of chiral 푝-wave states hosting Majorana zero modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The ABM state is realized in the A-phase of the SF 3He, which appears in high pressures and high temper- atures Vollhardt & Wölfle (1990), Volovik (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' At tem- peratures above the SF transition temperature, 푇 > 푇c ≈ 1– 2 mK, the normal Fermi liquid 3He maintains a high degree of symmetry 퐺 = 푆푂(3)푳 × 푆푂(3)푺 × 푈(1), (28) Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Masaki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Mizushima and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Nitta: Preprint submitted to Elsevier Page 7 of 34 Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors where 푆푂(3)푳, 푆푂(3)푺, and 푈(1) are the rotation symme- try in space, the rotational symmetry of the nuclear spin de- grees of freedom, and the global gauge symmetry, respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The tensor 퐴휇푖 transforms as a vector with respect to index 휇 under spin rotations, and, separately, as a vector with respect to index 푖 under orbital rotations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The order pa- rameter of the ABM state is then given by the complex form 퐴휇푗 = Δ푒푖휑 ̂푑휇( ̂푚푗 + 푖̂푛푗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (29) The ABM state is the condensation of Cooper pairs with the “ferromagnetic” orbital, and spontaneously breaks the time- reversal symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The orbital part of the order parame- ter is characterized by a set of three unit vectors forming the triad ( ̂풎, ̂풏, ̂풍), where ̂풍 = ̂풎 × ̂풏 denotes the orientation of the orbital angular momentum of Cooper pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The re- maining symmetry in the ABM state is 퐻A = 푆푂(2)푆푧 × 푆푂(2)퐿푧−휑 ×ℤ2, where 푆푂(2)푆푧 is the two-dimensional ro- tation symmetry in the spin space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The ABM state is also invariant under 푆푂(2)퐿푧−휑 which is the combined gauge- orbital symmetry, where the 푈(1) phase rotation, 휑 → 휑 + 훿휑, is compensated by the continuous rotation of the orbital part about ̂풍, ̂푚푗+푖 ̂푛푗 → 푒−푖훿휑( ̂푚′ 푗+푖 ̂푛′ 푗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In addition, ℤ2 is the mod-2 discrete symmetry ( ̂풅, ̂풎, ̂풏) → (− ̂풅, − ̂풎, −̂풏).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The manifold of the order parameter degeneracy is then given by 푅A ≃ 퐺∕퐻A ≃ 푆2 푺 × 푆푂(3)퐿푧,휑∕ℤ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (30) The two-sphere, 푆2 푺, is associated with the variation of ̂풅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The degeneracy space has an extra ℤ2 symmetry that the change from ̂풅 to − ̂풅 can be compensated by the phase ro- tation 휑 → 휑 + 휋.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The topologically stable linear defects in the ABM state are characterized by the group of the integers modulo 4 Voll- hardt & Wölfle (1990), Volovik (1992), Salomaa & Volovik (1987), Volovik (2003), 휋1(푅A) ≃ 휋1(푆푂(3)∕ℤ2) ≃ ℤ4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (31) There exist four different classes of topologically protected linear defects in the dipole-free case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The four linear defects can be categorized by the fractional topological charge, 푁A = 0, 1 2, 1, 3 2, (32) where 푁A = 3∕2 is topologically identical to 푁A = −1∕2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The representatives of 푁A = 0 and 푁A = 1∕2 classes in- clude continuous vortex such as the Anderson-Toulouse vor- tex and half quantum vortex (HQV), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Owing to 푁A = 2 = 0, a pure phase vortex with winding number 2 is continuously deformed into a nonsingular vortex without a core, that is, the Anderson-Toulouse vortex Anderson & Toulouse (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The 푁A = 1∕2 vortex is a combination of the half-wound 풅-disgyration with a half-integer value of the 푈(1) phase winding (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The extra ℤ2 symmetry allows us to take the half-integer value of the topological charge, because the 휋-phase jump arising from the half-winding of the 푈(1) phase (휑 = 휃∕2) can be canceled out by the change in the orientation of ̂풅 ( ̂풅 → − ̂풅).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The 푁A = 1 class in- cludes a pure phase vortex with odd winding number and the radial/tangential disgyrations without phase winding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The latter was originally introduced by de Gennes as 풍-textures with a singularity line De Gennes (1973), Ambegaokar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (1974).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The vortex with the fractional charge 푁A = 1∕2 is a harbor for spinless Majorana zero modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' We introduce the center-of-mass coordinate of Cooper pairs, 푹 = (휌, 휃, 푧), as ̂Δ(풌) → ̂Δ(풌, 푹), where 휌 = √ 푥2 + 푦2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The vortex core is located at 휌 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The vortex state is subject to the boundary condition at 휌 → ∞ where the orbital angular momentum of the Cooper pair is aligned to the 푧-axis (̂풍 ∥ ̂풛) and the 푈(1) phase 휑 continuously changes from 0 to 2휋휅 along the azimuthal (휃) direction, 퐴휇푖(휌 = ∞, 휃) = Δ푒푖휅휃 ̂푑휇(휃)(̂푥푗 + 푖 ̂푦푗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (33) Owing to the spontaneous breaking of the gauge-orbital symmetry, there are two classes for the vorticity 휅: Integer quantum vortices with 휅 ∈ ℤ and HQVs with 휅 ∈ ℤ∕2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In the HQVs, both the 푈(1) phase and ̂풅 rotate by 휋 about the vortex center (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In genral, the ̂풅-texture for HQVs is obtained as ̂풅(휃) = cos(휅sp휃)̂풙 + sin(휅sp휃)̂풚, (34) where 휅sp denotes the winding of ̂풅.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The HQV is character- ized by (휅, 휅sp) = (1∕2, ±1∕2), while the integer quantum vortex has (휅, 휅sp) = (1, 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' It is remarkable to notice that since the ABM state is the equal spin pairing state, the order parameter for the HQV is recast into the representation in the spin basis as ̂Δ = Δ [ 푒푖(휅−휅sp)휃 |↑↑⟩ + 푒푖(휅+휅sp)휃 |↓↓⟩ ] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (35) For the HQV with (휅, 휅sp) = (1∕2, 1∕2) the |↑↑⟩ Cooper pair possesses the spatially uniform phase, while the |↓↓⟩ pair has the phase winding of 2휋 around the vortex as in a conven- tional singly quantized vortex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Thus, the vortex-free state in the ↑ spin sector exhibits fully gapped quasiparticle exci- tations, while the low-lying structures in half quantum vor- tex are effectively describable with a singly quantized vor- tex in the ↓ spin sector, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=', the spin-polarized chiral 푝-wave SC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' An odd-vorticity vortex in the spin-polarized chiral sys- tem hosts a single spinless Majorana zero mode that obeys non-Abelian statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The existence of non-Abelian any- onic zero modes in half quantum vortices was first revealed by Ivanov, who developed the non-Abelian braiding statis- tics of vortices with spinless Majorana zero modes Ivanov (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In the bulk A-phase of the SF 3He, the formation of con- tinuous vortices with the ̂풍-texture, which are characterized by the topological charge 푁 = 0, is an obstacle to realizing the HQVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' As the orientation of the ̂풍-vector is associated with the orbital motion of the Cooper pair, the ̂풍-texture can be uniformly aligned in a parallel plate geometry with thick- ness 퐷.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The motion of Cooper pairs is confined in the two- dimensional plane and ̂풍 is locked perpendicular to the plates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Applying a magnetic field further restricts the orientation of ̂풅 to the two-dimensional plane perpendicular to the applied Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Masaki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Mizushima and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Nitta: Preprint submitted to Elsevier Page 8 of 34 Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors Figure 4: Schematic of the HQV realized in the ABM state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The color map shows the U(1) phase winding from 휑 = 0 (red) at 휃 to 휋 (blue) at 휃 = 2휋, and the arrows represent the texture of the ̂풅-vectors shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (34) with 휅sp = 1∕2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' field, which is a favorable situation to stabilize the HQVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In the parallel plate geometry with 퐷 = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='5 휇m, the measure- ments of NMR frequency shift observed that the ̂풅-vectors are confined to the two-dimensional plane perpendicular to ̂풍 Yamashita et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The experiment was performed in a rotating cryostat at ISSP, University of Tokyo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The parallel plates are rotated at the angular velocity ≲ 12rad∕s but no conclusive evidence of HQVs was observed Yamashita et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Although the SF 3He-A thin film provides an ideal platform for HQVs with Majorana zero modes, the realiza- tion of HQVs remains as a challenging task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Another promising route to realize HQVs with Majo- rana zero modes is to artificially introduce well-controlled disorders with high-porosity aerogel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In particular, the polar phase was observed in anisotropic aerogels consisting of uniaxially ordered alumina strands, called the nematic aerogels Dmitriev et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2015), Halperin (2019) [See Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 5(a)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The order parameter of the polar phase is given by 퐴휇푖 = Δ푒푖휑 ̂푑휇 ̂푧푖, where the orbital state of the Cooper pair (̂푧푖) is confined by the uniaxially anisotropic disorders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' As in the ABM state in the bulk 3He, the texture of the ̂풅-vector concomitant with the half-integer vorticity can realize HQVs in the polar phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In the polar phase, HQVs are energetically preferable to integer quantum vortices at zero magnetic fields and magnetic fields applied along the uniaxial anisotropy Nagamura & Ikeda (2018), Mineev (2014), Regan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Indeed, the HQVs were experimentally observed in nematic aerogels under rotation Autti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The HQVs were also created by temperature quench via the Kibble-Zurek mechanism Rysti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 5(a), the superfluid phase diagram in nematic aerogels is drastically changed from that of the bulk 3He without disorders, where the polar-distorted A and B (PdA and PdB) phases are stabilized in addition to the polar phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The NMR measurements performed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Mäkinen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2019) observed that the HQVs survive across the phase transition to the PdA phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' 4, the HQV is accompanied by the ̂풅-soliton in which the ̂풅 orientation rotates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Figure 5(b) shows the observed NMR spectra which have satellite peaks in addition to the (a) (b) Figure 5: (a) The experimental setup and the phase diagram in the liquid 3He with nematic disorders and (b) NMR spec- tra at pressure 푃 = 7 bar and 푇 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content='60푇c in the presence of a magnetic field perpendicular to the anisotropy direction of nematic disorders Mäkinen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2019), where 푇c is the crit- ical temperature of the bulk SF 3He without disorders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The disorders consist of nearly parallel Al2O3 strands, where the diameter and mean distance are 푑2 ≈ 8 nm and 푑1 ≈ 50 nm, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' In (b), the main peaks with green and magenta colors correspond to the signal of the bulk PdA phase, while the satellite peaks originate from the spin excitation bound to the ̂풅-solitons connecting pairs of HQVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The satellite peak remains unchanged after the thermal cycling illustrated by pur- ple arrows in (a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Both figures are taken from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Mäkinen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' main peak around the Larmor frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The main peak is a signal of the bulk PdA phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The satellite peak orig- inates from the spin excitation localized at the ̂풅-solitons connecting pairs of HQVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' The order parameter of the PdA phase is given by 퐴휇푖 = Δ푒푖휑 ̂푑휇( ̂풎 + 푖휀̂풏)푖, where ̂풎 is aligned along the axis of nematic aerogels and 휀 ∈ (0, 1) is the temperature- and pressure-dependent parameter on the distortion of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' (29) by nematic aerogels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Although the HQVs in the polar phase host no Majorana zero modes, the low energy structure of the HQVs in the PdA phase is Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Masaki, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Mizushima and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/B9FJT4oBgHgl3EQfsy1U/content/2301.11614v1.pdf'} +page_content=' Nitta: Preprint submitted to Elsevier Page 9 of 34 a b Rotation NMRpick-up coils 2 axis Pii log Pit +D +D +C +B) +(B +G +Network Entropy: +E +TiPii log Pi + Model human perception using free energy principle4 +A +B +C +FIG. 2. Quantifying the information of Bach’s music using the entropy of random walks on networks of note +transitions. (A) Entropy of Bach’s music networks (Sreal) compared with random networks of the same size (Srand). We report +the entropy of the corresponding random networks after averaging over 100 independent realizations. The error bars for Srand +indicate the standard error of the sample. (B) The entropy of Bach’s music networks (Sreal) compared with random networks +that preserve the in- and out-degree of each node (Sdeg). We report the entropy of the corresponding degree-preserving random +networks after averaging over 100 independent realizations. The error bars for Srand indicate the standard error of the sample. +(C) The entropy of the chorales as a function of the average in-degree heterogeneity Hin = Var(kin)/⟨kin⟩ (top) and out-degree +heterogeneity Hout = Var(kout)/⟨kout⟩ (bottom) of the networks. In panels (A) and (B), each data point represents a single +piece. Color and marker indicate the type of piece, as shown in the legend. The dashed line represents the line y = x. In panel +(C), the dotted line indicates the best linear fit, and the reported rs value is the Spearman correlation coefficient. +distribution numerically and use Eq. 2 to compute the +entropy of each piece. +To understand the amount of information produced +by the music networks, we compare them to random- +ized (or “null”) networks with equal number of nodes +and edges (see the Materials and Methods section A 5 for +details on generating null networks). If the note transi- +tions in Bach’s music do have distinct properties that al- +low them to communicate a large amount of information, +then we would expect Bach’s networks to contain more +information than random transition structures. By aver- +aging over 100 random networks for each piece, we find +that the real networks have consistently higher entropy— +thereby containing more information—than their ran- +dom counterparts (Fig. +2A). Moreover, by comparing +across pieces, we observe that the different kinds of com- +positions cluster together based on their entropy. The +chorales, typically meant to be sung by groups in eccle- +siastical settings, have a markedly lower entropy than +the rest of the compositions studied. By contrast, the +toccatas and preludes have a much higher entropy. It is +possible that the chorales’ functions of meditation, adora- +tion, and supplication are best supported by predictabil- +ity and hence low entropy, whereas the entertainment +functions of the toccatas and preludes are best supported +by unpredictability and hence high entropy. +We know that the node-level entropy is defined only +by the out-degrees of the nodes. Accordingly, it is use- +ful to assess differences between the true networks and +others wherein the node-level entropies have been fixed +by preserving the true degree distribution. To perform +this assessment, we compare the entropy of the real net- +works with another set of null models: randomized net- +works which preserve both the in- and out-degree of each +node (see the Methods and Materials section A 5 for de- +tails on generating these networks). +We observe that +the entropies of the networks are more or less preserved +(see Fig. 2B). Although this preservation is expected for +undirected networks (where the entropy is determined +only by the degree distribution), it need not exist for di- +rected networks (where the different stationary distribu- +tions contribute to the entropy). We therefore find that +the entropy of music networks is primarily determined +by their degree distributions rather than their stationary +distributions. +Heterogeneity in degrees favors higher entropy +To gain intuition for how the entropy of note tran- +sitions depends on network structure, consider the case +of unweighted and undirected networks. The network en- +tropy takes a particularly simple form, as shown in Eq. 3. +Following a Taylor expansion around the average degree +of the network (see the Materials and Methods section +A 2), one obtains: +S = log⟨k⟩ + Var(k) +2 ⟨k⟩2 + ... +(4) +where ⟨k⟩ is the average degree of the network and Var(k) +is the variance of the degrees. To first order, we see that + +5 +the entropy increases logarithmically with the average +degree of the network. To second order, the entropy in- +creases with the variance or the heterogeneity of the de- +grees, such that more information will be produced by +networks with heterogeneous (or broader) degree distri- +butions. We define the degree heterogeneity as: +H = Var(k) +⟨k⟩2 . +(5) +Many networks that we encounter in our daily lives are +characterized by heterogeneous degree distributions, typ- +ically with few high degree “hub” nodes and many low de- +gree nodes [36–38]. By contrast, regular graphs—which +have homogeneous degrees—produce random walks with +the least entropy. +Where does Bach’s music fall along this spectrum? We +found in Fig. 2A that Bach’s music networks have consis- +tently higher entropy than null networks with the same +number of nodes and edges (in other words, randomized +networks with the same average degree). In the Supple- +mentary Information Sec. B 4, we show that this higher +information content of Bach’s music networks is due to +higher heterogeneity in their in- and out-degree distri- +bution; that is, Bach’s music networks are more hetero- +geneous in their degrees than expected from transition +structures of their size, enabling them to pack more in- +formation into their structure. In (Fig. 2A), we also ob- +served that various pieces belonging to certain composi- +tions were clustered together in their entropy. Consistent +with this observation, we find that the pieces which are +clustered together in their entropy have very similar de- +grees (see Supplementary Information Sec. B 3). Exam- +ples include English suites, French suites, and chorales. +In contrast, fugues did not cluster together in their en- +tropy as much as other composition types and displayed +diverse average degrees. For the compositions that are +grouped together in their entropy, we find that the dif- +ferences observed among the pieces in the group can be +explained by their degree heterogeneity (see Supplemen- +tary Information Sec. B 4). We can, for example, see +this relation in the chorales where the pieces which have +a higher in- and out-degree heterogeneity tend to have a +higher entropy, despite having similar degrees (Fig. 2C). +We note that this relationship between the entropy and +degree heterogeneity holds even in our data set of di- +rected networks, likely because the in- and out-degrees +tend to be correlated. +IV. +HOW HUMANS PERCEIVE NETWORKS +OF INFORMATION +Communication systems, such as music or language, +convey information in sequences of discrete items. Hu- +mans then assimilate this information and build repre- +sentations of the underlying structure of inter-item rela- +tionships. The information that is perceived by a human +is the sum of the information present in the system and +Internal Estimates +0 +η +0 +1 +1/4 +Learned probability +Maximal accuracy +Minimal accuracy +Maximal complexity +Minimal complexity +Trade-off between accuracy and computational cost +Balanced between accuracy +and complexity +(i) +(ii) +(iii) +FIG. 3. How humans process networks of information. +Humans strike a balance between accuracy and complexity +when forming internal network models of the world. The pa- +rameter η quantifies this trade-off between accuracy and cost. +In panel (i), we see the example network built when solely +maximizing the accuracy (η → 0), which forms a perfect rep- +resentation of reality. However, building this network requires +perfect memory and is computationally expensive. In panel +(iii), we see the network built when solely minimizing the +computational cost (η → 1), in which all nodes are connected +to all other nodes, unlike the original network. Constructing +this network does not require significant cost, but it provides +no accuracy in representing the original information. +Hu- +mans tend to display intermediate values of η = 0.80 [31], +thereby constructing networks that preserve some but not all +of the true transition structure, as shown in panel (ii). Figure +adapted with permission from Ref. [32]. +the inaccuracies that stem from the imperfect cognitive +processes involved in perception [31]. In the previous sec- +tion, we focused on quantifying the actual information +present in the system (see Fig. 1B). We will now account +for the second piece: the inaccuracies that arise due to +the imperfect cognitive process of perceiving information +(see Fig. 1C). +When forming an internal network representation of +the information presented to them, humans seek to max- +imize the accuracy of their internal representation while +simultaneously minimizing the computational cost in- +volved in building it [30–32, 39]. One the one hand, a +human could learn the structure with no errors, forming +a perfectly accurate network of the transitions (Fig. 3(i)) +but that formation process would be computationally ex- +pensive. On the other hand, one could disregard accuracy +and have the least expensive representation (Fig. 3(iii)). +Most humans do something in between by recalling the +sequence of transitions sometimes accurately and some- +times inaccurately, thereby forming a fuzzy perception +of the true network (Fig. 3(ii)). Formally, the competi- +tion between computational complexity and accuracy can +be captured by a free energy model of people’s internal +representation [30]. The learned transition probabilities + +6 +under this model can be written as follows: +ˆP = (1 − η)P(I − ηP)−1, +(6) +where η ∈ [0, 1] captures the errors in representation. +Using this model, we can compute the learned network +for each musical piece. +Prior work indicates that, on +average, humans display an η = 0.80 in large-scale online +laboratory experiments [31]. +Given a network of note +transitions with transition probabilities P, we use this +empirically measured value of η = 0.8 to calculate the +average network that a human infers ˆP using Eq. 6. +V. +QUANTIFYING THE LEARNABILITY OF +NOTE TRANSITIONS +We are now prepared to investigate how a given music +network differs from the internal representation formed +by a human listener. +The closer the learned network +is to the original network, the more resilient the network +structure is to human errors in learning, and the network +is said to be more learnable. Mathematically, one can +quantify the deviations between the inferred network ( ˆP) +and the original network (P) using the Kullback-Leiber +(KL) divergence: +DKL(P|| ˆP) = − +� +i +πi +� +j +Pij log +ˆPij +Pij +, +(7) +where πi is the stationary distribution of the original +network. +The lower the KL-divergence, the closer the +learned transition structure is to the original transition +structure, and hence the more learnable the network. +Do Bach’s musical compositions possess distinct features +that facilitate human learning? How do pieces differ in +their learnability? +What are the structural differences +between the musical pieces that lead to such differences? +To answer these questions, for each musical piece, we +compute the KL-divergence between the true transition +probabilities P and the learned transition probabilities +ˆP. Then, to understand whether Bach’s music networks +are structured in a manner that improves their learnabil- +ity, we compare them against random networks with the +same number of nodes and edges. +The data confirms +our intuition (Fig. 4A): Bach’s music networks have a +lower KL-divergence than random networks of the same +size. Even if we compare against null networks with the +same in- and out-degree distributions, we still see that +Bach’s music networks have a lower KL-divergence (Fig. +4B). This finding suggests that the lower KL-divergence +of these networks cannot be explained by their degree +distributions alone. Additionally, we observe variations +in the KL-divergence among the different compositions +(Fig. 4). The chorales, at one extreme, seem to have the +highest KL-divergence, while the preludes have the lowest +KL-divergence. Our findings indicate that the note tran- +sitions in Bach’s music are structured in a manner that is +resilient to errors that humans make when learning infor- +mation. Further, learnability differs across composition +forms, with some being easier to learn than others. +A. +Transitive clustering +In the previous section, we saw that the differences +between the KL-divergences of the music networks and +the null networks could not be explained by the distri- +butions of degrees. Here, we seek to understand what +network property leads to the observed differences. Pre- +vious work has shown that in the case of undirected net- +works, the KL-divergence decreases with the density of +triangles in the network [31]. One can show this ana- +lytically by substituting the expression for the averaged +learned version of a network (Eq. 6) into the equation +for the KL-divergence (Eq. 7). This substitution gives +us an expression for the KL-divergence in terms of the +adjacency matrix of the original network: +DKL(P|| ˆP) = − log(1 − η) − +η +ln 2 +� +i +πi× +� +� +� +� +j +Aij +� +l +1 +kout +i +Ail +1 +kout +l +Alj +� +� +� + O(η2). +(8) +Here we see that the KL-divergence depends on a prod- +uct of the form AijAilAlj, which measures the transitive +relationships present in the network. More explicitly, it +depends on the number of directed triangles of the form +i → j → k and i → k. Musically, the presence of a larger +density of such triangles suggests that if there is a tran- +sition between notes i and j, and notes i and k, there is +likely also a transition between notes j and k. +To quantify the extent to which a network has clusters +of this form, we calculate the transitive clustering coef- +ficient of the network. For each node, this quantity is +measured by dividing the number of transitive triangles +that node i is a part of (∆T +i ) by the number of possible +directed triangles: +CT +i = +∆T +i +ktot +i +(ktot +i +− 1). +(9) +Here ktot +i +is the total degree (in + out) of the node. We +average this quantity over all nodes in the network to re- +port a single value for each piece. Eq. 8 indicates that the +KL-divergence will be smaller for networks with a large +number of transitive triangles. This intuition arises from +the fact that humans can easily make swap errors among +transitive relations. If node i is connected to node j and +node j links to node k, a human learner may erroneously +draw an edge between node i and node k. However, if +the network had an edge connecting node i to node k to +begin with, such an edge would not be an error. Hence, +we expect networks that have more transitive relations +to be more robust to errors made in learning. Indeed, we + +7 +B +D +C +A +FIG. 4. Quantifying the difference between the actual information and the perceived information in Bach’s +music networks by calculating the KL-divergence between the actual and perceived network. (A) KL-divergence +of the real music networks (Dreal +KL ) compared with random networks of the same size (Drand +KL ). We report the KL-divergence +of the corresponding random networks after averaging over 100 independent realizations. The error bars for Drand +KL +indicate +the standard error of the sample. (B) KL-divergence of the real music networks (Dreal +KL ) compared with random networks that +preserve the in- and out-degree of each node (Ddeg +KL ). We report the KL-divergence of the corresponding degree-preserving +random networks after averaging over 100 independent realizations. The error bars for Ddeg +KL indicate the standard error of +the sample. (C) KL-divergence of the real music networks as a function of the transitive clustering coefficient of the network +C = ⟨∆T +i /ktot +i +(ktot +i +− 1)⟩. (D) The transitive clustering coefficient of the real music networks compared with random networks +that preserve the in- and out-degree of each node. The dotted line indicates the line y = x. For the degree-preserving random +networks, we report the transitive clustering coefficient after averaging over 100 independent realizations, with error bars +denoting the standard error of the sample. In all the panels, each data point represents a single piece. Color and marker +indicate the type of piece, as shown in the legend. The dotted line in panels (A), (B), and (D) represents the line y = x. +observe that the KL-divergence of the music networks is +lower for networks that have a higher transitive cluster- +ing coefficient (Fig. +4C). +In fact, the real music net- +works have a higher transitive clustering coefficient than +degree-preserving random networks (Fig. 4D), suggest- +ing that this feature is not due to mere coincidence. From +Fig 4D, we make an interesting observation: the chorale +pieces generally have a higher transitive clustering coef- +ficient than expected from null networks that preserve +their size and degree distribution, while the preludes ap- +pear to have a lower transitive clustering coefficient than +the corresponding null networks. We probe this further +in the Supporting Information and identify meso-scale +structures that could lead to the observed differences be- +tween the compositional forms. +VI. +ACCOUNTING FOR NOTE TRANSITION +FREQUENCIES +So far, we have focused our attention on the infor- +mation content and perception of unweighted (or bi- +nary) note transition networks created from Bach’s mu- +sic. These networks only captured whether or not a tran- +sition exists between two notes and were not sensitive to +how frequently each transition occurs. The binary net- +works enabled us to probe how the structure of the tran- + +8 +A +B +C +FIG. 5. Accounting for the frequencies of the note transitions in our analysis. (A) Entropy of the weighted versions of +Bach’s music networks (Sweighted) compared with the corresponding unweighted versions (Sunweighted). (B) The KL-divergence +of the weighted versions of Bach’s music networks (Dreal,w +KL +) compared with the corresponding unweighted versions (Dreal +KL ). (C) +Top: Entropy of the weighted note transition networks (Sreal,w) compared with degree-preserving edge-rewired null networks +(Sdeg, w). Bottom: The KL-divergence of the weighted note transition networks (Dreal,w +KL +) compared with degree-preserving +edge-rewired null networks (Ddeg, w +KL +). In all panels, each data point represents a single piece. Color and marker indicate the +type of piece, as shown in the legend. The dashed line represents the line y = x. +sitions supports effective communication. +However, in +many real networks, not all transitions occur with the +same frequency. To reflect the different frequencies with +which transitions may occur, we construct networks in +which transitions are weighted according to this. For ex- +ample, if note i follows note j 90% of the time and note +k follows note j 10% of the time, the edge from node j to +node i will be more heavily weighted than the edge from +node j to node k (see the Materials and Methods section +A 1 for further details on network construction). Adding +this piece of information to the networks leads us to new +questions about the role that transition weights play in +communicating information to listeners. +For example, +how is the information generated by a random walk on +the network altered by differences in the frequencies of +transitions? In Bach’s music, do these differences in fre- +quencies make it easier for humans to learn the transition +networks? +A. +Weights reduce the surprisal of transitions +For unweighted networks, the node-level entropy of +a random walk is determined solely by the out-degree +(kout +i +), since each outgoing edge is traversed with prob- +ability Pij = 1/kout +i +. If the edges are weighted by their +transition frequencies, the Pij’s will no longer be uni- +formly distributed, and each outgoing edge will not have +an equal probability of being traversed. Hence, incorpo- +rating the edge weights reduces the node-level entropy. +This observation is intuitive since non-uniformities in any +distribution lead to decreases in entropy. However, ex- +tending this intuition to the entropy produced by the +entire network is not as straightforward, since one must +weigh the contribution of each node by the stationary +distribution of the random walkers, which cannot be ex- +pressed in closed form for directed networks. Generally, +we find that the entropy of weighted networks is still +lower than the corresponding unweighted networks (Fig. +5A). This finding suggests that the different weights re- +duce the overall surprisal generated by the networks. +B. +Weights reduce the deviations between the +learned network and the original network +Incorporating the transition frequencies also helps us +to understand the role that the weights play in the hu- +man inference of note transitions. We observe that the +weighted networks of note transitions have lower KL- +divergence than the binary networks (Fig. 5B). This ob- +servation suggests that the weights aid in forming more +accurate internal representations of the transition struc- +tures, thereby improving their learnability. +In light of these data, we next verify the role that the +network structure plays in the communicative success of +weighted networks by comparing the entropy and KL- +divergence of the weighted music networks with edge- +rewired null networks. +In the analysis on unweighted +networks, we observed that the entropy was primarily +driven by the degree distribution of the network and not +sensitive to the precise connectivity pattern. To make +this observation, we had compared the entropy of the +real music networks to randomized networks that pre- + +9 +served the exact degree distribution of each node and +hence, held the node-level entropies fixed. Along simi- +lar lines, here we make use of null models that keep the +node-level entropies fixed by preserving the in- and out- +degree of each node and the out-weights at each node +(see the Materials and Methods section for details on the +null models). By comparing the entropy of the weighted +music networks to the degree-preserving weighted null +models, we see that the entropies of real networks are +still more or less unchanged, although the real networks +have marginally higher entropies than the null networks +(Fig. +5C, top). +These results support our conclusion +that the entropy in the real networks is still primarily +driven by their degree distribution. When we compare +the KL-divergence of the real weighted networks with the +degree-preserving weighted null models, we find that the +real networks have a lower KL-divergence than the cor- +responding null networks (Fig. 5C, bottom). Together, +these results suggest that incorporating the weights into +our network analysis does not alter the effects of network +structure qualitatively. +Accounting for the note transition frequencies in our +network model leads to several interesting lines of inquiry. +For instance, is it the specific distribution of weights +that improves the learnability of music networks? Fu- +ture work could evaluate this possibility by comparing +the KL-divergence of the weighted networks with a class +of null models that preserve the skeleton of the network, +but permute the edge weights. It would also be interest- +ing to test whether higher edge weights are concentrated +in triangular clusters of the network, offering a potential +explanation for the lower KL-divergence of the weighted +networks compared to the binary networks. +VII. +DISCUSSION +In this article, we study music composed by J. S. Bach +through the lens of network science and information the- +ory. Viewing Bach’s musical compositions as networks of +note transitions, we quantify the information generated +by the note transitions and study how this information is +perceived by humans. We analyzed a total of 327 Bach +compositions spread over a wide range of compositional +forms, including preludes, fugues, inventions, cantatas, +English suites, French suites, chorales, Brandenburg con- +certos, toccatas, and concertos. For each musical piece, +we construct a network of note transitions by drawing di- +rected edges between notes that are played consecutively. +We then quantify the amount of information generated +by the network structure and find that different composi- +tional forms are grouped together based on their entropy. +Further, we find that the note transitions in Bach’s music +contain more information than expected from transition +structures of their size, which can be attributed to higher +heterogeneity in their degree distribution. +To quantify how the transition structure of Bach’s mu- +sic is perceived by a human, we use a mathematical model +for how humans infer networks of information [30, 31], +which allows us to estimate the average “learned” net- +work given any network of information. Using this model, +we compute the inferred version for each music network, +and quantify the information that arises due to discrep- +ancies between the original and inferred networks. We +find here that the discrepancies differ among the compo- +sitional forms. Moreover, Bach’s music networks main- +tain a consistently lower deviation between the original +and inferred version compared to randomized null net- +works of the same size and degree distribution. Probing +the structural features that enable these music networks +to be more resilient to biases in perception, we find that +this property is driven by a high density of transitive +triangular clusters in the network. +Finally, we study how the frequencies of transitions +influence the information content and perception of the +musical pieces, by weighing the transitions by the number +of times they occur. We find that the weights reduce the +overall entropy or surprisal of the transitions, and also +reduce the deviations between the inferred and actual +network, suggesting that the weights aid the learnability +of these transition structures. On comparing the infor- +mation content and learnability of the weighted networks +with degree-preserving null models, we find that qualita- +tively, our results relating the information content and +learnability to the network structure are still valid for +the weighted networks. +More generally, our findings here along with the re- +sults in Ref. [31] provide insight into features that make +a wide range of complex systems around us effective at +communicating information. To communicate informa- +tion successfully, networks of information in complex sys- +tems tend to be structured in a manner that allows them +to carry large amounts of information, while also being +robust to inaccuracies that humans make when infer- +ring relationships between items. +Networks which are +denser (have a higher average degree) produce more un- +predictable random walk sequences, and hence produce +more information (have a higher entropy). Further, for +networks of comparable average degree, more heteroge- +neous (higher variance in degree distribution) structures +produce more information than those more regular or ho- +mogeneous in their degree (Fig. 6A(i)). Additionally, we +find that networks which contain a large number of tri- +angular clusters can be inferred more accurately when +viewed through an observer’s imperfect cognitive appa- +ratus (Fig. 6A(ii)). Together, these findings suggest that +for networks of a given size, rapid and accurate commu- +nication of information is supported by structures that +are simultaneously heterogeneous and clustered (Fig. 6). +Future directions +Our study has focused on analyzing the note transi- +tions present in Bach’s music. It is important to note that +music is a multifaceted art form that encompasses a range +of structural and expressive elements. Future work could + +10 +Supports efficient communication +1 +Low KL-divergence +Easy to learn +High KL-divergence +Hard to learn +High Entropy +Contains more information +Low Entropy +Contains lesser information +Does not support effective communication +A. +B. +i. +ii. +i. +ii. +FIG. 6. +Network structures that support effective communication of information. +(A) Networks with a larger +variance or heterogeneity in their node degrees, as shown in panel (i), pack more information into their structure and have a +higher entropy. Clustering in the network, as shown in panel (ii), makes the structure more resilient to errors made by humans +when building an internal representation of the information, allowing the network to be inferred more accurately. Together, +these structures convey a large amount of information that can be learned by humans more accurately, and are hence more +efficient for communication. (B) Networks with lower variance in their node degrees, as shown in panel (i), carry relatively +lower information in their structure compared to networks that are of similar size but more heterogeneous in their degrees. A +lower tendency for nodes to form clusters, as shown in panel (ii), makes the network more susceptible to errors when humans +infer its transition structure. Together, these structures convey information less efficiently, rapidly, and accurately compared +to those shown in panel (A). +build upon our study by exploring other aspects of music, +for example, considering networks of transitions between +rhythms or harmonies. +Beyond music, our study can +also be extended to a range of complex systems present +around us—such as language and social networks. For +example, one could analyze works of literature and ask: +Does the entropy of noun transitions in various works of +Shakespeare differ based on their genre? +More specif- +ically, does the information content and learnability of +noun transitions or relationships between characters dif- +fer between tragedies and comedies? +By providing an +example of a systematic and comprehensive analysis of +the actual and perceived information in music, our study +complements and adds to the rich study of language, mu- +sic, and art as complex systems [25, 40, 41]. +Systematically analyzing the information that we ex- +tract from complex systems can provide new insights into +the human experience. A question that often arises in +the context of how humans experience music is: What +makes a musical composition appealing to the human +ear? +While individual preferences in music can vary +widely and is highly subjectively, there is still a gen- +eral agreement on certain composers being considered +“influential” or “great”. +This fact raises the possibil- +ity that there may be some inherent qualities that are +common to musical pieces which are widely considered +appealing. +Identifying such features might give us in- +sight into the creative process of composing music and +also complement existing work using AI to generate mu- +sic [42, 43]. Several attempts have been made to identify +such patterns. For example, Ref. [24] analyzed note tran- +sition networks in certain compositions by Bach, Chopin, +and Mozart as well as Chinese pop music, and sug- +gested that “good” music is characterized by the small- +world property [44] and heavy-tailed degree distributions. +On the other hand, Ref. [25] studied selected composi- +tions from Bach’s Well-Tempered Clavier and found non- +heavy-tailed degree distributions, suggesting that such +distributions are not necessary for music to be appeal- +ing. It would be interesting to devise future experiments +to determine whether our findings relate to the aesthetic +or emotional appeal of a piece. In our study, we found +that Bach’s music networks had a higher number of tran- +sitive triangular clusters, enabling them to be learned +more efficiently than arbitrary transition structures. Are +pieces with a larger number of these triangles also more +appealing to a listener? Future work assess this possi- +bility by conducting experiments that ask people to rate +Bach’s compositions and analyzing whether these ratings +correlate with the presence of triangular clusters. More +generally, our work focuses not solely on the informa- +tion inherent in the transition structure of music, but +also on how the information in this transition structure +is perceived by a human listener. This framework might +be useful in studying cognitive aspects of music and in +bridging patterns observed in data with cognitive theo- +ries of music. +In future work, it would be interesting to extend our +analysis to study how music networks evolve with time. +There are three potentially interesting lines of inquiry +here: First, how do the entropy and KL-divergence of +a musical piece change as the piece progresses? +Does + +11 +this temporal change differ among the various compo- +sitional forms? +Second, how has the music of a spe- +cific composer (whether Bach or otherwise) changed over +the course of their lifetime? Has it become more intri- +cate and complex, holding more information? Perhaps as +the composer gains experience, their compositions con- +vey information more efficiently and accurately, as re- +flected in a reduced KL-divergence? If the exact dates +of when each piece was composed were known, then the +framework used in our paper might provide answers to +these questions. Third, how has music of a given genre, +say classical music, changed over the years across com- +posers? Ref. [27], for example, studied the fluctuation in +pitch between adjacent notes in compositions by Bach, +Mozart, Beethoven, Mendelsohn, and Chopin, and found +that the largest pitch fluctuations of a composer gradu- +ally increased over time from Bach to Chopin. It would +be interesting to expand our analysis to different com- +posers, and see how the information and expectations +vary across composers and time. +Further considering how a genre changes with time, it +would be of interest to assess how various styles or gen- +res of music differ [45–47]. What are the key features by +which a listener distinguishes between music from two +eras, say the Classical and the Romantic eras? How do +the differences in structure then impact how the piece is +perceived by a listener? An analysis of the information +content and perception of various genres of music could +complement existing work in musicology, and potentially +aid in systematically classifying pieces into genres that +may not be a priori obvious. Classifying genres of music +could also be beneficial for audio streaming services, and +our framework could potentially complement existing ap- +proaches to musical genre classification [46, 48–51]. +Methodological considerations +Here we highlight the assumptions made in our study +and the resulting methodological constraints in our re- +search. +First, in constructing networks of note transi- +tions, the self loops present in the networks were ignored +to simplify our analysis. This choice restricted us to un- +derstanding only the structure of transitions between dif- +ferent notes in a musical piece. However, these self loops +may have interesting effects on the discrepancies between +the actual and perceived information content from the +network. Future work could include self loops, studying +their impact on the information content and learnability +of the network. Second, the production of information +from the underlying transition structure has been mod- +elled using Markov random walks. While this is a stan- +dard first step in understanding complex systems, in re- +ality, the transitions present in music possess long range +correlations and constraints to their structure. Including +these correlations (perhaps in the form of a biased ran- +dom walk with memory) would be a fruitful direction to +pursue to gain a better and more realistic understand- +ing of the information we encounter from real complex +systems around us. +VIII. +CONCLUSION +In this work, we analyze Bach’s musical compositions +as networks of note transitions conveying information to +humans. Recent studies have shown that the information +humans perceive from complex systems around them con- +sists of two parts: the information inherent in the system +and the information arising due to errors in their per- +ception [30, 31]. Analyzing the information from these +two parts, we find that different compositional forms can +be distinguished from one another. +Further, we gain +insight into structural features that enable these music +networks to communicate effectively: they communicate +more information by having more heterogeneous degrees, +and they convey information more accurately (minimiz- +ing the discrepancies with human inferences) by having +a higher density of transitive clusters (Fig. 6). Through +this quantitative analysis of Bach’s music, our findings +provide new methods to understand how humans share +and experience information around them. +ACKNOWLEDGMENTS +We thank Chris Macklin for an early conversation on +this topic and audience members who have asked prob- +ing questions about our earlier work in communication +networks. +These interactions motivated our continued +investigation in this space. +This particular research +was primarily supported by the Army Research Office +award number DCIST-W911NF-17-2-0181 and the Na- +tional Institutes of Mental Health award number 1-R21- +MH-124121-01. +D.S.B. would also like to acknowledge +additional support from the John D. and Catherine T. +MacArthur Foundation, the Alfred P. Sloan Foundation, +the Institute for Scientific Interchange Foundation, and +the Army Research Office (Grafton-W911NF-16-1-0474). +The content is solely the responsibility of the authors and +does not necessarily represent the official views of any of +the funding agencies. +CITATION DIVERSITY STATEMENT +Recent work in several fields of science has identi- +fied a bias in citation practices such that papers from +women and other minority scholars are under-cited rel- +ative to the number of such papers in the field [52–60]. +Here we sought to proactively consider choosing refer- +ences that reflect the diversity of the field in thought, +form of contribution, gender, race, ethnicity, and other +factors. First, we obtained the predicted gender of the +first and last author of each reference by using databases +that store the probability of a first name being carried by + +12 +a woman [56, 61]. By this measure (and excluding self- +citations to the first and last authors of our current pa- +per), our references contain 9.37% woman (first)/woman +(last), 18.67% man/woman, 19.29% woman/man, and +52.67% man/man. +This method is limited in that a) +names, pronouns, and social media profiles used to con- +struct the databases may not, in every case, be indica- +tive of gender identity and b) it cannot account for in- +tersex, non-binary, or transgender people. +Second, we +obtained predicted racial/ethnic category of the first and +last author of each reference by databases that store the +probability of a first and last name being carried by +an author of color [62, 63]. +By this measure (and ex- +cluding self-citations), our references contain 11.79% au- +thor of color (first)/author of color (last), 11.60% white +author/author of color, 16.05% author of color/white +author, and 60.56% white author/white author. +This +method is limited in that a) names and Florida Voter +Data to make the predictions may not be indicative of +racial/ethnic identity, and b) it cannot account for In- +digenous and mixed-race authors, or those who may face +differential biases due to the ambiguous racialization or +ethnicization of their names. We look forward to future +work that could help us to better understand how to sup- +port equitable practices in science. +Appendix A: Materials and Methods +1. +Data Collection and Network Construction +The music files were collected in the MIDI for- +mat from various sources. +The sources for the com- +positions analyzed are as follows: +preludes [64, 65], +fugues [64, 65], inventions[64, 65], cantatas[66], English +suites[67], French suites[67], chorales[65], Brandenburg +concertos[65], toccatas[67], and concertos[67]. The pre- +ludes and fugues are split based on whether they belong +to the first or second part of The Well-Tempered Clavier, +and are labelled ‘1’ or ‘2’. Certain compositions consist of +different movements and our data set has separate MIDI +files for each movement. We analyze each movement sep- +arately and average our measurements over them to yield +a single measured quantity for each piece, as indexed by +a unique BWV number. +The MIDI files were read in MATLAB using the +readmidi function in MATLAB [68] to obtain informa- +tion about the notes being played. Different instruments +in a piece are stored in separate channels within each +data file. The transitions between notes are calculated +separately for each instrument or track. We assign each +note present in a piece a node in the network, and notes +from different octaves are assigned distinct nodes. We +then draw an edge from note i to note j if there is a +transition between them. If there are multiple notes be- +ing played at a single time t (as is the case with chords), +edges are drawn from the previously played note to all +notes at time t, and from all the notes being played at +time t to the subsequent note(s). This procedure gives +us a directed binary network of note transitions. We also +construct weighted versions of these networks, where each +edge is weighted by the number of times the correspond- +ing transition occurs. +2. +Entropy of random walks on networks +We use random walks to model how a sequence of in- +formation is generated from an underlying network of +information. Under this model, a walker traverses the +network by picking an outgoing edge to traverse at each +node. Given a network with adjacency matrix A and ma- +trix element Aij, the probability that a walker transitions +from node i to node j in a standard Markov random walk +is Pij = Aij/kout +i +, where kout +i += � +j Gij is the out-degree +of a node. We are interested in quantifying how much +information is contained in the resulting sequence, which +is captured by the entropy of the random walk: +S = − +� +i +πi +� +j +Pij log Pij, +where π is the stationary distribution of the walkers, +which satisfies the condition Pπ = π. For the simplest +possible case of an undirected and unweighted network, +Pij = 1/ki and πi = ki/2E, where ki is the degree of +the ith node and E = � +i,j Aij/2 is the total number of +edges. The entropy in this case simplifies to: +S = 1 +2E +� +i +ki log ki = ⟨k log k⟩ +⟨k⟩ +. +(A1) +We can apply a Taylor expansion to this expression +around the average degree of the network, and thereby +obtain: +S = log⟨k⟩ + Var(k) +2 ⟨k⟩2 + ... +(A2) +Hence we find that the entropy of random walks increase +logarithmically with the average degree of the network. +Additionally, it grows as the variance of the degrees in- +creases. This formalization enables us to relate the in- +formation content of various music networks to their net- +work structure. +3. +Model for how humans learn networks +As discussed in the main text, when forming internal +representations of information around them, each human +arbitrates a trade-off between accuracy and cost [30, 31]. +In striking this balance, evidence suggests that humans +perform a fuzzy temporal integration of transition struc- +tures over time [29, 30, 69–71]. This process results in +humans connecting items in the sequence that are not +directly adjacent to each other. Mathematically, we can + +13 +express the inferred transition structure ˆP in terms of +the true transition structure P under this model of fuzzy +temporal integration as: +ˆP = +∞ +� +∆t=0 +f(∆t)P ∆t+1, +(A3) +where f(∆t) is the weight given to the higher powers of +P and is a decreasing function of ∆t. +The functional form of f(∆t) is obtained using a +free energy model that captures the accuracy-complexity +trade-off described in Ref. [30]. Under this theory, the +optimal distribution for f(∆t) is a Boltzmann distribu- +tion with a parameter β that quantifies the trade-off be- +tween cost and accuracy in forming an internal represen- +tation of the information: +f(∆t) = e−β∆t/Z, +(A4) +where Z = � e−β∆t = (1 − e−β)−1 is a normalization +constant. +Substituting this expression to simplify Eq. +A3, we obtain an equation that relates the inferred tran- +sition probabilities ˆP to the true transition probabilities +P: +ˆP =(1 − e−β)−1 +∞ +� +∆t=0 +e−β∆tP ∆t+1 +=(1 − η)P(I − ηP)−1, +(A5) +where η = e−β. Prior work has estimated the value of +η to be 0.8 from large-scale online experiments in hu- +mans [31]. Using this measured value of η, we use Eq. +A5 to calculate the learned network for any given music +network. +4. +KL-divergence +To quantify how much the distorted learned transition +structure ˆP differs from the original transition structure +P, we calculate the Kullback-Leiber (KL) divergence be- +tween the two transition structures. The Kullback-Leiber +divergence is a measure of how different a probability dis- +tribution is from a reference distribution, and is given by: +DKL(P|| ˆP) = − +� +i +πi +� +j +Pij log +ˆPij +Pij +, +(A6) +where ⃗π is the stationary probability distribution of the +transition matrix P, obtained by solving Pπ = π. The +KL-divergence between two quantities is always non- +negative and attains the value zero if and only if P = ˆP. +The larger the KL-divergence, the more the inferred net- +work ˆP differs from the original network. +Hence, this +quantity acts as a measure of the extent to which a net- +work gets scrambled by the inaccuracies of human of +learning—or in other words, how learnable a network +structure is. +5. +Null Models +We aim to identify distinct features in the music net- +works that enable them to convey information effectively. +To assess whether our observations are merely due to ran- +dom chance or are instead a unique feature of our dataset, +we compare our measurements on the real music networks +with the following null network models [72, 73]. +1. Null networks with the same number of nodes and +edges. These are obtained by generating random +networks with the same number of nodes and edges, +and enable us to assess whether the quantity we +have measured is to be expected merely based on +network size. +2. Degree-preserving null networks. +These are ran- +domized networks of the same size, with the ad- +ditional constraint that the in- and out-degrees of +each node in the network are preserved. Such net- +works are constructed by swapping edges between +pairs of nodes in the network iteratively, such that +the in- and out-degrees of each node are preserved +but the connectivity (or topology) of the network +is randomized. This class of null models enable us +to evaluate the role that connectivity or topology +plays in the quantity we are measuring. +We can generalize the degree-preserving null networks +to weighted networks. +We are interested in degree- +preserving randomized networks since these keep the +node-level entropies fixed and allow us to study the im- +pact of topology on the quantities we are measuring. In +the case of weighted networks, the node-level entropies +are determined by the out-weights and out-degrees of the +nodes. Hence, our procedure of swapping edges between +pairs of nodes in the network still works since it pre- +served the out-weights of each node in addition to the in- +and out-degrees. With these null models, we can bench- +mark the presence of the quantities we are interested in, +and identify the role that the connectivity pattern or size +plays. +6. +Transitive Clustering Coefficient +Along the lines of the clustering coefficient of a node +[44, 74], we define the transitive clustering coefficient as +a measure of the degree to which nodes in a directed net- +work tend to form transitive relationships. The transitive +clustering coefficient of a node i (for an unweighted graph +with no self loops) is given by: +CT +i = +∆T +i +ktot +i +(ktot +i +− 1), +(A7) +where ∆T +i denotes the number of transitive triangles that +node i is a part of and ktot +i +is the total degree (in + out) +of the node. The denominator simply counts the number + +14 +of triangles that could exist within the neighborhood of +node i. +FIG. 7. The 8 different possible triangles with node i as a +vertex in a directed graph. +The triangles which represent +transitive relationships are marked using the letter ’T’. +The possible directed triangles involving node i can +be divided into two categories—those representing cyclic +relationships and those representing transitive relation- +ships (Fig. 7). The number of transitive triangles involv- +ing node i that actually exist can be expressed in terms +of the adjacency matrix of the graph A, +CT +i = (A + AT )3 +ii − A3 +ii − (AT )3 +ii +2 ktot +i +(ktot +i +− 1) +. +(A8) +This expression counts a subset of the total number of +triangles, and is a special case of the expression derived +in Ref. [75]. We will use this expression to measure the +transitive clustering coefficient of each music networks. +Appendix B: Supplementary Information +1. +Introduction +In this Supplementary Information, we provide ex- +tended analysis and discussion to support the results pre- +sented in the main text. In Sec. B 2, we expand upon +our analysis of the information content of Bach’s music +networks and how it relates to network structure. In Sec. +B 5, we examine the transitive clustering coefficient more +closely and study meso-scale features that might explain +the differences observed across compositional forms. +2. +Information content +To better visualize the variation in information content +among the musical compositions, we assign each piece +an index number and plot the information entropy for +each piece as a function of its index number (Fig. 8A). +We observe here more clearly how different compositional +forms tend to have pieces clustered together in their en- +tropies. As reported in the main text, we find that the +chorales have a markedly lower entropy than the rest +of the compositions studied. +In contrast, the toccatas +and the second set of preludes have a much higher en- +tropy. +To relate the information entropy of the music +networks to their structure, we compare their entropy to +corresponding null networks (Fig. 2A and B in the main +text), where we conclude that the information entropy is +primarily determined by the degree distributions. In the +case of undirected and unweighted networks, the network +entropy depends upon the logarithm of the average de- +gree of the network and the heterogeneity in the degree +distribution (Eq. +4) to first and second order, respec- +tively [31, 35]. We now provide supplementary results +that relate the information entropy of the music networks +to their structure. +3. +Understanding the information entropy to first +order: average degree +On plotting the information entropy of the music net- +works as a function of their average degree (Fig. 8B), we +see that the differences in the information entropy of the +compositional forms to first order arise due to differences +in their average degrees. Although we observed in Fig. +8A that the compositional forms are clustered together +in their entropy, it is clear that some pieces—such as the +chorales, French suites, English suites, and cantatas— +are more tightly clustered than the fugues and first set of +preludes. These differences can be explained by the how +much the average degrees vary across pieces. In Fig. 9, +we plot the entropy of the music networks as a function +of the average network degree, separately for each com- +position type. Additionally, we also report the standard +deviation in the average degree of the pieces for each com- +position type. Studying these plots, we observe that the +English suites, French suites, and chorales (which clus- +tered more tightly in their entropies) have tighter degree +distributions, while the fugues (which are more spread +out in their entropy) display more diverse average de- +grees. +4. +Understanding the information entropy to +second order: degree heterogeneity +In Fig. +2A of the main text, we observed that the +entropy of the real music networks is larger than corre- +sponding randomized null networks with the same num- +ber of nodes and edges. Since the average degree is the +same for the two networks, we hypothesize that the differ- +ences arise due to higher in- and out-degree heterogene- +ity as per Eq. 4. To test our hypothesis, we compare the +in- and out-degree heterogeneity of the music networks +(calculated using Eq. 5) with their corresponding null +networks in Fig. 10. In general, we observe that Bach’s +music networks are indeed more heterogeneous than ex- +pected from the random networks of the same size. This +organization allows them to pack more information into +their structure. +The heterogeneity in degrees can also explain the dif- +ferences in entropies observed between pieces that are + +1 +2 +0 +2 +215 +A +B +FIG. 8. The entropy of Bach’s music networks and its relation to the average degree of the network. (A) The +entropy of Bach’s music networks (Sreal) indexed by the pieces. (B) The entropy of Bach’s music networks (Sreal) as a function +of the average degree of the network ⟨k⟩. Each data point in panels (A) and (B) represents a single piece. Colors and markers +indicate the type of pieces, as shown in the legend. +tightly clustered together in their entropy. As observed +earlier, compositions such as the chorales, French suites, +English suites, and cantatas have pieces that are clus- +tered together in their average degree and consequen- +tially, in their entropy. We expect that the differences +observed among the pieces in each group can be explained +by differences in their degree heterogeneity. In Fig. 11 +and Fig. 2C, we plot the entropies of the pieces that clus- +tered together as a function of their in- and out-degree +heterogeneity, and in general observe that the pieces with +higher heterogeneity have a higher information entropy. +However, we note that our sample size for most com- +positional forms is small and hence, we only report the +chorales in the main text. +5. +Further analysis of the transitive clustering +coefficient +In our analysis of the discrepancies between the ac- +tual and perceived information content of note transi- +tions in Bach’s musical compositions, we found that these +discrepancies were primarily driven by the presence of +transitive triangular clusters. These transitive triangular +clusters tend to bring the inferred network closer to the +actual network, making the network more learnable. As +shown in Fig. 12A, the real (unweighted) music networks +tend to have a higher transitive clustering coefficient than +random networks that preserve the degree of each node, +indicating that this is a distinct feature of the music net- +works that is not merely due to coincidence. The data +in Fig. 12A has a striking shape, which we elaborate on +and analyze in this section. First we observe that the +chorale pieces tend to have a higher transitive clustering +coefficient than expected from networks of their same +size and degree distribution. Second, although the pre- +ludes have a higher transitive clustering coefficient than +other compositional forms, the value was still lower than +expected from networks of their same size and degree +distribution. Indeed, by examining only the x-axis, we +notice that the null networks corresponding to the pre- +ludes have a higher transitive clustering coefficient than +the null networks corresponding to chorales. However, +by examining the y-axis, we see that the deviation be- +tween the real chorales and the prelude networks are not +that pronounced. We hypothesize that these differences +might be due to the presence of mesoscale features in the +networks, such as core-periphery structure. +a. +Core-periphery structure +Core-periphery structure in a network refers to the +presence of two components: a tightly connected “core” +and a sparsely connected “periphery. The core consists of +nodes which are well-connected to each other and to the +periphery, while the nodes in the periphery are sparsely +connected to one another and to the nodes in the core +[76, 77]. We hypothesize that the presence of a relatively +larger core might explain why the chorales have a higher +clustering coefficient than expected given their size and +degree. Similarly, a smaller than expected core for the +preludes might be explain why their clustering coefficient +was lower than expected from networks of the same size +and degree distribution. Since the core consists of nodes +that are well-connected to themselves and the periphery, + +16 +A +B +C +D +E +F +G +H +I +J +K +L +FIG. 9. The relation between the information entropy and the average degree of the music networks plotted +separately for each compositional form. The entropy of Bach’s music networks (Sreal) plotted against the average degree +of the network ⟨k⟩. Each data point represents a single piece. Colors and markers indicate the type of pieces, as shown in the +legend. +if there are a larger number of edges occurring within +the core and between the core and periphery than be- +tween the periphery nodes, it is likely that these edges +will form the clusters that we are interested in. We de- + +17 +A +B +FIG. 10. Comparing the heterogeneity of Bach’s music networks to randomized null networks of the same size. +(A) The in-degree heterogeneity of the music networks compared with random networks of the same size. (B) The out-degree +heterogeneity of the music networks compared with random networks of the same size. Each data point in panels (A) and (B) +represents a single piece. Colors and markers indicate the type of pieces, as shown in the legend. For each random network, +we report the in- and out- degree heterogeneity after averaging over 100 independent realizations. Error bars on the x-axis +represent the standard error of the sample. +A +B +C +D +FIG. 11. The relation between the information entropy of Bach’s music networks and its degree heterogeneity. +The entropy of Bach’s music networks (Sreal) plotted against the network in- and out-degree heterogeneity. Each data point +represents a single piece. Colors and markers indicate the type of pieces, as shown in the legend. The dotted line in each +panel indicates the best linear fit, and the reported rs value is the Spearman correlation coefficient between the x- and y-axis +variables. +note the edges between two nodes that belong to the +core by core-core (CC), those between nodes that belong +to the periphery by periphery-periphery (PP), and those +between the nodes in the core and the nodes in the pe- +riphery by core-periphery (CP). +To test our hypothesis, we compute the core-periphery + +18 +A +B +FIG. 12. Core-periphery analysis of the music networks. (A) The transitive clustering coefficient of the real music +networks compared to null networks that preserve the in- and out-degree of each node. For the degree-preserving null networks, +we report the average over 100 independent realizations, with error bars denoting the standard error of the sample. (B) The +ratio of the number of core-core (CC) edges and core-periphery (CP) edges to the number of periphery-periphery (PP) edges in +the real music networks compared to degree-preserving null networks. For the degree-preserving null networks, we report the +average value computed over 100 independent random graphs. In both panels, the dotted line indicates the line y = x. Colors +and markers indicate the type of piece, as shown in the legend. +structure for each music network using the method de- +scribed by Borgatti and Everett [77]. We then compute +the ratio of the sum of the number of core-core (CC) +edges and core-periphery (CP) edges to the number of +periphery-periphery (PP) edges for each network. +To +understand this ratio, we compare it to corresponding +degree-preserving null networks (Fig. 12B). Strikingly, +we observe that the chorales have a higher fraction of +edges that are within or emanating from the core than +expected from their corresponding null networks. +The +preludes are at the other end, and have a lower frac- +tion of edges that are within or emanating from the core +than expected from their corresponding null networks. +This pattern of findings suggests that the chorales have a +more pronounced core-periphery structure than expected +by chance, while the preludes have a less pronounced +core-periphery structure than expected. +Although the +preludes still have a slightly higher transitive clustering +coefficient than the other pieces, the differences are not +as pronounced as one would expect because of these dif- +ferences in their core-periphery structure. +By performing this additional analysis, we provide an +example of how the music networks display interesting +meso-scale structures that differ from one compositional +form to another, resulting in differences in how their net- +work structure is perceived. + +19 +[1] S. J. Mithen, The Singing Neanderthals: the origins of +music, language, mind and body (Harvard University +Press, 2005). +[2] W. T. Fitch, “The biology and evolution of music: +A comparative perspective,” Cognition 100, 173–215 +(2006). +[3] E. H. Hagen and P. Hammerstein, “Did neanderthals and +other early humans sing? seeking the biological roots of +music in the territorial advertisements of primates, li- +ons, hyenas, and wolves,” Musicae Scientiae 13, 291–320 +(2009). +[4] B. G. Levman, “The genesis of music and language,” Eth- +nomusicology 36, 147–170 (1992). +[5] N. Masataka, “Music, evolution and language,” Develop- +mental science 10, 35–39 (2007). +[6] G. F. Welch, M. Biasutti, J. MacRitchie, G. E. McPher- +son, and E. Himonides, “The impact of music on human +development and well-being,” (2020). +[7] I. Cross, “Music, cognition, culture, and evolution,” An- +nals of the New York Academy of sciences 930, 28–42 +(2001). +[8] S. McClary, “The impromptu that trod on a loaf: Or how +music tells stories,” Narrative 5, 20–35 (1997). +[9] E. Glennie, E. Mac Donald, et al., Musical communica- +tion (Oxford University Press on Demand, 2005). +[10] K. R Scherer and E. Coutinho, “How music creates emo- +tion: a multifactorial process approach,” The emotional +power of music: Multidisciplinary perspectives on mu- +sical arousal, expression, and social control , 121–145 +(2013). +[11] S. Koelsch, “Brain correlates of music-evoked emotions,” +Nature Reviews Neuroscience 15, 170–180 (2014). +[12] A. J. Blood and R. J. Zatorre, “Intensely pleasurable +responses to music correlate with activity in brain regions +implicated in reward and emotion,” Proceedings of the +National Academy of Sciences 98, 11818–11823 (2001). +[13] D. Huron, Sweet Anticipation: Music and the Psychology +of Expectation (The MIT Press, 2006). +[14] B. Tillmann, B. Poulin-Charronnat, +and E. Bigand, +“The role of expectation in music: +from the score to +emotions and the brain,” WIREs Cognitive Science 5, +105–113 (2014). +[15] L. B. Meyer, Emotion and Meaning in Music, ACLS Hu- +manities E-Book (University of Chicago Press, 1956). +[16] C. E. Shannon, “A mathematical theory of communica- +tion,” The Bell System Technical Journal 27, 379–423 +(1948). +[17] S. T. Piantadosi, H. Tily, and E. Gibson, “Word lengths +are optimized for efficient communication,” Proceedings +of the National Academy of Sciences 108, 3526–3529 +(2011). +[18] J. B. Plotkin and M. A. Nowak, “Language evolution and +information theory,” Journal of Theoretical Biology 205, +147–159 (2000). +[19] J.-P. Eckmann, E. Moses, +and D. Sergi, “Entropy of +dialogues creates coherent structures in e-mail traffic,” +Proceedings of the National Academy of Sciences 101, +14333–14337 (2004). +[20] K. Zhao, M. Karsai, and G. Bianconi, “Entropy of dy- +namical social networks,” PLOS ONE 6 (2011). +[21] M. Rosvall, A. Trusina, P. Minnhagen, +and K. Snep- +pen, “Networks and cities: An information perspective,” +Phys. Rev. Lett. 94, 028701 (2005). +[22] J. E. Cohen, “Information theory and music,” Behavioral +Science 7, 137–163 (1962). +[23] L. Hiller and C. Bean, “Information theory analyses of +four sonata expositions,” Journal of Music Theory 10, +96–137 (1966). +[24] X. F. Liu, K. T. Chi, and M. Small, “Complex network +structure of musical compositions: Algorithmic genera- +tion of appealing music,” Physica A: Statistical Mechan- +ics and its Applications 389, 126–132 (2010). +[25] F. Gomez, T. Lorimer, +and R. Stoop, “Complex net- +works of harmonic structure in classical music,” in Non- +linear Dynamics of Electronic Systems (Springer Inter- +national Publishing, Cham, 2014) pp. 262–269. +[26] J.-P. Boon, A. Noullez, and C. Mommen, “Complex dy- +namics and musical structure,” Interface 19, 3–14 (1990). +[27] L. Liu, J. Wei, H. Zhang, J. Xin, and J. Huang, “A sta- +tistical physics view of pitch fluctuations in the classical +music from bach to chopin: Evidence for scaling,” PLOS +ONE 8, 1–6 (2013). +[28] D. Kahneman, S. P. Slovic, P. Slovic, +and A. Tver- +sky, Judgment under uncertainty: Heuristics and biases +(Cambridge university press, 1982). +[29] P. Dayan, “Improving generalization for temporal dif- +ference learning: The successor representation,” Neural +computation 5, 613–624 (1993). +[30] C. W. Lynn, A. E. Kahn, N. Nyema, D. S. Bassett, “Ab- +stract representations of events arise from mental errors +in learning and memory,” Nature Communications , 2313 +(2020). +[31] C. W. Lynn, L. Papadopoulos, A. E. Kahn, and D. S. +Bassett, “Human information processing in complex net- +works,” Nature Physics 16, 965 (2020). +[32] C. W. Lynn and D. S. Bassett, “How humans learn +and represent networks,” Proceedings of the National +Academy of Sciences 117, 29407 (2020). +[33] G. +R. +Jagari, +P. +Pedram, +L. +Hedayatifar, +“Long- +range correlation and multifractality in Bach’s invention +pitches,” Journal of Statistical Mechanics: Theory and +Experiment 04 (2007). +[34] J. M. Moore, D. C. Corrˆea, +and M. Small, “Is bach’s +brain a markov chain? recurrence quantification to assess +markov order for short, symbolic, musical compositions,” +Chaos: An Interdisciplinary Journal of Nonlinear Science +28, 085715 (2018). +[35] J. Gomez-Gardenes and V. Latora, “Entropy rate of dif- +fusion processes on complex networks,” Physical Review +E 78, 065102 (2008). +[36] R. Albert, “Scale-free networks in cell biology,” Journal +of cell science 118, 4947–4957 (2005). +[37] K. Lerman, X. Yan, and X.-Z. Wu, “The” majority illu- +sion” in social networks,” PloS one 11, e0147617 (2016). +[38] A.-L. Barab´asi and R. Albert, “Emergence of scaling in +random networks,” Science 286, 509–512 (1999). +[39] A. E. Kahn, E. A. Karuza, J. M. Vettel, D. S. Bas- +sett, “Network constraints on learnability of probabilis- +tic motor sequences,” Nature Human Behavior , 936–947 +(2018). +[40] J. Stiller, D. Nettle, +and R. IM Dunbar, “The small +world of shakespeare’s plays,” Human Nature 14, 397– + +20 +408 (2003). +[41] Y.-M. Choi and H.-J. Kim, “A directed network of greek +and roman mythology,” Physica A: statistical Mechanics +and its Applications 382, 665–671 (2007). +[42] J. Thickstun, Z. Harchaoui, +and S. Kakade, “Learn- +ing features of music from scratch,” arXiv preprint +arXiv:1611.09827 (2016). +[43] I Liu, Bhiksha Ramakrishnan, et al., “Bach in 2014: Mu- +sic composition with recurrent neural network,” arXiv +preprint arXiv:1412.3191 (2014). +[44] D. J. Watts and S. H. Strogatz, “Collective dynamics of +‘small-world’ networks,” Nature 393, 440–442 (1998). +[45] P. H. R. Zivic, F. Shifres, +and G. A. Cecchi, “Percep- +tual basis of evolving western musical styles,” Proceed- +ings of the National Academy of Sciences 110, 10034– +10038 (2013). +[46] C. P´erez-Sancho, D. Rizo, and J. M. I˜nesta, “Genre clas- +sification using chords and stochastic language models,” +Connection Science 21, 145–159 (2009). +[47] D. K. Simonton, “Melodic structure and note transi- +tion probabilities: A content analysis of 15,618 classical +themes,” Psychology of Music 12, 3–16 (1984). +[48] G. Tzanetakis and P. Cook, “Musical genre classification +of audio signals,” IEEE Transactions on speech and audio +processing 10, 293–302 (2002). +[49] H. Soltau, T. Schultz, M. Westphal, +and A. Waibel, +“Recognition of music types,” in Proceedings of the 1998 +IEEE International Conference on Acoustics, Speech and +Signal Processing, ICASSP’98 (Cat. No. 98CH36181), +Vol. 2 (IEEE, 1998) pp. 1137–1140. +[50] T. Lidy, A. Schindler, et al., “Parallel convolutional neu- +ral networks for music genre and mood classification,” +MIREX2016 3 (2016). +[51] H. Bahuleyan, “Music genre classification using machine +learning techniques,” arXiv preprint arXiv:1804.01149 +(2018). +[52] Sara McLaughlin Mitchell, Samantha Lange, and Holly +Brus, “Gendered citation patterns in international re- +lations journals,” International Studies Perspectives 14, +485–492 (2013). +[53] Michelle +L +Dion, +Jane +Lawrence +Sumner, +and +Sara McLaughlin Mitchell, “Gendered citation patterns +across political science and social science methodology +fields,” Political Analysis 26, 312–327 (2018). +[54] Neven Caplar, Sandro Tacchella, +and Simon Birrer, +“Quantitative evaluation of gender bias in astronomical +publications from citation counts,” Nature Astronomy 1, +0141 (2017). +[55] Daniel Maliniak, Ryan Powers, and Barbara F Walter, +“The gender citation gap in international relations,” In- +ternational Organization 67, 889–922 (2013). +[56] Jordan D. Dworkin, Kristin A. Linn, Erin G. Teich, Perry +Zurn, Russell T. Shinohara, +and Danielle S. Bassett, +“The extent and drivers of gender imbalance in neuro- +science reference lists,” bioRxiv (2020). +[57] Maxwell A. Bertolero, Jordan D. Dworkin, Sophia U. +David, Claudia L´opez Lloreda, Pragya Srivastava, Jen- +nifer Stiso, Dale Zhou, Kafui Dzirasa, Damien A. Fair, +Antonia N. Kaczkurkin, Bianca Jones Marlin, Daphna +Shohamy, Lucina Q. Uddin, Perry Zurn, and Danielle S. +Bassett, “Racial and ethnic imbalance in neuroscience +reference lists and intersections with gender,” bioRxiv +(2020). +[58] Xinyi Wang, Jordan D. Dworkin, Dale Zhou, Jennifer +Stiso, Emily B Falk, Danielle S. Bassett, Perry Zurn, and +David M. Lydon-Staley, “Gendered citation practices in +the field of communication,” Annals of the International +Communication Association (2021). +[59] Paula Chatterjee and Rachel M Werner, “Gender dispar- +ity in citations in high-impact journal articles,” JAMA +Netw Open 4, e2114509 (2021). +[60] Jacqueline M Fulvio, Ileri Akinnola, and Bradley R Pos- +tle, “Gender (im)balance in citation practices in cognitive +neuroscience,” J Cogn Neurosci 33, 3–7 (2021). +[61] Dale Zhou, Eli J. Cornblath, Jennifer Stiso, Erin G. Te- +ich, Jordan D. Dworkin, Ann S. Blevins, and Danielle S. +Bassett, “Gender diversity statement and code notebook +v1.0,” (2020). +[62] Anurag Ambekar, Charles Ward, Jahangir Mohammed, +Swapna Male, and Steven Skiena, “Name-ethnicity clas- +sification from open sources,” in Proceedings of the 15th +ACM SIGKDD international conference on Knowledge +Discovery and Data Mining (2009) pp. 49–58. +[63] Gaurav Sood and Suriyan Laohaprapanon, “Predicting +race and ethnicity from the sequence of characters in a +name,” arXiv preprint arXiv:1805.02109 (2018). +[64] “Bach +central,” +http://www.bachcentral.com/ +midiindexcomplete.html. +[65] “Kern scores,” http://kern.humdrum.org/search?s=t& +keyword=Bach+Johann. +[66] “Bach cantatas website,” https://www.bach-cantatas. +com/Mus/BWV1-Mus.htm. +[67] “Suzu +midi,” +http://www.suzumidi.com/eng/bach4. +htm. +[68] “Midi file tools for matlab by ken schutte,” https:// +github.com/kts/matlab-midi. +[69] I. Momennejad, E. M. Russek, J. H. Cheong, M. M. +Botvinick, N. D. Daw, +and S. J. Gershman, “The suc- +cessor representation in human reinforcement learning,” +Nature human behaviour 1, 680–692 (2017). +[70] S. J. Gershman, C. D. Moore, M. T. Todd, K. A. Nor- +man, and P. B. Sederberg, “The successor representation +and temporal context,” Neural Computation 24, 1553– +1568 (2012). +[71] M. M. Garvert, R. J. Dolan, +and T. EJ Behrens, +“A map of abstract relational knowledge in the human +hippocampal–entorhinal cortex,” elife 6 (2017). +[72] M. E. J. Newman and M. Girvan, “Finding and evaluat- +ing community structure in networks,” Physical review +E 69, 026113 (2004). +[73] F. V´aˇsa and B. Miˇsi´c, “Null models in network neuro- +science,” Nature Reviews Neuroscience , 1–12 (2022). +[74] G. Szab´o, M. J. Alava, +and J. Kert´esz, “Clustering in +complex networks,” Lecture Notes in Physics 650, 139– +162 (2004). +[75] G. Fagiolo, “Clustering in complex directed networks,” +Physical Review E 76, 026107 (2007). +[76] M. P. Rombach, M. A. Porter, J. H. Fowler, +and P. J. +Mucha, “Core-periphery structure in networks,” SIAM +Journal on Applied mathematics 74, 167–190 (2014). +[77] S. P. Borgatti, M. G. Everett, “Models of core/periphery +structures,” Social Networks 21, 375–395 (2000). + diff --git a/BtAyT4oBgHgl3EQf4PqZ/content/tmp_files/load_file.txt b/BtAyT4oBgHgl3EQf4PqZ/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..6d92f4900d22f7bc6294fbae24d0490e1041b332 --- /dev/null +++ b/BtAyT4oBgHgl3EQf4PqZ/content/tmp_files/load_file.txt @@ -0,0 +1,1032 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf,len=1031 +page_content='Information content of note transitions in the music of J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bach Suman Kulkarni,1 Sophia U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' David,2, 3 Christopher W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Lynn,4, 5 and Dani S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bassett1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 6,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 7,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 8,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 9,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' ∗ 1Department of Physics & Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' College of Arts & Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' University of Pennsylvania,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Philadelphia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' PA 19104,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' USA 2Department of Bioengineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' School of Engineering & Applied Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' University of Pennsylvania,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Philadelphia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' PA 19104,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' USA 3Department of Psychology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Yale University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' New Haven,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' CT 06520,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' USA 4Initiative for the Theoretical Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Graduate Center,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' City University of New York,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' New York,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' NY 10016,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' USA 5Joseph Henry Laboratories of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Princeton University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Princeton,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' NJ 08544,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' USA 6Department of Electrical & Systems Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' School of Engineering & Applied Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' University of Pennsylvania,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Philadelphia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' PA 19104,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' USA 7Department of Neurology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Perelman School of Medicine,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' University of Pennsylvania,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Philadelphia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' PA 19104,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' USA 8Department of Psychiatry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Perelman School of Medicine,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' University of Pennsylvania,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Philadelphia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' PA 19104,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' USA 9Santa Fe Institute,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Santa Fe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' NM 87501,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' USA (Dated: January 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 2023) Music has a complex structure that expresses emotion and conveys information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Humans process that information through imperfect cognitive instruments that produce a gestalt, smeared version of reality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' What is the information that humans see?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' And how does their perception relate to (and dif- fer from) reality?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To address these questions quantitatively, we analyze J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bach’s music through the lens of network science and information theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Regarded as one of the greatest composers in the Western music tradition, Bach’s work is highly mathematically structured and spans a wide range of compositional forms, such as fugues and choral pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Conceptualizing each composition as a network of note transitions, we quantify the information contained in each piece and find that different kinds of compositions can be grouped together according to their information content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Moreover, we find that Bach’s music is structured for efficient communication;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' that is, it commu- nicates large amounts of information while maintaining small deviations of the inferred network from reality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We probe the network structures that enable this rapid and efficient communication of information—namely, high heterogeneity and strong clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Taken together, our findings shed new light on the information and network properties of Bach’s compositions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' More generally, we gain insight into features that make networks of information effective for communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' INTRODUCTION From Tibetan throat singing to Scottish piobaireachd to modern hip hop, music is a universal aspect of human culture, enjoyed by people of all ages from all around the world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' It has even been proposed that music is a funda- mental part of being human [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The earliest confirmed musical instruments are nearly 40,000 years old, and evi- dence suggests that vocal music began much earlier [2, 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' While it is a point of controversy, some scientists believe that communication through music arose even before lan- guage [1, 4, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Though styles, sounds, and instruments vary drastically from one culture and time period to an- other, it is indisputable that music has had a substantial impact on the development of humans and society [6, 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Making and listening to music is more than just a recre- ational activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Music is a medium of communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Through music we can tell stories [8], convey messages [9], and imbue the strongest of emotions [10–12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' It is ∗ To whom correspondence should be addressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' dsb@seas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='upenn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='edu a common human experience to feel pensive or despon- dent after hearing a slow song in a minor key or to feel carefree or energized after hearing an upbeat song in a major key.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' But how does something as abstract as mu- sic communicate so much?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Past literature has discussed music in terms of expectation and surprise [13, 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In or- der to be evolutionarily successful, our brains are adept at forming expectations based on prior events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' When these expectations are contradicted by an experience, we feel surprised.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' With surprise can come a host of other emotions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We may feel relief when the dissonant sound we expected was actually consonant, or we may feel dis- tress when the musical resolution we expected did not occur [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' But how do we quantify these expectations and surprises?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' How do we mathematically formalize the communicative success of a piece of music?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Fundamen- tally, music is comprised of fleeting and elusive sounds, and hence may appear hard to measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Even written on a page, the jumble of notes, rests, dynamic markings, and multilingual commands is daunting to describe with mathematical rigor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Here, we seek to extract order from music’s complexity by examining music through the lens of network science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' A network consists of nodes and edges—representing en- arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='00783v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='soc-ph] 2 Jan 2023 2 tities and the connections between them, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Conceptualizing each note as a node and each transition between two notes as an edge, we can build a network for any piece of music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Using music networks, we provide a comprehensive analysis of Bach’s compositions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bach is a natural case study given his prolific career, the wide appreciation his compositions have garnered, and the in- fluence he had over contemporaneous and subsequent composers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' His diverse compositions (from chorales to fugues) for a wide range of musicians (from singers to orchestra members) often share a fundamental underly- ing structure of repeated—and almost mathematical— musical themes and motifs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' These features of Bach’s compositions make them particularly interesting to study using a mathematical framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' As we listen to music, we form expectations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Upon hearing a particular note, we anticipate which notes might come next based on past transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The less likely the outcome, the more surprised we are upon hear- ing it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This “suprisal” can be quantified by the Shan- non information entropy [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Ideas from information theory have led to illuminating insights in a wide range of settings, including language [17, 18], social networks [19, 20], transportation patterns [21] and music [22, 23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We draw upon these ideas to shed light on the features of Bach’s music that make it successful in communicating information to the human mind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Prior research has at- tempted to quantitatively identify patterns and features that might be present across different kinds of music [24– 27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' However, understanding how humans perceive these patterns is more nuanced and complex than simply eval- uating the structure of compositions because humans are not perfect learners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Rather, humans assimilate patterns of information presented to them through imperfect per- ceptual systems, sacrificing the accuracy of their internal representation to conserve computational energy [28–30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This trade-off between the accuracy of the inferred transi- tion structure and the computational cost involved in its formation results in a slightly distorted version of tran- sition networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The “learned” version of a network can be calculated using previous models of human percep- tion [31, 32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Networks for which the inferred version maintains a low deviation from the true network can be considered efficient in communicating information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This framework thus provides insight into the communicative success of a network, from the point of view of how the network interacts with our imperfect perceptual systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In this work, we apply information theory to note tran- sition networks constructed from Bach’s musical compo- sitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We seek to quantify the amount of information in these networks and understand what patterns or features allow these networks to successfully hold and accurately convey information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We begin by studying the informa- tion entropy of each piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Here, we find that Bach’s music contains more information than expected from typ- ical (or random) transition structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Strikingly, certain composition forms are clustered together based on their information content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We hypothesize that the higher in- formation content in Bach’s music and the differences observed across musical pieces can be explained by the heterogeneity in node degrees (or the number of distinct pitches that follow a given note).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Next, to determine how accurately the transition structure of a composition can be inferred by a human observer, we use a free energy model of how humans perceive networks of information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We hypothesize that Bach’s music networks maintain a low deviation between the learned and original network, and this property is driven by tight clustering in the net- work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Additionally, we find that certain compositional forms can be distinguished based on the discrepancies between the original and the inferred network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Our find- ings illuminate how these music networks are structured to convey large amounts of information rapidly and accu- rately, thereby supporting successful communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' By performing this systematic study of how the information in a complex system, like music, is structured and per- ceived by humans, our work provides a new perspective on how humans experience the world around them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' MUSIC AS A NETWORK OF NOTE TRANSITIONS We study a wide range of Bach’s compositions in- cluding: preludes, fugues, inventions, cantatas, English suites, French suites, chorales, Brandenburg concertos, toccatas, and concertos (see Materials and Methods sec- tion A 1 for further details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The audio files for these pieces were collected and read in MIDI format, from which the sequence of notes was extracted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Each note present in a piece is represented as a node in the network, with notes from different octaves represented as distinct nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The transitions between notes are calculated sep- arately for different instruments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' If there is a transition from note i to note j, then we draw a directed edge from node i to node j (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 1A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' For chords, where multiple notes occur at the same time, edges are drawn between all notes in the first chord to all notes in the second chord.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To simplify our analysis, we remove any self loops in the network, thereby restricting ourselves to understanding the structure of transitions to the next different note in the piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We begin by examining unweighted networks of note transitions to focus on how the network structure alone impacts the information content and perception of a musical piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' After understanding the skeleton of the transitions, we then add weights to the edges based on how frequently various transitions occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This procedure allows us to disentangle the effects of the network struc- ture (comprising the set of possible note transitions) and edge weights (comprising the note transition probabili- ties).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' QUANTIFYING THE INFORMATION IN NETWORKS We seek to measure the amount of information pro- duced by a sequence of notes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=" Although note sequences 3 F D G D B C A B G E G E G E C G A B E G' D F E' C G A B E G' D F E' B A E D G' E' Model information production using random walks (iii) Network Entropy: (ii) Node-level Entropy: Model human perception using free energy principle C G A B E G' D F E' B." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' A High Low Original Network Inferred Network Low High (i) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' By treating music as a network of note transitions, we build a model for how information is produced and the network is perceived by humans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (A) An example of a network constructed from a musical piece using the method described in our paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' At the top, we show a toy musical piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Below, we show the network in which notes are nodes and transitions between notes, whether isolated or played simultaneously as part of a chord, are directed edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The direction of the edge matches the temporal direction of the transition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (B) The model of information production using random walks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (i) An example of a random walk on the network of note transitions is shown using the blue dotted line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' At each node, the walker chooses an outgoing edge to traverse, each weighted with equal probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This walk generates a sequence of notes as shown below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (ii) The amount of information, or the entropy, generated when a walker traverses an edge from a node depends on the number of edges emanating from the node (called the degree of the node).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' When traversing nodes with a high versus low degree, the walker has more choices for which edge to pick and hence, such a transition generates more information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Thus, nodes with a higher degree (right) are said to have higher entropy than nodes with a low degree (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (iii) To calculate the entropy of the entire network, one needs to weigh the contribution of each node by the probability that a walker will occupy it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' For networks with the same average degree, those with a wider range of degrees (right) have a higher entropy than those with a narrower range of degrees (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (C) The model for how humans form internal estimates of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Humans perceive sequences of information presented to them through imperfect perceptual systems, which results in an imperfect internal representation of the network (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This inexact inferred version of the network contains extra edges due to biases that stem from imperfect perception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The color bar indicates the weight assigned to an edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Based on models for this fuzzy perception, humans are most likely to jumble up transitive relationships, as shown on the right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Therefore, networks with a large number of these triangular clusters are resilient to the inaccuracies in human perception and are easier to learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' can have long-range temporal dependencies [33, 34], as a first analytical step, we focus on the Markov transition structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' That is, we study the information contained in individual note transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This information is quan- tified by the Shannon entropy of a random walk on the network [16, 35] (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 1B;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' see also the Materials and Methods section A 2 for further details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Given a net- work of transitions, the contribution of the ith node to the entropy can be written in terms of the entries of the transition probability matrix P as: Si = − � j Pij log Pij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (1) In the case of directed unweighted networks, Pij = 1/kout i , where kout i is the out-degree of the node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Hence, for unweighted networks, the node-level entropy is Si = log (kout i ), which is solely determined by the out-degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To calculate the entropy of the entire network, the con- tributions of the nodes are weighted by their stationary distribution—the probability that a walker ends up at node i after infinite time—which we denote by πi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The entropy of the network is then [35]: S = � i πiSi = − � i πi � j Pij log Pij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (2) For undirected and unweighted networks, the stationary distribution has a simple analytical form πi = ki/2E, where ki is the degree of node i, and E is the total number of edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The network entropy is then: S = 1 2E � i ki log ki.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (3) By contrast, for directed networks the stationary dis- tribution depends on the detailed structure of the net- work and cannot be written in closed form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Hence, for our directed music networks, we calculate the stationary Model information production using random walks Node-level Entropy: G F Si= >Pii log Pit D D C B) (B G Network Entropy: E TiPii log Pi Model human perception using free energy principle4 A B C FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Quantifying the information of Bach’s music using the entropy of random walks on networks of note transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (A) Entropy of Bach’s music networks (Sreal) compared with random networks of the same size (Srand).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We report the entropy of the corresponding random networks after averaging over 100 independent realizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The error bars for Srand indicate the standard error of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (B) The entropy of Bach’s music networks (Sreal) compared with random networks that preserve the in- and out-degree of each node (Sdeg).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We report the entropy of the corresponding degree-preserving random networks after averaging over 100 independent realizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The error bars for Srand indicate the standard error of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (C) The entropy of the chorales as a function of the average in-degree heterogeneity Hin = Var(kin)/⟨kin⟩ (top) and out-degree heterogeneity Hout = Var(kout)/⟨kout⟩ (bottom) of the networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In panels (A) and (B), each data point represents a single piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Color and marker indicate the type of piece, as shown in the legend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The dashed line represents the line y = x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In panel (C), the dotted line indicates the best linear fit, and the reported rs value is the Spearman correlation coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' distribution numerically and use Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 2 to compute the entropy of each piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To understand the amount of information produced by the music networks, we compare them to random- ized (or “null”) networks with equal number of nodes and edges (see the Materials and Methods section A 5 for details on generating null networks).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' If the note transi- tions in Bach’s music do have distinct properties that al- low them to communicate a large amount of information, then we would expect Bach’s networks to contain more information than random transition structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' By aver- aging over 100 random networks for each piece, we find that the real networks have consistently higher entropy— thereby containing more information—than their ran- dom counterparts (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 2A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Moreover, by comparing across pieces, we observe that the different kinds of com- positions cluster together based on their entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The chorales, typically meant to be sung by groups in eccle- siastical settings, have a markedly lower entropy than the rest of the compositions studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' By contrast, the toccatas and preludes have a much higher entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' It is possible that the chorales’ functions of meditation, adora- tion, and supplication are best supported by predictabil- ity and hence low entropy, whereas the entertainment functions of the toccatas and preludes are best supported by unpredictability and hence high entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We know that the node-level entropy is defined only by the out-degrees of the nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Accordingly, it is use- ful to assess differences between the true networks and others wherein the node-level entropies have been fixed by preserving the true degree distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To perform this assessment, we compare the entropy of the real net- works with another set of null models: randomized net- works which preserve both the in- and out-degree of each node (see the Methods and Materials section A 5 for de- tails on generating these networks).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We observe that the entropies of the networks are more or less preserved (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 2B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Although this preservation is expected for undirected networks (where the entropy is determined only by the degree distribution), it need not exist for di- rected networks (where the different stationary distribu- tions contribute to the entropy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We therefore find that the entropy of music networks is primarily determined by their degree distributions rather than their stationary distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Heterogeneity in degrees favors higher entropy To gain intuition for how the entropy of note tran- sitions depends on network structure, consider the case of unweighted and undirected networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The network en- tropy takes a particularly simple form, as shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Following a Taylor expansion around the average degree of the network (see the Materials and Methods section A 2), one obtains: S = log⟨k⟩ + Var(k) 2 ⟨k⟩2 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (4) where ⟨k⟩ is the average degree of the network and Var(k) is the variance of the degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To first order, we see that 5 the entropy increases logarithmically with the average degree of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To second order, the entropy in- creases with the variance or the heterogeneity of the de- grees, such that more information will be produced by networks with heterogeneous (or broader) degree distri- butions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We define the degree heterogeneity as: H = Var(k) ⟨k⟩2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (5) Many networks that we encounter in our daily lives are characterized by heterogeneous degree distributions, typ- ically with few high degree “hub” nodes and many low de- gree nodes [36–38].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' By contrast, regular graphs—which have homogeneous degrees—produce random walks with the least entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Where does Bach’s music fall along this spectrum?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We found in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 2A that Bach’s music networks have consis- tently higher entropy than null networks with the same number of nodes and edges (in other words, randomized networks with the same average degree).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In the Supple- mentary Information Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' B 4, we show that this higher information content of Bach’s music networks is due to higher heterogeneity in their in- and out-degree distri- bution;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' that is, Bach’s music networks are more hetero- geneous in their degrees than expected from transition structures of their size, enabling them to pack more in- formation into their structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 2A), we also ob- served that various pieces belonging to certain composi- tions were clustered together in their entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Consistent with this observation, we find that the pieces which are clustered together in their entropy have very similar de- grees (see Supplementary Information Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' B 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Exam- ples include English suites, French suites, and chorales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In contrast, fugues did not cluster together in their en- tropy as much as other composition types and displayed diverse average degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' For the compositions that are grouped together in their entropy, we find that the dif- ferences observed among the pieces in the group can be explained by their degree heterogeneity (see Supplemen- tary Information Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' B 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We can, for example, see this relation in the chorales where the pieces which have a higher in- and out-degree heterogeneity tend to have a higher entropy, despite having similar degrees (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 2C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We note that this relationship between the entropy and degree heterogeneity holds even in our data set of di- rected networks, likely because the in- and out-degrees tend to be correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' HOW HUMANS PERCEIVE NETWORKS OF INFORMATION Communication systems, such as music or language, convey information in sequences of discrete items.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Hu- mans then assimilate this information and build repre- sentations of the underlying structure of inter-item rela- tionships.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The information that is perceived by a human is the sum of the information present in the system and Internal Estimates 0 η 0 1 1/4 Learned probability Maximal accuracy Minimal accuracy Maximal complexity Minimal complexity Trade-off between accuracy and computational cost Balanced between accuracy and complexity (i) (ii) (iii) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' How humans process networks of information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Humans strike a balance between accuracy and complexity when forming internal network models of the world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The pa- rameter η quantifies this trade-off between accuracy and cost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In panel (i), we see the example network built when solely maximizing the accuracy (η → 0), which forms a perfect rep- resentation of reality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' However, building this network requires perfect memory and is computationally expensive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In panel (iii), we see the network built when solely minimizing the computational cost (η → 1), in which all nodes are connected to all other nodes, unlike the original network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Constructing this network does not require significant cost, but it provides no accuracy in representing the original information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Hu- mans tend to display intermediate values of η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='80 [31], thereby constructing networks that preserve some but not all of the true transition structure, as shown in panel (ii).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Figure adapted with permission from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' the inaccuracies that stem from the imperfect cognitive processes involved in perception [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In the previous sec- tion, we focused on quantifying the actual information present in the system (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 1B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We will now account for the second piece: the inaccuracies that arise due to the imperfect cognitive process of perceiving information (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 1C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' When forming an internal network representation of the information presented to them, humans seek to max- imize the accuracy of their internal representation while simultaneously minimizing the computational cost in- volved in building it [30–32, 39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' One the one hand, a human could learn the structure with no errors, forming a perfectly accurate network of the transitions (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 3(i)) but that formation process would be computationally ex- pensive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' On the other hand, one could disregard accuracy and have the least expensive representation (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 3(iii)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Most humans do something in between by recalling the sequence of transitions sometimes accurately and some- times inaccurately, thereby forming a fuzzy perception of the true network (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 3(ii)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Formally, the competi- tion between computational complexity and accuracy can be captured by a free energy model of people’s internal representation [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The learned transition probabilities 6 under this model can be written as follows: ˆP = (1 − η)P(I − ηP)−1, (6) where η ∈ [0, 1] captures the errors in representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Using this model, we can compute the learned network for each musical piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Prior work indicates that, on average, humans display an η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='80 in large-scale online laboratory experiments [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Given a network of note transitions with transition probabilities P, we use this empirically measured value of η = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='8 to calculate the average network that a human infers ˆP using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' QUANTIFYING THE LEARNABILITY OF NOTE TRANSITIONS We are now prepared to investigate how a given music network differs from the internal representation formed by a human listener.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The closer the learned network is to the original network, the more resilient the network structure is to human errors in learning, and the network is said to be more learnable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Mathematically, one can quantify the deviations between the inferred network ( ˆP) and the original network (P) using the Kullback-Leiber (KL) divergence: DKL(P|| ˆP) = − � i πi � j Pij log ˆPij Pij , (7) where πi is the stationary distribution of the original network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The lower the KL-divergence, the closer the learned transition structure is to the original transition structure, and hence the more learnable the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Do Bach’s musical compositions possess distinct features that facilitate human learning?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' How do pieces differ in their learnability?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' What are the structural differences between the musical pieces that lead to such differences?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To answer these questions, for each musical piece, we compute the KL-divergence between the true transition probabilities P and the learned transition probabilities ˆP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Then, to understand whether Bach’s music networks are structured in a manner that improves their learnabil- ity, we compare them against random networks with the same number of nodes and edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The data confirms our intuition (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 4A): Bach’s music networks have a lower KL-divergence than random networks of the same size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Even if we compare against null networks with the same in- and out-degree distributions, we still see that Bach’s music networks have a lower KL-divergence (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 4B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This finding suggests that the lower KL-divergence of these networks cannot be explained by their degree distributions alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Additionally, we observe variations in the KL-divergence among the different compositions (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The chorales, at one extreme, seem to have the highest KL-divergence, while the preludes have the lowest KL-divergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Our findings indicate that the note tran- sitions in Bach’s music are structured in a manner that is resilient to errors that humans make when learning infor- mation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Further, learnability differs across composition forms, with some being easier to learn than others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Transitive clustering In the previous section, we saw that the differences between the KL-divergences of the music networks and the null networks could not be explained by the distri- butions of degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Here, we seek to understand what network property leads to the observed differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Pre- vious work has shown that in the case of undirected net- works, the KL-divergence decreases with the density of triangles in the network [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' One can show this ana- lytically by substituting the expression for the averaged learned version of a network (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 6) into the equation for the KL-divergence (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This substitution gives us an expression for the KL-divergence in terms of the adjacency matrix of the original network: DKL(P|| ˆP) = − log(1 − η) − η ln 2 � i πi× � � � � j Aij � l 1 kout i Ail 1 kout l Alj � � � + O(η2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (8) Here we see that the KL-divergence depends on a prod- uct of the form AijAilAlj, which measures the transitive relationships present in the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' More explicitly, it depends on the number of directed triangles of the form i → j → k and i → k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Musically, the presence of a larger density of such triangles suggests that if there is a tran- sition between notes i and j, and notes i and k, there is likely also a transition between notes j and k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To quantify the extent to which a network has clusters of this form, we calculate the transitive clustering coef- ficient of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' For each node, this quantity is measured by dividing the number of transitive triangles that node i is a part of (∆T i ) by the number of possible directed triangles: CT i = ∆T i ktot i (ktot i − 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (9) Here ktot i is the total degree (in + out) of the node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We average this quantity over all nodes in the network to re- port a single value for each piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 8 indicates that the KL-divergence will be smaller for networks with a large number of transitive triangles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This intuition arises from the fact that humans can easily make swap errors among transitive relations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' If node i is connected to node j and node j links to node k, a human learner may erroneously draw an edge between node i and node k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' However, if the network had an edge connecting node i to node k to begin with, such an edge would not be an error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Hence, we expect networks that have more transitive relations to be more robust to errors made in learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Indeed, we 7 B D C A FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Quantifying the difference between the actual information and the perceived information in Bach’s music networks by calculating the KL-divergence between the actual and perceived network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (A) KL-divergence of the real music networks (Dreal KL ) compared with random networks of the same size (Drand KL ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We report the KL-divergence of the corresponding random networks after averaging over 100 independent realizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The error bars for Drand KL indicate the standard error of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (B) KL-divergence of the real music networks (Dreal KL ) compared with random networks that preserve the in- and out-degree of each node (Ddeg KL ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We report the KL-divergence of the corresponding degree-preserving random networks after averaging over 100 independent realizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The error bars for Ddeg KL indicate the standard error of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (C) KL-divergence of the real music networks as a function of the transitive clustering coefficient of the network C = ⟨∆T i /ktot i (ktot i − 1)⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (D) The transitive clustering coefficient of the real music networks compared with random networks that preserve the in- and out-degree of each node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The dotted line indicates the line y = x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' For the degree-preserving random networks, we report the transitive clustering coefficient after averaging over 100 independent realizations, with error bars denoting the standard error of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In all the panels, each data point represents a single piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Color and marker indicate the type of piece, as shown in the legend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The dotted line in panels (A), (B), and (D) represents the line y = x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' observe that the KL-divergence of the music networks is lower for networks that have a higher transitive cluster- ing coefficient (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 4C).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In fact, the real music net- works have a higher transitive clustering coefficient than degree-preserving random networks (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 4D), suggest- ing that this feature is not due to mere coincidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' From Fig 4D, we make an interesting observation: the chorale pieces generally have a higher transitive clustering coef- ficient than expected from null networks that preserve their size and degree distribution, while the preludes ap- pear to have a lower transitive clustering coefficient than the corresponding null networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We probe this further in the Supporting Information and identify meso-scale structures that could lead to the observed differences be- tween the compositional forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' ACCOUNTING FOR NOTE TRANSITION FREQUENCIES So far, we have focused our attention on the infor- mation content and perception of unweighted (or bi- nary) note transition networks created from Bach’s mu- sic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' These networks only captured whether or not a tran- sition exists between two notes and were not sensitive to how frequently each transition occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The binary net- works enabled us to probe how the structure of the tran- 8 A B C FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Accounting for the frequencies of the note transitions in our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (A) Entropy of the weighted versions of Bach’s music networks (Sweighted) compared with the corresponding unweighted versions (Sunweighted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (B) The KL-divergence of the weighted versions of Bach’s music networks (Dreal,w KL ) compared with the corresponding unweighted versions (Dreal KL ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (C) Top: Entropy of the weighted note transition networks (Sreal,w) compared with degree-preserving edge-rewired null networks (Sdeg, w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bottom: The KL-divergence of the weighted note transition networks (Dreal,w KL ) compared with degree-preserving edge-rewired null networks (Ddeg, w KL ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In all panels, each data point represents a single piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Color and marker indicate the type of piece, as shown in the legend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The dashed line represents the line y = x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' sitions supports effective communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' However, in many real networks, not all transitions occur with the same frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To reflect the different frequencies with which transitions may occur, we construct networks in which transitions are weighted according to this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' For ex- ample, if note i follows note j 90% of the time and note k follows note j 10% of the time, the edge from node j to node i will be more heavily weighted than the edge from node j to node k (see the Materials and Methods section A 1 for further details on network construction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Adding this piece of information to the networks leads us to new questions about the role that transition weights play in communicating information to listeners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' For example, how is the information generated by a random walk on the network altered by differences in the frequencies of transitions?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In Bach’s music, do these differences in fre- quencies make it easier for humans to learn the transition networks?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Weights reduce the surprisal of transitions For unweighted networks, the node-level entropy of a random walk is determined solely by the out-degree (kout i ), since each outgoing edge is traversed with prob- ability Pij = 1/kout i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' If the edges are weighted by their transition frequencies, the Pij’s will no longer be uni- formly distributed, and each outgoing edge will not have an equal probability of being traversed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Hence, incorpo- rating the edge weights reduces the node-level entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This observation is intuitive since non-uniformities in any distribution lead to decreases in entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' However, ex- tending this intuition to the entropy produced by the entire network is not as straightforward, since one must weigh the contribution of each node by the stationary distribution of the random walkers, which cannot be ex- pressed in closed form for directed networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Generally, we find that the entropy of weighted networks is still lower than the corresponding unweighted networks (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 5A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This finding suggests that the different weights re- duce the overall surprisal generated by the networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Weights reduce the deviations between the learned network and the original network Incorporating the transition frequencies also helps us to understand the role that the weights play in the hu- man inference of note transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We observe that the weighted networks of note transitions have lower KL- divergence than the binary networks (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 5B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This ob- servation suggests that the weights aid in forming more accurate internal representations of the transition struc- tures, thereby improving their learnability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In light of these data, we next verify the role that the network structure plays in the communicative success of weighted networks by comparing the entropy and KL- divergence of the weighted music networks with edge- rewired null networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In the analysis on unweighted networks, we observed that the entropy was primarily driven by the degree distribution of the network and not sensitive to the precise connectivity pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To make this observation, we had compared the entropy of the real music networks to randomized networks that pre- 9 served the exact degree distribution of each node and hence, held the node-level entropies fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Along simi- lar lines, here we make use of null models that keep the node-level entropies fixed by preserving the in- and out- degree of each node and the out-weights at each node (see the Materials and Methods section for details on the null models).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' By comparing the entropy of the weighted music networks to the degree-preserving weighted null models, we see that the entropies of real networks are still more or less unchanged, although the real networks have marginally higher entropies than the null networks (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 5C, top).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' These results support our conclusion that the entropy in the real networks is still primarily driven by their degree distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' When we compare the KL-divergence of the real weighted networks with the degree-preserving weighted null models, we find that the real networks have a lower KL-divergence than the cor- responding null networks (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 5C, bottom).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Together, these results suggest that incorporating the weights into our network analysis does not alter the effects of network structure qualitatively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Accounting for the note transition frequencies in our network model leads to several interesting lines of inquiry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' For instance, is it the specific distribution of weights that improves the learnability of music networks?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Fu- ture work could evaluate this possibility by comparing the KL-divergence of the weighted networks with a class of null models that preserve the skeleton of the network, but permute the edge weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' It would also be interest- ing to test whether higher edge weights are concentrated in triangular clusters of the network, offering a potential explanation for the lower KL-divergence of the weighted networks compared to the binary networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' DISCUSSION In this article, we study music composed by J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bach through the lens of network science and information the- ory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Viewing Bach’s musical compositions as networks of note transitions, we quantify the information generated by the note transitions and study how this information is perceived by humans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We analyzed a total of 327 Bach compositions spread over a wide range of compositional forms, including preludes, fugues, inventions, cantatas, English suites, French suites, chorales, Brandenburg con- certos, toccatas, and concertos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' For each musical piece, we construct a network of note transitions by drawing di- rected edges between notes that are played consecutively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We then quantify the amount of information generated by the network structure and find that different composi- tional forms are grouped together based on their entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Further, we find that the note transitions in Bach’s music contain more information than expected from transition structures of their size, which can be attributed to higher heterogeneity in their degree distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To quantify how the transition structure of Bach’s mu- sic is perceived by a human, we use a mathematical model for how humans infer networks of information [30, 31], which allows us to estimate the average “learned” net- work given any network of information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Using this model, we compute the inferred version for each music network, and quantify the information that arises due to discrep- ancies between the original and inferred networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We find here that the discrepancies differ among the compo- sitional forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Moreover, Bach’s music networks main- tain a consistently lower deviation between the original and inferred version compared to randomized null net- works of the same size and degree distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Probing the structural features that enable these music networks to be more resilient to biases in perception, we find that this property is driven by a high density of transitive triangular clusters in the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Finally, we study how the frequencies of transitions influence the information content and perception of the musical pieces, by weighing the transitions by the number of times they occur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We find that the weights reduce the overall entropy or surprisal of the transitions, and also reduce the deviations between the inferred and actual network, suggesting that the weights aid the learnability of these transition structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' On comparing the infor- mation content and learnability of the weighted networks with degree-preserving null models, we find that qualita- tively, our results relating the information content and learnability to the network structure are still valid for the weighted networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' More generally, our findings here along with the re- sults in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [31] provide insight into features that make a wide range of complex systems around us effective at communicating information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To communicate informa- tion successfully, networks of information in complex sys- tems tend to be structured in a manner that allows them to carry large amounts of information, while also being robust to inaccuracies that humans make when infer- ring relationships between items.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Networks which are denser (have a higher average degree) produce more un- predictable random walk sequences, and hence produce more information (have a higher entropy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Further, for networks of comparable average degree, more heteroge- neous (higher variance in degree distribution) structures produce more information than those more regular or ho- mogeneous in their degree (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 6A(i)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Additionally, we find that networks which contain a large number of tri- angular clusters can be inferred more accurately when viewed through an observer’s imperfect cognitive appa- ratus (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 6A(ii)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Together, these findings suggest that for networks of a given size, rapid and accurate commu- nication of information is supported by structures that are simultaneously heterogeneous and clustered (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Future directions Our study has focused on analyzing the note transi- tions present in Bach’s music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' It is important to note that music is a multifaceted art form that encompasses a range of structural and expressive elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Future work could 10 Supports efficient communication 1 Low KL-divergence Easy to learn High KL-divergence Hard to learn High Entropy Contains more information Low Entropy Contains lesser information Does not support effective communication A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' ii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' ii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Network structures that support effective communication of information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (A) Networks with a larger variance or heterogeneity in their node degrees, as shown in panel (i), pack more information into their structure and have a higher entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Clustering in the network, as shown in panel (ii), makes the structure more resilient to errors made by humans when building an internal representation of the information, allowing the network to be inferred more accurately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Together, these structures convey a large amount of information that can be learned by humans more accurately, and are hence more efficient for communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (B) Networks with lower variance in their node degrees, as shown in panel (i), carry relatively lower information in their structure compared to networks that are of similar size but more heterogeneous in their degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' A lower tendency for nodes to form clusters, as shown in panel (ii), makes the network more susceptible to errors when humans infer its transition structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Together, these structures convey information less efficiently, rapidly, and accurately compared to those shown in panel (A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' build upon our study by exploring other aspects of music, for example, considering networks of transitions between rhythms or harmonies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Beyond music, our study can also be extended to a range of complex systems present around us—such as language and social networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' For example, one could analyze works of literature and ask: Does the entropy of noun transitions in various works of Shakespeare differ based on their genre?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' More specif- ically, does the information content and learnability of noun transitions or relationships between characters dif- fer between tragedies and comedies?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' By providing an example of a systematic and comprehensive analysis of the actual and perceived information in music, our study complements and adds to the rich study of language, mu- sic, and art as complex systems [25, 40, 41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Systematically analyzing the information that we ex- tract from complex systems can provide new insights into the human experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' A question that often arises in the context of how humans experience music is: What makes a musical composition appealing to the human ear?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' While individual preferences in music can vary widely and is highly subjectively, there is still a gen- eral agreement on certain composers being considered “influential” or “great”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This fact raises the possibil- ity that there may be some inherent qualities that are common to musical pieces which are widely considered appealing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Identifying such features might give us in- sight into the creative process of composing music and also complement existing work using AI to generate mu- sic [42, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Several attempts have been made to identify such patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' For example, Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [24] analyzed note tran- sition networks in certain compositions by Bach, Chopin, and Mozart as well as Chinese pop music, and sug- gested that “good” music is characterized by the small- world property [44] and heavy-tailed degree distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' On the other hand, Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [25] studied selected composi- tions from Bach’s Well-Tempered Clavier and found non- heavy-tailed degree distributions, suggesting that such distributions are not necessary for music to be appeal- ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' It would be interesting to devise future experiments to determine whether our findings relate to the aesthetic or emotional appeal of a piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In our study, we found that Bach’s music networks had a higher number of tran- sitive triangular clusters, enabling them to be learned more efficiently than arbitrary transition structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Are pieces with a larger number of these triangles also more appealing to a listener?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Future work assess this possi- bility by conducting experiments that ask people to rate Bach’s compositions and analyzing whether these ratings correlate with the presence of triangular clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' More generally, our work focuses not solely on the informa- tion inherent in the transition structure of music, but also on how the information in this transition structure is perceived by a human listener.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This framework might be useful in studying cognitive aspects of music and in bridging patterns observed in data with cognitive theo- ries of music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In future work, it would be interesting to extend our analysis to study how music networks evolve with time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' There are three potentially interesting lines of inquiry here: First, how do the entropy and KL-divergence of a musical piece change as the piece progresses?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Does 11 this temporal change differ among the various compo- sitional forms?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Second, how has the music of a spe- cific composer (whether Bach or otherwise) changed over the course of their lifetime?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Has it become more intri- cate and complex, holding more information?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Perhaps as the composer gains experience, their compositions con- vey information more efficiently and accurately, as re- flected in a reduced KL-divergence?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' If the exact dates of when each piece was composed were known, then the framework used in our paper might provide answers to these questions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Third, how has music of a given genre, say classical music, changed over the years across com- posers?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [27], for example, studied the fluctuation in pitch between adjacent notes in compositions by Bach, Mozart, Beethoven, Mendelsohn, and Chopin, and found that the largest pitch fluctuations of a composer gradu- ally increased over time from Bach to Chopin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' It would be interesting to expand our analysis to different com- posers, and see how the information and expectations vary across composers and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Further considering how a genre changes with time, it would be of interest to assess how various styles or gen- res of music differ [45–47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' What are the key features by which a listener distinguishes between music from two eras, say the Classical and the Romantic eras?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' How do the differences in structure then impact how the piece is perceived by a listener?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' An analysis of the information content and perception of various genres of music could complement existing work in musicology, and potentially aid in systematically classifying pieces into genres that may not be a priori obvious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Classifying genres of music could also be beneficial for audio streaming services, and our framework could potentially complement existing ap- proaches to musical genre classification [46, 48–51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Methodological considerations Here we highlight the assumptions made in our study and the resulting methodological constraints in our re- search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' First, in constructing networks of note transi- tions, the self loops present in the networks were ignored to simplify our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This choice restricted us to un- derstanding only the structure of transitions between dif- ferent notes in a musical piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' However, these self loops may have interesting effects on the discrepancies between the actual and perceived information content from the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Future work could include self loops, studying their impact on the information content and learnability of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Second, the production of information from the underlying transition structure has been mod- elled using Markov random walks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' While this is a stan- dard first step in understanding complex systems, in re- ality, the transitions present in music possess long range correlations and constraints to their structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Including these correlations (perhaps in the form of a biased ran- dom walk with memory) would be a fruitful direction to pursue to gain a better and more realistic understand- ing of the information we encounter from real complex systems around us.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' VIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' CONCLUSION In this work, we analyze Bach’s musical compositions as networks of note transitions conveying information to humans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Recent studies have shown that the information humans perceive from complex systems around them con- sists of two parts: the information inherent in the system and the information arising due to errors in their per- ception [30, 31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Analyzing the information from these two parts, we find that different compositional forms can be distinguished from one another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Further, we gain insight into structural features that enable these music networks to communicate effectively: they communicate more information by having more heterogeneous degrees, and they convey information more accurately (minimiz- ing the discrepancies with human inferences) by having a higher density of transitive clusters (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Through this quantitative analysis of Bach’s music, our findings provide new methods to understand how humans share and experience information around them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' ACKNOWLEDGMENTS We thank Chris Macklin for an early conversation on this topic and audience members who have asked prob- ing questions about our earlier work in communication networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' These interactions motivated our continued investigation in this space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This particular research was primarily supported by the Army Research Office award number DCIST-W911NF-17-2-0181 and the Na- tional Institutes of Mental Health award number 1-R21- MH-124121-01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' would also like to acknowledge additional support from the John D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' and Catherine T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' MacArthur Foundation, the Alfred P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Sloan Foundation, the Institute for Scientific Interchange Foundation, and the Army Research Office (Grafton-W911NF-16-1-0474).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The content is solely the responsibility of the authors and does not necessarily represent the official views of any of the funding agencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' CITATION DIVERSITY STATEMENT Recent work in several fields of science has identi- fied a bias in citation practices such that papers from women and other minority scholars are under-cited rel- ative to the number of such papers in the field [52–60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Here we sought to proactively consider choosing refer- ences that reflect the diversity of the field in thought, form of contribution, gender, race, ethnicity, and other factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' First, we obtained the predicted gender of the first and last author of each reference by using databases that store the probability of a first name being carried by 12 a woman [56, 61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' By this measure (and excluding self- citations to the first and last authors of our current pa- per), our references contain 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='37% woman (first)/woman (last), 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='67% man/woman, 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='29% woman/man, and 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='67% man/man.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This method is limited in that a) names, pronouns, and social media profiles used to con- struct the databases may not, in every case, be indica- tive of gender identity and b) it cannot account for in- tersex, non-binary, or transgender people.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Second, we obtained predicted racial/ethnic category of the first and last author of each reference by databases that store the probability of a first and last name being carried by an author of color [62, 63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' By this measure (and ex- cluding self-citations), our references contain 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='79% au- thor of color (first)/author of color (last), 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='60% white author/author of color, 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='05% author of color/white author, and 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='56% white author/white author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This method is limited in that a) names and Florida Voter Data to make the predictions may not be indicative of racial/ethnic identity, and b) it cannot account for In- digenous and mixed-race authors, or those who may face differential biases due to the ambiguous racialization or ethnicization of their names.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We look forward to future work that could help us to better understand how to sup- port equitable practices in science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Appendix A: Materials and Methods 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Data Collection and Network Construction The music files were collected in the MIDI for- mat from various sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The sources for the com- positions analyzed are as follows: preludes [64, 65], fugues [64, 65], inventions[64, 65], cantatas[66], English suites[67], French suites[67], chorales[65], Brandenburg concertos[65], toccatas[67], and concertos[67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The pre- ludes and fugues are split based on whether they belong to the first or second part of The Well-Tempered Clavier, and are labelled ‘1’ or ‘2’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Certain compositions consist of different movements and our data set has separate MIDI files for each movement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We analyze each movement sep- arately and average our measurements over them to yield a single measured quantity for each piece, as indexed by a unique BWV number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The MIDI files were read in MATLAB using the readmidi function in MATLAB [68] to obtain informa- tion about the notes being played.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Different instruments in a piece are stored in separate channels within each data file.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The transitions between notes are calculated separately for each instrument or track.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We assign each note present in a piece a node in the network, and notes from different octaves are assigned distinct nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We then draw an edge from note i to note j if there is a transition between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' If there are multiple notes be- ing played at a single time t (as is the case with chords), edges are drawn from the previously played note to all notes at time t, and from all the notes being played at time t to the subsequent note(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This procedure gives us a directed binary network of note transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We also construct weighted versions of these networks, where each edge is weighted by the number of times the correspond- ing transition occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Entropy of random walks on networks We use random walks to model how a sequence of in- formation is generated from an underlying network of information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Under this model, a walker traverses the network by picking an outgoing edge to traverse at each node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Given a network with adjacency matrix A and ma- trix element Aij, the probability that a walker transitions from node i to node j in a standard Markov random walk is Pij = Aij/kout i , where kout i = � j Gij is the out-degree of a node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We are interested in quantifying how much information is contained in the resulting sequence, which is captured by the entropy of the random walk: S = − � i πi � j Pij log Pij, where π is the stationary distribution of the walkers, which satisfies the condition Pπ = π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' For the simplest possible case of an undirected and unweighted network, Pij = 1/ki and πi = ki/2E, where ki is the degree of the ith node and E = � i,j Aij/2 is the total number of edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The entropy in this case simplifies to: S = 1 2E � i ki log ki = ⟨k log k⟩ ⟨k⟩ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (A1) We can apply a Taylor expansion to this expression around the average degree of the network, and thereby obtain: S = log⟨k⟩ + Var(k) 2 ⟨k⟩2 + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (A2) Hence we find that the entropy of random walks increase logarithmically with the average degree of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Additionally, it grows as the variance of the degrees in- creases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This formalization enables us to relate the in- formation content of various music networks to their net- work structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Model for how humans learn networks As discussed in the main text, when forming internal representations of information around them, each human arbitrates a trade-off between accuracy and cost [30, 31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In striking this balance, evidence suggests that humans perform a fuzzy temporal integration of transition struc- tures over time [29, 30, 69–71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This process results in humans connecting items in the sequence that are not directly adjacent to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Mathematically, we can 13 express the inferred transition structure ˆP in terms of the true transition structure P under this model of fuzzy temporal integration as: ˆP = ∞ � ∆t=0 f(∆t)P ∆t+1, (A3) where f(∆t) is the weight given to the higher powers of P and is a decreasing function of ∆t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The functional form of f(∆t) is obtained using a free energy model that captures the accuracy-complexity trade-off described in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Under this theory, the optimal distribution for f(∆t) is a Boltzmann distribu- tion with a parameter β that quantifies the trade-off be- tween cost and accuracy in forming an internal represen- tation of the information: f(∆t) = e−β∆t/Z, (A4) where Z = � e−β∆t = (1 − e−β)−1 is a normalization constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Substituting this expression to simplify Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' A3, we obtain an equation that relates the inferred tran- sition probabilities ˆP to the true transition probabilities P: ˆP =(1 − e−β)−1 ∞ � ∆t=0 e−β∆tP ∆t+1 =(1 − η)P(I − ηP)−1, (A5) where η = e−β.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Prior work has estimated the value of η to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='8 from large-scale online experiments in hu- mans [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Using this measured value of η, we use Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' A5 to calculate the learned network for any given music network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' KL-divergence To quantify how much the distorted learned transition structure ˆP differs from the original transition structure P, we calculate the Kullback-Leiber (KL) divergence be- tween the two transition structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The Kullback-Leiber divergence is a measure of how different a probability dis- tribution is from a reference distribution, and is given by: DKL(P|| ˆP) = − � i πi � j Pij log ˆPij Pij , (A6) where ⃗π is the stationary probability distribution of the transition matrix P, obtained by solving Pπ = π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The KL-divergence between two quantities is always non- negative and attains the value zero if and only if P = ˆP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The larger the KL-divergence, the more the inferred net- work ˆP differs from the original network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Hence, this quantity acts as a measure of the extent to which a net- work gets scrambled by the inaccuracies of human of learning—or in other words, how learnable a network structure is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Null Models We aim to identify distinct features in the music net- works that enable them to convey information effectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To assess whether our observations are merely due to ran- dom chance or are instead a unique feature of our dataset, we compare our measurements on the real music networks with the following null network models [72, 73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Null networks with the same number of nodes and edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' These are obtained by generating random networks with the same number of nodes and edges, and enable us to assess whether the quantity we have measured is to be expected merely based on network size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Degree-preserving null networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' These are ran- domized networks of the same size, with the ad- ditional constraint that the in- and out-degrees of each node in the network are preserved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Such net- works are constructed by swapping edges between pairs of nodes in the network iteratively, such that the in- and out-degrees of each node are preserved but the connectivity (or topology) of the network is randomized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This class of null models enable us to evaluate the role that connectivity or topology plays in the quantity we are measuring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We can generalize the degree-preserving null networks to weighted networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We are interested in degree- preserving randomized networks since these keep the node-level entropies fixed and allow us to study the im- pact of topology on the quantities we are measuring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In the case of weighted networks, the node-level entropies are determined by the out-weights and out-degrees of the nodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Hence, our procedure of swapping edges between pairs of nodes in the network still works since it pre- served the out-weights of each node in addition to the in- and out-degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' With these null models, we can bench- mark the presence of the quantities we are interested in, and identify the role that the connectivity pattern or size plays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Transitive Clustering Coefficient Along the lines of the clustering coefficient of a node [44, 74], we define the transitive clustering coefficient as a measure of the degree to which nodes in a directed net- work tend to form transitive relationships.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The transitive clustering coefficient of a node i (for an unweighted graph with no self loops) is given by: CT i = ∆T i ktot i (ktot i − 1), (A7) where ∆T i denotes the number of transitive triangles that node i is a part of and ktot i is the total degree (in + out) of the node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The denominator simply counts the number 14 of triangles that could exist within the neighborhood of node i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The 8 different possible triangles with node i as a vertex in a directed graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The triangles which represent transitive relationships are marked using the letter ’T’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The possible directed triangles involving node i can be divided into two categories—those representing cyclic relationships and those representing transitive relation- ships (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The number of transitive triangles involv- ing node i that actually exist can be expressed in terms of the adjacency matrix of the graph A, CT i = (A + AT )3 ii − A3 ii − (AT )3 ii 2 ktot i (ktot i − 1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (A8) This expression counts a subset of the total number of triangles, and is a special case of the expression derived in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We will use this expression to measure the transitive clustering coefficient of each music networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Appendix B: Supplementary Information 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Introduction In this Supplementary Information, we provide ex- tended analysis and discussion to support the results pre- sented in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' B 2, we expand upon our analysis of the information content of Bach’s music networks and how it relates to network structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' B 5, we examine the transitive clustering coefficient more closely and study meso-scale features that might explain the differences observed across compositional forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Information content To better visualize the variation in information content among the musical compositions, we assign each piece an index number and plot the information entropy for each piece as a function of its index number (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 8A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We observe here more clearly how different compositional forms tend to have pieces clustered together in their en- tropies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' As reported in the main text, we find that the chorales have a markedly lower entropy than the rest of the compositions studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In contrast, the toccatas and the second set of preludes have a much higher en- tropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To relate the information entropy of the music networks to their structure, we compare their entropy to corresponding null networks (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 2A and B in the main text), where we conclude that the information entropy is primarily determined by the degree distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In the case of undirected and unweighted networks, the network entropy depends upon the logarithm of the average de- gree of the network and the heterogeneity in the degree distribution (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 4) to first and second order, respec- tively [31, 35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We now provide supplementary results that relate the information entropy of the music networks to their structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Understanding the information entropy to first order: average degree On plotting the information entropy of the music net- works as a function of their average degree (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 8B), we see that the differences in the information entropy of the compositional forms to first order arise due to differences in their average degrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Although we observed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 8A that the compositional forms are clustered together in their entropy, it is clear that some pieces—such as the chorales, French suites, English suites, and cantatas— are more tightly clustered than the fugues and first set of preludes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' These differences can be explained by the how much the average degrees vary across pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 9, we plot the entropy of the music networks as a function of the average network degree, separately for each com- position type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Additionally, we also report the standard deviation in the average degree of the pieces for each com- position type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Studying these plots, we observe that the English suites, French suites, and chorales (which clus- tered more tightly in their entropies) have tighter degree distributions, while the fugues (which are more spread out in their entropy) display more diverse average de- grees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Understanding the information entropy to second order: degree heterogeneity In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 2A of the main text, we observed that the entropy of the real music networks is larger than corre- sponding randomized null networks with the same num- ber of nodes and edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Since the average degree is the same for the two networks, we hypothesize that the differ- ences arise due to higher in- and out-degree heterogene- ity as per Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To test our hypothesis, we compare the in- and out-degree heterogeneity of the music networks (calculated using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 5) with their corresponding null networks in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In general, we observe that Bach’s music networks are indeed more heterogeneous than ex- pected from the random networks of the same size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This organization allows them to pack more information into their structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The heterogeneity in degrees can also explain the dif- ferences in entropies observed between pieces that are 1 2 0 2 215 A B FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The entropy of Bach’s music networks and its relation to the average degree of the network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (A) The entropy of Bach’s music networks (Sreal) indexed by the pieces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (B) The entropy of Bach’s music networks (Sreal) as a function of the average degree of the network ⟨k⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Each data point in panels (A) and (B) represents a single piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Colors and markers indicate the type of pieces, as shown in the legend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' tightly clustered together in their entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' As observed earlier, compositions such as the chorales, French suites, English suites, and cantatas have pieces that are clus- tered together in their average degree and consequen- tially, in their entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We expect that the differences observed among the pieces in each group can be explained by differences in their degree heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 11 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 2C, we plot the entropies of the pieces that clus- tered together as a function of their in- and out-degree heterogeneity, and in general observe that the pieces with higher heterogeneity have a higher information entropy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' However, we note that our sample size for most com- positional forms is small and hence, we only report the chorales in the main text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Further analysis of the transitive clustering coefficient In our analysis of the discrepancies between the ac- tual and perceived information content of note transi- tions in Bach’s musical compositions, we found that these discrepancies were primarily driven by the presence of transitive triangular clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' These transitive triangular clusters tend to bring the inferred network closer to the actual network, making the network more learnable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 12A, the real (unweighted) music networks tend to have a higher transitive clustering coefficient than random networks that preserve the degree of each node, indicating that this is a distinct feature of the music net- works that is not merely due to coincidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The data in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 12A has a striking shape, which we elaborate on and analyze in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' First we observe that the chorale pieces tend to have a higher transitive clustering coefficient than expected from networks of their same size and degree distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Second, although the pre- ludes have a higher transitive clustering coefficient than other compositional forms, the value was still lower than expected from networks of their same size and degree distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Indeed, by examining only the x-axis, we notice that the null networks corresponding to the pre- ludes have a higher transitive clustering coefficient than the null networks corresponding to chorales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' However, by examining the y-axis, we see that the deviation be- tween the real chorales and the prelude networks are not that pronounced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We hypothesize that these differences might be due to the presence of mesoscale features in the networks, such as core-periphery structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Core-periphery structure Core-periphery structure in a network refers to the presence of two components: a tightly connected “core” and a sparsely connected “periphery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The core consists of nodes which are well-connected to each other and to the periphery, while the nodes in the periphery are sparsely connected to one another and to the nodes in the core [76, 77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We hypothesize that the presence of a relatively larger core might explain why the chorales have a higher clustering coefficient than expected given their size and degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Similarly, a smaller than expected core for the preludes might be explain why their clustering coefficient was lower than expected from networks of the same size and degree distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Since the core consists of nodes that are well-connected to themselves and the periphery, 16 A B C D E F G H I J K L FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The relation between the information entropy and the average degree of the music networks plotted separately for each compositional form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The entropy of Bach’s music networks (Sreal) plotted against the average degree of the network ⟨k⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Each data point represents a single piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Colors and markers indicate the type of pieces, as shown in the legend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' if there are a larger number of edges occurring within the core and between the core and periphery than be- tween the periphery nodes, it is likely that these edges will form the clusters that we are interested in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We de- 17 A B FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Comparing the heterogeneity of Bach’s music networks to randomized null networks of the same size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (A) The in-degree heterogeneity of the music networks compared with random networks of the same size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (B) The out-degree heterogeneity of the music networks compared with random networks of the same size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Each data point in panels (A) and (B) represents a single piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Colors and markers indicate the type of pieces, as shown in the legend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' For each random network, we report the in- and out- degree heterogeneity after averaging over 100 independent realizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Error bars on the x-axis represent the standard error of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' A B C D FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The relation between the information entropy of Bach’s music networks and its degree heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The entropy of Bach’s music networks (Sreal) plotted against the network in- and out-degree heterogeneity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Each data point represents a single piece.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Colors and markers indicate the type of pieces, as shown in the legend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The dotted line in each panel indicates the best linear fit, and the reported rs value is the Spearman correlation coefficient between the x- and y-axis variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' note the edges between two nodes that belong to the core by core-core (CC), those between nodes that belong to the periphery by periphery-periphery (PP), and those between the nodes in the core and the nodes in the pe- riphery by core-periphery (CP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To test our hypothesis, we compute the core-periphery 18 A B FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Core-periphery analysis of the music networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (A) The transitive clustering coefficient of the real music networks compared to null networks that preserve the in- and out-degree of each node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' For the degree-preserving null networks, we report the average over 100 independent realizations, with error bars denoting the standard error of the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' (B) The ratio of the number of core-core (CC) edges and core-periphery (CP) edges to the number of periphery-periphery (PP) edges in the real music networks compared to degree-preserving null networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' For the degree-preserving null networks, we report the average value computed over 100 independent random graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' In both panels, the dotted line indicates the line y = x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Colors and markers indicate the type of piece, as shown in the legend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' structure for each music network using the method de- scribed by Borgatti and Everett [77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' We then compute the ratio of the sum of the number of core-core (CC) edges and core-periphery (CP) edges to the number of periphery-periphery (PP) edges for each network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' To understand this ratio, we compare it to corresponding degree-preserving null networks (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 12B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Strikingly, we observe that the chorales have a higher fraction of edges that are within or emanating from the core than expected from their corresponding null networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' The preludes are at the other end, and have a lower frac- tion of edges that are within or emanating from the core than expected from their corresponding null networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' This pattern of findings suggests that the chorales have a more pronounced core-periphery structure than expected by chance, while the preludes have a less pronounced core-periphery structure than expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Although the preludes still have a slightly higher transitive clustering coefficient than the other pieces, the differences are not as pronounced as one would expect because of these dif- ferences in their core-periphery structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' By performing this additional analysis, we provide an example of how the music networks display interesting meso-scale structures that differ from one compositional form to another, resulting in differences in how their net- work structure is perceived.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 19 [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Mithen, The Singing Neanderthals: the origins of music, language, mind and body (Harvard University Press, 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [2] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Fitch, “The biology and evolution of music: A comparative perspective,” Cognition 100, 173–215 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [3] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Hagen and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Hammerstein, “Did neanderthals and other early humans sing?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' seeking the biological roots of music in the territorial advertisements of primates, li- ons, hyenas, and wolves,” Musicae Scientiae 13, 291–320 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [4] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Levman, “The genesis of music and language,” Eth- nomusicology 36, 147–170 (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [5] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Masataka, “Music, evolution and language,” Develop- mental science 10, 35–39 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [6] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Welch, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Biasutti, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' MacRitchie, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' McPher- son, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Himonides, “The impact of music on human development and well-being,” (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [7] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Cross, “Music, cognition, culture, and evolution,” An- nals of the New York Academy of sciences 930, 28–42 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [8] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' McClary, “The impromptu that trod on a loaf: Or how music tells stories,” Narrative 5, 20–35 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [9] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Glennie, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Mac Donald, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=', Musical communica- tion (Oxford University Press on Demand, 2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [10] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' R Scherer and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Coutinho, “How music creates emo- tion: a multifactorial process approach,” The emotional power of music: Multidisciplinary perspectives on mu- sical arousal, expression, and social control , 121–145 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [11] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Koelsch, “Brain correlates of music-evoked emotions,” Nature Reviews Neuroscience 15, 170–180 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [12] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Blood and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Zatorre, “Intensely pleasurable responses to music correlate with activity in brain regions implicated in reward and emotion,” Proceedings of the National Academy of Sciences 98, 11818–11823 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [13] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Huron, Sweet Anticipation: Music and the Psychology of Expectation (The MIT Press, 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [14] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Tillmann, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Poulin-Charronnat, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bigand, “The role of expectation in music: from the score to emotions and the brain,” WIREs Cognitive Science 5, 105–113 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [15] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Meyer, Emotion and Meaning in Music, ACLS Hu- manities E-Book (University of Chicago Press, 1956).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [16] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Shannon, “A mathematical theory of communica- tion,” The Bell System Technical Journal 27, 379–423 (1948).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [17] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Piantadosi, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Tily, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Gibson, “Word lengths are optimized for efficient communication,” Proceedings of the National Academy of Sciences 108, 3526–3529 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [18] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Plotkin and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Nowak, “Language evolution and information theory,” Journal of Theoretical Biology 205, 147–159 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [19] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Eckmann, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Moses, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Sergi, “Entropy of dialogues creates coherent structures in e-mail traffic,” Proceedings of the National Academy of Sciences 101, 14333–14337 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [20] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Zhao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Karsai, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bianconi, “Entropy of dy- namical social networks,” PLOS ONE 6 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [21] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Rosvall, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Trusina, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Minnhagen, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Snep- pen, “Networks and cities: An information perspective,” Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 94, 028701 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [22] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Cohen, “Information theory and music,” Behavioral Science 7, 137–163 (1962).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [23] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Hiller and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bean, “Information theory analyses of four sonata expositions,” Journal of Music Theory 10, 96–137 (1966).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [24] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Liu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Chi, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Small, “Complex network structure of musical compositions: Algorithmic genera- tion of appealing music,” Physica A: Statistical Mechan- ics and its Applications 389, 126–132 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [25] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Gomez, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Lorimer, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Stoop, “Complex net- works of harmonic structure in classical music,” in Non- linear Dynamics of Electronic Systems (Springer Inter- national Publishing, Cham, 2014) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 262–269.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [26] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Boon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Noullez, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Mommen, “Complex dy- namics and musical structure,” Interface 19, 3–14 (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [27] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Liu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Wei, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Xin, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Huang, “A sta- tistical physics view of pitch fluctuations in the classical music from bach to chopin: Evidence for scaling,” PLOS ONE 8, 1–6 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [28] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Kahneman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Slovic, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Slovic, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Tver- sky, Judgment under uncertainty: Heuristics and biases (Cambridge university press, 1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [29] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Dayan, “Improving generalization for temporal dif- ference learning: The successor representation,” Neural computation 5, 613–624 (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [30] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Lynn, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Kahn, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Nyema, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bassett, “Ab- stract representations of events arise from mental errors in learning and memory,” Nature Communications , 2313 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [31] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Lynn, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Papadopoulos, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Kahn, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bassett, “Human information processing in complex net- works,” Nature Physics 16, 965 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [32] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Lynn and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bassett, “How humans learn and represent networks,” Proceedings of the National Academy of Sciences 117, 29407 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [33] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Jagari, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Pedram, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Hedayatifar, “Long- range correlation and multifractality in Bach’s invention pitches,” Journal of Statistical Mechanics: Theory and Experiment 04 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [34] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Moore, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Corrˆea, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Small, “Is bach’s brain a markov chain?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' recurrence quantification to assess markov order for short, symbolic, musical compositions,” Chaos: An Interdisciplinary Journal of Nonlinear Science 28, 085715 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [35] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Gomez-Gardenes and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Latora, “Entropy rate of dif- fusion processes on complex networks,” Physical Review E 78, 065102 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [36] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Albert, “Scale-free networks in cell biology,” Journal of cell science 118, 4947–4957 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [37] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Lerman, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Yan, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Wu, “The” majority illu- sion” in social networks,” PloS one 11, e0147617 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [38] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Barab´asi and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Albert, “Emergence of scaling in random networks,” Science 286, 509–512 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [39] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Kahn, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Karuza, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Vettel, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bas- sett, “Network constraints on learnability of probabilis- tic motor sequences,” Nature Human Behavior , 936–947 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [40] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Stiller, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Nettle, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' IM Dunbar, “The small world of shakespeare’s plays,” Human Nature 14, 397– 20 408 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [41] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Choi and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Kim, “A directed network of greek and roman mythology,” Physica A: statistical Mechanics and its Applications 382, 665–671 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [42] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Thickstun, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Harchaoui, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Kakade, “Learn- ing features of music from scratch,” arXiv preprint arXiv:1611.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='09827 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [43] I Liu, Bhiksha Ramakrishnan, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=', “Bach in 2014: Mu- sic composition with recurrent neural network,” arXiv preprint arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='3191 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [44] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Watts and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Strogatz, “Collective dynamics of ‘small-world’ networks,” Nature 393, 440–442 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [45] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Zivic, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Shifres, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Cecchi, “Percep- tual basis of evolving western musical styles,” Proceed- ings of the National Academy of Sciences 110, 10034– 10038 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [46] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' P´erez-Sancho, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Rizo, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' I˜nesta, “Genre clas- sification using chords and stochastic language models,” Connection Science 21, 145–159 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [47] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Simonton, “Melodic structure and note transi- tion probabilities: A content analysis of 15,618 classical themes,” Psychology of Music 12, 3–16 (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [48] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Tzanetakis and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Cook, “Musical genre classification of audio signals,” IEEE Transactions on speech and audio processing 10, 293–302 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [49] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Soltau, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Schultz, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Westphal, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Waibel, “Recognition of music types,” in Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP’98 (Cat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 98CH36181), Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 2 (IEEE, 1998) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 1137–1140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [50] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Lidy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Schindler, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=', “Parallel convolutional neu- ral networks for music genre and mood classification,” MIREX2016 3 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [51] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bahuleyan, “Music genre classification using machine learning techniques,” arXiv preprint arXiv:1804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='01149 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [52] Sara McLaughlin Mitchell, Samantha Lange, and Holly Brus, “Gendered citation patterns in international re- lations journals,” International Studies Perspectives 14, 485–492 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [53] Michelle L Dion, Jane Lawrence Sumner, and Sara McLaughlin Mitchell, “Gendered citation patterns across political science and social science methodology fields,” Political Analysis 26, 312–327 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [54] Neven Caplar, Sandro Tacchella, and Simon Birrer, “Quantitative evaluation of gender bias in astronomical publications from citation counts,” Nature Astronomy 1, 0141 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [55] Daniel Maliniak, Ryan Powers, and Barbara F Walter, “The gender citation gap in international relations,” In- ternational Organization 67, 889–922 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [56] Jordan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Dworkin, Kristin A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Linn, Erin G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Teich, Perry Zurn, Russell T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Shinohara, and Danielle S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bassett, “The extent and drivers of gender imbalance in neuro- science reference lists,” bioRxiv (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [57] Maxwell A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bertolero, Jordan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Dworkin, Sophia U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' David, Claudia L´opez Lloreda, Pragya Srivastava, Jen- nifer Stiso, Dale Zhou, Kafui Dzirasa, Damien A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Fair, Antonia N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Kaczkurkin, Bianca Jones Marlin, Daphna Shohamy, Lucina Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Uddin, Perry Zurn, and Danielle S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bassett, “Racial and ethnic imbalance in neuroscience reference lists and intersections with gender,” bioRxiv (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [58] Xinyi Wang, Jordan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Dworkin, Dale Zhou, Jennifer Stiso, Emily B Falk, Danielle S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bassett, Perry Zurn, and David M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Lydon-Staley, “Gendered citation practices in the field of communication,” Annals of the International Communication Association (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [59] Paula Chatterjee and Rachel M Werner, “Gender dispar- ity in citations in high-impact journal articles,” JAMA Netw Open 4, e2114509 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [60] Jacqueline M Fulvio, Ileri Akinnola, and Bradley R Pos- tle, “Gender (im)balance in citation practices in cognitive neuroscience,” J Cogn Neurosci 33, 3–7 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [61] Dale Zhou, Eli J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Cornblath, Jennifer Stiso, Erin G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Te- ich, Jordan D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Dworkin, Ann S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Blevins, and Danielle S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Bassett, “Gender diversity statement and code notebook v1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='0,” (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [62] Anurag Ambekar, Charles Ward, Jahangir Mohammed, Swapna Male, and Steven Skiena, “Name-ethnicity clas- sification from open sources,” in Proceedings of the 15th ACM SIGKDD international conference on Knowledge Discovery and Data Mining (2009) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' 49–58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [63] Gaurav Sood and Suriyan Laohaprapanon, “Predicting race and ethnicity from the sequence of characters in a name,” arXiv preprint arXiv:1805.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='02109 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [64] “Bach central,” http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='bachcentral.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='com/ midiindexcomplete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='html.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [65] “Kern scores,” http://kern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='humdrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='org/search?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='s=t& keyword=Bach+Johann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [66] “Bach cantatas website,” https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='bach-cantatas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' com/Mus/BWV1-Mus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='htm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [67] “Suzu midi,” http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='suzumidi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='com/eng/bach4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' htm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [68] “Midi file tools for matlab by ken schutte,” https:// github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content='com/kts/matlab-midi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [69] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Momennejad, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Russek, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Cheong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Botvinick, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Daw, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Gershman, “The suc- cessor representation in human reinforcement learning,” Nature human behaviour 1, 680–692 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [70] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Gershman, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Moore, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Todd, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Nor- man, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Sederberg, “The successor representation and temporal context,” Neural Computation 24, 1553– 1568 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [71] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Garvert, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Dolan, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' EJ Behrens, “A map of abstract relational knowledge in the human hippocampal–entorhinal cortex,” elife 6 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [72] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Newman and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Girvan, “Finding and evaluat- ing community structure in networks,” Physical review E 69, 026113 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [73] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' V´aˇsa and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Miˇsi´c, “Null models in network neuro- science,” Nature Reviews Neuroscience , 1–12 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [74] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Szab´o, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Alava, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Kert´esz, “Clustering in complex networks,” Lecture Notes in Physics 650, 139– 162 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [75] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Fagiolo, “Clustering in complex directed networks,” Physical Review E 76, 026107 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [76] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Rombach, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Porter, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Fowler, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Mucha, “Core-periphery structure in networks,” SIAM Journal on Applied mathematics 74, 167–190 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' [77] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Borgatti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} +page_content=' Everett, “Models of core/periphery structures,” Social Networks 21, 375–395 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/BtAyT4oBgHgl3EQf4PqZ/content/2301.00783v1.pdf'} diff --git a/BtE4T4oBgHgl3EQfeA0g/content/2301.05095v1.pdf b/BtE4T4oBgHgl3EQfeA0g/content/2301.05095v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..771eb0230ebd34bae8ce6fadb8e6fcc6965775c8 --- /dev/null +++ b/BtE4T4oBgHgl3EQfeA0g/content/2301.05095v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2f0506f157f1a266406cedfecb93de920110b5b6ba4cd7036bae4842d6392743 +size 6758859 diff --git a/CNE1T4oBgHgl3EQfVwTa/vector_store/index.faiss b/CNE1T4oBgHgl3EQfVwTa/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..8254ac2fb8d3542158771ad2fe8e39e2373cda9a --- /dev/null +++ b/CNE1T4oBgHgl3EQfVwTa/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b67d9d03e9d20ba329deb493846355deec9ba44184072e1507e7a1312f7949d7 +size 6094893 diff --git a/CtE0T4oBgHgl3EQfQQAs/vector_store/index.pkl b/CtE0T4oBgHgl3EQfQQAs/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..616a92cfe80c4ae8432c6e939b2b7a49fda39748 --- /dev/null +++ b/CtE0T4oBgHgl3EQfQQAs/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e8d110fb83f3c8af8d636e00814bedc46234d9d1911eeb07b4e614914bec5151 +size 433440 diff --git a/DdAzT4oBgHgl3EQfwf7y/vector_store/index.pkl b/DdAzT4oBgHgl3EQfwf7y/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..01b49e117accbc2747d667626da9c8a246f2c14b --- /dev/null +++ b/DdAzT4oBgHgl3EQfwf7y/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a5eeaf14de544b45d3b49ce1b5504a69282183ec0dcc6b56424fbe06a5c869c5 +size 239563 diff --git a/FdE1T4oBgHgl3EQfEwOD/content/tmp_files/2301.02894v1.pdf.txt b/FdE1T4oBgHgl3EQfEwOD/content/tmp_files/2301.02894v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..229b5d5f75b4a1564b7b0c9ab704dabcc718b1ec --- /dev/null +++ b/FdE1T4oBgHgl3EQfEwOD/content/tmp_files/2301.02894v1.pdf.txt @@ -0,0 +1,673 @@ +XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE +Quantum Encryption in Phase Space using +Displacement Operator for QPSK Data Modulation + + + + +Randy Kuang +Quantropi Inc. +Ottawa, Canada +randy.kuang@quantropi.com +ORCID: 000-0002-5567-2192 + + +Adrian Chan +Quantropi Inc. +Ottawa, Canada +adrian.chan@quantropi.com + + + + + +Abstract—Quantum Public Key Distribution or QPKE with +the randomized phase shift gate was proposed by Kuang and +Bettenburg in 2020. It has been implemented theoretically with +simulations and experimentally over existing fiber optical +networks since then. QPKE can be considered as an RSA-type +scheme in optical analogue domain. QPKE was renamed as +Quantum Encryption in Phase Space or QEPS to reflect the +encryption of coherent states in phase space. QEPS with the phase +shift gate can only be applied to data modulation scheme with +phase shift keying such as quadrature phase shift keying or QPSK. +It would leak data information in amplitude once it is applied to +quadrature amplitude modulation or QAM schemes. Kuang and +Chan recently proposed a new version of QEPS called Quantum +Encryption in Phase Space with the displacement gate or QEPS-d. +It demonstrated to overcome the limitation of QEPS with the +phase shift gate. We introduced a reduced displacement operator +by ignoring the global phase factor then the reduced displacement +operators are commutable. This commutability helps our +implementation at both transmission and receiving. An arbitrary +displacement operator can be decoupled into a standard QAM +modulation with a phase shift modulation to ease our encryption +and decryption. This paper simulates the QEPS-d encryption for +QPSK data modulation to demonstrate how QEPS-d works. +Keywords—quantum cryptography, post-quantum cryptography, +PQC, quantum encryption, coherent state, phase shift gate, +displacement gate, quadrature amplitude modulation, QAM, +quadrature phase shift keying, QPSK +I. INTRODUCTION + After Shor proposed his algorithm with quantum bit or qubit +for integer factorization in 1994 [1], it has been well-understood +that classical public key algorithms such as RSA based on the +factorization problem, Diffie-Hellman or elliptic Diffie- +Hellman based on the discrete logarithm are breakable once fault +tolerate quantum computers are available. However, breaking +RSA-2048 requires a fault tolerate quantum computer to have +more than 4000 logic qubits or 4 million physical qubits. The +latest released IBM quantum computer Osprey offers 433 +physical qubits [2]. The IBM roadmap shows that they will +release their next quantum computer Condor with 1121 qubits +in 2023 and qubits will raise over 100,000 in 2026. Very +recently, Yan, et al. proposed a new algorithm by combining +classical lattice reduction with quantum optimization called +Sublinear-resource Quantum Integer Factorization (SQIF) [3]. +SQIF works in a noise quantum computer with a quantum +resource reduction or qubits of 4 magnitudes from 4 million of +physical qubits to less than 400 physical qubits. They have +demonstrated it for a 48-bit integer factorization with as little as +a 10-qubit quantum processor. +National Institute of Standards and Technology or NIST +started the standardization process in the late of 2017 and +completed its three rounds in 2021 [4] and announced its final +standardized algorithms for key encapsulation mechanism or +KEM and digital signature algorithms [5]. The lattice-based +Kyber [6] becomes the standardized winner for KEM and the +lattice-based Dillithium [7] and Falcon [8], as well as hash- +based SPHINCS+ [9] become the standardized algorithms for +digital signature. NIST continues its standardization for KEM in +its round 4 and reopens its standardization of digital signature +for submissions in the early 2023. +Some major cryptanalyses have made NIST finalists +vulnerable in 2022. Beullens broke Rainbow signature with a +laptop over a weekend [10], Robert broke SIDH [11] and +Castryck and Decru made its more efficient to break SIDH level +I in one hour with a single core computer [12]. Wenger, et al. +reported their secret recovery of lattice-based PQC with +machine learning by training the transformer with 300,000 +samples and achieved the complete secret recovery for up to a +mid-size lattice dimension. +Some recent developments in PQC KEM and digital +signature were proposed by Kuang’s team, called Multivariate +Polynomial Public Key or MPPK by leveraging the NP- +complete problem of the Modular Diophantine Equation +Problem [14, 15, 16, 17]. MPPK offers relatively small public +key size, cipher size, and signature size, comparable to the +classical public key schemes. They also outperform NIST +finalists in performances of key generation, encryption, +decryption, signing and verification. MPPK could become good +alternatives to NIST finalists for generic use cases. MPPK +digital signature scheme is planned to participate in the NIST +reopening submission for digital signature. +On the other hand, Quantum Key Distribution or QKD was +developed over three decades since it was proposed in 1984. +Shor and Preskill proved that QKD offers the information +theoretical security in 2000 [18]. It has become commercial +ready for a distance at around 100km. To break the distance + +boundary, Lucamarini, et. Al. proposed Twin-Field QKD or TF- +QKD in 2018 [19]. TF-QKD has been widely explored since +then and the longest distance of 830km was reported by Wang, +et al. in 2022 [20]. QKD generally offers a key rate at kbps level +and TF-QKD [20] achieved a key rate at 0.014 bps at 830km, +requiring more than 5 hours to establish a 256 bits of AES key. + Considering the pre-shared secret for QKD authentication, +Kuang and Bettenburg in 2020 proposed a new mechanism +using Quantum Permutation Pad or QPP to digitally distribute +quantum random [21]. The pre-shared secret is not only used for +authentication but also used to map to a QPP pad for encoding +at the sender and decoding at the receiver. QPP is implemented +into matrices operating on data column vector or Dirac ket. +Permutation matrix is unitary and reversable, so the decoding +side uses the reversed QPP. Kuang and Barbeau proposed a +universal quantum safe cryptography using QPP in 2022 [22]. +QPP has been developed as a platform for digital QKD and +benchmarked by Deutsche Telekom in 2022 [23]. Leveraging +the quantum gate property of QPP, quantum encryption with +QPP implemented inside quantum computers was reported by +Kuang and Perepechaenko in 2022 [24], Perepechaenko and +Kuang in 2022 [25, 26]. +To eliminate the pre-shared key in quantum key distribution +in coherent optical domain, Kuang and Bettenburg in 2020 +proposed Quantum Public Key Envelope or QPKE using +randomized phase shift gate in a round-trip scheme [27], +leveraging the self-shared random secret to drive the phase shift +encoding without the specific requirement of the pre-shared +secret. QPKE was designed to operate in the existing coherent +optical networks with the same coherent detection module. It has +been simulated and experimentally implemented through the +collaborations with McGill University [28, 29, 30, 31]. QPKE +mimics the RSA-type public key scheme in coherent optical +domain. The experiment implementation with off-shelf optical +modules demonstrated the speed at 200 gbps for a distance 80km +between two communication peers. To mimicking its +implementation in a symmetric fashion with a pre-shared secret, +QPKE was renamed as Quantum Encryption in Phase Space or +QEPS with the randomized phase shift gate, reflecting to its +possible implementation in photonic quantum computer with +phase shift gate. There is one limitation of QEPS with phase shift +gate, or only applicable for data modulation schemes with phase +shift keying such as QPSK or M-PSK. Once the data modulation +is quadrature amplitude modulation or QAM, the amplitude bits +would be leaked out. +To overcome this limitation, Kuang and Chan recently +proposed to use coherent displacement operator ����� where � +denotes a coherent state [32]. This paper will report its +simulation results with QPSK data modulation. Section 2 will +briefly summarize the QEPS with the displacement operator and +section 3 will present the simulation result and the conclusion is +at the end. +II. QEPS WITH DISPLACEMENT OPERATOR +A. Coherent State and Displacement Operator + +A coherent state is the specific quantum state of quantum +harmonic oscillator denoted by a Dirac ket |�⟩ where � is a +complex variable in the phase space. � can be expressed either +in terms of in-phase and quadrature as � = �� + � �� or +amplitude and phase � = |�|���. Then a coherent state can be +written as + +|�⟩ = ��� + � ��� = | |�|��� ⟩ + (1) +And the displacement operator is defined with creation and +annihilation operators ��� and �� through following equation + + +|�⟩ = �� �� ���∗ �� |0⟩ = ����� |0⟩ + (2) +So + + +����� = �� �� ���∗ �� + (3) +which indicates the displacement operator is unitary and +reversable: + + +������ = ��� �� ���∗ ��� +� += ���−�� = ��� ��� (4) +Let’s apply the displacement operator ����� to a coherent state +|�⟩ + ����� |�⟩ = ����� ����� |0⟩ = ��!∗��∗!���� + ��|0⟩ (5) +And in the same way +����� |�⟩ = ����� ����� |0⟩ = �!�∗�!∗����� + ��|0⟩ (6) +So, it is clear that ����� and ����� are not commutable due to the +global phase factor ��!∗��∗! but that does not impact our +physical measurements on the amplitude and phase of a coherent +state. Therefore, we can ignore the global phase factor and +introduce +a +reduced +displacement +operator +"#��� = + ���!∗$�∗!�����. Then the reduced displacement operator "#��� +and "#��� are commutable. +B. QEPS with Reduced Displacement Operator +From Eq. (5), QEPS encryption with a reduced displacement +operator "#��� can be expressed as follows +"#��� |�⟩ = "#�� + ��|0⟩ = |� + �⟩ = |%⟩ (7) +with |�⟩ to be a plain coherent state, "#��� to be an encryption +operator and |%⟩ to be the encrypted cipher coherent state. Eq. +(7) indicates that QEPS encryption with the reduced +displacement operator or QEPS-d essentially performs an +addition of two coherent states |�⟩ and |�⟩ as shown in Fig. 1. +A general displacement operator would change both the +amplitude and phase of a plain coherent state. But it can also +only change the phase of the plain coherent as shown in Fig. 1. +In this special case, the displacement operator behaves like a +phase shift operator. +The encryptor "#��� can be controlled by a pre-shared secret +in a symmetric encryption or a self-shared secret in an +asymmetric encryption as shown in QPKE [27]. In the ideal +communication case, the receiver would decrypt the cipher +coherent state |%⟩ with "#� ��� = "#�−�� : "#� ���|%⟩ = +"#�−��|%⟩ = |−� + %⟩ = |�⟩. +In coherent optical communications, optical line path would +impact a coherent state during transmission from the sender to +the receiver such as dispersion, attenuation, polarization, noise, + +environment factors, etc. Thanks to the digital signal processing +or DSP, all those impacts could be compensated and corrected +in the electrical digital domain. Based on that, we only consider +the encryption and decryption in the ideal transmission situation. +A displacement operator can be decomposed into two or +more displacement operators as follows +"#��� = "#�� � "#��&� … "#��(� +And +"#���|�⟩ = "#�� � "#��&� … "#��(�|�⟩ + = |� + �& + ⋯ �( + �⟩ +This decomposition feature helps us to ease the implementation +of a general displacement operator with two operators: "#�� � +implemented with a standard modulation such as QAM and +"#��&� with a phase shift operator. By doing that, we can +overcome the weakness of original QPKE scheme [27]. +III. QEPS-D SIMULATION +The simulation is performed with OptiSystem and the +simulation layout is illustrated in Fig. 2. The major modules are +explained in the figure caption. The only extra components are +needed to discuss here are QEPS and RNG. All others are +common for typical coherent optical communications. The +random number generator or RNG should be a cryptographic +PRNG or pseudo–Quantum Random Number Generator or +pQRNG [33] with generated random number meeting +cryptographic requirement. pQRNG is capable to take upto 16 +KB of the pre-shared secret and produces pseudo random +number with excellent randomness [33]. QEPS consists of two +operators: "#�� � implemented with standard data modulation +such as 16-QAM or QPSK and "#��&� implemented with a +random phase shift operator. These two operators together offer +a coherent encryption with a generic displacement operator +"#���. QEPS produces a complex modulation form based on the +rand number generated from RNG module. The complex +modulation form dictates the signal generator to produce +voltages for IQ modulator. In Fig. 2, we omitted the data input +which is combined with QEPS. Once the coherent states are +generated from CW and pass IQ Modulator, their amplitude and +phase would be modulated by IQ modulator then the encrypted +cipher coherent states are transmitted over 80 km fiber to +coherent detector at the receiver side. Typical coherent detection +is applied to produce electrical digital signal and QEPS-d +decryption is done before DSP processing. The simulation +parameters are given in Table 1. +We simulated QEPS encryption with the reduced +displacement operator for QPSK data modulations and plot +constellation diagrams in 3 cases: +1. Constellation right after coherent detection as shown in Fig. +3. This constellation diagram displays the detections of +cipher coherent states together with fiber path impacts. +2. Constellation diagram after applying the digital signal +processing as shown in Fig. 4. +TABLE 1. SIMULATION PARAMETERS ARE TABULATED. + +Layout +Parameter +Sequence length +Baudrate +PM period +65,536 bits +28 Gbaud +1024 +CW Laser and +LO Laser +Center wavelength +Power +Linewidth +Azimuth +1550 nm +5 dBm +0.1 MHz +0.45 degree +IQ Modulator +Extinction ratio +Switching bias +Insertion loss +20 dB +3 V +5 dB +EDFA +Forward pump power +Forward pump wavelength +Loss at 1550 nm +Loss at 980 nm +13-14 mW +980 nm +0.1dB/m +0.15 dB/m +Optical Fiber +Length (1 spool) +Attenuation +Dispersion +Dispersion slope +Differential group delay +Effective area +80 km +0.2 dB/km +0.3 16.75 ps/nm/km +0.4 0.075 ps/nm2/km +0.5 0.2ps/km +80 μm2 +Figure 1. Illustration of QEPS-d is plotted in the phase space. A +special case of QEPS with phase shift operator is also plotted for +demonstration purpose of a general displacement operator "#���. +Figure 2. Simulation layout is illustrated. CW: continuous wave +source, IQ Modulator: in-phase and quadrature modulator, +,, .,and ++/ , .0: in-phase and quadrature components for IQ modulator, QEPS: +coherent encryption module driven by a random number generator or +RNG seeded with a pre-shared secret, EDFA: Erbium-Doped Fiber +Amplifier, Coherent Receiver: coherent detection, LO: local oscillator, +QEPS and DSP: digital QEPS decryption and DSP. +QEPS +and +DSP + +Qy +LO +DSP +Signal Generator +Quantum +QEPS +Encoding : +RNGAliceTransmitter +Bob Receiver +BPF +Ix +Digital +cW +IQModulator +Qx +Phase De- +80 km +Coherent +EDFA +EDFA +randomiz +Ix +Qx +Receiver +1y +ationandy) =a(α)Iβ)= [α +β) +a(a) +lα) +Iβ) +p3. Constellation after applying digital QEPS decryption and +DSP compensations as shown in Fig. 5. + +Fig. 3 is used to mimic the attacker’s coherent detection by +assuming the attacker taped good portion of the transmitted +cipher coherent signals. Then he/she would obtain a coherent +constellation diagram as shown in Fig. 3, which is randomly +scattered points. Then we also assume that the attacker knows +the data modulation scheme to be QPSK so he/she can apply +DSP to compensate and correct the impacts from the fiber path. +After applying DSP processing, he/she obtains a constellation +diagram as shown in Fig. 4 with a huge Bit-Error-Rate or BER +at 0.38. That means, it is impossible to extract any meaningful +transmitted data. If we carefully look at Fig. 4, we will notice +that there is a square-typed band with 2-unit amplitude, +indicating two QPSK modulations through QEPS-d encryption +"#�� � on a QPSK data modulation. The square band reflects the +phase shift operator "#��&� driving by the random number +generated from RNG. The central disk reflects the QPSK data +modulations have the opposite phases of "#�� � so they cancel +out and give the “zero” amplitudes. + +In QPSK data modulation scheme, data values are +modulated into phases not in amplitude, so Fig. 4 would not leak +transmitted data information. So, they transmission is totally +secure. +Coherent detection turns coherent optical domain into +coherent electrical domain so digital signal processing can +compensate and correct the impacts from the optical path. That +is fantastic for QEPS encryption: encryption in coherent optical +domain or analogue encryption then decryption in electrical +digital domain before DSP processing. That means, QEPS +encryption is an analogue encryption which blocks attackers to +Figure 3. Constellation diagram of directly detected cipher coherent +states is displayed. +Figure 4. Constellation diagram of directly detected cipher coherent +states is displayed after applying the DSP processing. The BER is +0.38. +Figure 5. Constellation diagram of QEPS decryption and DSP +processing. BER is 0. + +Electrical Constellation Visualizer +2 +-1 +0 +2 +Amplitude -I (a.u.)Electrical Constellation Visualizer +Amplitude +C +2 +1 +0 +2 +Amplitude -I (a.u.)Electrical Constelation Visualizer_1 +山 +'n'e) +Q : +-10 m +0 +10 m +Amplitude -I (a.u.)extract transmitted digital data. Of course, one can apply AES +encryption in data then transmit with coherent optical +communications which would allow attackers to extract AES +ciphertexts. That is the major difference between QEPS and +other encryption schemes. +Leveraging the feature of coherent detection, we apply +QEPS-d decryption with "#�−�� driving by the synchronized +RNG seeded with the pre-shared secret. Fig. 5 illustrates the +constellation diagram with QEPS-d decryption then DSP +processing. It is clearly seen that a QPSK constellation with +BER to be zero. +The described technique in the above can be implemented in +a round trip as shown in QPKE [27, 30] where Alice becomes +Alice Transmission and Alice receiving with a self-shared +random secret for encryption and decryption then Bob only +performs data modulations, Alice would securely extract Bob’s +transmitted data without pre-share secret. Using this way, one +trick needs to be remembered: phase shift operator must be in a +reverse +order +of +transmission +side. +The +round-trip +implementation can be also used for true random number +distributions, as an alternative of traditional QKD but the key +rate can be dramatically increased to 100s gbps. For example, in +this simulation, we could achieve 56 gbps with a single +polarization and 112 gbps with dual polarizations. +The distance can be extended with EDFA amplification as +what we have used in today’s coherent optical communications. + +IV. CONCLUSION +We briefly introduced QEPS with the reduced displacement +operator proposed in [32] and applied it for QPSK data +modulation +with +QPSK +implementation +of +the +first +displacement operator "#�� � and a randomized phase shift +operator of the second displacement operator "#��&� . The +simulation demonstrates QEPS-d offers security in analogue +domain encryption and the transmitted cipher coherent states +can not be extracted without knowing the pre-shared secret in +symmetric implementation mode. It can be also implemented in +a roundtrip scheme without the pre-shared secret which can be +used +for +key +distributions +over +coherent +optical +communications. The simulation shows that we can achieve 56 +gbps distributions rate with a single polarization and 112 gbps +with dual polarizations. As what we have demonstrated in [32] +that the displacement operator can also be implemented with +QAM schemes such as 16-QAM or 32-QAM. That makes +QEPS-d be a generic encryption in coherent optical domain or +analogue encryption. In the future, we plan to implement it +experimentally. + +REFERENCES +[1] Shor, P.W. (1994). "Algorithms for quantum computation: discrete +logarithms and factoring". Proceedings 35th Annual Symposium on +Foundations of Computer Science. IEEE Comput. Soc. Press: 124– +134. doi:10.1109/sfcs.1994.365700. +[2] IBM, https://newsroom.ibm.com/2022-11-09-IBM-Unveils-400-Qubit- +Plus-Quantum-Processor-and-Next-Generation-IBM-Quantum-System- +Two. +[3] Yan, Bao, et al. "Factoring integers with sublinear resources on a +superconducting quantum processor." arXiv preprint arXiv:2212.12372 +(2022). +[4] Dustin Moody: Status Update on the 3rd Round. NIST, Online: +https://csrc.nist.gov/CSRC/media/Presentations/status-update-on-the- +3rd-round/images-media/session-1-moody-nist-round-3-update. +pdf. Accessed: 2022-05-23 +[5] NIST: Status Report on the Third Round of the NIST Post-Quantum +Cryptography Standardization Process. https://csrc.nist.gov/publications/ +detail/nistir/8413/final (2022) +[6] Bos J, Ducas L, Kiltz E, Lepoint T, Lyubashevsky V, Schanck JM, +Schwabe P, Seiler G, Stehle D (2018) CRYSTALS - Kyber: A CCA- +secure module-lattice-based KEM. 2018 IEEE European Symposium on +Security and Privacy (EuroS P), pp 353–367. +[7] Lyubashevsky V (2009) Fiat-Shamir with aborts: Applications to lattice +and factoring-based signatures. Advances in Cryptology – ASIACRYPT +2009, ed Matsui M (Springer Berlin Heidelberg, Berlin, Heidelberg), pp +598–616. +[8] Gentry C, Peikert C, Vaikuntanathan V (2008) Trapdoors for hard lattices +and new cryptographic constructions. Proceedings of the Fortieth Annual +ACM Symposium on Theory of Computing STOC ’08 (Association for +Computing Machinery, New York, NY, USA), pp 197–206. +https://doi.org/10.1145/1374376.1374407. +[9] Bernstein DJ, Hulsing ¨ A (2019) Decisional second-preimage resistance: +When does SPR imply PRE? Advances in Cryptology – ASIACRYPT +2019, eds Galbraith SD, Moriai S (Springer International Publishing, +Cham), pp 33–62. +[10] Beullens, W.: Breaking Rainbow Takes a Weekend on a Laptop. +Cryptology +ePrint +Archive, +Paper +2022/214. +https://eprint.iacr.org/2022/214 (2022). +[11] Robert, D.: Breaking SIDH in polynomial time. Cryptology ePrint +Archive, Paper 2022/1038. https://eprint.iacr.org/2022/1038 (2022). +[12] Castryck, W., Decru, T.: An efficient key recovery attack on SIDH +(preliminary version). Cryptology ePrint Archive, Paper 2022/975. +https://eprint.iacr.org/2022/975 (2022). +[13] Wenger, E., Chen, M., Charton, F., Lauter, K.: SALSA: Attacking Lattice +Cryptography with Transformers. Cryptology ePrint Archive, Paper +2022/935. https://eprint.iacr.org/2022/935 (2022). +[14] Kuang, R., Perepechaenko, M. & Barbeau, M. A new quantum-safe +multivariate polynomial public key digital signature algorithm. Sci +Rep 12, 13168 (2022). https://doi.org/10.1038/s41598-022-15843-x +[15] Kuang, R., Perepechaenko, M. & Barbeau, M. A new post-quantum +multivariate polynomial public key encapsulation algorithm. Quantum Inf +Process 21, 360 (2022). https://doi.org/10.1007/s11128-022-03712-5 +[16] R. Kuang, M. Perepechaenko, R. Toth and M. Barbeau, "Benchmark +Performance of a New Quantum-Safe Multivariate Polynomial Digital +Signature Algorithm," 2022 IEEE International Conference on Quantum +Computing and Engineering (QCE), 2022, pp. 454-464, doi: +10.1109/QCE53715.2022.00067. +[17] R. Kuang and M. Perepechaenko, "Digital Signature Performance of a +New +Quantum +Safe +Multivariate +Polynomial +Public +Key +Algorithm," 2022 7th International Conference on Computer and +Communication +Systems +(ICCCS), +2022, +pp. +419-424, +doi: +10.1109/ICCCS55155.2022.9846785. +[18] Shor PW, Preskill J. Simple proof of security of the BB84 quantum key +distribution protocol Physical Review Letters. 2000 Jul;85(2):441-444. +DOI: 10.1103/physrevlett.85.441. PMID: 10991303. +[19] Lucamarini, M., Yuan, Z.L., Dynes, J.F., Shields, A.J.: Overcoming the +rate–distance limit of quantum key distribution without quantum +repeaters. Nature 557(7705), 400–403 (2018). +[20] Wang, S., Yin, ZQ., He, DY. et al. Twin-field quantum key distribution +over +830-km +fibre. Nat. +Photon. 16, +154–161 +(2022). +https://doi.org/10.1038/s41566-021-00928-2 +[21] R. Kuang and N. Bettenburg, "Shannon Perfect Secrecy in a Discrete +Hilbert Space," 2020 IEEE International Conference on Quantum +Computing and Engineering (QCE), 2020, pp. 249-255, doi: +10.1109/QCE49297.2020.00039. + +[22] Kuang, R., Barbeau, M. Quantum permutation pad for universal quantum- +safe +cryptography. Quantum +Inf +Process 21, +211 +(2022). +https://doi.org/10.1007/s11128-022-03557-y. +[23] D. Lou et al., "Benchmark Performance of Digital QKD Platform Using +Quantum Permutation Pad," in IEEE Access, vol. 10, pp. 107066-107076, +2022, doi: 10.1109/ACCESS.2022.3212738. +[24] Kuang, R., Perepechaenko, M. Quantum encryption with quantum +permutation pad in IBMQ systems. EPJ Quantum Technol. 9, 26 +(2022). https://doi.org/10.1140/epjqt/s40507-022-00145-y. +[25] M. Perepechaenko and R. Kuang, "Quantum Encrypted Communication +between Two IBMQ Systems Using Quantum Permutation Pad," 2022 +11th International Conference on Communications, Circuits and Systems +(ICCCAS), +2022, +pp. +146-152, +doi: +10.1109/ICCCAS55266.2022.9824836. +[26] M. Perepechaenko and R. Kuang, “Quantum encryption and decryption +in IBMQ systems using quantum Permutation Pad,” Journal of +Communications, vol. 17, no. 12, December 2022. +[27] R. Kuang and N. Bettenburg, "Quantum Public Key Distribution using +Randomized Glauber States," 2020 IEEE International Conference on +Quantum Computing and Engineering (QCE), 2020, pp. 191-196, doi: +10.1109/QCE49297.2020.00032. +[28] A. Chan, M. Khalil, K. A. Shahriar, L. R. Chen, D. V. Plant and R. Kuang, +"Security Analysis of a Next Generation TF-QKD for Secure Public Key +Distribution with Coherent Detection over Classical Optical Fiber +Networks," 2021 7th International Conference on Computer and +Communications +(ICCC), +2021, +pp. +416-420, +doi: +10.1109/ICCC54389.2021.9674320. +[29] A. Chan, M. Khalil, K. A. Shahriar, L. R. Chen, D. V. Plant and R. Kuang, +"On the Security of an Optical Layer Encryption Using Coherent-based +TF-QKD in Classical Optical Fiber Links," 2022 4th International +Conference on Computer Communication and the Internet (ICCCI), 2022, +pp. 105-110, doi: 10.1109/ICCCI55554.2022.9850244. +[30] K. A. Shahriar, M. Khalil, A. Chan, L. R. Chen, R. Kuang and D. V. Plant, +"Physical-Layer Secure Optical Communication Based on Randomized +Phase Space in Pseudo-3-Party Infrastructure," 2022 Conference on +Lasers and Electro-Optics (CLEO), 2022, pp. 1-2. +[31] K. A. Shahriar, M. Khalil, A. Chan, L. R. Chen, R. Kuang and D. V. Plant, +"Security Performance of Physical-Layer Encryption Based on +Randomized Phase Space in Optical Fiber Communication," 2022 IEEE +Photonics +Conference +(IPC), +2022, +pp. +1-2, +doi: +10.1109/IPC53466.2022.9975665. +[32] Kuang, R., Chan A.. Quantum encryption in Phase Space with +Displacement Operators. EPJ Quantum Technol., submitted (2022) +[33] R. Kuang, D. Lou, A. He, C. McKenzie and M. Redding, "Pseudo +Quantum Random Number Generator with Quantum Permutation +Pad," 2021 IEEE International Conference on Quantum Computing and +Engineering +(QCE), +2021, +pp. +359-364, +doi: +10.1109/QCE52317.2021.00053. + + diff --git a/FdE1T4oBgHgl3EQfEwOD/content/tmp_files/load_file.txt b/FdE1T4oBgHgl3EQfEwOD/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..16448b0037c485ff8161d66828f4a367e69c922b --- /dev/null +++ b/FdE1T4oBgHgl3EQfEwOD/content/tmp_files/load_file.txt @@ -0,0 +1,463 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf,len=462 +page_content='XXX-X-XXXX-XXXX-X/XX/$XX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='00 ©20XX IEEE Quantum Encryption in Phase Space using Displacement Operator for QPSK Data Modulation Randy Kuang Quantropi Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Ottawa, Canada randy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='kuang@quantropi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='com ORCID: 000-0002-5567-2192 Adrian Chan Quantropi Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Ottawa, Canada adrian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='chan@quantropi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='com Abstract—Quantum Public Key Distribution or QPKE with the randomized phase shift gate was proposed by Kuang and Bettenburg in 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' It has been implemented theoretically with simulations and experimentally over existing fiber optical networks since then.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' QPKE can be considered as an RSA-type scheme in optical analogue domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' QPKE was renamed as Quantum Encryption in Phase Space or QEPS to reflect the encryption of coherent states in phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' QEPS with the phase shift gate can only be applied to data modulation scheme with phase shift keying such as quadrature phase shift keying or QPSK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' It would leak data information in amplitude once it is applied to quadrature amplitude modulation or QAM schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Kuang and Chan recently proposed a new version of QEPS called Quantum Encryption in Phase Space with the displacement gate or QEPS-d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' It demonstrated to overcome the limitation of QEPS with the phase shift gate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' We introduced a reduced displacement operator by ignoring the global phase factor then the reduced displacement operators are commutable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' This commutability helps our implementation at both transmission and receiving.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' An arbitrary displacement operator can be decoupled into a standard QAM modulation with a phase shift modulation to ease our encryption and decryption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' This paper simulates the QEPS-d encryption for QPSK data modulation to demonstrate how QEPS-d works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Keywords—quantum cryptography, post-quantum cryptography, PQC, quantum encryption, coherent state, phase shift gate, displacement gate, quadrature amplitude modulation, QAM, quadrature phase shift keying, QPSK I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' INTRODUCTION After Shor proposed his algorithm with quantum bit or qubit for integer factorization in 1994 [1], it has been well-understood that classical public key algorithms such as RSA based on the factorization problem, Diffie-Hellman or elliptic Diffie- Hellman based on the discrete logarithm are breakable once fault tolerate quantum computers are available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' However, breaking RSA-2048 requires a fault tolerate quantum computer to have more than 4000 logic qubits or 4 million physical qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The latest released IBM quantum computer Osprey offers 433 physical qubits [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The IBM roadmap shows that they will release their next quantum computer Condor with 1121 qubits in 2023 and qubits will raise over 100,000 in 2026.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Very recently, Yan, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' proposed a new algorithm by combining classical lattice reduction with quantum optimization called Sublinear-resource Quantum Integer Factorization (SQIF) [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' SQIF works in a noise quantum computer with a quantum resource reduction or qubits of 4 magnitudes from 4 million of physical qubits to less than 400 physical qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' They have demonstrated it for a 48-bit integer factorization with as little as a 10-qubit quantum processor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' National Institute of Standards and Technology or NIST started the standardization process in the late of 2017 and completed its three rounds in 2021 [4] and announced its final standardized algorithms for key encapsulation mechanism or KEM and digital signature algorithms [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The lattice-based Kyber [6] becomes the standardized winner for KEM and the lattice-based Dillithium [7] and Falcon [8], as well as hash- based SPHINCS+ [9] become the standardized algorithms for digital signature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' NIST continues its standardization for KEM in its round 4 and reopens its standardization of digital signature for submissions in the early 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Some major cryptanalyses have made NIST finalists vulnerable in 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Beullens broke Rainbow signature with a laptop over a weekend [10], Robert broke SIDH [11] and Castryck and Decru made its more efficient to break SIDH level I in one hour with a single core computer [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Wenger, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' reported their secret recovery of lattice-based PQC with machine learning by training the transformer with 300,000 samples and achieved the complete secret recovery for up to a mid-size lattice dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Some recent developments in PQC KEM and digital signature were proposed by Kuang’s team, called Multivariate Polynomial Public Key or MPPK by leveraging the NP- complete problem of the Modular Diophantine Equation Problem [14, 15, 16, 17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' MPPK offers relatively small public key size, cipher size, and signature size, comparable to the classical public key schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' They also outperform NIST finalists in performances of key generation, encryption, decryption, signing and verification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' MPPK could become good alternatives to NIST finalists for generic use cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' MPPK digital signature scheme is planned to participate in the NIST reopening submission for digital signature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' On the other hand, Quantum Key Distribution or QKD was developed over three decades since it was proposed in 1984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Shor and Preskill proved that QKD offers the information theoretical security in 2000 [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' It has become commercial ready for a distance at around 100km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' To break the distance boundary, Lucamarini, et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' proposed Twin-Field QKD or TF- QKD in 2018 [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' TF-QKD has been widely explored since then and the longest distance of 830km was reported by Wang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' in 2022 [20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' QKD generally offers a key rate at kbps level and TF-QKD [20] achieved a key rate at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='014 bps at 830km, requiring more than 5 hours to establish a 256 bits of AES key.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Considering the pre-shared secret for QKD authentication, Kuang and Bettenburg in 2020 proposed a new mechanism using Quantum Permutation Pad or QPP to digitally distribute quantum random [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The pre-shared secret is not only used for authentication but also used to map to a QPP pad for encoding at the sender and decoding at the receiver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' QPP is implemented into matrices operating on data column vector or Dirac ket.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Permutation matrix is unitary and reversable, so the decoding side uses the reversed QPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Kuang and Barbeau proposed a universal quantum safe cryptography using QPP in 2022 [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' QPP has been developed as a platform for digital QKD and benchmarked by Deutsche Telekom in 2022 [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Leveraging the quantum gate property of QPP, quantum encryption with QPP implemented inside quantum computers was reported by Kuang and Perepechaenko in 2022 [24], Perepechaenko and Kuang in 2022 [25, 26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' To eliminate the pre-shared key in quantum key distribution in coherent optical domain, Kuang and Bettenburg in 2020 proposed Quantum Public Key Envelope or QPKE using randomized phase shift gate in a round-trip scheme [27], leveraging the self-shared random secret to drive the phase shift encoding without the specific requirement of the pre-shared secret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' QPKE was designed to operate in the existing coherent optical networks with the same coherent detection module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' It has been simulated and experimentally implemented through the collaborations with McGill University [28, 29, 30, 31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' QPKE mimics the RSA-type public key scheme in coherent optical domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The experiment implementation with off-shelf optical modules demonstrated the speed at 200 gbps for a distance 80km between two communication peers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' To mimicking its implementation in a symmetric fashion with a pre-shared secret, QPKE was renamed as Quantum Encryption in Phase Space or QEPS with the randomized phase shift gate, reflecting to its possible implementation in photonic quantum computer with phase shift gate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' There is one limitation of QEPS with phase shift gate, or only applicable for data modulation schemes with phase shift keying such as QPSK or M-PSK.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Once the data modulation is quadrature amplitude modulation or QAM, the amplitude bits would be leaked out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' To overcome this limitation, Kuang and Chan recently proposed to use coherent displacement operator ����� where � denotes a coherent state [32].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' This paper will report its simulation results with QPSK data modulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Section 2 will briefly summarize the QEPS with the displacement operator and section 3 will present the simulation result and the conclusion is at the end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' QEPS WITH DISPLACEMENT OPERATOR A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Coherent State and Displacement Operator A coherent state is the specific quantum state of quantum harmonic oscillator denoted by a Dirac ket |�⟩ where � is a complex variable in the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' � can be expressed either in terms of in-phase and quadrature as � = �� + � �� or amplitude and phase � = |�|���.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Then a coherent state can be ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='written as ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='|�⟩ = ��� + � ��� = | |�|��� ⟩ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='(1) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='And the displacement operator is defined with creation and ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='annihilation operators ��� and �� through following equation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='|�⟩ = �� �� ���∗ �� |0⟩ = ����� |0⟩ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='(2) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='So ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='����� = �� �� ���∗ �� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='(3) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='which indicates the displacement operator is unitary and ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='reversable: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='������ = ��� �� ���∗ ��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='= ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='���−�� = ��� ��� ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='(4) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='Let’s apply the displacement operator ����� to a coherent state ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='|�⟩ ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='����� |�⟩ = ����� ����� |0⟩ = ��!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='∗��∗!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='���� + ��|0⟩ (5) And in the same way ����� |�⟩ = ����� ����� |0⟩ = �!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='�∗�!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='∗����� + ��|0⟩ (6) So, it is clear that ����� and ����� are not commutable due to the global phase factor ��!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='∗��∗!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' but that does not impact our physical measurements on the amplitude and phase of a coherent state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Therefore, we can ignore the global phase factor and introduce a reduced displacement operator "#��� = ���!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='∗$�∗!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='�����.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Then the reduced displacement operator "#��� and "#��� are commutable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' QEPS with Reduced Displacement Operator From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' (5), QEPS encryption with a reduced displacement operator "#��� can be expressed as follows "#��� |�⟩ = "#�� + ��|0⟩ = |� + �⟩ = |%⟩ (7) with |�⟩ to be a plain coherent state, "#��� to be an encryption operator and |%⟩ to be the encrypted cipher coherent state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' (7) indicates that QEPS encryption with the reduced displacement operator or QEPS-d essentially performs an addition of two coherent states |�⟩ and |�⟩ as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' A general displacement operator would change both the amplitude and phase of a plain coherent state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' But it can also only change the phase of the plain coherent as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' In this special case, the displacement operator behaves like a phase shift operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The encryptor "#��� can be controlled by a pre-shared secret in a symmetric encryption or a self-shared secret in an asymmetric encryption as shown in QPKE [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' In the ideal communication case, the receiver would decrypt the cipher coherent state |%⟩ with "#� ��� = "#�−�� : "#� ���|%⟩ = "#�−��|%⟩ = |−� + %⟩ = |�⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' In coherent optical communications, optical line path would impact a coherent state during transmission from the sender to the receiver such as dispersion, attenuation, polarization, noise, environment factors, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Thanks to the digital signal processing or DSP, all those impacts could be compensated and corrected in the electrical digital domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Based on that, we only consider the encryption and decryption in the ideal transmission situation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' A displacement operator can be decomposed into two or more displacement operators as follows "#��� = "#�� � "#��&� … "#��(� And "#���|�⟩ = "#�� � "#��&� … "#��(�|�⟩ = |� + �& + ⋯ �( + �⟩ This decomposition feature helps us to ease the implementation of a general displacement operator with two operators: "#�� � implemented with a standard modulation such as QAM and "#��&� with a phase shift operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' By doing that, we can overcome the weakness of original QPKE scheme [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' QEPS-D SIMULATION The simulation is performed with OptiSystem and the simulation layout is illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The major modules are explained in the figure caption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The only extra components are needed to discuss here are QEPS and RNG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' All others are common for typical coherent optical communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The random number generator or RNG should be a cryptographic PRNG or pseudo–Quantum Random Number Generator or pQRNG [33] with generated random number meeting cryptographic requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' pQRNG is capable to take upto 16 KB of the pre-shared secret and produces pseudo random number with excellent randomness [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' QEPS consists of two operators: "#�� � implemented with standard data modulation such as 16-QAM or QPSK and "#��&� implemented with a random phase shift operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' These two operators together offer a coherent encryption with a generic displacement operator "#���.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' QEPS produces a complex modulation form based on the rand number generated from RNG module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The complex modulation form dictates the signal generator to produce voltages for IQ modulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 2, we omitted the data input which is combined with QEPS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Once the coherent states are generated from CW and pass IQ Modulator, their amplitude and phase would be modulated by IQ modulator then the encrypted cipher coherent states are transmitted over 80 km fiber to coherent detector at the receiver side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Typical coherent detection is applied to produce electrical digital signal and QEPS-d decryption is done before DSP processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The simulation parameters are given in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' We simulated QEPS encryption with the reduced displacement operator for QPSK data modulations and plot constellation diagrams in 3 cases: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Constellation right after coherent detection as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' This constellation diagram displays the detections of cipher coherent states together with fiber path impacts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Constellation diagram after applying the digital signal processing as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' TABLE 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' SIMULATION PARAMETERS ARE TABULATED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Layout Parameter Sequence length Baudrate PM period 65,536 bits 28 Gbaud 1024 CW Laser and LO Laser Center wavelength Power Linewidth Azimuth 1550 nm 5 dBm 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1 MHz 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='45 degree IQ Modulator Extinction ratio Switching bias Insertion loss 20 dB 3 V 5 dB EDFA Forward pump power Forward pump wavelength Loss at 1550 nm Loss at 980 nm 13-14 mW 980 nm 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1dB/m 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='15 dB/m Optical Fiber Length (1 spool) Attenuation Dispersion Dispersion slope Differential group delay Effective area 80 km 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='2 dB/km 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='3 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='75 ps/nm/km 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='075 ps/nm2/km 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='2ps/km 80 μm2 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Illustration of QEPS-d is plotted in the phase space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' A special case of QEPS with phase shift operator is also plotted for demonstration purpose of a general displacement operator "#���.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Simulation layout is illustrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' CW: continuous wave source, IQ Modulator: in-phase and quadrature modulator, +,, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=',and +/ , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='0: in-phase and quadrature components for IQ modulator, QEPS: coherent encryption module driven by a random number generator or RNG seeded with a pre-shared secret, EDFA: Erbium-Doped Fiber Amplifier, Coherent Receiver: coherent detection, LO: local oscillator, QEPS and DSP: digital QEPS decryption and DSP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' QEPS and DSP Qy LO DSP Signal Generator Quantum QEPS Encoding : RNGAliceTransmitter Bob Receiver BPF Ix Digital cW IQModulator Qx Phase De- 80 km Coherent EDFA EDFA randomiz Ix Qx Receiver 1y ationandy) =a(α)Iβ)= [α +β) a(a) lα) Iβ) p3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Constellation after applying digital QEPS decryption and DSP compensations as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 3 is used to mimic the attacker’s coherent detection by assuming the attacker taped good portion of the transmitted cipher coherent signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Then he/she would obtain a coherent constellation diagram as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 3, which is randomly scattered points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Then we also assume that the attacker knows the data modulation scheme to be QPSK so he/she can apply DSP to compensate and correct the impacts from the fiber path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' After applying DSP processing, he/she obtains a constellation diagram as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 4 with a huge Bit-Error-Rate or BER at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' That means, it is impossible to extract any meaningful transmitted data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' If we carefully look at Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 4, we will notice that there is a square-typed band with 2-unit amplitude, indicating two QPSK modulations through QEPS-d encryption "#�� � on a QPSK data modulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The square band reflects the phase shift operator "#��&� driving by the random number generated from RNG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The central disk reflects the QPSK data modulations have the opposite phases of "#�� � so they cancel out and give the “zero” amplitudes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' In QPSK data modulation scheme, data values are modulated into phases not in amplitude, so Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 4 would not leak transmitted data information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' So, they transmission is totally secure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Coherent detection turns coherent optical domain into coherent electrical domain so digital signal processing can compensate and correct the impacts from the optical path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' That is fantastic for QEPS encryption: encryption in coherent optical domain or analogue encryption then decryption in electrical digital domain before DSP processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' That means, QEPS encryption is an analogue encryption which blocks attackers to Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Constellation diagram of directly detected cipher coherent states is displayed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Constellation diagram of directly detected cipher coherent states is displayed after applying the DSP processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The BER is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Constellation diagram of QEPS decryption and DSP processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' BER is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Electrical Constellation Visualizer 2 1 0 2 Amplitude -I (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' )Electrical Constellation Visualizer Amplitude C 2 1 0 2 Amplitude -I (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=" )Electrical Constelation Visualizer_1 山 'n'e) Q : 10 m 0 10 m Amplitude -I (a." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' )extract transmitted digital data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Of course, one can apply AES encryption in data then transmit with coherent optical communications which would allow attackers to extract AES ciphertexts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' That is the major difference between QEPS and other encryption schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Leveraging the feature of coherent detection, we apply QEPS-d decryption with "#�−�� driving by the synchronized RNG seeded with the pre-shared secret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 5 illustrates the constellation diagram with QEPS-d decryption then DSP processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' It is clearly seen that a QPSK constellation with BER to be zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The described technique in the above can be implemented in a round trip as shown in QPKE [27, 30] where Alice becomes Alice Transmission and Alice receiving with a self-shared random secret for encryption and decryption then Bob only performs data modulations, Alice would securely extract Bob’s transmitted data without pre-share secret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Using this way, one trick needs to be remembered: phase shift operator must be in a reverse order of transmission side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The round-trip implementation can be also used for true random number distributions, as an alternative of traditional QKD but the key rate can be dramatically increased to 100s gbps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' For example, in this simulation, we could achieve 56 gbps with a single polarization and 112 gbps with dual polarizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The distance can be extended with EDFA amplification as what we have used in today’s coherent optical communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' CONCLUSION We briefly introduced QEPS with the reduced displacement operator proposed in [32] and applied it for QPSK data modulation with QPSK implementation of the first displacement operator "#�� � and a randomized phase shift operator of the second displacement operator "#��&� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The simulation demonstrates QEPS-d offers security in analogue domain encryption and the transmitted cipher coherent states can not be extracted without knowing the pre-shared secret in symmetric implementation mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' It can be also implemented in a roundtrip scheme without the pre-shared secret which can be used for key distributions over coherent optical communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' The simulation shows that we can achieve 56 gbps distributions rate with a single polarization and 112 gbps with dual polarizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' As what we have demonstrated in [32] that the displacement operator can also be implemented with QAM schemes such as 16-QAM or 32-QAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' That makes QEPS-d be a generic encryption in coherent optical domain or analogue encryption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' In the future, we plan to implement it experimentally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' REFERENCES [1] Shor, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' "Algorithms for quantum computation: discrete logarithms and factoring".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Proceedings 35th Annual Symposium on Foundations of Computer Science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' IEEE Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Press: 124– 134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1109/sfcs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='365700.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [2] IBM, https://newsroom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='ibm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='com/2022-11-09-IBM-Unveils-400-Qubit- Plus-Quantum-Processor-and-Next-Generation-IBM-Quantum-System- Two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [3] Yan, Bao, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' "Factoring integers with sublinear resources on a superconducting quantum processor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='" arXiv preprint arXiv:2212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='12372 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [4] Dustin Moody: Status Update on the 3rd Round.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' NIST, Online: https://csrc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='nist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='gov/CSRC/media/Presentations/status-update-on-the- 3rd-round/images-media/session-1-moody-nist-round-3-update.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Accessed: 2022-05-23 [5] NIST: Status Report on the Third Round of the NIST Post-Quantum Cryptography Standardization Process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' https://csrc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='nist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='gov/publications/ detail/nistir/8413/final (2022) [6] Bos J, Ducas L, Kiltz E, Lepoint T, Lyubashevsky V, Schanck JM, Schwabe P, Seiler G, Stehle D (2018) CRYSTALS - Kyber: A CCA- secure module-lattice-based KEM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 2018 IEEE European Symposium on Security and Privacy (EuroS P), pp 353–367.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [7] Lyubashevsky V (2009) Fiat-Shamir with aborts: Applications to lattice and factoring-based signatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Advances in Cryptology – ASIACRYPT 2009, ed Matsui M (Springer Berlin Heidelberg, Berlin, Heidelberg), pp 598–616.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [8] Gentry C, Peikert C, Vaikuntanathan V (2008) Trapdoors for hard lattices and new cryptographic constructions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing STOC ’08 (Association for Computing Machinery, New York, NY, USA), pp 197–206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1145/1374376.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1374407.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [9] Bernstein DJ, Hulsing ¨ A (2019) Decisional second-preimage resistance: When does SPR imply PRE?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Advances in Cryptology – ASIACRYPT 2019, eds Galbraith SD, Moriai S (Springer International Publishing, Cham), pp 33–62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [10] Beullens, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=': Breaking Rainbow Takes a Weekend on a Laptop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Cryptology ePrint Archive, Paper 2022/214.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' https://eprint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='iacr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='org/2022/214 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [11] Robert, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=': Breaking SIDH in polynomial time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Cryptology ePrint Archive, Paper 2022/1038.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' https://eprint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='iacr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='org/2022/1038 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [12] Castryck, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=', Decru, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=': An efficient key recovery attack on SIDH (preliminary version).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Cryptology ePrint Archive, Paper 2022/975.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' https://eprint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='iacr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='org/2022/975 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [13] Wenger, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=', Chen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=', Charton, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=', Lauter, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=': SALSA: Attacking Lattice Cryptography with Transformers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Cryptology ePrint Archive, Paper 2022/935.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' https://eprint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='iacr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='org/2022/935 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [14] Kuang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=', Perepechaenko, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' & Barbeau, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' A new quantum-safe multivariate polynomial public key digital signature algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Sci Rep 12, 13168 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1038/s41598-022-15843-x [15] Kuang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=', Perepechaenko, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' & Barbeau, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' A new post-quantum multivariate polynomial public key encapsulation algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Quantum Inf Process 21, 360 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1007/s11128-022-03712-5 [16] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Kuang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Perepechaenko, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Toth and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Barbeau, "Benchmark Performance of a New Quantum-Safe Multivariate Polynomial Digital Signature Algorithm," 2022 IEEE International Conference on Quantum Computing and Engineering (QCE), 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 454-464, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1109/QCE53715.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='00067.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [17] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Kuang and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Perepechaenko, "Digital Signature Performance of a New Quantum Safe Multivariate Polynomial Public Key Algorithm," 2022 7th International Conference on Computer and Communication Systems (ICCCS), 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 419-424, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1109/ICCCS55155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='9846785.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [18] Shor PW, Preskill J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Simple proof of security of the BB84 quantum key distribution protocol Physical Review Letters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 2000 Jul;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='85(2):441-444.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' DOI: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1103/physrevlett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='441.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' PMID: 10991303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [19] Lucamarini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=', Yuan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=', Dynes, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=', Shields, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' : Overcoming the rate–distance limit of quantum key distribution without quantum repeaters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Nature 557(7705), 400–403 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [20] Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=', Yin, ZQ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=', He, DY.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Twin-field quantum key distribution over 830-km fibre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Photon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 16, 154–161 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1038/s41566-021-00928-2 [21] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Kuang and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Bettenburg, "Shannon Perfect Secrecy in a Discrete Hilbert Space," 2020 IEEE International Conference on Quantum Computing and Engineering (QCE), 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 249-255, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1109/QCE49297.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='00039.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [22] Kuang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=', Barbeau, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Quantum permutation pad for universal quantum- safe cryptography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Quantum Inf Process 21, 211 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1007/s11128-022-03557-y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [23] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Lou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=', "Benchmark Performance of Digital QKD Platform Using Quantum Permutation Pad," in IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 107066-107076, 2022, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1109/ACCESS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='3212738.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [24] Kuang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=', Perepechaenko, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Quantum encryption with quantum permutation pad in IBMQ systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' EPJ Quantum Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 9, 26 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1140/epjqt/s40507-022-00145-y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [25] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Perepechaenko and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Kuang, "Quantum Encrypted Communication between Two IBMQ Systems Using Quantum Permutation Pad," 2022 11th International Conference on Communications, Circuits and Systems (ICCCAS), 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 146-152, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1109/ICCCAS55266.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='9824836.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [26] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Perepechaenko and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Kuang, “Quantum encryption and decryption in IBMQ systems using quantum Permutation Pad,” Journal of Communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 12, December 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [27] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Kuang and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Bettenburg, "Quantum Public Key Distribution using Randomized Glauber States," 2020 IEEE International Conference on Quantum Computing and Engineering (QCE), 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 191-196, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1109/QCE49297.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='00032.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [28] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Chan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Khalil, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Shahriar, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Chen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Plant and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Kuang, "Security Analysis of a Next Generation TF-QKD for Secure Public Key Distribution with Coherent Detection over Classical Optical Fiber Networks," 2021 7th International Conference on Computer and Communications (ICCC), 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 416-420, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1109/ICCC54389.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='9674320.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [29] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Chan, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Khalil, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Shahriar, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Chen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Plant and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Kuang, "On the Security of an Optical Layer Encryption Using Coherent-based TF-QKD in Classical Optical Fiber Links," 2022 4th International Conference on Computer Communication and the Internet (ICCCI), 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 105-110, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1109/ICCCI55554.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='9850244.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [30] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Shahriar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Khalil, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Chan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Chen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Kuang and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Plant, "Physical-Layer Secure Optical Communication Based on Randomized Phase Space in Pseudo-3-Party Infrastructure," 2022 Conference on Lasers and Electro-Optics (CLEO), 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 1-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [31] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Shahriar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Khalil, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Chan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Chen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Kuang and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Plant, "Security Performance of Physical-Layer Encryption Based on Randomized Phase Space in Optical Fiber Communication," 2022 IEEE Photonics Conference (IPC), 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 1-2, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1109/IPC53466.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='9975665.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' [32] Kuang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=', Chan A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='. Quantum encryption in Phase Space with Displacement Operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' EPJ Quantum Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=', submitted (2022) [33] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Kuang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Lou, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' He, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' McKenzie and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' Redding, "Pseudo Quantum Random Number Generator with Quantum Permutation Pad," 2021 IEEE International Conference on Quantum Computing and Engineering (QCE), 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content=' 359-364, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='1109/QCE52317.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} +page_content='00053.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/FdE1T4oBgHgl3EQfEwOD/content/2301.02894v1.pdf'} diff --git a/FtE1T4oBgHgl3EQfXARM/content/2301.03121v1.pdf b/FtE1T4oBgHgl3EQfXARM/content/2301.03121v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b58bbdbb27fba7ef43263693e5996c2ff656a063 --- /dev/null +++ b/FtE1T4oBgHgl3EQfXARM/content/2301.03121v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e3f0c7b8e6adff218510f5c9b642074e9da12bb8db7481ead94b7433ab854748 +size 29400169 diff --git a/GNAyT4oBgHgl3EQfSvfA/content/2301.00093v1.pdf b/GNAyT4oBgHgl3EQfSvfA/content/2301.00093v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d3ecce9395ddb83b56c05d11b53a2728e3bb4feb --- /dev/null +++ b/GNAyT4oBgHgl3EQfSvfA/content/2301.00093v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:91d92313dd280401d9c86fb00620713a0703e0cc9cdbcb11013a8c36e6bc641f +size 742454 diff --git a/GNAyT4oBgHgl3EQfSvfA/vector_store/index.pkl b/GNAyT4oBgHgl3EQfSvfA/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..a84f0587e2eef16f73c00427bc7aa52b60cc67a4 --- /dev/null +++ b/GNAyT4oBgHgl3EQfSvfA/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d7cc8d6b670d718bc04e61b14d3155ee234dc5d4ab7c0aea84bd4164f633b83e +size 204042 diff --git a/GNE0T4oBgHgl3EQfhQF8/vector_store/index.faiss b/GNE0T4oBgHgl3EQfhQF8/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..3904544cbb77e323d1ad7ded8c3b1798ee092c45 --- /dev/null +++ b/GNE0T4oBgHgl3EQfhQF8/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:bcf1dd003bb048cbfd85bf31d4610a5d81a30ff34e40f44f3d412f803a363a71 +size 6750253 diff --git a/HNE4T4oBgHgl3EQfgg1T/vector_store/index.faiss b/HNE4T4oBgHgl3EQfgg1T/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..994608f987f3e09b122e973def96a019ada1f9d4 --- /dev/null +++ b/HNE4T4oBgHgl3EQfgg1T/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a769ec20dd16b38cb7870fc0b72c176ba2d83392089377d8184fb561c2657c7e +size 6619181 diff --git a/JdAyT4oBgHgl3EQfsPlo/content/2301.00573v1.pdf b/JdAyT4oBgHgl3EQfsPlo/content/2301.00573v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..35946b6483eb1241cf047b766920be7de642d928 --- /dev/null +++ b/JdAyT4oBgHgl3EQfsPlo/content/2301.00573v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e60c7b01143d2c903bdaf648b19422ba6690b1e6cd3e5e73ceb5dc78c543af8c +size 458286 diff --git a/JdAyT4oBgHgl3EQfsPlo/vector_store/index.pkl b/JdAyT4oBgHgl3EQfsPlo/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..0c801e614276b201a56d567591599c0f4bdd33ce --- /dev/null +++ b/JdAyT4oBgHgl3EQfsPlo/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b78565e323d289233460d3043ee4270ea678d066b07c48d15d4f5f35802880f6 +size 122004 diff --git a/KNAyT4oBgHgl3EQff_hn/content/2301.00350v1.pdf b/KNAyT4oBgHgl3EQff_hn/content/2301.00350v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c79e2c97d88c3a56333b77fd77e52457ee65ae9c --- /dev/null +++ b/KNAyT4oBgHgl3EQff_hn/content/2301.00350v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e79cb60156a81045f5424364821efafd59a4861d617c68a30e569827cea7cdd7 +size 1218728 diff --git a/KNAyT4oBgHgl3EQff_hn/vector_store/index.faiss b/KNAyT4oBgHgl3EQff_hn/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..1d320b5fbc3f0d367e65f985fd7c491345cf9e25 --- /dev/null +++ b/KNAyT4oBgHgl3EQff_hn/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:741c60a8a676c3764e29886ef09749535539746bff01ffcae16f2ad3a6748b50 +size 1507373 diff --git a/KNE3T4oBgHgl3EQfAQkY/content/tmp_files/2301.04255v1.pdf.txt b/KNE3T4oBgHgl3EQfAQkY/content/tmp_files/2301.04255v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..b74d22e4c4ecb3cc813bf1bc71a85d57d317987f --- /dev/null +++ b/KNE3T4oBgHgl3EQfAQkY/content/tmp_files/2301.04255v1.pdf.txt @@ -0,0 +1,915 @@ +Quantum tracking control of the orientation of symmetric top molecules +Alicia B. Magann,1, 2, ∗ Tak-San Ho,3 Christian Arenz,3, 4 and Herschel A. Rabitz3, † +1Department of Chemical & Biological Engineering, +Princeton University, Princeton, New Jersey 08544, USA +2Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA +3Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA +4School of Electrical, Computer and Energy Engineering, +Arizona State University, Tempe, Arizona 85281, USA +(Dated: January 12, 2023) +The goal of quantum tracking control is to identify shaped fields to steer observable expectation values along +designated time-dependent tracks. The fields are determined via an iteration-free procedure, which is based on +inverting the underlying dynamical equations governing the controlled observables. In this article, we generalize +the ideas in Phys. Rev. A 98, 043429 (2018) to the task of orienting symmetric top molecules in 3D. To +this end, we derive equations for the control fields capable of directly tracking the expected value of the 3D +dipole orientation vector along a desired path in time. We show this framework can be utilized for tracking the +orientation of linear molecules as well, and present numerical illustrations of these principles for symmetric top +tracking control problems. +I. +INTRODUCTION +The desire to selectively manipulate molecular dynamics +using external fields is a decades-old dream that has mo- +tivated a broad range of research pursuits [1–3], includ- +ing the development of quantum optimal control (QOC) +theory [4]. The goal of QOC is to identify fields to con- +trol the dynamics of a quantum system, such that the sys- +tem achieves a desired control objective at a designated +target time t = T. The task of identifying an optimal +field is typically accomplished by iterative optimization +methods [5–7]. Although these methods can be compu- +tationally demanding, QOC has nonetheless found broad +applications, ranging from quantum computing [8, 9] to +chemical reactions [10–13]. +In this article, we focus on another formulation, quan- +tum tracking control (QTC) [14–16], for designing con- +trol fields to accurately track the temporal path of an +observable of interest. The origins of QTC are in engi- +neering control theory, which has explored tracking con- +trol in a range of settings including linear [17], nonlinear +[18], and bilinear [19] systems. For quantum-mechanical +applications, tracking control principles have been ap- +plied towards the numerical study of systems including +a qubit [20], a single atom [21], and various molecular +[14–16, 22, 23] and solid-state systems [24–26]. +∗ abmagan@sandia.gov +† hrabitz@princeton.edu +Figure 1. In this article, we formulate QTC for controlling +the 3D orientation of symmetric top molecules, such as fluo- +romethane, shown here. The control procedure involves de- +signing three orthogonal fields (black) in order to drive the +molecule’s 3D dipole vector along a desired time-dependent +track (red). The three fields can be determined by solving an +inverse equation, without the need for optimization. +The aim of QTC is to find tracking control field(s) ε(t) +that drive one or multiple observable expectation values +⟨O⟩(t) ≡ ⟨ψ(t)|O|ψ(t)⟩ along desired time-dependent +“tracks” ⟨O⟩d(t) for a chosen time interval t ∈ [0, T]. +This is carried out by directly inverting the underlying +dynamical equation governing ⟨O⟩(t) in order to solve +for ε(t) [14–16]. Because it does not require any iterative +optimization, QTC can be computationally advantageous +arXiv:2301.04255v1 [quant-ph] 11 Jan 2023 + +compared with usual QOC schemes. +A challenge facing QTC is the potential presence of sin- +gularities in the corresponding direct inversion procedure +[27]. That is, attempts to exactly track arbitrary time- +dependent observable paths can produce unphysical, dis- +continuous control fields [28] and deviations from the +desired tracks. However, if singularities can be avoided, +QTC offers an appealing, iteration-free approach for de- +signing fields to control quantum systems. +Here, we consider applications of QTC to orienting sym- +metric top molecules. The control of molecular orien- +tation has applications spanning high harmonic genera- +tion [29] and chemical reaction enhancement [30–32], +and has been the subject of numerous experimental [33– +35] and theoretical [36–42] studies. In particular, QTC +of molecular rotor orientation in 2D has been explored +[22]. In this work, we extend this prior work to linear and +symmetric top molecules in 3D. We note that although +the controllability of linear and symmetric top molecules +has been the subject of other studies [43, 44], to the best +of our knowledge, the suitability of symmetric tops for +QTC has thus far not been explored. +The remainder of the paper is organized as follows. We +begin by outlining the symmetric top rotor model and +derive QTC equations for the control fields to track its +orientation. We go on to describe computational methods +for solving the QTC equations by expanding the wave +function in terms of angular momentum eigenfunctions +of the symmetric top and address the QTC singularity +issue. We then show how the formulation of QTC for +symmetric top molecules can be reduced to the case of +a linear rotor. We conclude with numerical illustrations +and an outlook. +II. +SYMMETRIC TOP MOLECULES IN 3D +We consider a symmetric top molecule with dynamics +governed by the time-dependent Schr¨odinger equation, +i ∂ +∂t|ψ(t)⟩ = H(t)|ψ(t)⟩ , +(1) +where ℏ = 1 and the time-dependent Hamiltonian is +H(t) = H0 − µ · ε(t) +(2) +in terms of (1) the field-free Hamiltonian H0, (2) three +orthogonal control fields εX(t), εY (t), and εZ(t), i.e., +where ε(t) = ˆXεX(t) + ˆY εY (t) + ˆZεZ(t), and (3) the +components of the dipole moment µ = ˆXµX + ˆY µY + +ˆZµZ, where ˆX, ˆY , and ˆZ denote the three Cartesian unit +vectors in the laboratory, space-fixed frame of reference. +Given the symmetry of the molecule, the dipole moment +is along the principal, molecular, body-fixed ˆz-axis, such +that µ = ˆzµz, where µz = µz, µ is the magnitude of the +dipole moment, and z is the body-fixed position opera- +tor. Noting that vectors represented in body-fixed coor- +dinates ˆx, ˆy, and ˆz and space-fixed coordinates ˆX, ˆY , and +ˆZ can be related via Euler angles θ ∈ [0, π], φ ∈ [0, 2π], +and χ ∈ [0, 2π], as per Fig. 2, the components of the +dipole moment in the space-fixed frame are then given +by +µX = µX = µ sin θ cos φ, +µY = µY = µ sin θ sin φ, +µZ = µZ = µ cos θ, +(3) +where X, Y, Z denote the space-fixed position operators, +expressed using Euler angles θ, φ. +The molecule is assumed to be a rigid rotor, and the field- +free symmetric top Hamiltonian is given by [45] +H0 = B(J2 +x + J2 +y) + CJ2 +z , +(4) +where B and C are rotational constants and Jx, Jy, and +Jz, respectively, denote angular momentum projection +operators in the molecular frame, given by the relations +Jx = −i cos χ +� +cot θ ∂ +∂χ − +1 +sin θ +∂ +∂φ +� +− i sin χ ∂ +∂θ, +Jy = i sin χ +� +cot θ ∂ +∂χ − +1 +sin θ +∂ +∂φ +� +− i cos χ ∂ +∂θ, +(5) +and +Jz = −i ∂ +∂χ. +(6) +Figure 2. Diagram showing (θ, φ, χ) Euler angle relations be- +tween laboratory space-fixed ˆ +X, ˆY , and ˆZ coordinates (black) +and molecular body-fixed ˆx, ˆy, and ˆz coordinates (red). +2 + +2 +X +D +y +Y +CAs a result, the total angular momentum can be written +as +J2 = − +� +∂2 +∂θ2 + cot θ ∂ +∂θ + +1 +sin2 θ +� ∂2 +∂φ2 + ∂2 +∂χ2 +− 2 cos θ +∂2 +∂φ∂χ +�� +(7) +and the field-free Hamiltonian becomes +H0 = −B +� ∂2 +∂θ2 + cot θ ∂ +∂θ + cot2 θ ∂2 +∂χ2 +− 2cot θ +sin θ +∂2 +∂χ∂φ + +1 +sin2 θ +∂2 +∂φ2 +� +− C ∂2 +∂χ2 . +(8) +III. +QUANTUM TRACKING CONTROL EQUATIONS +FOR SYMMETRIC TOP ORIENTATION +Here, we apply the QTC framework [14–16, 22] to track- +ing a symmetric top molecule’s 3D orientation using +three orthogonal QTC fields. The time-dependent sym- +metric top orientation is defined as +⟨R⟩(t) = ˆX⟨X⟩(t) + ˆY ⟨Y ⟩(t) + ˆZ⟨Z⟩(t), +(9) +which is the instantaneous expectation value, at time t, of +the position vector operator R ≡ ˆXX + ˆY Y + ˆZZ. By +differentiating ⟨R⟩(t) with respect to t once we obtain +d⟨R⟩(t) +dt += i⟨[H0, R]⟩(t), +(10) +which has no explicit dependence on ε(t). By further +differentiating Eq. (10) with respect to t we obtain +d2⟨R⟩(t) +dt2 += ⟨[µ · ε(t), [H0, R]]⟩(t) − ⟨[H0, [H0, R]]⟩(t). +(11) +Eq. (11) can be expressed as a single matrix equation +b(t) = A(t)ε(t), where ε(t) = (εX(t), εY (t), εZ(t))T , +the components of the matrix A(t) are given by +AX,X(t) = ⟨[µX, [H0, X]]⟩(t) = 2µB⟨Y 2 + Z2⟩(t) +AY,Y (t) = ⟨[µY , [H0, Y ]]⟩(t) = 2µB⟨Z2 + X2⟩(t) +AZ,Z(t) = ⟨[µZ, [H0, Z]]⟩(t) = 2µB⟨X2 + Y 2⟩(t) +AX,Y (t) = AY,X(t) = ⟨[µY , [H0, X]]⟩(t) += −2µB⟨XY ⟩(t) +AY,Z(t) = AZ,Y (t) = ⟨[µZ, [H0, Y ]]⟩(t) += −2µB⟨Y Z⟩(t) +AZ,X(t) = AX,Z(t) = ⟨[µX, [H0, Z]]⟩(t) += −2µB⟨ZX⟩(t), +(12) +and the components of the vector b(t) read +b(t) = d2⟨R⟩d(t) +dt2 +⟨+⟨[H0, [H0, R]]⟩(t). +(13) +Here the subscript “d” denotes the predefined or “desig- +nated” path in time to be tracked, ⟨R⟩d(t). +The QTC fields can be found by inverting A(t), i.e., as- +suming the inverse of A(t) exists at all times t, and solv- +ing the resultant QTC equations, +ε(t) = A−1(t)b(t), +(14) +as follows. First, the initial field values ε(0) are com- +puted at time t = 0, by evaluating (14) for an initial +state |ψ(0)⟩. The next step is to evolve the system for- +ward in time by integrating the Schr¨odinger equation (1) +over a small time step ∆t, where this evolution depends +on ε(0). Then, the state that results from this forward +propagation, |ψ(∆t)⟩, can be substituted into Eq. (14) to +compute ε(∆t) associated with time t = ∆t. This proce- +dure is then repeated for all remaining time steps, where +each forward step k − 1 → k involves the following two +computational steps (i) and (ii): +(i) |ψ(k∆t)⟩ = e−iH +� +ε +� +(k−1)∆t +�� +∆t|ψ +� +(k − 1)∆t +� +⟩ +(ii) ε(k∆t) = A−1� +|ψ(k∆t)⟩ +� +b +� +|ψ(k∆t)⟩ +� +. +The computational details associated with steps (i) and +(ii) are given in Sec. IV. As mentioned above, this pro- +cedure requires that A(t) is invertible at all times. A +singularity is obtained when A(t) is not invertible, im- +plying that det(A(t)) = 0. We proceed by investigating +this case in more detail below. +From Eq. (12) it can be readily shown that the determi- +nant of the matrix A, suppressing the t-dependence, can +be written as +det(A) = (2µB)3�� +⟨X2⟩ + ⟨Y 2⟩ +�� +⟨Y 2⟩⟨X2⟩ − ⟨XY ⟩2� ++ +� +⟨Y 2⟩ + ⟨Z2⟩ +�� +⟨Y 2⟩⟨Z2⟩ − ⟨Y Z⟩2� ++ +� +⟨Z2⟩ + ⟨X2⟩ +�� +⟨X2⟩⟨Z2⟩ − ⟨XZ⟩2� ++ 2 +� +⟨X2⟩⟨Y 2⟩⟨Z2⟩ − ⟨XY ⟩⟨Y Z⟩⟨XZ⟩ +�� +≥ 0 +(15) +The Cauchy-Schwarz inequalities between the state vec- +tors X|ψ(t)⟩, Y |ψ(t)⟩, and Z|ψ(t)⟩, which can be ex- +pressed in general as +⟨ϕ1|ϕ1⟩⟨ϕ2|ϕ2⟩ ≥ |⟨ϕ1|ϕ2⟩|2 +(16) +for any two state vectors |ϕ1⟩ and |ϕ2⟩, implies that Eq. +(15) is positive semidefinite, as indicated. To see that +3 + +this holds for the final line in Eq. (15), we begin with the +following relations from Cauchy-Schwarz, +⟨X2⟩⟨Y 2⟩ ≥ ⟨XY ⟩2 +⟨Y 2⟩⟨Z2⟩ ≥ ⟨Y Z⟩2 +⟨Z2⟩⟨X2⟩ ≥ ⟨ZX⟩2 +(17) +which may be rearranged by taking products as, +⟨X2⟩2⟨Y 2⟩2⟨Z2⟩2 ≥ ⟨XY ⟩2⟨Y Z⟩2⟨ZX⟩2. +(18) +Taking the square root of both sides then yields the de- +sired result that +⟨X2⟩⟨Y 2⟩⟨Z2⟩ ≥ ⟨XY ⟩⟨Y Z⟩⟨ZX⟩. +(19) +The equality sign (i.e., a singularity) in Eq. (15) can +arise if and only if X|ψ(t)⟩, Y |ψ(t)⟩, and Z|ψ(t)⟩ are +all linearly dependent. The QTC singularity issue will +be addressed in Sec. IV below where we describe our +computational methods for solving Eq. (14). +IV. +COMPUTATIONAL METHODS +The numerical computation of the QTC fields according +to Eq. (14) requires evaluations of the expectation val- +ues for the associated operators. Here, we study QTC +of symmetric top molecules in the |JKM⟩ eigenbasis of +the drift Hamiltonian, which is given in Eq. (8) and can +be rearranged as +H0 = BJ2 + (C − B)J2 +z +(20) +leading to the eigenvalue equation +H0 |JKM⟩ = +� +BJ(J + 1) + (C − B)K2� +|JKM⟩ +(21) +where J = 0, 1, 2, · · · is the total rotational angular +momentum quantum number, K = 0, ±1, ±2, · · · , ±J +is the projection of the angular momentum onto the +molecule-fixed z-axis, and M = 0, ±1, ±2, · · · , ±J is +the projection of the angular momentum onto the labora- +tory frame Z-axis. Eq. (21) can be obtained in a straight- +forward manner from Eq. (20) using the standard an- +gular momentum matrix element relations Jz|JKM⟩ = +K|JKM⟩ and J2|JKM⟩ = J(J + 1)|JKM⟩. In this +section, we obtain matrix element relations in this basis +in order to carry out the two computational steps outlined +in Sec. III that must be taken at each forward time step, +i.e., (i) solving the time-dependent Schr¨odinger equation, +Eq. (1) and (ii) solving the QTC equations, Eq. (14). +(i) Solving Eq. (1): +We begin by expanding the state of a symmetric top as +|ψ(t)⟩ = +� +JKM +⟨JKM|ψ(t)⟩|JKM⟩, +(22) +The expansion coefficients are governed by the equation +i d +dt⟨JKM|ψ(t)⟩ += +� +J′K′M ′ +⟨JKM|H0|J′K′M ′⟩⟨J′K′M ′|ψ(t)⟩ +− +� +J′K′M ′ +µ⟨JKM|X|J′K′M ′⟩⟨J′K′M ′|ψ(t)⟩εX(t) +− +� +J′K′M ′ +µ⟨JKM|Y |J′K′M ′⟩⟨J′K′M ′|ψ(t)⟩εY (t) +− +� +J′K′M ′ +µ⟨JKM|Z|J′K′M ′⟩⟨J′K′M ′|ψ(t)⟩εZ(t), +(23) +where +⟨JKM|H0|J′K′M ′⟩ = BJ(J +1)+(C−B)K2 (24) +for J′ = J, K′ = K, and M ′ = M, and +⟨JKM|X|J′K′M ′⟩ = −N +√ +2(−1)2+2J′+M ′−K′+2M +2 +� +m=−1,1 +m +� +J +1 +J′ +M m −M ′ +� � +J +1 +J′ +K 0 −K′ +� +, +⟨JKM|Y |J′K′M ′⟩ = N +√ +2(−1)2+2J′+M ′−K′+2M +2i +� +m=−1,1 +� +J +1 +J′ +M m −M ′ +� � +J +1 +J′ +K 0 −K′ +� +, +(25) +with J′ = J ± 1, K′ = K, and M ′ = M ± 1, and +⟨JKM|Z|J′K′M ′⟩ = N(−1)2+2J′+M ′−K′+2M +� +J +1 +J′ +M 0 −M ′ +� � +J +1 +J′ +K 0 −K′ +� +, +(26) +4 + +with J′ = J ± 1, K′ = K, and M ′ = M, in terms +of 3j symbols, where N = +� +(2J + 1)(2J′ + 1) [46– +48]. The selection rules associated with Eqs. (25) and +(26) can be used to accelerate the computation of the as- +sociated matrix elements. The selection rules also imply +that fields coupling to the system via X, Y, Z can only be +used to drive transitions in the quantum numbers J, M, +while K is conserved. +(ii) Solving Eq. (14): +Eqs. (25) and (26) provide the matrix element relations +needed for obtaining the elements of A(t) in the QTC +Eq. +(14) (i.e., see Eq. +(12)) in the |JKM⟩ eigen- +basis. +The computation of b(t) requires matrix ele- +ment relations for the triple commutators of the form +[H0, [H0, R]], i.e., +⟨JKM|[H0, [H0, R]]|J′K′M ′⟩ += +� +B +� +J(J + 1) − J′(J′ + 1) +��2 +⟨JKM|R|J′K′M ′⟩. +(27) +The issue of det(A(t)) = 0 in Eq. (15) can be clarified +as follows. We will show that the state vectors X|ψ(t)⟩, +Y |ψ(t)⟩, and Z|ψ(t)⟩ are linearly independent of each +other. Specifically, X|ψ(t)⟩, Y |ψ(t)⟩, and Z|ψ(t)⟩ can +be, respectively, further written in terms of the basis +|JKM⟩, as +X|ψ(t)⟩ = +� +JKM +� +� +J′K′M ′ +⟨JKM|X|J′K′M ′⟩⟨J′K′M ′|ψ(t)⟩ +� +|JKM⟩, +Y |ψ(t)⟩ = +� +JKM +� +� +J′K′M ′ +⟨JKM|Y |J′K′M ′⟩⟨J′K′M ′|ψ(t)⟩ +� +|JKM⟩, +(28) +and +Z|ψ(t)⟩ = +� +JKM +� +� +J′K′M ′ +⟨JKM|Z|J′K′M ′⟩⟨J′K′M ′|ψ(t)⟩ +� +|JKM⟩, +(29) +which, from Eqs. (25) and (26), can be seen to be lin- +early independent, since the expansion coefficients for +X|ψ(t)⟩, Y |ψ(t)⟩, and Z|ψ(t)⟩ in the |JKM⟩ basis are +all distinct for bases truncated at some finite, albeit suf- +ficiently large, value Jmax (which is set to 30 in all of +our calculations in Sec. VI). As a result, we conclude +that det(A(t)) > 0 and that singularities will not appear +when solving the QTC Eqs. (14). +V. +REDUCTION TO THE CASE OF LINEAR +MOLECULES +Figure 3. Diagram showing (θ, φ) relation between laboratory +frame fixed ( ˆ +X, ˆY , ˆZ) coordinates (black) and molecular ori- +entation vector (red) +Linear molecules possess only one axis of rotation and +their Hamiltonian is given by, +H0 = BL2 +(30) +where +L2 = − +� +1 +sin θ +∂ +∂θ +� +sin θ ∂ +∂θ +� ++ +1 +sin2 θ +∂2 +∂φ2 +� +(31) +and has no explicit χ-dependence, as depicted in Fig. 3. +This yields an expression for det(A) that is equal to Eq. +(15). The matrix elements required to study QTC of lin- +ear molecules in their eigenbasis can be found using the +matrix element relations obtained for symmetric tops and +setting K = 0. +VI. +NUMERICAL ILLUSTRATIONS +We have derived the QTC equations, Eq. (14), for con- +trolling symmetric top orientation, and we now present +numerical illustrations of this approach. For our illus- +trations, we consider the symmetric top molecule flu- +oromethane, with principal rotational constant B += +5 + +Z +Y +X5.182 cm−1 and second rotational constant C += +0.852 cm−1 [49]. +The magnitude of the dipole mo- +ment is given by µ = 1.847 Debye [50]. +The sys- +tem is represented in the |JKM⟩ basis, with basis el- +ements |000⟩, · · · , |30, ±30, ±30⟩. We consider desig- +nated tracks ⟨X⟩d(t), ⟨Y ⟩d(t), and ⟨Z⟩d(t) given by +⟨X⟩d(t) ≡ 0.2e− +� +t−0.8T +T/8 +�2 +sin(8Bt) +⟨Y ⟩d(t) ≡ 0.2e− +� +t−0.8T +T/8 +�2 +cos(8Bt) +⟨Z⟩d(t) ≡ 0.2e− +� +t−T +T/8 +�2 +cos(8Bt) +(32) +where T = 5/B is the terminal time and 30,000 time +points are used for the calculations. +Fig. +4 shows a +3D plot comparing these designated ⟨X⟩d(t), ⟨Y ⟩d(t), +and ⟨Z⟩d(t) trajectories with the actual tracks ⟨X⟩(t), +⟨Y ⟩(t), and ⟨Z⟩(t) that are followed when the molecule +is initialized in |ψ(0)⟩ = |000⟩, |100⟩, |110⟩, |200⟩. We +see that the curves in Fig. 4 are all superimposed, indi- +cating that QTC is successful. Meanwhile, Fig. 5 shows +the QTC fields determined via Eq. (14) that are found +to drive ⟨X⟩(t), ⟨Y ⟩(t), and ⟨Z⟩(t) along these desig- +nated trajectories for the four initial conditions we con- +sider. We note that as per Sec. (V), the fields εX(t), +εY (t), and εZ(t) and the tracks associated with |ψ(0)⟩ = +|000⟩, |100⟩, |200⟩ are the same fields and tracks for a +3D linear rotor with rotational constant B, initialized as +|ψ(0)⟩ = |00⟩, |10⟩, |20⟩. +VII. +CONCLUSIONS +In this article, we have explored how QTC can be applied +to design fields to orient symmetric top molecules, and +have derived expressions for the QTC fields for driving +the molecular orientation along time-dependent tracks. +We also obtained matrix element relations to facilitate +studying QTC of symmetric tops in the |JKM⟩ symmet- +ric top eigenbasis, and presented numerical illustrations +of the QTC procedure for driving orientation dynamics +in these systems. In order to realize associated experi- +mental demonstrations, molecular rotors could be inves- +tigated using, e.g., laser and evaporative cooling methods +to create ultracold molecules, and then trapping them in +an optical lattice [51]. Then, the creation of shaped mi- +crowave fields needed for QTC could be explored using +arbitrary waveform generators [52, 53]. +Looking ahead, this QTC formulation could be extended +towards studying the control of so-called molecular su- +perrotors [54], e.g. +by selecting tracks to create very +rapid rotational dynamics. Furthermore, the prospects of +Figure 4. The designated tracks ⟨X⟩d(t), ⟨Y ⟩d(t), and ⟨Z⟩d(t) +given in Eq. (32) are plotted as a black curve inside of the +⟨X⟩2(t) + ⟨Y ⟩2(t) + ⟨Z⟩2(t) = 1 unit sphere. Then, the QTC +tracks ⟨X⟩(t), ⟨Y ⟩(t), and ⟨Z⟩(t) followed by the system are +plotted in color. The different colors correspond to different +initial conditions |ψ(0)⟩ = |000⟩, |100⟩, |110⟩, |200⟩. +applying QTC towards the control of arrays of coupled +molecular rotors, e.g. for applications in quantum infor- +mation science [55–57], could be studied as well. For +the latter, the study of coupled molecules will likely re- +quire high-dimensional modeling to represent the system +dynamics, given that the model dimension scales expo- +nentially in the number of degrees of freedom. As such, +numerically exact simulations of coupled molecular ro- +tors may not be computationally feasible. However, such +challenges may be addressable through the use of suit- +able approximation frameworks for the quantum dynam- +ics, e.g. [58–61]. +ACKNOWLEDGMENTS +A.B.M. acknowledges support from the U.S. Department +of Energy, Office of Science, Office of Advanced Scien- +tific Computing Research, Department of Energy Com- +putational Science Graduate Fellowship under Award +No. DE-FG02-97ER25308, as well as support from San- +dia National Laboratories’ Laboratory Directed Research +and Development Program under the Truman Fellow- +ship. +H.A.R. acknowledges support from DOE under +6 + +(a) +(b) +(c) +Figure 5. The QTC fields εX(τ), εY (τ), and εZ(τ) are plotted +as a function of the nondimensionalized time τ ≡ Bt in panels +(a), (b), and (c), respectively. The different colors correspond to +different initial conditions |ψ(0)⟩ = |000⟩, |100⟩, |110⟩, |200⟩. +Grant No. DE-FG02-02ER15344. T.S.H. acknowledges +support from the Army Research Office W911NF-19-1- +0382. +Sandia National Laboratories is a multimission labora- +tory managed and operated by National Technology & +Engineering Solutions of Sandia, LLC, a wholly owned +subsidiary of Honeywell International Inc., for the U.S. +Department of Energy’s National Nuclear Security Ad- +ministration under contract DE-NA0003525. This paper +describes objective technical results and analysis. Any +subjective views or opinions that might be expressed in +the paper do not necessarily represent the views of the +U.S. Department of Energy or the United States Govern- +ment. +This report was prepared as an account of work spon- +sored by an agency of the United States Government. +Neither the United States Government nor any agency +thereof, nor any of their employees, makes any warranty, +express or implied, or assumes any legal liability or re- +sponsibility for the accuracy, completeness, or useful- +ness of any information, apparatus, product, or process +disclosed, or represents that its use would not infringe +privately owned rights. Reference herein to any specific +commercial product, process, or service by trade name, +trademark, manufacturer, or otherwise does not neces- +sarily constitute or imply its endorsement, recommenda- +tion, or favoring by the United States Government or any +agency thereof. The views and opinions of authors ex- +pressed herein do not necessarily state or reflect those of +the United States Government or any agency thereof. +[1] C. Brif, R. Chakrabarti, and H. Rabitz, Control of quan- +tum phenomena: past, present and future, New J. Phys. +12, 075008 (2010). +[2] S. J. Glaser, U. Boscain, T. Calarco, C. P. Koch, W. K¨ock- +enberger, R. Kosloff, I. Kuprov, B. Luy, S. Schirmer, +T. Schulte-Herbr¨uggen, D. Sugny, and F. K. Wilhelm, +Training schr¨odinger’s cat: quantum optimal control, Eur. +Phys. J. D 69, 279 (2015). +[3] C. P. Koch, Controlling open quantum systems: tools, +achievements, and limitations, J. Phys. Condens. Matter +28, 213001 (2016). +[4] A. P. Peirce, M. A. Dahleh, and H. Rabitz, Optimal con- +trol of quantum-mechanical systems: Existence, numer- +ical approximation, and applications, Phys. Rev. A 37, +4950 (1988). +[5] T. Caneva, T. Calarco, and S. Montangero, Chopped +random-basis quantum optimization, Phys. Rev. A 84, +022326 (2011). +[6] Y. Maday and G. Turinici, New formulations of monoton- +ically convergent quantum control algorithms, J. Chem. +Phys. 118, 8191 (2003). +[7] W. Zhu and H. Rabitz, A rapid monotonically convergent +iteration algorithm for quantum optimal control over the +expectation value of a positive definite operator, J. Chem. +Phys. 109, 385 (1998). +[8] F. Dolde, V. Bergholm, Y. Wang, I. Jakobi, B. Nayde- +nov, S. Pezzagna, J. Meijer, F. Jelezko, P. Neumann, +T. Schulte-Herbr¨uggen, J. Biamonte, and J. Wrachtrup, +High-fidelity spin entanglement using optimal control, +Nat. Commun. 5, 3371 (2014). +[9] G. Waldherr, Y. Wang, S. Zaiser, M. Jamali, T. Schulte- +Herbr¨uggen, H. Abe, T. Ohshima, J. Isoya, J. F. Du, +P. Neumann, and J. Wrachtrup, Quantum error correc- +tion in a solid-state hybrid spin register, Nature 506, 204 +(2014). +[10] A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, +V. Seyfried, M. Strehle, and G. Gerber, Control of chem- +ical reactions by feedback-optimized phase-shaped fem- +tosecond laser pulses, Science 282, 919 (1998). +[11] R. J. Levis, G. M. Menkir, and H. Rabitz, Selective bond +7 + +dissociation and rearrangement with optimally tailored, +strong-field laser pulses, Science 292, 709 (2001). +[12] N. H. Damrauer, C. Dietl, G. Krampert, S. H. Lee, K. H. +Jung, and G. Gerber, Control of bond-selective photo- +chemistry in CH2BrCl using adaptive femtosecond pulse +shaping, Eur. Phys. J. D 20, 71 (2002). +[13] G. Vogt, G. Krampert, P. Niklaus, P. Nuernberger, and +G. Gerber, Optimal control of photoisomerization, Phys. +Rev. Lett. 94, 068305 (2005). +[14] P. Gross, H. Singh, H. Rabitz, K. Mease, and G. M. +Huang, Inverse quantum-mechanical control: A means +for design and a test of intuition, Phys. Rev. A 47, 4593 +(1993). +[15] Y. Chen, P. Gross, V. Ramakrishna, H. Rabitz, and +K. Mease, Competitive tracking of molecular objectives +described by quantum mechanics, J. Chem. Phys. 102 +(1995). +[16] Y. Chen, P. Gross, V. Ramakrishna, H. Rabitz, K. Mease, +and H. Singh, Control of Classical Regime Molecular Ob- +jectives -Applications of Tracking and Variations on the +Theme*, Automatica 33, 1617 (1997). +[17] R. Brockett and M. Mesarovic, The reproducibility of +multivariable systems, J. Math. Anal. Appl. 11, 548 +(1965). +[18] R. M. Hirschorn, Invertibility of Nonlinear Control Sys- +tems, SIAM J. Control Optim. 17 (1979). +[19] C. K. Ong, G. M. Huang, T. J. Tarn, and J. W. Clark, In- +vertibility of quantum-mechanical control systems, Math. +Systems Theory 17, 335 (1984). +[20] D. A. Lidar and S. Schneider, Stabilizing qubit coherence +via tracking-control, Quantum Inf. Comput. 5 (2005). +[21] A. G. Campos, D. I. Bondar, R. Cabrera, and H. A. Rab- +itz, How to make distinct dynamical systems appear spec- +trally identical, Phys. Rev. Lett. 118, 083201 (2017). +[22] A. Magann, T.-S. Ho, and H. Rabitz, Singularity-free +quantum tracking control of molecular rotor orientation, +Phys. Rev. A 98, 043429 (2018). +[23] A. B. Magann, G. McCaul, H. A. Rabitz, and D. I. Bon- +dar, Sequential optical response suppression for chemical +mixture characterization, Quantum 6, 626 (2022). +[24] G. McCaul, C. Orthodoxou, K. Jacobs, G. H. Booth, and +D. I. Bondar, Controlling arbitrary observables in cor- +related many-body systems, Phys. Rev. A 101, 053408 +(2020). +[25] G. McCaul, C. Orthodoxou, K. Jacobs, G. H. Booth, +and D. I. Bondar, Driven imposters: Controlling expecta- +tions in many-body systems, Phys. Rev. Lett. 124, 183201 +(2020). +[26] G. McCaul, A. F. King, and D. I. Bondar, Optical indis- +tinguishability via twinning fields, Phys. Rev. Lett. 127, +113201 (2021). +[27] W. Zhu, M. Smit, and H. Rabitz, Managing singular be- +havior in the tracking control of quantum dynamical ob- +servables, J. Chem. Phys. 110 (1999). +[28] R. Hirschornf and J. Davis, Output Tracking for Nonlinear +Systems with Singular Points, SIAM J. Control Optim. 25 +(1987). +[29] P. M. Kraus, A. Rupenyan, and H. J. W¨orner, Phys. Rev. +Lett. 109, 233903 (2012). +[30] P. R. Brooks, Science 193, 11 (1976). +[31] R. N. Zare, Science 279, 1875 (1998). +[32] T. P. Rakitzis, A. J. van den Brom, and M. H. M. Janssen, +Science 303, 1852 (2004). +[33] S. De, I. Znakovskaya, D. Ray, F. Anis, N. G. Johnson, +I. A. Bocharova, M. Magrakvelidze, B. D. Esry, C. L. +Cocke, I. V. Litvinyuk, and M. F. Kling, Field-free ori- +entation of co molecules by femtosecond two-color laser +fields, Phys. Rev. Lett. 103, 153002 (2009). +[34] K. Oda, M. Hita, S. Minemoto, and H. Sakai, All-optical +molecular orientation, Phys. Rev. Lett. 104, 213901 +(2010). +[35] S. Fleischer, Y. Zhou, R. W. Field, and K. A. Nelson, +Molecular orientation and alignment by intense single- +cycle thz pulses, Phys. Rev. Lett. 107, 163603 (2011). +[36] K. Hoki and Y. Fujimura, Chem. Phys. 267, 187 (2001). +[37] J. Salomon, C. M. Dion, and G. Turinici, J. Chem. Phys. +123, 144310 (2005). +[38] G. Turinici and H. Rabitz, J. Phys. A 43, 105303 (2010). +[39] M. Yoshida and Y. Ohtsuki, Chem. Phys. Lett. 633, 169 +(2015). +[40] H. Yu, T.-S. Ho, and H. Rabitz, Phys. Chem. Chem. Phys. +20, 13008 (2018). +[41] T. Szidarovszky, M. Jono, and K. Yamanouchi, Li- +mao: +Cross-platform software for simulating laser- +induced alignment and orientation dynamics of linear- +, symmetric-and asymmetric tops, Comput. Phys. Com- +mun. 228, 219 (2018). +[42] A. Ma, A. B. Magann, T.-S. Ho, and H. Rabitz, Opti- +mal control of coupled quantum systems based on the +first-order magnus expansion: Application to multiple +dipole-dipole-coupled molecular rotors, Phys. Rev. A 102, +013115 (2020). +[43] U. Boscain, M. Caponigro, and M. Sigalotti, Multi-input +schr¨odinger equation: controllability, tracking, and appli- +cation to the quantum angular momentum, J. Differ. Equ. +256, 3524 (2014). +[44] U. Boscain, E. Pozzoli, and M. Sigalotti, Classical and +quantum controllability of a rotating symmetric molecule, +SIAM J Control Optim. 59, 156 (2021). +[45] R. N. Zare, Angular momentum : understanding spa- +tial aspects in chemistry and physics (Wiley, New York +; Toronto, 1988). +[46] P. C. Cross, R. M. Hainer, and G. W. King, The asym- +metric rotor ii. calculation of dipole intensities and line +classification, J. Chem. Phys. 12, 210 (1944). +[47] R. N. Zare, Molecular level-crossing spectroscopy, J. +Chem. Phys. 45, 4510 (1966). +[48] H. W. Kroto, Molecular Rotation Spectra (Dover Publica- +tions, Inc, New York, 1992). +[49] D. Papousek, Y. Hsu, H. Chen, P. Pracna, S. Klee, and +M. Winnewisser, Far infrared spectrum and ground state +parameters of 12ch3f, Journal of Molecular Spectroscopy +159, 33 (1993). +[50] B. Starck, R. Tischer, and M. Winnewisser, Molecular +constants from microwave, molecular beam, and electron +spin resonance spectroscopy · 1 introduction: Datasheet +from landolt-b¨ornstein - group ii molecules and radicals · +volume 6: “molecular constants from microwave, molec- +8 + +ular beam, and electron spin resonance spectroscopy” in +springermaterials +(https://doi.org/10.1007/10201226 1), +copyright 1974 Springer-Verlag Berlin Heidelberg. +[51] M. A. Baranov, M. Dalmonte, G. Pupillo, and P. Zoller, +Condensed Matter Theory of Dipolar Quantum Gases, +Chem. Rev. 112, 5012 (2012). +[52] J. Yao, Photonic generation of microwave arbitrary wave- +forms, Opt. Commun. 284, 3723 (2011). +[53] I. Lin, J. McKinney, and A. Weiner, Photonic synthesis +of broadband microwave arbitrary waveforms applicable +to ultra-wideband communication, IEEE Microw. Wirel. +Compon. Lett 15, 226 (2005). +[54] A. Korobenko, A. A. Milner, and V. Milner, Direct obser- +vation, study, and control of molecular superrotors, Phys. +Rev. Lett. 112, 113004 (2014). +[55] D. DeMille, Phys. Rev. Lett. 88, 067901 (2002). +[56] L. Bomble, P. Pellegrini, P. Ghesqui`ere, and M. Desouter- +Lecomte, Phys. Rev. A 82, 062323 (2010). +[57] Q. Wei, Y. Cao, S. Kais, B. Friedrich, and D. Herschbach, +ChemPhysChem 17, 3714 (2016). +[58] M. Messina, K. R. Wilson, and J. L. Krause, Quan- +tum control of multidimensional systems: Implementa- +tion within the time?dependent hartree approximation, J. +Chem. Phys. 104, 173 (1996). +[59] M. Schr¨oder, J.-L. Carre´on-Macedo, and A. Brown, Im- +plementation of an iterative algorithm for optimal control +of molecular dynamics into mctdh, Phys. Chem. Chem. +Phys. 10, 850 (2008). +[60] A. Magann, L. Chen, T.-S. Ho, and H. Rabitz, Quantum +optimal control of multiple weakly interacting molecu- +lar rotors in the time-dependent hartree approximation, J. +Chem. Phys. 150, 164303 (2019). +[61] P. Doria, T. Calarco, and S. Montangero, Optimal control +technique for many-body quantum dynamics, Phys. Rev. +Lett. 106, 190501 (2011). +9 + diff --git a/KNE3T4oBgHgl3EQfAQkY/content/tmp_files/load_file.txt b/KNE3T4oBgHgl3EQfAQkY/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..24d18bf4b039ccddb2d910582cf34bee24f737ef --- /dev/null +++ b/KNE3T4oBgHgl3EQfAQkY/content/tmp_files/load_file.txt @@ -0,0 +1,763 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf,len=762 +page_content='Quantum tracking control of the orientation of symmetric top molecules Alicia B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Magann,1, 2, ∗ Tak-San Ho,3 Christian Arenz,3, 4 and Herschel A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rabitz3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' † 1Department of Chemical & Biological Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Princeton University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Princeton,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' New Jersey 08544,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' USA 2Center for Computing Research,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Sandia National Laboratories,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Albuquerque,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' New Mexico 87185,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' USA 3Department of Chemistry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Princeton University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Princeton,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' New Jersey 08544,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' USA 4School of Electrical,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Computer and Energy Engineering,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Arizona State University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Tempe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Arizona 85281,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' USA (Dated: January 12,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 2023) The goal of quantum tracking control is to identify shaped fields to steer observable expectation values along designated time-dependent tracks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The fields are determined via an iteration-free procedure, which is based on inverting the underlying dynamical equations governing the controlled observables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' In this article, we generalize the ideas in Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A 98, 043429 (2018) to the task of orienting symmetric top molecules in 3D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' To this end, we derive equations for the control fields capable of directly tracking the expected value of the 3D dipole orientation vector along a desired path in time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' We show this framework can be utilized for tracking the orientation of linear molecules as well, and present numerical illustrations of these principles for symmetric top tracking control problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' INTRODUCTION The desire to selectively manipulate molecular dynamics using external fields is a decades-old dream that has mo- tivated a broad range of research pursuits [1–3], includ- ing the development of quantum optimal control (QOC) theory [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The goal of QOC is to identify fields to con- trol the dynamics of a quantum system, such that the sys- tem achieves a desired control objective at a designated target time t = T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The task of identifying an optimal field is typically accomplished by iterative optimization methods [5–7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Although these methods can be compu- tationally demanding, QOC has nonetheless found broad applications, ranging from quantum computing [8, 9] to chemical reactions [10–13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' In this article, we focus on another formulation, quan- tum tracking control (QTC) [14–16], for designing con- trol fields to accurately track the temporal path of an observable of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The origins of QTC are in engi- neering control theory, which has explored tracking con- trol in a range of settings including linear [17], nonlinear [18], and bilinear [19] systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' For quantum-mechanical applications, tracking control principles have been ap- plied towards the numerical study of systems including a qubit [20], a single atom [21], and various molecular [14–16, 22, 23] and solid-state systems [24–26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' ∗ abmagan@sandia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='gov † hrabitz@princeton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='edu Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' In this article, we formulate QTC for controlling the 3D orientation of symmetric top molecules, such as fluo- romethane, shown here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The control procedure involves de- signing three orthogonal fields (black) in order to drive the molecule’s 3D dipole vector along a desired time-dependent track (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The three fields can be determined by solving an inverse equation, without the need for optimization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The aim of QTC is to find tracking control field(s) ε(t) that drive one or multiple observable expectation values ⟨O⟩(t) ≡ ⟨ψ(t)|O|ψ(t)⟩ along desired time-dependent “tracks” ⟨O⟩d(t) for a chosen time interval t ∈ [0, T].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' This is carried out by directly inverting the underlying dynamical equation governing ⟨O⟩(t) in order to solve for ε(t) [14–16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Because it does not require any iterative optimization, QTC can be computationally advantageous arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='04255v1 [quant-ph] 11 Jan 2023 compared with usual QOC schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A challenge facing QTC is the potential presence of sin- gularities in the corresponding direct inversion procedure [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' That is, attempts to exactly track arbitrary time- dependent observable paths can produce unphysical, dis- continuous control fields [28] and deviations from the desired tracks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' However, if singularities can be avoided, QTC offers an appealing, iteration-free approach for de- signing fields to control quantum systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Here, we consider applications of QTC to orienting sym- metric top molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The control of molecular orien- tation has applications spanning high harmonic genera- tion [29] and chemical reaction enhancement [30–32], and has been the subject of numerous experimental [33– 35] and theoretical [36–42] studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' In particular, QTC of molecular rotor orientation in 2D has been explored [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' In this work, we extend this prior work to linear and symmetric top molecules in 3D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' We note that although the controllability of linear and symmetric top molecules has been the subject of other studies [43, 44], to the best of our knowledge, the suitability of symmetric tops for QTC has thus far not been explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The remainder of the paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' We begin by outlining the symmetric top rotor model and derive QTC equations for the control fields to track its orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' We go on to describe computational methods for solving the QTC equations by expanding the wave function in terms of angular momentum eigenfunctions of the symmetric top and address the QTC singularity issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' We then show how the formulation of QTC for symmetric top molecules can be reduced to the case of a linear rotor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' We conclude with numerical illustrations and an outlook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' SYMMETRIC TOP MOLECULES IN 3D We consider a symmetric top molecule with dynamics governed by the time-dependent Schr¨odinger equation, i ∂ ∂t|ψ(t)⟩ = H(t)|ψ(t)⟩ , (1) where ℏ = 1 and the time-dependent Hamiltonian is H(t) = H0 − µ · ε(t) (2) in terms of (1) the field-free Hamiltonian H0, (2) three orthogonal control fields εX(t), εY (t), and εZ(t), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=', where ε(t) = ˆXεX(t) + ˆY εY (t) + ˆZεZ(t), and (3) the components of the dipole moment µ = ˆXµX + ˆY µY + ˆZµZ, where ˆX, ˆY , and ˆZ denote the three Cartesian unit vectors in the laboratory, space-fixed frame of reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Given the symmetry of the molecule, the dipole moment is along the principal, molecular, body-fixed ˆz-axis, such that µ = ˆzµz, where µz = µz, µ is the magnitude of the dipole moment, and z is the body-fixed position opera- tor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Noting that vectors represented in body-fixed coor- dinates ˆx, ˆy, and ˆz and space-fixed coordinates ˆX, ˆY , and ˆZ can be related via Euler angles θ ∈ [0, π], φ ∈ [0, 2π], and χ ∈ [0, 2π], as per Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 2, the components of the dipole moment in the space-fixed frame are then given by µX = µX = µ sin θ cos φ, µY = µY = µ sin θ sin φ, µZ = µZ = µ cos θ, (3) where X, Y, Z denote the space-fixed position operators, expressed using Euler angles θ, φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The molecule is assumed to be a rigid rotor, and the field- free symmetric top Hamiltonian is given by [45] H0 = B(J2 x + J2 y) + CJ2 z , (4) where B and C are rotational constants and Jx, Jy, and Jz, respectively, denote angular momentum projection operators in the molecular frame, given by the relations Jx = −i cos χ � cot θ ∂ ∂χ − 1 sin θ ∂ ∂φ � − i sin χ ∂ ∂θ, Jy = i sin χ � cot θ ∂ ∂χ − 1 sin θ ∂ ∂φ � − i cos χ ∂ ∂θ, (5) and Jz = −i ∂ ∂χ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (6) Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Diagram showing (θ, φ, χ) Euler angle relations be- tween laboratory space-fixed ˆ X, ˆY , and ˆZ coordinates (black) and molecular body-fixed ˆx, ˆy, and ˆz coordinates (red).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 2 2 X D y Y CAs a result, the total angular momentum can be written as J2 = − � ∂2 ∂θ2 + cot θ ∂ ∂θ + 1 sin2 θ � ∂2 ∂φ2 + ∂2 ∂χ2 − 2 cos θ ∂2 ∂φ∂χ �� (7) and the field-free Hamiltonian becomes H0 = −B � ∂2 ∂θ2 + cot θ ∂ ∂θ + cot2 θ ∂2 ∂χ2 − 2cot θ sin θ ∂2 ∂χ∂φ + 1 sin2 θ ∂2 ∂φ2 � − C ∂2 ∂χ2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (8) III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' QUANTUM TRACKING CONTROL EQUATIONS FOR SYMMETRIC TOP ORIENTATION Here, we apply the QTC framework [14–16, 22] to track- ing a symmetric top molecule’s 3D orientation using three orthogonal QTC fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The time-dependent sym- metric top orientation is defined as ⟨R⟩(t) = ˆX⟨X⟩(t) + ˆY ⟨Y ⟩(t) + ˆZ⟨Z⟩(t), (9) which is the instantaneous expectation value, at time t, of the position vector operator R ≡ ˆXX + ˆY Y + ˆZZ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' By differentiating ⟨R⟩(t) with respect to t once we obtain d⟨R⟩(t) dt = i⟨[H0, R]⟩(t), (10) which has no explicit dependence on ε(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' By further differentiating Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (10) with respect to t we obtain d2⟨R⟩(t) dt2 = ⟨[µ · ε(t), [H0, R]]⟩(t) − ⟨[H0, [H0, R]]⟩(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (11) Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (11) can be expressed as a single matrix equation b(t) = A(t)ε(t),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' where ε(t) = (εX(t),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' εY (t),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' εZ(t))T ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' the components of the matrix A(t) are given by AX,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='X(t) = ⟨[µX,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [H0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' X]]⟩(t) = 2µB⟨Y 2 + Z2⟩(t) AY,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='Y (t) = ⟨[µY ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [H0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Y ]]⟩(t) = 2µB⟨Z2 + X2⟩(t) AZ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='Z(t) = ⟨[µZ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [H0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Z]]⟩(t) = 2µB⟨X2 + Y 2⟩(t) AX,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='Y (t) = AY,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='X(t) = ⟨[µY ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [H0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' X]]⟩(t) = −2µB⟨XY ⟩(t) AY,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='Z(t) = AZ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='Y (t) = ⟨[µZ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [H0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Y ]]⟩(t) = −2µB⟨Y Z⟩(t) AZ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='X(t) = AX,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='Z(t) = ⟨[µX,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [H0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Z]]⟩(t) = −2µB⟨ZX⟩(t),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (12) and the components of the vector b(t) read b(t) = d2⟨R⟩d(t) dt2 ⟨+⟨[H0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [H0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' R]]⟩(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (13) Here the subscript “d” denotes the predefined or “desig- nated” path in time to be tracked, ⟨R⟩d(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The QTC fields can be found by inverting A(t), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=', as- suming the inverse of A(t) exists at all times t, and solv- ing the resultant QTC equations, ε(t) = A−1(t)b(t), (14) as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' First, the initial field values ε(0) are com- puted at time t = 0, by evaluating (14) for an initial state |ψ(0)⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The next step is to evolve the system for- ward in time by integrating the Schr¨odinger equation (1) over a small time step ∆t, where this evolution depends on ε(0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Then, the state that results from this forward propagation, |ψ(∆t)⟩, can be substituted into Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (14) to compute ε(∆t) associated with time t = ∆t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' This proce- dure is then repeated for all remaining time steps, where each forward step k − 1 → k involves the following two computational steps (i) and (ii): (i) |ψ(k∆t)⟩ = e−iH � ε � (k−1)∆t �� ∆t|ψ � (k − 1)∆t � ⟩ (ii) ε(k∆t) = A−1� |ψ(k∆t)⟩ � b � |ψ(k∆t)⟩ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The computational details associated with steps (i) and (ii) are given in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' As mentioned above, this pro- cedure requires that A(t) is invertible at all times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A singularity is obtained when A(t) is not invertible, im- plying that det(A(t)) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' We proceed by investigating this case in more detail below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' From Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (12) it can be readily shown that the determi- nant of the matrix A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' suppressing the t-dependence,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' can be written as det(A) = (2µB)3�� ⟨X2⟩ + ⟨Y 2⟩ �� ⟨Y 2⟩⟨X2⟩ − ⟨XY ⟩2� + � ⟨Y 2⟩ + ⟨Z2⟩ �� ⟨Y 2⟩⟨Z2⟩ − ⟨Y Z⟩2� + � ⟨Z2⟩ + ⟨X2⟩ �� ⟨X2⟩⟨Z2⟩ − ⟨XZ⟩2� + 2 � ⟨X2⟩⟨Y 2⟩⟨Z2⟩ − ⟨XY ⟩⟨Y Z⟩⟨XZ⟩ �� ≥ 0 (15) The Cauchy-Schwarz inequalities between the state vec- tors X|ψ(t)⟩,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Y |ψ(t)⟩,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' and Z|ψ(t)⟩,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' which can be ex- pressed in general as ⟨ϕ1|ϕ1⟩⟨ϕ2|ϕ2⟩ ≥ |⟨ϕ1|ϕ2⟩|2 (16) for any two state vectors |ϕ1⟩ and |ϕ2⟩,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' implies that Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (15) is positive semidefinite, as indicated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' To see that 3 this holds for the final line in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (15), we begin with the following relations from Cauchy-Schwarz, ⟨X2⟩⟨Y 2⟩ ≥ ⟨XY ⟩2 ⟨Y 2⟩⟨Z2⟩ ≥ ⟨Y Z⟩2 ⟨Z2⟩⟨X2⟩ ≥ ⟨ZX⟩2 (17) which may be rearranged by taking products as, ⟨X2⟩2⟨Y 2⟩2⟨Z2⟩2 ≥ ⟨XY ⟩2⟨Y Z⟩2⟨ZX⟩2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (18) Taking the square root of both sides then yields the de- sired result that ⟨X2⟩⟨Y 2⟩⟨Z2⟩ ≥ ⟨XY ⟩⟨Y Z⟩⟨ZX⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (19) The equality sign (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=', a singularity) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (15) can arise if and only if X|ψ(t)⟩, Y |ψ(t)⟩, and Z|ψ(t)⟩ are all linearly dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The QTC singularity issue will be addressed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' IV below where we describe our computational methods for solving Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' COMPUTATIONAL METHODS The numerical computation of the QTC fields according to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (14) requires evaluations of the expectation val- ues for the associated operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Here, we study QTC of symmetric top molecules in the |JKM⟩ eigenbasis of the drift Hamiltonian, which is given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (8) and can be rearranged as H0 = BJ2 + (C − B)J2 z (20) leading to the eigenvalue equation H0 |JKM⟩ = � BJ(J + 1) + (C − B)K2� |JKM⟩ (21) where J = 0, 1, 2, · · · is the total rotational angular momentum quantum number, K = 0, ±1, ±2, · · · , ±J is the projection of the angular momentum onto the molecule-fixed z-axis, and M = 0, ±1, ±2, · · · , ±J is the projection of the angular momentum onto the labora- tory frame Z-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (21) can be obtained in a straight- forward manner from Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (20) using the standard an- gular momentum matrix element relations Jz|JKM⟩ = K|JKM⟩ and J2|JKM⟩ = J(J + 1)|JKM⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' In this section, we obtain matrix element relations in this basis in order to carry out the two computational steps outlined in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' III that must be taken at each forward time step, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=', (i) solving the time-dependent Schr¨odinger equation, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (1) and (ii) solving the QTC equations, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (i) Solving Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (1): We begin by expanding the state of a symmetric top as |ψ(t)⟩ = � JKM ⟨JKM|ψ(t)⟩|JKM⟩,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (22) The expansion coefficients are governed by the equation i d dt⟨JKM|ψ(t)⟩ = � J′K′M ′ ⟨JKM|H0|J′K′M ′⟩⟨J′K′M ′|ψ(t)⟩ − � J′K′M ′ µ⟨JKM|X|J′K′M ′⟩⟨J′K′M ′|ψ(t)⟩εX(t) − � J′K′M ′ µ⟨JKM|Y |J′K′M ′⟩⟨J′K′M ′|ψ(t)⟩εY (t) − � J′K′M ′ µ⟨JKM|Z|J′K′M ′⟩⟨J′K′M ′|ψ(t)⟩εZ(t),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (23) where ⟨JKM|H0|J′K′M ′⟩ = BJ(J +1)+(C−B)K2 (24) for J′ = J,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' K′ = K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' and M ′ = M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' and ⟨JKM|X|J′K′M ′⟩ = −N √ 2(−1)2+2J′+M ′−K′+2M 2 � m=−1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='1 m � J 1 J′ M m −M ′ � � J 1 J′ K 0 −K′ � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' ⟨JKM|Y |J′K′M ′⟩ = N √ 2(−1)2+2J′+M ′−K′+2M 2i � m=−1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='1 � J 1 J′ M m −M ′ � � J 1 J′ K 0 −K′ � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (25) with J′ = J ± 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' K′ = K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' and M ′ = M ± 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' and ⟨JKM|Z|J′K′M ′⟩ = N(−1)2+2J′+M ′−K′+2M � J 1 J′ M 0 −M ′ � � J 1 J′ K 0 −K′ � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (26) 4 with J′ = J ± 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' K′ = K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' and M ′ = M,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' in terms of 3j symbols,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' where N = � (2J + 1)(2J′ + 1) [46– 48].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The selection rules associated with Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (25) and (26) can be used to accelerate the computation of the as- sociated matrix elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The selection rules also imply that fields coupling to the system via X, Y, Z can only be used to drive transitions in the quantum numbers J, M, while K is conserved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (ii) Solving Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (14): Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (25) and (26) provide the matrix element relations needed for obtaining the elements of A(t) in the QTC Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (14) (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=', see Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (12)) in the |JKM⟩ eigen- basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The computation of b(t) requires matrix ele- ment relations for the triple commutators of the form [H0, [H0, R]], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=', ⟨JKM|[H0, [H0, R]]|J′K′M ′⟩ = � B � J(J + 1) − J′(J′ + 1) ��2 ⟨JKM|R|J′K′M ′⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (27) The issue of det(A(t)) = 0 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (15) can be clarified as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' We will show that the state vectors X|ψ(t)⟩, Y |ψ(t)⟩, and Z|ψ(t)⟩ are linearly independent of each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Specifically, X|ψ(t)⟩, Y |ψ(t)⟩, and Z|ψ(t)⟩ can be, respectively, further written in terms of the basis |JKM⟩, as X|ψ(t)⟩ = � JKM � � J′K′M ′ ⟨JKM|X|J′K′M ′⟩⟨J′K′M ′|ψ(t)⟩ � |JKM⟩, Y |ψ(t)⟩ = � JKM � � J′K′M ′ ⟨JKM|Y |J′K′M ′⟩⟨J′K′M ′|ψ(t)⟩ � |JKM⟩, (28) and Z|ψ(t)⟩ = � JKM � � J′K′M ′ ⟨JKM|Z|J′K′M ′⟩⟨J′K′M ′|ψ(t)⟩ � |JKM⟩, (29) which, from Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (25) and (26), can be seen to be lin- early independent, since the expansion coefficients for X|ψ(t)⟩, Y |ψ(t)⟩, and Z|ψ(t)⟩ in the |JKM⟩ basis are all distinct for bases truncated at some finite, albeit suf- ficiently large, value Jmax (which is set to 30 in all of our calculations in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' VI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' As a result, we conclude that det(A(t)) > 0 and that singularities will not appear when solving the QTC Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' REDUCTION TO THE CASE OF LINEAR MOLECULES Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Diagram showing (θ, φ) relation between laboratory frame fixed ( ˆ X, ˆY , ˆZ) coordinates (black) and molecular ori- entation vector (red) Linear molecules possess only one axis of rotation and their Hamiltonian is given by, H0 = BL2 (30) where L2 = − � 1 sin θ ∂ ∂θ � sin θ ∂ ∂θ � + 1 sin2 θ ∂2 ∂φ2 � (31) and has no explicit χ-dependence, as depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' This yields an expression for det(A) that is equal to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (15).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The matrix elements required to study QTC of lin- ear molecules in their eigenbasis can be found using the matrix element relations obtained for symmetric tops and setting K = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' NUMERICAL ILLUSTRATIONS We have derived the QTC equations, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (14), for con- trolling symmetric top orientation, and we now present numerical illustrations of this approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' For our illus- trations, we consider the symmetric top molecule flu- oromethane, with principal rotational constant B = 5 Z Y X5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='182 cm−1 and second rotational constant C = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='852 cm−1 [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The magnitude of the dipole mo- ment is given by µ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='847 Debye [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The sys- tem is represented in the |JKM⟩ basis, with basis el- ements |000⟩, · · · , |30, ±30, ±30⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' We consider desig- nated tracks ⟨X⟩d(t), ⟨Y ⟩d(t), and ⟨Z⟩d(t) given by ⟨X⟩d(t) ≡ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='2e− � t−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='8T T/8 �2 sin(8Bt) ⟨Y ⟩d(t) ≡ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='2e− � t−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='8T T/8 �2 cos(8Bt) ⟨Z⟩d(t) ≡ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='2e− � t−T T/8 �2 cos(8Bt) (32) where T = 5/B is the terminal time and 30,000 time points are used for the calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 4 shows a 3D plot comparing these designated ⟨X⟩d(t), ⟨Y ⟩d(t), and ⟨Z⟩d(t) trajectories with the actual tracks ⟨X⟩(t), ⟨Y ⟩(t), and ⟨Z⟩(t) that are followed when the molecule is initialized in |ψ(0)⟩ = |000⟩, |100⟩, |110⟩, |200⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' We see that the curves in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 4 are all superimposed, indi- cating that QTC is successful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Meanwhile, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 5 shows the QTC fields determined via Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (14) that are found to drive ⟨X⟩(t), ⟨Y ⟩(t), and ⟨Z⟩(t) along these desig- nated trajectories for the four initial conditions we con- sider.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' We note that as per Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (V), the fields εX(t), εY (t), and εZ(t) and the tracks associated with |ψ(0)⟩ = |000⟩, |100⟩, |200⟩ are the same fields and tracks for a 3D linear rotor with rotational constant B, initialized as |ψ(0)⟩ = |00⟩, |10⟩, |20⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' CONCLUSIONS In this article, we have explored how QTC can be applied to design fields to orient symmetric top molecules, and have derived expressions for the QTC fields for driving the molecular orientation along time-dependent tracks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' We also obtained matrix element relations to facilitate studying QTC of symmetric tops in the |JKM⟩ symmet- ric top eigenbasis, and presented numerical illustrations of the QTC procedure for driving orientation dynamics in these systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' In order to realize associated experi- mental demonstrations, molecular rotors could be inves- tigated using, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=', laser and evaporative cooling methods to create ultracold molecules, and then trapping them in an optical lattice [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Then, the creation of shaped mi- crowave fields needed for QTC could be explored using arbitrary waveform generators [52, 53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Looking ahead, this QTC formulation could be extended towards studying the control of so-called molecular su- perrotors [54], e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' by selecting tracks to create very rapid rotational dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Furthermore, the prospects of Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The designated tracks ⟨X⟩d(t), ⟨Y ⟩d(t), and ⟨Z⟩d(t) given in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' (32) are plotted as a black curve inside of the ⟨X⟩2(t) + ⟨Y ⟩2(t) + ⟨Z⟩2(t) = 1 unit sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Then, the QTC tracks ⟨X⟩(t), ⟨Y ⟩(t), and ⟨Z⟩(t) followed by the system are plotted in color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The different colors correspond to different initial conditions |ψ(0)⟩ = |000⟩, |100⟩, |110⟩, |200⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' applying QTC towards the control of arrays of coupled molecular rotors, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' for applications in quantum infor- mation science [55–57], could be studied as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' For the latter, the study of coupled molecules will likely re- quire high-dimensional modeling to represent the system dynamics, given that the model dimension scales expo- nentially in the number of degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' As such, numerically exact simulations of coupled molecular ro- tors may not be computationally feasible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' However, such challenges may be addressable through the use of suit- able approximation frameworks for the quantum dynam- ics, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [58–61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' ACKNOWLEDGMENTS A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' acknowledges support from the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Department of Energy, Office of Science, Office of Advanced Scien- tific Computing Research, Department of Energy Com- putational Science Graduate Fellowship under Award No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' DE-FG02-97ER25308, as well as support from San- dia National Laboratories’ Laboratory Directed Research and Development Program under the Truman Fellow- ship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' acknowledges support from DOE under 6 (a) (b) (c) Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The QTC fields εX(τ), εY (τ), and εZ(τ) are plotted as a function of the nondimensionalized time τ ≡ Bt in panels (a), (b), and (c), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The different colors correspond to different initial conditions |ψ(0)⟩ = |000⟩, |100⟩, |110⟩, |200⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' DE-FG02-02ER15344.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' acknowledges support from the Army Research Office W911NF-19-1- 0382.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Sandia National Laboratories is a multimission labora- tory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=', for the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Department of Energy’s National Nuclear Security Ad- ministration under contract DE-NA0003525.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' This paper describes objective technical results and analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Department of Energy or the United States Govern- ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' This report was prepared as an account of work spon- sored by an agency of the United States Government.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or re- sponsibility for the accuracy, completeness, or useful- ness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not neces- sarily constitute or imply its endorsement, recommenda- tion, or favoring by the United States Government or any agency thereof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' The views and opinions of authors ex- pressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [1] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Brif, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chakrabarti, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rabitz, Control of quan- tum phenomena: past, present and future, New J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 12, 075008 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [2] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Glaser, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Boscain, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Calarco, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Koch, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' K¨ock- enberger, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Kosloff, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Kuprov, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Luy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Schirmer, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Schulte-Herbr¨uggen, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Sugny, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Wilhelm, Training schr¨odinger’s cat: quantum optimal control, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' D 69, 279 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [3] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Koch, Controlling open quantum systems: tools, achievements, and limitations, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Condens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Matter 28, 213001 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Peirce, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Dahleh, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rabitz, Optimal con- trol of quantum-mechanical systems: Existence, numer- ical approximation, and applications, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A 37, 4950 (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [5] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Caneva, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Calarco, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Montangero, Chopped random-basis quantum optimization, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A 84, 022326 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [6] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Maday and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Turinici, New formulations of monoton- ically convergent quantum control algorithms, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 118, 8191 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [7] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Zhu and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rabitz, A rapid monotonically convergent iteration algorithm for quantum optimal control over the expectation value of a positive definite operator, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 109, 385 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [8] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Dolde, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Bergholm, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Wang, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Jakobi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Nayde- nov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Pezzagna, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Meijer, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Jelezko, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Neumann, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Schulte-Herbr¨uggen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Biamonte, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Wrachtrup, High-fidelity spin entanglement using optimal control, Nat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 5, 3371 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [9] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Waldherr, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Wang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Zaiser, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Jamali, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Schulte- Herbr¨uggen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Abe, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Ohshima, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Isoya, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Du, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Neumann, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Wrachtrup, Quantum error correc- tion in a solid-state hybrid spin register, Nature 506, 204 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [10] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Assion, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Baumert, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Bergt, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Brixner, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Kiefer, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Seyfried, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Strehle, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Gerber, Control of chem- ical reactions by feedback-optimized phase-shaped fem- tosecond laser pulses, Science 282, 919 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [11] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Levis, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Menkir, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rabitz, Selective bond 7 dissociation and rearrangement with optimally tailored, strong-field laser pulses, Science 292, 709 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [12] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Damrauer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Dietl, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Krampert, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Jung, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Gerber, Control of bond-selective photo- chemistry in CH2BrCl using adaptive femtosecond pulse shaping, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' D 20, 71 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [13] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Vogt, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Krampert, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Niklaus, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Nuernberger, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Gerber, Optimal control of photoisomerization, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 94, 068305 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [14] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Gross, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Singh, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rabitz, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Mease, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Huang, Inverse quantum-mechanical control: A means for design and a test of intuition, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A 47, 4593 (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [15] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Gross, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Ramakrishna, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rabitz, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Mease, Competitive tracking of molecular objectives described by quantum mechanics, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 102 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [16] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Gross, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Ramakrishna, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rabitz, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Mease, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Singh, Control of Classical Regime Molecular Ob- jectives -Applications of Tracking and Variations on the Theme*, Automatica 33, 1617 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [17] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Brockett and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Mesarovic, The reproducibility of multivariable systems, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Anal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 11, 548 (1965).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [18] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Hirschorn, Invertibility of Nonlinear Control Sys- tems, SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Control Optim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 17 (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [19] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Ong, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Huang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Tarn, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Clark, In- vertibility of quantum-mechanical control systems, Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Systems Theory 17, 335 (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [20] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Lidar and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Schneider, Stabilizing qubit coherence via tracking-control, Quantum Inf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 5 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [21] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Campos, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Bondar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Cabrera, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rab- itz, How to make distinct dynamical systems appear spec- trally identical, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 118, 083201 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [22] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Magann, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Ho, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rabitz, Singularity-free quantum tracking control of molecular rotor orientation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A 98, 043429 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [23] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Magann, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' McCaul, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rabitz, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Bon- dar, Sequential optical response suppression for chemical mixture characterization, Quantum 6, 626 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [24] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' McCaul, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Orthodoxou, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Jacobs, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Booth, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Bondar, Controlling arbitrary observables in cor- related many-body systems, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A 101, 053408 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [25] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' McCaul, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Orthodoxou, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Jacobs, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Booth, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Bondar, Driven imposters: Controlling expecta- tions in many-body systems, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 124, 183201 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [26] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' McCaul, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' King, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Bondar, Optical indis- tinguishability via twinning fields, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 127, 113201 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [27] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Zhu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Smit, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rabitz, Managing singular be- havior in the tracking control of quantum dynamical ob- servables, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 110 (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [28] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Hirschornf and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Davis, Output Tracking for Nonlinear Systems with Singular Points, SIAM J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Control Optim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 25 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [29] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Kraus, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rupenyan, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' W¨orner, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 109, 233903 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [30] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Brooks, Science 193, 11 (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [31] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Zare, Science 279, 1875 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [32] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rakitzis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' van den Brom, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Janssen, Science 303, 1852 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [33] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' De, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Znakovskaya, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Ray, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Anis, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Johnson, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Bocharova, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Magrakvelidze, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Esry, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Cocke, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Litvinyuk, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Kling, Field-free ori- entation of co molecules by femtosecond two-color laser fields, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 103, 153002 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [34] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Oda, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Hita, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Minemoto, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Sakai, All-optical molecular orientation, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 104, 213901 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [35] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Fleischer, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Zhou, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Field, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Nelson, Molecular orientation and alignment by intense single- cycle thz pulses, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 107, 163603 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [36] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Hoki and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Fujimura, Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 267, 187 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [37] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Salomon, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Dion, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Turinici, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 123, 144310 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [38] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Turinici and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rabitz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A 43, 105303 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [39] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Yoshida and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Ohtsuki, Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 633, 169 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [40] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Yu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Ho, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rabitz, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 20, 13008 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [41] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Szidarovszky, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Jono, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Yamanouchi, Li- mao: Cross-platform software for simulating laser- induced alignment and orientation dynamics of linear- , symmetric-and asymmetric tops, Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Com- mun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 228, 219 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [42] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Ma, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Magann, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Ho, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rabitz, Opti- mal control of coupled quantum systems based on the first-order magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A 102, 013115 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [43] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Boscain, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Caponigro, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Sigalotti, Multi-input schr¨odinger equation: controllability, tracking, and appli- cation to the quantum angular momentum, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Differ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Equ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 256, 3524 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [44] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Boscain, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Pozzoli, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Sigalotti, Classical and quantum controllability of a rotating symmetric molecule, SIAM J Control Optim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 59, 156 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [45] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Zare, Angular momentum : understanding spa- tial aspects in chemistry and physics (Wiley, New York ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Toronto, 1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [46] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Cross, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Hainer, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' King, The asym- metric rotor ii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' calculation of dipole intensities and line classification, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 12, 210 (1944).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [47] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Zare, Molecular level-crossing spectroscopy, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 45, 4510 (1966).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [48] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Kroto, Molecular Rotation Spectra (Dover Publica- tions, Inc, New York, 1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [49] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Papousek, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Hsu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Pracna, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Klee, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Winnewisser, Far infrared spectrum and ground state parameters of 12ch3f, Journal of Molecular Spectroscopy 159, 33 (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [50] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Starck, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Tischer, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Winnewisser, Molecular constants from microwave, molecular beam, and electron spin resonance spectroscopy · 1 introduction: Datasheet from landolt-b¨ornstein - group ii molecules and radicals · volume 6: “molecular constants from microwave, molec- 8 ular beam, and electron spin resonance spectroscopy” in springermaterials (https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='1007/10201226 1), copyright 1974 Springer-Verlag Berlin Heidelberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [51] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Baranov, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Dalmonte, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Pupillo, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Zoller, Condensed Matter Theory of Dipolar Quantum Gases, Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 112, 5012 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [52] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Yao, Photonic generation of microwave arbitrary wave- forms, Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 284, 3723 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [53] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Lin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' McKinney, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Weiner, Photonic synthesis of broadband microwave arbitrary waveforms applicable to ultra-wideband communication, IEEE Microw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Wirel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Compon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Lett 15, 226 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [54] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Korobenko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Milner, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Milner, Direct obser- vation, study, and control of molecular superrotors, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 112, 113004 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [55] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' DeMille, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 88, 067901 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [56] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Bomble, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Pellegrini, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Ghesqui`ere, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Desouter- Lecomte, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' A 82, 062323 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [57] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Wei, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Cao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Kais, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Friedrich, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Herschbach, ChemPhysChem 17, 3714 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [58] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Messina, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Wilson, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Krause, Quan- tum control of multidimensional systems: Implementa- tion within the time?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='dependent hartree approximation, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 104, 173 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [59] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Schr¨oder, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Carre´on-Macedo, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Brown, Im- plementation of an iterative algorithm for optimal control of molecular dynamics into mctdh, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 10, 850 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [60] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Magann, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Ho, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rabitz, Quantum optimal control of multiple weakly interacting molecu- lar rotors in the time-dependent hartree approximation, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 150, 164303 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' [61] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Doria, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Calarco, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Montangero, Optimal control technique for many-body quantum dynamics, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 106, 190501 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} +page_content=' 9' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNE3T4oBgHgl3EQfAQkY/content/2301.04255v1.pdf'} diff --git a/LdE1T4oBgHgl3EQfZAQe/content/tmp_files/2301.03144v1.pdf.txt b/LdE1T4oBgHgl3EQfZAQe/content/tmp_files/2301.03144v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..75b4f1a0d9b2518eb381e5b04433ee0b3f666245 --- /dev/null +++ b/LdE1T4oBgHgl3EQfZAQe/content/tmp_files/2301.03144v1.pdf.txt @@ -0,0 +1,3093 @@ +MNRAS 000, 1–15 (2021) +Preprint 10 January 2023 +Compiled using MNRAS LATEX style file v3.0 +Evidence of high-mass star formation through multi-scale mass accretion +in hub-filament-system clouds +Hong-Li Liu,⋆1 Anandmayee Tej,⋆2 Tie Liu,⋆3,4 Patricio Sanhueza,5,6 Shengli Qin,1 Jinhua He,7,8,9 +Paul F. Goldsmith,10 Guido Garay,9 Sirong Pan,1 Kaho Morii,5,11 Shanghuo Li,12, Amelia Stutz,13,14 +Ken’ichi Tatematsu,5 Feng-Wei Xu,15,16 Leonardo Bronfman,9 Anindya Saha,2 Namitha Issac,17 Tapas Baug,18 +L. Viktor Toth,19 Lokesh Dewangan,20 Ke Wang,15,16 Jianwen Zhou,21 Chang Won Lee,22,23 Dongting Yang,1 +Anxu Luo,1 Xianjin Shen,1 Yong Zhang,24 Yue-Fang Wu,15,16 Zhiyuan Ren,21 Xun-Chuan Liu,3 +Archana Soam,25 Siju Zhang,15,16 Qiu-Yi Luo,3 +Affiliations are listed at the end of the paper +Accepted 2023 January 3; Received 2022 December 6; in original form 2022 September 13 +ABSTRACT +We present a statistical study of a sample of 17 hub-filament-system (HFS) clouds of high-mass star formation using high- +angular resolution (∼ 1–2′′) ALMA 1.3 mm and 3 mm continuum data. The sample includes 8 infrared (IR)-dark and 9 IR- +bright types, which correspond to an evolutionary sequence from the IR-dark to IR-bright stage. The central massive clumps +and their associated most massive cores are observed to follow a trend of increasing mass (M) and mass surface density (Σ) with +evolution from IR-dark to IR-bright stage. In addition, a mass-segregated cluster of young stellar objects (YSOs) are revealed in +both IR-dark and IR-bright HFSs with massive YSOs located in the hub and the population of low-mass YSOs distributed over +larger areas. Moreover, outflow feedback in all HFSs are found to escape preferentially through the inter-filamentary diffuse +cavities, suggesting that outflows would render a limited effect on the disruption of the HFSs and ongoing high-mass star +formation therein. From the above observations, we suggest that high-mass star formation in the HFSs can be described by a +multi-scale mass accretion/transfer scenario, from hub-composing filaments through clumps down to cores, that can naturally +lead to a mass-segregated cluster of stars. +Key words: stars: formation – stars: massive; ISM: individual objects: hub filament system; ISM: clouds. +1 INTRODUCTION +High-mass stars are fundamental components of the universe, sig- +nificantly impacting a multitude of astrophysical processes, for in- +stance, the structure and evolution of the universe and its con- +stituents (e.g., Larson 2003). Understanding how high-mass stars +form has therefore long been an active area of astrophysical research +(e.g., Motte, Bontemps, & Louvet 2018). It is generally accepted +that high-mass stars form in clusters probably as a result of the hi- +erarchical, multi-scale fragmentation process from clouds, through +filaments, clumps and cores, down to seeds of star formation (e.g., +Zhang et al. 2009; Wang et al. 2011, 2014; Beuther et al. 2018; Yuan +et al. 2018; V´azquez-Semadeni et al. 2019; Li et al. 2019, 2020b; +Padoan et al. 2020; Kumar et al. 2020; Liu et al. 2022a,b; Hacar +et al. 2022; Chevance et al. 2022). Under this paradigm, filaments +as a “conveyor belt” play a critical role in transporting gas material +between the scales above and below (e.g., Longmore et al. 2014; +V´azquez-Semadeni et al. 2019; Padoan et al. 2020; Kumar et al. +2020). +Indeed, filaments have been observed to be ubiquitous in the inter- +stellar medium (ISM), and the sites of star formation in both nearby +⋆ E-mail: hongliliu2012@gmail.com; tej@iist.ac.in; liutie@shao.ac.cn +low-mass and distant high-mass star-forming clouds (e.g., Andr´e et +al. 2010, 2019; Molinari et al. 2010; Stutz & Gould 2016; Guo et al. +2021; Yuan et al. 2021). Crisscrossing filaments result in a special +web that can comprise of three or more filaments converging toward +a central web node. Defined as hub-filament systems (HFSs), these +web networks are considered as a unique category of filaments for +star formation, especially for high-mass star formation (e.g., Myers +2009; Kumar et al. 2020). In the definition of HFS, the web node +is defined as the hub while the associated individual filaments are +defined as the hub-composing filaments. In general, the central hub +has a lower aspect ratio but a higher column density, which are in +contrast to the high aspect ratio and low column density observed in +the hub-composing filaments (e.g., Myers 2009; Kumar et al. 2020). +The hierarchical density structure discussed above can promote +high-mass star formation. This is supported by several observational +studies that include both single dish and interferometric observations +from the far-infrared (IR) to millimeter regime (e.g., Schneider et al. +2012; Liu et al. 2012; Peretto et al. 2013; Williams et al. 2018; Yuan +et al. 2018; Issac et al. 2019; Kumar et al. 2020; Anderson et al. +2021; Beltr´an et al. 2022; Liu et al. 2022a,b; Sanhueza et al. 2021; +Saha et al. 2022; Zhou et al. 2022; Thomasson et al. 2022). These +studies reveal that young massive stellar clusters appear in HFSs +with the high-mass stars being preferentially formed in the hubs. +© 2021 The Authors +arXiv:2301.03144v1 [astro-ph.GA] 9 Jan 2023 + +2 +H.-L. Liu et al. +Longitudinal gas flows along the hub-composing filaments, which +are observed in several HFSs to converge toward the hub at typical +flow rates of ∼ 10−4–10−3 M⊙ yr−1, have been demonstrated to +account for the required mass accretion (e.g., Yuan et al. 2018; Chen +et al. 2019; Trevi˜no-Morales et al. 2019; Liu et al. 2022a). +The above scenario advocates for further detailed observational +studies of HFSs from the perspective of high-mass star forma- +tion and for the development of theoretical models. For instance, +the latest-generation models such as “global hierarchical collapse” +(GHC, V´azquez-Semadeni et al. 2019) and “inertial-inflow” (I2, +Padoan et al. 2020), which in terms of the accretion process could +be complementary to the two proposed competing theories of “tur- +bulent core accretion” (McKee & Tan 2003) and “competitive ac- +cretion” (Bonnell et al. 2001). The merits of these latest-generation +models can be attributed to the envisioned multi-scale gas accretion, +from clouds to the seeds of star formation, which was proposed in +earlier times as “clump-fed” accretion in simulations of Wang et al. +(2010), but not fully developed to the cloud scales due to the compu- +tation limitation at that time. In addition, the HFSs are often repro- +duced to be a common signature in the multi-scale accretion models +as the preferential system of cluster and high-mass star formation. +However, the major driver of multi-scale gas accretion (e.g., gravity, +and/or turbulence) is predicted to be different in different models +(e.g., Liu et al. 2022b). This is inferred from our previous ALMA +observations, at ∼ 2′′ resolution, toward a well-studied, high-mass +star-forming filamentary IRDC, G034.43+00.24 (e.g., Sanhueza et +al. 2010; Sakai et al. 2013; Foster et al. 2014; Liu et al. 2020, G34 +hereafter). G34 can be regarded as an HFS with the hub located at +the MM1 clump (see Fig. 1 of Liu et al. 2022a,b). Our investiga- +tions have revealed multi-scale accretion process from cloud down +to the seeds of star formation and the scale-dependent nature of gas +kinematics of the multi-scale, hierarchical density structures. Inter- +preting our results in the framework of both GHC and I2 models, +we conclude that the scale-dependent combined effect of turbulence +and gravity is essential to explain the multi-scale, dynamical accre- +tion process responsible for high-mass star formation in G34. +In this paper, we aim to carry out a statistical study of a sample +of 17 high-mass star forming HFSs using high-angular resolution +(∼1–2 ′′) ALMA continuum data. The sample was selected partic- +ularly to contain two different infrared (IR) characteristics (i.e., 8 +IR-dark and 9 IR-bright objects) since these two IR types can rep- +resent two different evolutionary stages (see Sect. 2.1). The purpose +of this study is to gain insights into high-mass star formation sce- +narios in HFS clouds by analysing the hierarchical structures of the +HFSs as a function of evolution of high-mass star formation. The pa- +per is organised as follows: Sect. 2 briefly describes the selection of +the HFS sample and the ALMA data used, Sect. 3 presents analysis +on the hierarchical structures of the HFSs (i.e., clouds, clumps, and +cores), star formation therein, and the effect of outflow feedback on +star formation. Sect. 4 discusses the multi-scale accretion scenario, +from the core through clump up to the cloud scales, and Sect. 5 gives +a comprehensive summary of the results obtained. +2 SAMPLE AND ALMA DATA +2.1 Sample +The sample investigated here consists of 17 HFS clouds selected +from the ASHES (The ALMA Survey of 70 µm Dark High-mass +Clumps in Early Stages; Sanhueza et al. 2019; Li et al. 2020; Saba- +tini et al. 2022) and the ATOMS (ALMA Three-millimeter Obser- +vations of Massive Star-forming regions; Liu et al. (2020a,b, 2021)) +surveys. The selection is based on their morphological appearance +in the Spitzer 8 µm image (see Fig. 1). The selected HFS cloud is re- +quired to be globally seen as an HFS morphology in 8 µm emission +with at least three hub-composing filaments intersecting at the cen- +tral hub (see Fig. 1). The hub-composing filaments appear as elon- +gated dark lanes against bright 8 µm background emission. With the +matching angular resolution (i.e., 2′′) as that of the ALMA data, the +Spitzer image facilitates the ALMA analysis of the identified HFSs. +The selected HFSs are classified into 8 IR-dark and 9 IR-bright +HFS clouds based on the lack or presence of IR emission in the cen- +tral hubs. The IR-dark sample (i.e., HFSs 1–8) is from the ASHES +survey where the hubs are identified as IR-dark clumps from 3.6 +to 70 µm (Sanhueza et al. 2019). In contrast, the hubs of the IR- +bright HFSs (i.e., HFSs 9–17), selected from the ATOMS survey, are +bright in the same IR regime. This, in essence, is a reflection of the +bolometric luminosity (Lbol) of the embedded young stellar objects +(YSOs) in the hubs. Making a simple assumption, the Lbol of YSOs +in these hubs is assumed to approximately represent that of their host +HFSs (see Table 1). While the absence of compact IR emission can +qualify the central hubs of IR-dark HFSs as prestellar candidates, +being 70 µm dark does not always imply absolute lack of star forma- +tion (e.g., Li et al. 2019, 2020; Morii et al. 2021; Tafoya et al. 2021; +Sakai et al. 2022). Hence, the lack of YSOs here could also indicate +a relatively quiescent star formation stage with very low bolomet- +ric luminosities (i.e., Lbol ≲ 300 L⊙, see Table 1). On the other +hand, the central hubs of the IR-bright HFSs have high-luminosity +(Lbol ≳ 104 L⊙, see Table 1) IRAS sources typical of high-mass +stars, thus suggesting an active star formation stage. Interestingly, +even with the relatively limited sample of HFSs investigated in this +study strikingly different regimes of Lbol/Mclump ratios are seen +for the IR-dark and IR-bright HFSs (see Sect. 3.1). This lends strong +support to the inference that two different star-formation stages are +probed with these two IR types. +The basic parameters (e.g., source name, distance, and luminos- +ity) of the selected sample are listed in Table 1. They have a median +distance of ∼ 3.6 kpc in a range of ∼ 1.3–5.4 kpc with the IR-dark +HFSs (∼ 3.9 kpc) being on average around 1.4 times farther than the +IR-bright ones (∼ 2.7 kpc). It is worth noting that the 9 IR-bright +HFSs selected here have been reported by Zhou et al. (2022) as part +of a statistical study to identify and study HFSs in a large sample of +146 active massive protoclusters based on the H13CO+ (1–0) line +data from the same ATOMS survey. Among the sample studied by +Zhou et al. (2022), these 9 IR-bright HFSs stand out in terms of +the 8 µm appearance of their hub-composing filaments as elongated +dark lanes. +Figure 1 presents an example of the large-scale appearance of the +selected 17 HFSs studied here in the Spitzer 8 µm image. Overlaid +in gray contours on the image is ATLASGAL 870 µm continuum +representative of cold, dense dust thermal emission. The size of the +images was adjusted to recover the complete presence of the global +HFS appearance in 8 µm emission. As shown in the figure, the global +HFS appearance can be identified for all 17 HFS clouds with the +hub-composing filaments intersecting at the centrally located hub. +The hub-composing filaments seen as elongated dark lanes at 8 µm +have associated 870 µm dust emission representative of cold and +dense material, indicating that the filaments are essentially high den- +sity structures. +2.2 ALMA data +We made use of the combined 12m+7m continuum data from +ASHES (project IDs: 2015.1.01539.S, PI: Patricio Sanhueza), and +MNRAS 000, 1–15 (2021) + +High-mass star formation in HFS cloud +3 +Figure 1. Images showing examples of the IR-dark (left) and bright (right) HFS clouds at Spitzer 8 µm. The contours represent 870 µm dust continuum from +the ATLASGAL survey (Schuller et al. 2009). The solid circles represent the compact dust clumps (Sect. 3.1). The dashed loop/circle demarcates the central +subcloud field covered by our ALMA observations. The dashed curves identify the filamentary structures. The 8.0 µm beam (i.e., 2′′) are shown at the bottom +right-hand corner of the corresponding panel. The image size for each HFS is determined individually to recover the full view of its HFS morphology at 8 µm. +Table 1. Parameters of the HFSs and their central clumps. +HFS cloud +Alias +RA +DEC +d +Lbol +Tdust +F int. +870µm +Mclump +Σclump +ID +J2000 +J2000 +kpc +log(L⊙) +K +Jy +M⊙ +g cm−2 +1 +G010.991-00.082 +18:10:06.58 +-19:27:46.44 +3.7 +1.7 +12.0 +1.94 +355 +0.38 +2 +G014.492-00.139 +18:17:22.08 +-16:24:59.40 +3.9 +2.5 +13.0 +3.89 +685 +0.73 +3 +G028.273-00.167 +18:43:31.27 +-4:13:18.48 +5.1 +1.6 +12.0 +1.05 +365 +0.39 +4 +G331.372-00.116 +16:11:34.08 +-51:34:56.28 +5.4 +1.6 +14.0 +0.90 +266 +0.28 +5 +G340.222-00.167 +16:48:30.74 +-45:11:04.56 +4.0 +1.6 +15.0 +1.07 +155 +0.17 +6 +G340.232-00.146 +16:48:27.46 +-45:09:48.24 +3.9 +1.1 +14.0 +1.16 +179 +0.19 +7 +G341.039-00.114 +16:51:14.21 +-44:31:24.24 +3.6 +1.8 +14.3 +1.21 +153 +0.16 +8 +G343.489-00.416 +17:01:01.34 +-42:48:07.92 +2.9 +0.8 +10.3 +1.04 +156 +0.17 +9 +I13484-6100 +13:51:58.51 +-61:15:42.84 +5.4 +4.8 +31.8 +4.10 +600 +0.64 +10 +I15394-5358 +15:43:16.46 +-54:07:15.24 +1.8 +3.7 +34.0 +29.69 +482 +0.51 +11 +I15520-5234 +15:55:48.62 +-52:43:05.88 +2.6 +5.1 +32.2 +38.82 +733 +0.78 +12 +I16272-4837 +16:30:59.11 +-48:43:53.40 +2.9 +4.3 +23.1 +17.64 +748 +0.80 +13 +I16351-4722 +16:38:50.69 +-47:27:58.68 +3.0 +4.9 +30.4 +25.43 +649 +0.69 +14 +I16424-4531 +16:46:06.36 +-45:36:44.64 +2.6 +3.9 +24.6 +6.70 +153 +0.16 +15 +I17016-4124 +17:05:11.18 +-41:29:05.28 +1.4 +5.3 +32.0 +51.16 +975 +1.04 +16 +I17233-3606 +17:26:42.74 +-36:09:18.00 +1.3 +4.6 +29.9 +123.33 +201 +0.21 +17 +I18507+0121 +18:53:18.12 ++1:25:24.24 +3.7 +3.5 +22.7 +13.34 +882 +0.94 +Note: The distance d of the HFSs comes from Sanhueza et al. (2019) for HFSs 1–8, and Liu et al. (2021) for HFSs 9–17. The bolometric luminosity Lbol of +the HFSs is approximately represented by that of their centrally located young stellar objects (YSOs, Bronfman, Nyman, & May 1996; Contreras et al. 2013; +Liu et al. 2020a,b, 2021). +ATOMS (project ID: 2019.1.00685.S; PI: Tie Liu) surveys. Detailed +discussion on the scientific goals, observing set-ups, and data reduc- +tion can be found in Sanhueza et al. (2019); Liu et al. (2020a,b, +2021). Briefly, the two surveys observed the central area of ra- +dius ∼ 31–39′′ of our selected HFSs (see the dashed loop in +Fig. 1) in different observing modes at different wavelengths, i.e., +the 1.3 mm mosaic mode for ASHES, and 3 mm pointing observing +mode for ATOMS. In addition, the synthesized beams of the com- +bined 12m+7m continuum data of the two surveys are different with +∼ 1.2′′ for ASHES and ∼ 2.0′′ for ATOMS. However, the two sur- +veys have similar field of views (FoVs, i.e., ∼ 62′′ for ASHES and +78′′ for ATOMS). Given their typical distances (see Sect. 2.1), the +IR-dark and bright HFSs selected from the respective ASHES, and +ATOMS surveys have very close linear-scale FoVs (i.e., ∼ 1.0 pc +and ∼ 1.2 pc, respectively). This rather close agreement of FoVs +ensures detailed high-resolution analysis (e.g., for cores) over al- +most the same spatial scales for most of the HFSs studied here. The +ASHES and ATOMS surveys have a maximum angular recoverable +MNRAS 000, 1–15 (2021) + +HFS9/I13484-6100 +8μm +-61°12'00" +RA: 13:51:57.86 +Dec: -61:14:01.68 +13'00" +Dec (J2000) +14'00" +15'00" +16'00" +0.5pc/ +. +13h52m10s +s00 +51m50s +40s +RA (J2000)HFS1/G010.991-00.082 +-19°26'30' +8μm +RA:18:10:06.79 +Dec: -19:27:B4.56 +27'00" +Dec (J2000) +30" +28'00" +30" +0.5pc +18h10m10s +08s +06s +04s +02s +RA (J2000)4 +H.-L. Liu et al. +scale of 19′′ and 60′′, respectively, for the combined data. Note that +the different angular resolutions and maximum recoverable scales +may lead to some observation biases to the properties of cores (e.g., +mass), which will be discussed in Sect. 3.2.3. In addition, the typ- +ical sensitivities of the combined continuum data for ASHES and +ATOMS are ∼ 0.1 mJy beam−1 (Sanhueza et al. 2019) at 1.3 mm +and ∼ 0.3 mJy beam−1 at 3 mm (Liu et al. 2022a), respectively, +which correspond to a mass sensitivity of ∼ 0.04 M⊙ (for a temper- +ature of 15 K typical of IR-dark cases), and ∼ 1.2 M⊙ (for 25 K typ- +ical of IR-bright cases), respectively, at a typical distance of 3.6 kpc +(see Sect. 3.1 for mass calculation). +3 RESULTS AND ANALYSIS +3.1 Clumps in the HFSs +Clumps are one of the characteristic hierarchical structures of the +HFS clouds. From Fig. 1, one can see that each HFS has a domi- +nant central clump. Generally, such density structures can be identi- +fied using several widely-used algorithms, such as Dendrogram and +CASA-imfit. However, the use of these algorithms is limited by the +intensity contrast of the clumps with respect to their natal clouds es- +pecially for the IR-dark HFSs studied here where the contrast is low +(see Fig. 1). In these cases, the extracted clumps tend to have a large +aspect ratio of > 3 (i.e., ratio of the major to minor axis) indica- +tive of more than one entity within them. To avoid inaccurate clump +identification for these low-contrast cases and to maintain unifor- +mity, we define a circular aperture to enclose the enhanced 870 µm +emission in the central area of both IR-dark and bright HFSs anal- +ysed here. From a careful scrutiny of the 870 µm maps of the entire +sample, an optimum aperture with radius 0.25 pc is found suitable to +encompass most of the 870 µm emission (see Fig. A1). Hence, we +consider this as the radius of the clump, Rclump. Given this defini- +tion, the integrated flux (F int +870µm) of the central clumps in all HFSs +were extracted from the ATLASGAL 870 µm image. In addition, +we retrieved the dust temperature (Tdust) of the clumps from San- +hueza et al. (2019) for those in the IR-dark HFSs and from Liu et al. +(2020a) for those in the IR-bright HFSs. With the above parameters, +the clump mass (Mclump) was computed following Eqs. B1–B2 of +Liu et al. (2021). In the computation, we assumed the gas-to-dust +mass ratio to be Rgd = 100, and the dust opacity per gram of dust +to be k870µm = 1.78 cm2 g−1, which corresponds to the opacity of +dust grains with thin ice mantles at gas densities of 106 cm−3 (Os- +senkopf & Henning 1994). The mass surface density (Σclump) of +the clumps was derived from Σclump = Mclump/(πR2 +clump). The +derived parameters are listed in Table 1. According to Sanhueza et +al. (2017, 2019), the uncertainty of both Mclump and Σclump could +be about 50%, which accounts for the combined uncertainties from +k870µm (∼ 30%), Rgd (∼ 20%), Td (∼ 20%), and the kinematic +distance (∼ 10%). +The central clumps have a median Mclump of ∼ 223 M⊙ in a +range of [153, 685] M⊙ in the IR-dark HFSs. For the IR-bright +HFSs, the median Mclump is ∼649 M⊙ in a range of [153, 975] M⊙. +Σclump has a median value of 0.24 g cm−2 in a range of [0.16, +0.73] g cm−2 in the IR-dark HFSs, and 0.69 g cm−2 in a range of +[0.16, 1.04] g cm−2 in the IR-bright HFSs. Overall, the estimated +Σclump values in all HFSs studied here satisfy the empirical high- +mass star formation threshold of Σcrit ⩾ 0.05 g cm−2, which was +derived from the mass-size relationship established using the AT- +LASGAL massive clumps containing high-mass star-forming signa- +tures (e.g., methanol masers, and HII regions, Urquhart et al. 2014). +This provides evidence that the central clumps in both IR-dark and +IR-bright HFSs are dense enough to form high-mass stars. Evidence +of high-mass star formation in the IR-dark HFSs (i.e., HFSs 1–8) +has been suggested in Sanhueza et al. (2019), while the same infer- +ence in the IR-bright HFSs (i.e., HFSs 9–17) is strengthened by their +associated high luminosities of Lbol ≳ 104 L⊙ (see Table 1). +To quantitatively describe the evolutionary stage of clumps that +can represent the stage of their natal HFSs in terms of high-mass +star formation, we consider the bolometric luminosity to mass ra- +tio Lbol/Mclump, where the bolometric luminosity of each clump, +Lbol, can be found in Table 1. This is approximately taken to be +the luminosity of their centrally located YSOs (Bronfman, Nyman, +& May 1996; Contreras et al. 2013; Liu et al. 2020a,b, 2021) This +ratio is independent of distance, and has been widely used as an +indicator of the evolutionary stage of clumps (e.g., Guzm´an et al. +2015; Liu et al. 2021). The clumps in IR-dark and bright HFSs +have a median Lbol/Mclump value of 0.14 L⊙/M⊙ in a range of +[0.04, 0.46] L⊙/M⊙, and a median value of 105 L⊙/M⊙ in a range +of [3.58, 204.62] L⊙/M⊙, respectively. The ratio Lbol/Mclump has +been used as a diagnostic tool to probe the evolutionary stages of ob- +served clumps (e.g., Urquhart et al. 2014; Giannetti et al. 2017; Elia +et al. 2022). Based on the results discussed in these papers, values of +Lbol/Mclump ≲ 2 have been associated with a very early evolution- +ary phase of mass accretion and possibly the beginning of protostel- +lar activity. Whereas, ratios between 2–40 are shown to represent +a later evolutionary phase where the protostar grows in mass with +continuing accretion reaching the zero age main sequence around +Lbol/Mclump ∼ 10. Beyond a ratio of ≳ 40, onset of radio emission +with detection of hypercompact and UCHII regions. This strongly +supports our conjecture that the ensemble of 8 IR-dark HFSs are +at an earlier stage of high-mass star formation than that of the 9 +IR-bright HFSs (see Sect. 2.1). Following this evolution, an over- +all increasing trend of both Mclump and Σclump can be found from +the IR-dark (223 M⊙ and 0.24 g cm−2) to IR-bright (649 M⊙ and +0.69 g cm−2) stage of HFSs. +3.2 Cores in the HFSs +3.2.1 Core identification +The high-resolution (1.2′′–2′′) ALMA continuum data, that corre- +spond to linear scales 0.02 and 0.03 pc at the typical distances of the +IR-dark and bright HFSs, respectively, enable the identification of +compact cores where stars could form. A total of 224 compact cores +in the 8 IR-dark HFSs have already been identified from ASHES +1.3 mm continuum by Sanhueza et al. (2019). Slightly different ap- +proaches have been implemented in Sanhueza et al. (2019) and Liu +et al. (2021) to identify compact cores. While the former study +used the Dendrogram algorithm, the later used a two-step process +in which the initial identification was carried out using Dendrogram +then followed by CASA–imfit to estimate the parameters. Examining +the performance of both schemes (especially for the low-mass cores +in the IR-dark HFSs) and to maintain uniformity, we use Dendro- +gram alone to extract cores in the 9 IR-bright HFSs from ATOMS +3 mm, combined 12m+7m continuum data. It is worth mentioning +here that there are a suite of clump/core identification algorithms +available (e.g., Clumpfind by Williams, de Geus, & Blitz 1994; getsf +by Men’shchikov 2021) and Dendrogram is one such robust algo- +rithm widely used in similar studies (e.g., Rosolowsky et al. 2008; +Ginsburg et al. 2016; Offner et al. 2022). While a comparative study, +which is beyond the focus of this paper, would help highlight the +MNRAS 000, 1–15 (2021) + +High-mass star formation in HFS cloud +5 +Table 2. Parameters of cores in HFSs. +HFS cloud +Core ID +RA +DEC +Rcore +Rcore +F int. +cont +Mcore +Σcore +Assoc. +J2000 +J2000 +′′ +AU +mJy +M⊙ +g cm−2 +HFS9 +ALMA1 +13:51:58.35 +-61:15:41.9 +1.53 +8242 +56.63 +289.9 +12.07 +1,2 +HFS9 +ALMA2 +13:51:55.31 +-61:16:05.4 +1.57 +8467 +3.40 +17.4 +0.69 +0 +HFS9 +ALMA3 +13:52:00.74 +-61:15:53.2 +1.89 +10190 +4.70 +24.1 +0.66 +0 +HFS9 +ALMA4 +13:51:57.10 +-61:15:51.0 +1.69 +9143 +4.66 +23.9 +0.81 +4 +HFS9 +ALMA5 +13:51:58.09 +-61:15:38.8 +1.79 +9639 +3.43 +17.6 +0.53 +0 +HFS9 +ALMA6 +13:51:58.58 +-61:15:33.9 +0.98 +5280 +2.94 +15.0 +1.53 +4 +HFS9 +ALMA7 +13:51:57.87 +-61:15:31.8 +0.99 +5323 +2.86 +14.6 +1.46 +4 +HFS9 +ALMA8 +13:52:01.76 +-61:15:25.0 +1.16 +6267 +1.86 +9.5 +0.69 +0 +HFS9 +ALMA9 +13:51:57.56 +-61:16:06.4 +0.71 +3851 +0.86 +4.4 +0.84 +4 +HFS9 +ALMA10 +13:52:03.09 +-61:15:53.5 +0.69 +3700 +0.84 +4.3 +0.89 +0 +HFS9 +ALMA11 +13:51:58.29 +-61:15:45.9 +1.57 +8496 +1.93 +9.9 +0.39 +4 +HFS9 +ALMA12 +13:51:59.32 +-61:15:41.1 +1.64 +8839 +2.79 +14.3 +0.52 +4 +HFS10 +ALMA1 +15:43:18.94 +-54:07:35.6 +1.08 +1962 +8.69 +5.1 +3.71 +2,4 +HFS10 +ALMA2 +15:43:16.62 +-54:07:14.8 +2.80 +5095 +254.36 +147.9 +16.12 +2,4 +HFS10 +ALMA3 +15:43:18.36 +-54:07:34.1 +2.87 +5213 +17.49 +10.2 +1.06 +0 +HFS10 +ALMA4 +15:43:14.23 +-54:07:27.7 +1.13 +2059 +1.75 +1.0 +0.68 +0 +HFS10 +ALMA5 +15:43:16.91 +-54:07:22.4 +3.83 +6973 +7.55 +4.4 +0.26 +0 +HFS10 +ALMA6 +15:43:16.07 +-54:07:10.9 +2.13 +3884 +3.80 +2.2 +0.41 +0 +HFS10 +ALMA7 +15:43:17.15 +-54:07:07.5 +1.51 +2739 +2.58 +1.5 +0.57 +0 +HFS10 +ALMA8 +15:43:16.96 +-54:06:59.4 +1.14 +2082 +2.94 +1.7 +1.12 +0 +HFS10 +ALMA9 +15:43:15.76 +-54:07:22.7 +1.42 +2577 +1.81 +1.1 +0.45 +0 +HFS10 +ALMA10 +15:43:18.49 +-54:07:17.7 +0.70 +1277 +0.64 +0.4 +0.64 +0 +HFS11 +ALMA1 +15:55:48.46 +-52:43:07.9 +2.16 +5723 +190.43 +234.7 +20.27 +1,3 +HFS11 +ALMA2 +15:55:46.39 +-52:43:23.5 +1.07 +2838 +11.30 +13.9 +4.89 +4 +HFS11 +ALMA3 +15:55:47.93 +-52:43:13.8 +2.53 +6693 +32.84 +40.5 +2.56 +0 +HFS11 +ALMA4 +15:55:48.99 +-52:43:12.0 +1.02 +2714 +9.26 +11.4 +4.38 +0 +HFS11 +ALMA5 +15:55:48.87 +-52:43:02.9 +2.43 +6430 +28.63 +35.3 +2.41 +0 +HFS11 +ALMA6 +15:55:46.18 +-52:43:00.7 +0.67 +1774 +4.14 +5.1 +4.58 +0 +HFS12 +ALMA1 +16:30:58.82 +-48:43:53.9 +1.58 +4601 +156.58 +234.3 +31.30 +1,2 +HFS12 +ALMA2 +16:30:58.61 +-48:43:57.4 +2.44 +7128 +4.75 +7.1 +0.40 +0 +HFS12 +ALMA3 +16:30:59.26 +-48:43:53.0 +1.45 +4219 +2.41 +3.6 +0.57 +0 +HFS12 +ALMA4 +16:30:57.17 +-48:43:54.4 +1.18 +3449 +1.81 +2.7 +0.64 +0 +HFS12 +ALMA5 +16:30:57.37 +-48:43:39.6 +2.29 +6685 +22.57 +33.8 +2.14 +2,4 +HFS12 +ALMA6 +16:31:01.53 +-48:44:05.2 +0.73 +2128 +0.84 +1.3 +0.79 +0 +HFS12 +ALMA7 +16:30:59.32 +-48:43:51.1 +0.84 +2439 +1.19 +1.8 +0.85 +0 +HFS13 +ALMA1 +16:38:50.55 +-47:28:01.8 +2.34 +7078 +179.71 +287.7 +16.24 +1,3 +HFS13 +ALMA2 +16:38:51.68 +-47:28:20.2 +0.71 +2155 +1.47 +2.4 +1.43 +4 +HFS13 +ALMA3 +16:38:51.24 +-47:28:13.9 +1.13 +3410 +4.56 +7.3 +1.78 +4 +HFS13 +ALMA4 +16:38:50.06 +-47:28:04.2 +3.25 +9812 +11.91 +19.1 +0.56 +4 +HFS13 +ALMA5 +16:38:49.70 +-47:27:55.7 +0.82 +2485 +2.50 +4.0 +1.83 +4 +HFS13 +ALMA6 +16:38:50.61 +-47:27:52.4 +1.45 +4377 +3.73 +6.0 +0.88 +0 +HFS13 +ALMA7 +16:38:51.42 +-47:27:48.1 +1.24 +3750 +2.02 +3.2 +0.65 +4 +HFS13 +ALMA8 +16:38:51.77 +-47:28:10.0 +0.81 +2432 +1.20 +1.9 +0.92 +4 +HFS13 +ALMA9 +16:38:53.98 +-47:28:02.8 +0.66 +2000 +1.03 +1.6 +1.16 +0 +HFS13 +ALMA10 +16:38:51.60 +-47:27:56.2 +0.79 +2397 +1.21 +1.9 +0.95 +4 +HFS13 +ALMA11 +16:38:50.28 +-47:27:47.3 +0.83 +2504 +1.47 +2.4 +1.06 +0 +HFS14 +ALMA1 +16:46:06.08 +-45:36:43.2 +1.76 +4625 +28.41 +34.5 +4.56 +1,2 +HFS14 +ALMA2 +16:46:07.30 +-45:36:40.9 +1.16 +3053 +12.53 +15.2 +4.62 +4 +HFS14 +ALMA3 +16:46:06.88 +-45:36:52.2 +2.15 +5639 +8.07 +9.8 +0.87 +4 +HFS14 +ALMA4 +16:46:04.59 +-45:36:53.9 +1.09 +2877 +0.99 +1.2 +0.41 +0 +HFS14 +ALMA5 +16:46:05.99 +-45:36:51.5 +0.75 +1966 +1.63 +2.0 +1.45 +4 +HFS14 +ALMA6 +16:46:05.72 +-45:36:48.3 +0.99 +2611 +1.82 +2.2 +0.92 +4 +HFS14 +ALMA7 +16:46:05.04 +-45:36:47.1 +0.78 +2059 +0.52 +0.6 +0.42 +4 +HFS14 +ALMA8 +16:46:07.65 +-45:36:39.1 +1.36 +3573 +2.38 +2.9 +0.64 +0 +HFS14 +ALMA9 +16:46:08.43 +-45:36:36.5 +0.83 +2181 +0.75 +0.9 +0.54 +0 +HFS14 +ALMA10 +16:46:06.55 +-45:36:39.9 +3.16 +8309 +5.35 +6.5 +0.27 +4 +HFS15 +ALMA1 +17:05:11.15 +-41:29:07.0 +1.74 +2380 +271.70 +89.5 +44.69 +3,4 +HFS15 +ALMA2 +17:05:10.23 +-41:29:33.0 +1.07 +1467 +13.24 +4.4 +5.73 +0 +HFS15 +ALMA3 +17:05:09.52 +-41:29:06.3 +0.85 +1167 +9.58 +3.2 +6.55 +0 +HFS15 +ALMA4 +17:05:11.84 +-41:29:01.3 +0.95 +1300 +5.38 +1.8 +2.97 +0 +HFS15 +ALMA5 +17:05:09.57 +-41:28:57.4 +0.99 +1351 +5.62 +1.9 +2.87 +0 +HFS15 +ALMA6 +17:05:10.92 +-41:28:47.3 +1.71 +2340 +14.29 +4.7 +2.43 +0 +HFS15 +ALMA7 +17:05:09.40 +-41:29:28.1 +0.79 +1078 +4.47 +1.5 +3.59 +0 +HFS15 +ALMA8 +17:05:12.17 +-41:29:08.5 +0.80 +1089 +4.79 +1.6 +3.76 +0 +HFS16 +ALMA1 +17:26:42.56 +-36:09:18.2 +2.15 +2885 +623.10 +196.4 +66.75 +1,3 +HFS16 +ALMA2 +17:26:43.61 +-36:09:17.1 +1.50 +2002 +207.04 +65.3 +46.03 +4 +HFS16 +ALMA3 +17:26:42.96 +-36:09:40.0 +0.74 +985 +2.98 +0.9 +2.74 +4 +HFS16 +ALMA4 +17:26:40.26 +-36:09:36.0 +1.20 +1611 +5.06 +1.6 +1.74 +0 +HFS16 +ALMA5 +17:26:45.12 +-36:09:19.8 +0.71 +948 +3.38 +1.1 +3.35 +0 +HFS16 +ALMA6 +17:26:42.95 +-36:09:13.3 +2.28 +3054 +31.69 +10.0 +3.03 +2,4 +HFS16 +ALMA7 +17:26:43.59 +-36:09:09.3 +1.07 +1436 +10.35 +3.3 +4.47 +4 +HFS16 +ALMA8 +17:26:42.12 +-36:09:20.7 +1.12 +1500 +5.18 +1.6 +2.05 +0 +HFS16 +ALMA9 +17:26:43.38 +-36:09:19.6 +1.83 +2449 +16.63 +5.2 +2.47 +0 +HFS17 +ALMA1 +18:53:18.64 ++1:24:46.5 +1.03 +3801 +8.84 +21.2 +4.16 +3,4 +HFS17 +ALMA2 +18:53:18.07 ++1:25:25.3 +1.88 +6952 +158.09 +379.9 +22.23 +1,2 +HFS17 +ALMA3 +18:53:18.41 ++1:24:54.2 +1.23 +4559 +10.00 +24.0 +3.27 +4 +HFS17 +ALMA4 +18:53:18.33 ++1:25:13.2 +0.90 +3338 +4.41 +10.6 +2.69 +4 +HFS17 +ALMA5 +18:53:18.53 ++1:25:18.1 +0.87 +3220 +5.02 +12.1 +3.29 +4 +HFS17 +ALMA6 +18:53:18.23 ++1:25:19.9 +2.08 +7680 +3.84 +9.2 +0.44 +2,4 +HFS17 +ALMA7 +18:53:18.07 ++1:25:30.1 +2.15 +7958 +5.11 +12.3 +0.55 +0 +HFS17 +ALMA8 +18:53:18.66 ++1:25:27.5 +1.13 +4193 +5.00 +12.0 +1.93 +4 +HFS17 +ALMA9 +18:53:18.51 ++1:25:37.3 +2.11 +7801 +7.06 +17.0 +0.79 +0 +HFS17 +ALMA10 +18:53:18.75 ++1:26:00.4 +1.03 +3824 +5.05 +12.1 +2.35 +4 +HFS17 +ALMA11 +18:53:18.72 ++1:24:44.1 +1.15 +4248 +2.26 +5.4 +0.85 +0 +HFS17 +ALMA12 +18:53:18.43 ++1:24:46.2 +1.37 +5070 +2.12 +5.1 +0.56 +0 +HFS17 +ALMA13 +18:53:18.34 ++1:25:09.8 +1.15 +4269 +2.48 +6.0 +0.92 +0 +Note: This table includes only the parameters of cores in the nine IR-bright HFSs, while the same parameters of the cores in the eight IR-dark HFSs are +referred to tables 3, and 4 of Sanhueza et al. (2019). F int. +cont represents the integrated 3 mm continuum flux of the cores. Core association ranges from 0 to 4, +where 0 = prestellar candidate, 1 = molecular outflow, 2 = hot core, 3 = compact HII region, and 4 = point-like 8/24 µm object. +MNRAS 000, 1–15 (2021) + +6 +H.-L. Liu et al. +103 +104 +Rcore [AU] +10 +2 +10 +1 +100 +101 +102 +103 +Mcore [M ] +(a1) +IR-dark +3.0 +3.5 +4.0 +4.5 +5.0 +d [kpc] +103 +104 +Rcore [AU] +10 +2 +10 +1 +100 +101 +102 +103 +Mcore [M ] +(a2) +IR-bright +2 +3 +4 +5 +d [kpc] +IR dark +IR bright +Cores in the HFSs +1 +0 +1 +2 +log(Mcore) [M ] +(a3) +-0.33 +1.03 +-0.74 +-0.01 +0.59 +1.44 +-1.50 +0.89 +-0.06 +2.27 +103 +104 +Rcore [AU] +10 +1 +100 +101 +102 +core [g cm +2] +(b1) +IR-dark +3.0 +3.5 +4.0 +4.5 +5.0 +d [kpc] +103 +104 +Rcore [AU] +10 +1 +100 +101 +102 +core [g cm +2] +(b2) +IR-bright +2 +3 +4 +5 +d [kpc] +IR dark +IR bright +Cores in the HFSs +2 +1 +0 +1 +2 +log( +core) [g cm +2] +(b3) +-0.96 +0.34 +-1.18 +-0.68 +0.14 +0.77 +-1.68 +0.02 +-0.66 +1.54 +Figure 2. Panels (a1–a3): mass (Mcore) distribution of cores. Panels a1, and a2 show the Mcore distribution against the radius of cores located in the IR-dark, +and IR-bright HFSs, respectively. The colors of dots in both panels represent the distances of the cores. Panel a3 displays a box-whisker plot summarising the +Mcore distribution of the cores in the two IR types of HFSs. Panels (b1–b3): same as Panels (a1–a3) but for the mass surface density (Σcore) distribution. In +the box-whisker plots, the numbers associated with the boxes from the top to bottom represent the upper quartile, median (inside the box), and lower quartile, +respectively. The red crosses indicate the outliers outside 1.5 times the interquartile range either above the upper quartile or below the lower quartile. +101 +102 +103 +Mcore, 12m + 7m [M ] +101 +102 +103 +Mcore, 12m [M ] +Figure 3. Comparison between determinations of the masses of the mas- +sive cores from the nine IR-bright HFSs, each having one clump. The core +masses were derived first from the ATOMS 12m data alone, and second the +combined 12m+7m data. The dashed line indicates equal mass from each set +of observations. +nuances of each, the overall interpretation based on the retrieved pa- +rameters would remain the same. +Following Sanhueza et al. (2019), an intensity threshold of 2.5 σ, +a step of 1.0 σ (the rms noise of the continuum data, see Sect. 2.2), +and a minimum number of pixels equal to those contained in each +synthesized beam (half of the beam considered in Sanhueza et al. +2019) were used as input parameters. The algorithm identifies the +small structures, called ”leaves”, which cannot further break up into +smaller structures, and are thus defined here as cores. Finally, cores +with integrated flux densities less than 4 σ were excluded to avoid +spurious identification, where 4 σ was determined from the corre- +sponding negative level (i.e., −4 σ) within which the interferometric +sidelobe effects cannot be ruled out. A total of 86 compact cores are +obtained in the 9 IR-bright HFSs. The parameters retrieved from the +Dendrogram analysis are listed in Table 2. These include the core +coordinates, radius (Rcore), and integrated flux (F int +cont). The same +parameters for the compact cores in the 8 IR-dark HFSs are referred +to Tables 3 and 4 of Sanhueza et al. (2019). +The number of the cores in the IR-bright HFSs found in this study +is about four times greater than that reported in Liu et al. (2021) for +the same regions. Apart from the slightly different parameter used, a +possible reason is the use of the higher resolution 12m data for core +extraction in Liu et al. (2021) as opposed to the combined 12m+7m +data used here, which will be discussed below. Similar differences +were noted by Sanhueza et al. (2019) where inclusion of more ex- +tended emission with the 7m array leads to detection of 20% greater +number of cores. +3.2.2 Star-forming nature of cores +The star-forming activity in cores can be inferred from YSO sig- +natures such as outflows, hot cores, compact HII regions. Li et al. +(2020) provided the catalogues of CO and SiO outflows associated +with the cores in the IR-dark HFSs while the association of hot cores +and HII regions with the cores in the IR-bright HFSs are tabulated in +Liu et al. (2021), who complied these based on the detection of rich +complex organic molecular lines, and H40α line. Presence of point- +like 24 µm or slightly extended but compact 8 µm sources, which +are likely to be candidate YSOs and hence could be considered as +signposts of star formation. These associations are listed in the last +column of Table 2. In total, 112 out of 310 cores are protostellar ones +associated with one or more star-forming signatures (see above). The +remaining 198 cores without any of these signatures are treated here +as prestellar candidates. +3.2.3 Derived parameters of cores +From the parameters (e.g., radius Rcore, and integrated flux F int. +cont.) +of the cores derived from the Dendrogram analysis discussed in +Sect. 3.2.1, other parameters such as mass and mass surface den- +sities can be estimated. Cores without detectable star-forming sig- +natures are roughly assigned the temperature of their natal clumps. +For cores with associated star-forming signatures, the temperature +MNRAS 000, 1–15 (2021) + +High-mass star formation in HFS cloud +7 +was assumed to be 50 K for those associated with outflows (San- +hueza et al. 2019), and 100 K for those associated either with hot +cores or compact HII regions (Liu et al. 2021). The mass (Mcore) +and mass surface density (Σcore) parameters of the cores were cal- +culated following the same approach outlined in Sect. 3.1, where the +dust opacities per gram of dust were adjusted to be 0.9 cm2 g−1 for +1 mm and 0.2 cm2 g−1 for 3 mm according to Ossenkopf & Henning +(1994). The uncertainties of Mcore and Σcore are around ∼ 50% (see +Sect. 3.1). The derived physical parameters are listed in Table 2. +It is worth noting that for those five cores associated with compact +HII regions (see Table 2) that lie in five of nine IR-bright HFSs (i.e., +HFSs 11, 13, 15, 16, 17), the continuum flux of cores would have +contribution from both dust thermal emission and free-free emission. +The values tabulated have been subtracted for the free-free emission +component. To estimate the contribution of free-free emission, we +used the H40α hydrogen recombination line observations under the +assumption of local thermodynamical equilibrium and optically thin +emission. The free-free emission intensity was estimated via the fol- +lowing relation (e.g., Motte et al. 2022): +Sff = 1.43 × 10−4SRRL[ +ν +GHz]−1.1[Te +K ]1.15(1 + NHe +NH )−1, +(1) +where SRRL is the integrated intensity of H40α over its velocity +extent; ν = 99.0 GHz is the rest frequency of H40α observed +in the ATOMS data; and we assume the electron temperature of +Te = 6000 K as well as a relative abundance of helium to hydrogen +of NHe/NH = 0.08. We assume an upper limit of Te = 6000 K to +avoid over subtraction of free-free continuum for the small scale ex- +tracted cores (Liu et al. 2015). The above estimated free-free emis- +sion intensity was subsequently subtracted from the 3 mm contin- +uum image to yield the dust continuum emission image. +Figure 2 (a–b) show the distribution of Mcore and Σcore as a func- +tion of Rcore for the cores in both IR-dark and bright HFSs. The +colors in dots in the figure indicate the distance distribution. The +cores in both IR types of HFSs have a similar radius range of [0.9, +10]×103 AU, with an average radius ratio of ∼ 1.4 of cores in the +IR-dark HFSs to those in the IR-bright HFSs. As suggested by Lou- +vet et al. 2021, this can be understood since the similar typical spatial +resolutions of the ALMA observations toward the two IR-type HFSs +can yield the close derived sizes of the extracted cores. +Considering the median values of the mass and mass surface den- +sity in the IR-bright HFSs (5.7 M⊙ and 1.4 g cm−2) and the IR-dark +HFSs (1.0 M⊙ and 0.4 g cm−2), it is seen that the mass and mass +surface density is higher by factors of 6 and 3, respectively in the +IR-bright HFSs (Fig. 2 c). From Fig. 2 (a–b), this difference can be +seen to be independent of the source distance. Instead, it could be +in part a result of the observation bias caused by the different maxi- +mum recoverable scales (MRS) in the ASHES (∼ 20′′) and ATOMS +(∼ 60′′) combined 12m+7m data. As suggested in Sanhueza et al. +(2019), the higher MRS of the ATOMS combined data could intrin- +sically lead to higher fluxes and thus flux-derived parameters (e.g., +mass and mass surface densities) of cores. Different mass sensitiv- +ity of the surveys could also contribute since in the higher sensitiv- +ity ASHES data, more low-mass cores are detected. However, it is +worth noting that this observation bias could not affect significantly +the most massive cores (i.e., nine cores with the highest Mcore and +Σcore values in panels a–b), as can be seen from Fig. 3. Hence, in +the analysis that follows, we focus on the most massive cores in the +IR-bright sample of HFSs. In Fig. 3, we compare the masses esti- +mated from the ATOMS 12m continuum data alone with a MRS +of ∼ 18 ′′(similar to the MRS of the ASHES data) with that de- +rived from the 12m+7m combined data having a MRS of ∼ 60′′. +From this comparison, we estimate a nominal factor of ∼1.3 on av- +erage higher mass estimates for the cores extracted in the IR-bright +HFSs using ATOMS 12m+7m data. As is also seen in the figure, +the most massive cores in the IR-bright HFSs can be clearly distin- +guished from the majority of low mass cores in the distributions of +both Mcore and Σcore (see Fig. 2 a2 and b2). This trend could be ei- +ther a consequence of the limited HFS sample investigated here or +the evolutionary phase of the IR-bright HFSs, the latter being related +to their preferred central location and sufficiently long accretion his- +tory. Certainly, larger sample of such IR-dark and IR-bright HFSs +are required to examine the above possibilities. +3.3 YSOs in the HFSs +Investigating the spatial distribution of associated YSOs helps in un- +derstanding star formation in HFSs. From the 24 µm point source +catalogue of the Galactic plane from Spitzer/MIPSGAL (Gutermuth +& Heyer 2015), we searched for point sources associated with the +HFS sample studied here, and obtained their 24 µm photometric +fluxes. Here, we have used different search areas depending on the +spatial extent of the HFSs in the 8 µm image (i.e., image size in +Fig. 1, 1.5′–4.8′). In addition to the catalogued sources, we identified +ten bright, point-like sources in the 24 µm MIPSGAL images that +were not included in the MIPSGAL point source catalogue. These +were identified in the HFSs 9, 11, 13, 14, 15, 16, and 17. For these +sources, the photometry was performed manually using appropriate +circular annulus whose inner and outer radii can represent well the +point-like source and its associated background. +Since the typical distance of the HFSs studied here is ∼ 3.6 kpc, +some of the 24 µm point sources obtained above could be fore- +ground/background stars along the line of sight of the HFSs. To al- +leviate this, we correlate the identified sources with Gaia EDR3 data +within a radius of 2′′. The parallax distances of the Gaia-matched +sources were subsequently calculated. As a rough approximation, +we assume that the sources with distance estimates more than 10% +of the nearest HFS’s distance are foreground/background stars. It +is to be noted that only a few sources were filtered out as fore- +ground/background stars. Finally, 175 point sources that are likely +associated with the HFSs studied here are retained for further anal- +ysis. +Furthermore, we classify the identified YSOs cross-matching +(within 2′′ radius) using the SPICY catalogue that compiles +∼ 120,000 Spitzer/IRAC candidate YSOs for the Inner Galactic +Midplane (Kuhn et al. 2021). This catalogue contains five classes of +YSOs, including Class I, Flat-spectrum, Class II, Class III, and “Un- +certain” YSOs that cannot be placed in any of the above four classes. +Class I YSOs are highly embedded protostars with the bolometric lu- +minosity dominated by a spherical infalling envelope; Class II YSOs +are young stars surrounded by a substantial accreting disk; Class III +YSOs are young stars with most of their disk mass being dissipated. +Flat spectrum YSOs are those in between Class I and Class II. From +the above exercise, 122 of the 175 detected 24 µm sources are clas- +sified as YSOs (29 and 93 in the IR-dark and IR-bright HFSs, re- +spectively) and 53 as “unknown” sources. To confirm the nature of +the “unknown” sources requires detailed investigation of the photo- +metric information over multiple wavelengths, which is beyond the +scope of this work. +The YSO luminosity can be directly linked to the star-formation +process, i.e., either low or high-mass star formation. In previous +studies, the 24 µm photometric flux of both low and high-mass pro- +tostellar sources was found to correlate well with their bolometric +luminosity (Lbol, e.g., Dunham et al. 2008; Ragan et al. 2012). Ap- +MNRAS 000, 1–15 (2021) + +8 +H.-L. Liu et al. +Table 3. Statistical number of outflows in HFSs. +HFS ID +N (outflow lobes) +Filament-aligned +Filament-not-aligned (%) +HFS1 +5 +2 +3 (60 ) +HFS2 +10 +0 +10 (100) +HFS3 +3 +0 +3 (100) +HFS4 +7 +1 +6 (86 ) +HFS5 +– +– +– (– ) +HFS6 +2 +0 +2 (100) +HFS7 +13 +1 +12 (92 ) +HFS8 +3 +0 +3 (100) +HFS9 +2 +0 +2 (100) +HFS10 +2 +0 +2 (100) +HFS11 +1 +0 +1 (100) +HFS12 +2 +0 +2 (100) +HFS13 +2 +0 +2 (100) +HFS14 +2 +0 +2 (100) +HFS15 +2 +1 +1 (50 ) +HFS16 +2 +0 +2 (100) +HFS17 +7 +1 +6 (80 ) +Note: The statistics was made from Li et al. (2020) and Baug et al. 2022 +(under preparation). +plying this empirical correlation, we estimated the luminosities of +the 175 candidate YSOs from their 24 µm fluxes. Except for the one +luminous YSO (Lbol ∼ 104 L⊙; see Fig. 6), the candidate YSOs in +the IR-dark HFSs have low luminosities of Lbol < 103 L⊙ . Note +that the location of the one luminous YSO is more than 1 pc from +the central hub of HFS 3, and thus do not conflict with the classifica- +tion of the host HFS as IR-dark type. In case of the IR-bright HFSs, +the majority of the candidate YSOs are also found to have low lu- +minosities though there are 12 high-luminosity sources found with +Lbol ∼ [104, 105] L⊙. The presence of a significant population of +high-luminosity YSOs in the IR-bright HFSs agrees well with their +more evolved stage inferred earlier. +3.4 Effects of outflow feedback on star formation +The final stellar mass depends not only on the initial mass reser- +voir of the natal clump but also on the mass accretion from the hub- +composing filaments. However, several observational studies (e.g., +Schneider et al. 2020) and theoretical simulations have shown the +profound influence of stellar and protostellar feedback processes like +collimated jets and bipolar outflows (e.g., Wang et al. 2010; Offner +& Chaban 2017; Guszejnov et al. 2020, 2021; Verliat et al. 2022), +and radiative heating (e.g., Bate 2009, 2012; Krumholz & Thompson +2012; Hennebelle et al. 2020, 2022; Grudi´c et al. 2022) in inhibiting +mass accretion. Hence, for the protostar to grow in mass requires +the strong accretion inflow to be least impacted by the above feed- +back processes in the early stages. As discussed in Dale & Bonnell +(2011); Kumar et al. (2020), ionizing radiation, stellar wind and ion- +izing gas (HII regions) are found to channel out through pre-existing, +inter-filamentary voids without dispelling the natal clump or inhibit- +ing the mass inflow through filaments. In this study, we focus on +the influence of outflows since these are pronounced in our HFSs +sample. +The protostar’s spin, and hence the orientation of the outflows, is +inherited from the core scale where the angular momentum is hi- +erarchically transferred from the natal cloud through the filament +onto the star-forming core. Given that the large-scale filamentary in- +flow is either onto the short axes of the filament or along the long +axis, the alignment of the outflows is expected to be either prefer- +entially parallel or perpendicular to the filament. Anathpindika & +Whitworth (2008) found observational evidence that outflows are +preferentially aligned perpendicular to the filaments. In compari- +son, observational results presented by Davis et al. (2009) and more +recently by Stephens et al. (2017); Baug et al. (2021) reveal no +preferred outflow-filament orientation. Several other studies have +shown that the rotation of the protostar could be independent of +the parent filament (e.g., Tatematsu et al. 2016) or could evolve +significantly during formation (e.g., Lee et al. 2016; Offner et al. +2016). The outflow-filament alignment has implication on the form- +ing protocluster in HFSs. If the outflows run along the individual fil- +aments, the filament-rooted longitudinal mass flows will be inhibited +or halted which will significantly hinder the mass growth of young +stars embedded in the central hubs (e.g., Wang et al. 2010). +To understand the potential effect of outflows on star formation in +the HFSs studied here, we compiled the parameters (i.e., position, +and orientation) of the associated outflows from Li et al. (2020) +and Baug et al. (2022; under preparation). Li et al. (2020) have +catalogued the CO and SiO outflows of the 8 IR-dark HFSs (i.e., +HFSs 1–8) taken from the ASHES survey data at ∼ 1.3 mm (see +Sect. 2), while Baug et al. (2022) provide the HCO+ outflows of the +9 IR-bright HFSs (i.e., HFSs 9–17) taken from the ATOMS survey +data at ∼ 3 mm (see Sect. 2). As indicated in Table 3, we obtain 60 +outflow lobes for all the HFSs investigated here, where 38 and 22 +outflow lobes are associated with the IR-dark and IR-bright HFSs, +respectively. Note that we have considered the individual lobes of +outflows here instead of the entire outflow entities. +The location and orientation of the identified outflows are dis- +played in Fig. 4, where the red/blue arrows indicate the estimated +orientation and extent of the red/blue-shifted lobes. As evident from +the figure, most of the outflows have spatial extents smaller than +the dimension of the host HFS subclouds (i.e., the central dense re- +gions covered by ALMA observations). This result indicates that the +outflows might have not escaped the dense regions of the HFSs in +early stages of star formation. However, this result may be an ob- +servational consequence due to the lack of total power in the anal- +ysis made in the ASHES and ATOMS surveys. But, if the outflows +can escape the dense regions of the HFSs, then their direction can +be traced by extending the identified outflows. These are shown as +white arrows in the figure. +The statistics of the outflows and their orientation are tabulated +in Table 3. For HFS 5 there are no identifiable outflows while HFS 1 +and 15 have 60 %, and 50% of filament-aligned outflows, respec- +tively. Except for these three HFSs, all the other HFSs have the ma- +jority of outflows (i.e., ⩾ 86%) not aligned with the individual fil- +aments. There are a couple of caveats in the above analysis which +need to be highlighted here. Firstly, the outflow identifications in the +two studies used here are probably incomplete due to the presence +of multiple overlapping outflows which tend to occur in high-mass +star formation regions. Secondly, projection effects would also in- +fluence the observed orientations. Last but not the least, one needs +to study more number of HFSs-outflow systems to enable a more +robust statistical investigation. Keeping the above caveats in mind, +our results show that the observed outflows (1) do not preferentially +align parallel or perpendicular to the filaments and (2) tend to be +oriented toward the voids of the hub-composing filaments. This sug- +gests that, similar to the effect of other feedback processes, outflows +render a limited effect on filamentary mass inflow and thus on the +mass growth of young stars being formed in the centrally located +hubs. +Moreover, the inference obtained above agrees with the quanti- +tative analysis of the related energies. For the IR-dark HFSs, Li et +al. (2020) found that the outflow-induced turbulence cannot sustain +the internal turbulence of the natal clumps as the outflow energy +rate is around two orders of magnitude less than the turbulent en- +MNRAS 000, 1–15 (2021) + +High-mass star formation in HFS cloud +9 +Figure 4. Zoom-in images of Spitzer 8 µm and 24 µm for the central regions of the IR-dark (in top row) and bright (in bottom row) HFS clouds. The contours +represent 870 µm dust continuum from the ATLASGAL survey (Schuller et al. 2009). The blue/red arrows are blue/red-shifted outflowing lobes identified +by Li et al. (2020). They are purposely extended as white arrows for easy comparison of the relative orientation between the outflows and hub-composing +filaments. The dashed loop delineates the central subcloud field covered by our ALMA observations. The red circles indicate the cores identified from the +ALMA continuum data. The dashed curves identify the filamentary structures. The 8.0 and 24 µm beams are shown at the bottom right-hand corner of the +corresponding panel. +ergy dissipation rate. These authors also infer the outflow energy to +be much smaller than the gravitational energy of the clumps. For +the more evolved IR-bright HFSs investigated here, three of which +(i.e.., HFSs 11–13) were studied in terms of the outflow dynamics in +Baug et al. (2021), they argued that the kinetic energy of outflows +alone cannot balance the gravitational binding energy of the hosting +clumps. Taken together, these results indicate the limited effect of +outflows on the destruction of their host HFSs in early stages and +thus on the progress of star formation therein. However, as men- +tioned above, a larger sample and improved statistics on filament- +outflow alignment is required to conclusively interpret simulations +of outflow feedback (e.g., Wang et al. 2010; Offner & Chaban 2017; +Guszejnov et al. 2020, 2021; Verliat et al. 2022) in the context of +HFSs. +MNRAS 000, 1–15 (2021) + +HFS9/I13484-6100 +8μm +24μm +-61°15'00" +8 +8 +Dec (J2000) +30" +12 +12 +1 +10 +3 +16'00" +9 +2 +30" +0.1pc +0.1pc +. +00s +51m56s +52s +RA (J2000)HFS1 /G010.991-0b.082 +8μm +24pm +-19°27'00" +Dec (J2000) +30" +16 +16 +X224 +224 +302 +28'00" +25 +19.0 +19 +13 +13 +1512 +1 +6 +6 +30" +0.1pc +0.1pc +. +18h10m10s +08s +06s +04s +RA (J2000)10 +H.-L. Liu et al. +0.00 +0.25 +0.50 +0.75 +1.00 +offset [pc] +10 +1 +100 +101 +102 +(b) ALMA cores in IR-bright HFSs +100 +200 +300 +Mcore (M ) +10 +1 +100 +101 +102 +core [g cm +2] +(a) ALMA cores in IR-dark HFSs +10 +20 +30 +Mcore (M ) +Figure 5. Distribution of mass surface density of cores in the HFSs against +distance from the HFS centre. The colors in circles reflect the mass distribu- +tion of the cores. Panels (a) and (b) display the cores in the IR-dark, and IR- +bright HFSs, respectively. In both panels, the protostellar cores are indicated +in circles with inserted pluses while candidate starless cores are in empty +circles. Circles with black dots inside are the centrally located most massive +cores. The vertical dotted lines indicate the average distance weighted by the +mass surface density of cores, i.e., 0.16 pc in panel a, and 0.04 pc in panel b. +4 DISCUSSION +4.1 Spatial distribution of cores and YSOs +Cores in the HFSs +Figure 5 shows the distribution of the mass surface density (Σcore) +of the cores as a function of the distance from the centre of the host +HFSs. The centre is defined to be the position where the intensity +of the 870 µm emission peaks. Circles with inserted plus symbols +distinguish the protostellar cores from that of the candidate star- +less ones. The centrally located most massive core of each HFS has +an additional dot symbol included. Further, the plotted circles are +colour-coded to represent the core mass (Mcore) distribution. Sev- +eral interesting trends can be deciphered from these plots and are +discussed below. +The number of cores is more in the central region with only a +sparse population seen beyond ∼0.5 pc. The massive and dense +cores in the IR-dark HFSs are located within ∼0.25 pc, whereas, +in IR-bright HFSs these are confined to the innermost region of +∼0.05 pc. All nine centrally located most massive cores in IR-bright +HFSs are forming high-mass stars as inferred from the associated +high luminosities of > 104 L⊙. This supports the scenario that in +HFSs, the central areas of hubs are preferential sites for high-mass +star formation where mass accretion occurs from the hub-composing +filaments. The ideal location of such cores in IR-dark HFSs also +qualifies them as potential high-mass star-forming cores. +The steep gradient seen in the spatial distribution of the most mas- +sive and dense cores towards the inner most region in IR-bright HFSs +suggests a more centrally peaked clustering as opposed to the wider +distribution observed in the IR-dark HFSs. That is, the spatial distri- +bution of massive dense cores peaks at ∼ 0.16 pc in IR-dark HFSs, +but at ∼ 0.04 pc in IR-bright HFSs, as indicated in the dotted lines in +the figure. These represent the average distance from the HFS centre +weighted by the mass surface density over all the cores in each IR +type of HFSs. The wider distribution of massive cores in the IR-dark +hubs is in good agreement with the results of Sanhueza et al. (2019). +These authors propose that cores in IR-dark HFSs originate from +hierarchical subclustering rather than from centrally peaked cluster- +ing. The observed difference in the two IR types could suggest trans- +formation to a centrally peaked clustering following the evolution of +the host HFSs from the IR-dark to IR-bright stages. +Scarcity of high-mass prestellar cores (of Mcore ⩾ 30 M⊙ over +the 0.1 pc scale, e.g., Sanhueza et al. 2017, 2019), the progenitors of +high-mass stars, is observed in our sample of IR-dark HFSs. Here, +none of the detected cores have masses greater than the threshold de- +fined above. This allows us to conjecture that high-mass star forma- +tion could involve a dynamical, continuous mass accretion with evo- +lution, which will be discussed further in Sect. 4.2. If we consider the +prestellar cores in the IR-bright sample, only 11 (∼ 13% of cores) +have mass estimates greater than 30 M⊙. For these to form high- +mass stars, the same mass accretion process should ensue. However, +the starless or prestellar nature of those cores needs to be confirmed +through future higher-resolution observations with a more sensitive +outflow tracer (e.g., CO 1–0), +YSOs in the HFS clouds +Figure 6 presents the distribution of bolometric luminosity (Lbol) +of candidate YSOs against the distance from the centre of the host +HFSs. In the IR-dark HFSs, the YSO’s luminosity distribution is +nearly constant at a low luminosity level (i.e., ∼ 100 L⊙) typi- +cal of low-mass protostars, regardless of the distance of the YSOs +from the centre of the HFSs. Only one YSO with Lbol ∼ 104 L⊙, +that is typical of high-mass protostars, is found at distance > 1 pc +from the centre of the host HFSs. Furthermore, only two HFSs (i.e., +HFSs 6, and 8) have identified YSOs (one each) within the hub- +clump (i.e., central clump in the hub) region and their luminosities +are low (i.e., Lbol ≲ 100 L⊙). In the case of the IR-bright HFSs, +except for the three YSOs having Lbol ∼ 103–104 L⊙ located in a +distance range of [1.6, 2.1] pc from the center of HFS 13, all of the +YSOs show a decreasing trend in luminosity from high (≳ 104 L⊙) +to low (< 100 L⊙) luminosity values with the distance from the +centre of the host HFSs up to ∼ 2 pc, beyond which the YSOs +display nearly constant low luminosity values. Note that given the +not so high luminsities (i.e., < 104 L⊙) of the above mentioned +three luminous YSOs far from the centre of the host HFS 13, we +assume that they could represent a cluster of intermediate and/or +low-mass young stars instead of high-mass protostars, which agrees +with the apparent multiplicity of these three YSOs seen at 8 µm but +not well resolved at 24 µm. In view of this, the observed decreas- +ing trend suggests a luminosity/mass-segregated cluster formation +picture in the IR-bright stage of HFSs, in which high-mass stars +represented by high luminosities prefer to form in the central area +of HFSs (i.e., the hub-clump region), while low-mass stars repre- +sented by low luminosities tend to form in the outskirts of HFSs +up to several pc. In addition, the number of high-luminosity YSOs +of Lbol > 104 L⊙ found in IR-bright HFSs is larger (eleven; see +star symbols in Fig. 6b) compared to the IR-dark HFSs where only +one are detected. Moreover, almost each of the IR-bright HFSs has +a corresponding high-luminosity YSO within the hub-clump region, +in contrast to the absence of high-luminosity YSOs within the same +region of the IR-dark HFSs. The above distribution of YSOs pos- +sibly implies an evolutionary sequence from a relatively quiescent, +IR-dark phase to an active, IR-bright phase. +MNRAS 000, 1–15 (2021) + +High-mass star formation in HFS cloud +11 +0.0 +0.5 +1.0 +1.5 +2.0 +2.5 +offset [pc] +(b) +(b) +(b) +(b) +(b) +(b) +(b) +(b) +(b) +HFS9 +HFS10 +HFS11 +HFS12 +HFS13 +HFS14 +HFS15 +HFS16 +HFS17 +0 +1 +2 +3 +4 +5 +offset [pc] +0 +2 +4 +6 +log(Lbol) [L⊙] +(a) +(a) +(a) +(a) +(a) +(a) +(a) +HFS1 +HFS2 +HFS3 +HFS4 +HFS6 +HFS7 +HFS8 +Figure 6. Luminosity of YSOs bright at 24 µm associated with the IR-dark (panel a) and IR-bright HFSs (panel b) as a function of the distance from the HFS +centre. The dashed lines indicate the typical size of the centrally-located clump for all HFSs, as defined in Fig. 5. Stars having luminosity above 104 L⊙ are +shown as star symbols as opposed to those having luminosity below 104 L⊙ shown as triangle symbols. +4.2 Multi-scale mass transfer and high-mass star formation +Figure 7 presents the mass distribution of the central massive clumps +of the HFSs (in panel a) and their embedded massive cores (in +panel b) against the Lbol/Mclump ratio of the clumps. The colors +in circles in the figure represent the mass surface density of the +sources. Note that, for this analysis, we have only considered the +most massive cores since 1) they are (potential) sites of high-mass +star formation, and 2) their mass and surface density estimates are +not significantly affected by the observation bias caused by the dif- +ferent MRSs associated with the ASHES and ATOMS data (see +Sect. 3.2.3). As shown in the figure, the IR-dark and IR-bright stages +of HFSs can be well represented by the Lbol/Mclump ratios of the +clumps. The mass and mass surface density of the central clumps +show a marginal increase of a factor of ∼ 3 (on average) from the +IR-dark to IR-bright stage. In comparison, for the embedded mas- +sive cores, the estimated values of the above parameters are en- +hanced by a factor of ∼ 24 (on average) from the IR-dark to IR- +bright stage. Additionally, as previously discussed (see Sect. 4.1), +high-mass protostars (i.e., with Lbol ≳ 104 L⊙) are only identi- +fied in the IR-bright HFSs. These results suggest that sufficient mass +accumulation from the large-scale, hub-composing filaments is re- +quired for the central clumps in IR-dark HFSs to evolve to clumps +with high-mass protostars in IR-bright HFSs. This process would +continue till the hub-composing filaments are completely dispersed +by stellar feedback (e.g., stellar winds, and ionization). Further, the +associated massive cores accumulate the required mass from their +natal clumps. Thus, a multi-scale mass accretion/transfer scenario +unfolds in HFSs, where the mass accretion/transfer proceeds from +the large-scale hub-composing filaments, through clumps, down to +cores where high-mass stars finally form. Consistent with the ob- +served trend, the mass and mass surface density of the clumps, and +cores should be higher in the IR-bright stage of HFSs since the ac- +cretion timescales of these density structures are more extended in +the more evolved stage as along as the large-scale hub-composing +filaments contain sufficient gas material. This multi-scale mass ac- +cretion process has also been observed toward one of the HFSs stud- +ied here (i.e., HFS 17) in Liu et al. (2022a). These authors reveal the +presence of the multi-scale mass accretion flows, i.e., accretion from +clumps onto cores, and that from cores to embedded protostars. +The above results from a selected sub-sample of the ASHES +and ATOMS surveys agree well with the filament to cluster (i.e., +F2C) evolutionary sequence discussed in a recent statistical study +by Kumar et al. (2020). Based on a large sample of ∼ 3700 candi- +date HFSs using far-infrared Herschel dust continuum maps at 70– +500 µm from the Hi-Gal survey, these authors propose four stages +involved in the formation of high-mass stars in the context of HFSs. +These are: I) formation of individual dense filaments by mechanisms +such as cloud-cloud collisions, and compression from local turbu- +lence; II) flow driven filaments overlap wherein intra-filamentary +matter in the HFS cloud combine to form a hub with density am- +plification making them more conducive to star formation as com- +pared to the filaments; III) formation of high-mass stars in the den- +sity amplified hub where the generated gravitational potential differ- +ence between the hub and the filaments can trigger and direct the +filament-rooted longitudinal flows toward the centrally-located hub. +IV) formation of “classical” (optically visible) HII regions in the +hub along with a small embedded cluster of stars. In this stage, the +radiation pressure and ionization feedback from the newly forming +massive stars channel out of the hub through the inter-filamentary +diffuse cavities. These four stages, where a multi-scale mass accre- +tion/transfer process can be expected from hub-composing filaments +through clumps (hubs) to cores (i.e., Stage II and III), finally lead to +a mass-segregated embedded cluster with high-mass stars preferen- +tially formed in the hub and low-mass stars in the hub-composing +filaments. +From the observational study presented here, the IR-dark HFSs +resemble Stage II, where the density-enhanced hub has formed and +is in a relatively quiescent phase of star formation. Presence of low- +luminosity YSOs outside the hub-clump region implies onset of low- +mass star formation in the HFS cloud and/or individual filaments +while the longitudinal flows continue to feed matter to the central +hub which are devoid of high-luminosity sources. In comparison, +the observational features seen in IR-bright HFSs are characteris- +tic of Stage III. In this sample, in addition to a similar picture of +low-mass star formation in the entire HFS cloud, a small, mass- +segregated embedded cluster of YSOs (see Fig. 6b), in which high- +luminosity YSOs (≳ 104 L⊙) typical of high-mass protostars are +preferentially located in the hub-clump region. Interestingly, the ori- +entation of outflows along the low density, inter-filamentary voids +(see Sect. 3.4) also gives clues for channelling out radiation pressure +MNRAS 000, 1–15 (2021) + +12 +H.-L. Liu et al. +10 +1 +100 +101 +102 +Lbol/Mclump [L /M ] +102 +103 +Mclump [M ] +HFS14 +HFS16 +(a) +IR-bright +IR-dark +0.2 +0.4 +0.6 +0.8 +1.0 +clump [g cm +2] +10 +1 +100 +101 +102 +Lbol/Mclump [L /M ] +101 +102 +103 +Mmax +core [M ] +(b) +IR-bright +IR-dark +20 +40 +60 +core [g cm +2] +Figure 7. Mass distribution of the central massive clumps (panel a) and their embedded most massive cores (panel b) in the two IR types of HFS against the the +Lbol/Mclump ratio of the clumps. The color-coded circles reflect the mass surface density of the sources. The Lbol/Mclump ratio of the clumps represent the +evolutionary stage of high-mass star formation of the HFSs. +and ionization feedback in the next evolutionary stage (IV) of the +classical HII regions. +Recent studies of molecular clouds found evidence for multi-scale +hierarchical fragmentation cascade (i.e., from clouds, through fila- +ments, clumps and cores, down to protostars, see e.g., Elia et al. +2018; Thomasson et al. 2022) probably as a major vector of star +formation. In conjunction with the latest theoretical models such as +GHC (V´azquez-Semadeni et al. 2019) and I2 (Padoan et al. 2020), +there seems to be a general consensus which can favor high-mass +star formation in HFSs through a multi-scale mass accretion/transfer +process that finally can lead to a mass-segregated cluster of stars. +Notwithstanding the selection bias (see Sect. 3.2.3), one may con- +sider the observed distinct mass distribution of the central massive +clumps and their most massive cores as an evidence for the above +processes in play in HFSs. Towards the above efforts and to put +more robust constraints to theoretical models, companion papers +(e.g., Yang, D.T. et al. 2022, in prep.) are in the pipeline on high- +resolution, multi-scale (i.e., from hub-composing filaments, clumps, +to cores) kinematic and dynamical studies dedicated to the HFSs in- +vestigated here using the spectral line data from the same surveys. +For example, the GHC and I2 models agree on gravity-driven mass– +accretion on small scales (e.g., cores), however, they predict two dis- +tinct drivers on larger scales for the multi-scale mass accretion pro- +cess. The former strongly favors a gravity–driven hierarchical mass +accretion while the latter advocates for a turbulence–driven mass in- +flow/accretion, which can be disentangled with the multi-scale kine- +matic and dynamical studies. +5 SUMMARY AND CONCLUSIONS +We have presented a statistical study of a sample of 17 high-mass +star formation HFSs using high-angular resolution (∼ 1–2′′) ALMA +1.3 mm and 3 mm continuum data. The statistical results have helped +shed light on the high-mass star formation scenario in HFSs. Our +main results can be summarised as follows: +• The 17 HFSs are selected from the target lists of the ASHES +1.3 mm and ATOMS 3 mm surveys. They are identifiable in the +Spitzer 8 µm image with hub-composing filaments intersecting at +the central hub. All the hub-composing filaments appear as elon- +gated dark lanes in 8 µm emission. Based on the different IR types +of the hubs, the HFSs are divided into 8 IR-dark and 9 IR-bright +HFSs. The IR-dark HFSs contain an IR-dark hub without detectable +IR emission shortward of 70 µm, while the IR-bright HFSs have +an IR-bright hub with high-mass protostars in the same wavelength +regime. The two IR types can represent an evolutionary sequence of +high-mass star formation HFSs from the IR-dark to IR-bright stage. +• The 17 central massive clumps are identified in their natal HFSs +from the available ATLASGAL 870 µm continuum data. In addition, +310 embedded cores are extracted from the ALMA continuum data, +including 224 from the IR-dark HFSs, and 86 from the IR-bright +HFSs. +• The massive, dense cores in the two IR types of HFSs are pre- +dominantly distributed in the central hub-clump region of HFSs of +radius 0.25 pc. For IR-dark HFSs, the cores peak within ∼ 0.16 pc +of the centre displaying a hierarchical sub-clustering mode. This +transforms to a centrally-peaked clustering mode in IR-bright HFSs +where the cores peak within ∼ 0.04 pc of the centre. +• The central massive clumps and their associated most massive +cores in HFSs show a trend of increasing mass and mass surface +density with the evolution of HFSs from the IR-dark to IR-bright +stage. This could be a natural result of the multi-scale mass accre- +tion/transfer scenario in HFSs from the hub-composing filaments +through clumps to cores. +• A total of 122 candidate YSOs associated with the 17 +HFSs are retrieved from the combined catalogues of the archival +Spitzer/MIPSGAL 24 µm point sources and the Spitzer/IRAC candi- +date YSOs. Their stellar bolometric luminosities are estimated from +the 24 µm flux. From the spatial distributions of YSOs in the HFSs, +we find the picture of a mass-segregated cluster of YSOs in which +high-luminosity YSOs typical of high-mass protostars are preferen- +tially located in the central hub-clump region, and surrounded by a +population of low-luminosity YSOs typical of low-mass protostars +in the entire HFS cloud extending to several parsecs. +• From qualitative analysis of the relative orientation between +the outflow and hub-composing filaments in all the HFSs studied +here, most of the outflows are found oriented toward the lower den- +sity inter-filamentary cavities. This suggests that outflow feedback +would have a limited effect on the disruption of the HFS clouds and +ongoing star formation therein. +From the observed facts of the trend on multi-scales (i.e., clumps +and cores) of increasing mass and mass surface density with evolu- +tion from IR-dark to IR-bright stage, the mass-segregated cluster of +YSOs, and the preferential escape directions of outflow feedback, +we conclude that high-mass star formation in the HFSs can be de- +scribed by a multi-scale mass accretion/transfer scenario, from hub- +MNRAS 000, 1–15 (2021) + +High-mass star formation in HFS cloud +13 +composing filaments through clumps down to cores, that can natu- +rally lead to a mass-segregated cluster of stars. To reveal the detailed +physics related to the multi-scale accretion scenario requires further +investigations, which will be carried out in our future multi-scale +kinematic and dynamical studies dedicated to the HFSs investigated +here using the high-resolution spectral line data from both ATOMS +and ASHES surveys. +ACKNOWLEDGEMENTS +We thank the anonymous referee for comments and suggestions +that greatly improved the quality of this paper. This work has +been supported by the National Key R&D Program of China +(No. 2022YFA1603101). H.-L. Liu is supported by National Nat- +ural Science Foundation of China (NSFC) through the grant +No.12103045. T. Liu acknowledges the supports by NSFC through +grants No.12073061 and No.12122307. PS was partially supported +by a Grant-in-Aid for Scientific Research (KAKENHI Number +22H01271) of the Japan Society for the Promotion of Science +(JSPS). S.-L. Qin is supported by NSFC under No.12033005. AS +gratefully acknowledges support by the Fondecyt Regular (project +code 1220610). This research was carried out in part at the Jet +Propulsion Laboratory, which is operated by the California Insti- +tute of Technology under a contract with the National Aeronau- +tics and Space Administration (80NM0018D0004). G.G., AS and +L.B. gratefully acknowledges support by the ANID BASAL projects +ACE210002 and FB210003. C.W.L. is supported by the Basic Sci- +ence Research Program through the National Research Founda- +tion of Korea (NRF) funded by the Ministry of Education, Sci- +ence and Technology(NRF-2019R1A2C1010851), and by the Ko- +rea Astronomy and Space Science Institute grant funded by the Ko- +rea government (MSIT) (Project No. 2022-1-840-05). This work +is supported by the international partnership program of Chinese +Academy of Sciences through grant No.114231KYSB20200009, +and Shanghai Pujiang Program 20PJ1415500. This paper makes use +of the following ALMA data: ADS/JAO.ALMA#2019.1.00685.S +and 2015.1.01539.S. ALMA is a partnership of ESO (represent- +ing its member states), NSF (USA), and NINS (Japan), together +with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Re- +public of Korea), in cooperation with the Republic of Chile. The +Joint ALMA Observatory is operated by ESO, AUI/NRAO, and +NAOJ. This research made use of astrodendro, a Python package +to compute dendrograms of Astronomical data (http://www. +dendrograms.org/). This research made use of Astropy, a +community-developed core Python package for Astronomy (As- +tropy Collaboration et al. 2018). +DATA AVAILABILITY +The data underlying this article will be shared on reasonable request +to the corresponding author. +REFERENCES +Anderson M., Peretto N., Ragan S. E., Rigby A. J., Avison A., +Duarte-Cabral A., Fuller G. A., et al., 2021, MNRAS, 508, 2964. +doi:10.1093/mnras/stab2674 +Andr´e P., Men’shchikov A., Bontemps S., K¨onyves V., Motte F., Schnei- +der N., Didelon P., et al., 2010, A&A, 518, L102. doi:10.1051/0004- +6361/201014666 +Andr´e P., Arzoumanian D., K¨onyves V., Shimajiri Y., Palmeirim P., 2019, +A&A, 629, L4. doi:10.1051/0004-6361/201935915 +Anathpindika S., Whitworth A. P., 2008, A&A, 487, 605. doi:10.1051/0004- +6361:200810308 +Astropy Collaboration, Price-Whelan A. M., Sip˝ocz B. M., G¨unther H. M., +Lim P. L., Crawford S. M., Conseil S., et al., 2018, AJ, 156, 123. +doi:10.3847/1538-3881/aabc4f +Bate +M. +R., +2009, +MNRAS, +392, +1363. +doi:10.1111/j.1365- +2966.2008.14165.x +Bate +M. +R., +2012, +MNRAS, +419, +3115. +doi:10.1111/j.1365- +2966.2011.19955.x +Baug T., Wang K., Liu T., Wu Y.-F., Li D., Zhang Q., Tang M., et al., 2021, +MNRAS, 507, 4316. doi:10.1093/mnras/stab1902 +Beltr´an M. T., Rivilla V. M., Kumar M. S. N., Cesaroni R., Galli D., 2022, +A&A, 660, L4. doi:10.1051/0004-6361/202243361 +Beuther H., Mottram J. C., Ahmadi A., Bosco F., Linz H., Henning +T., Klaassen P., et al., 2018, A&A, 617, A100. doi:10.1051/0004- +6361/201833021 +Bonnell I. A., Bate M. R., Clarke C. J., Pringle J. E., 2001, MNRAS, 323, +785. doi:10.1046/j.1365-8711.2001.04270.x +Bronfman L., Nyman L.-A., May J., 1996, A&AS, 115, 81 +Chen H.-R. V., Zhang Q., Wright M. C. H., Busquet G., Lin Y., Liu H. B., +Olguin F. A., et al., 2019, ApJ, 875, 24. doi:10.3847/1538-4357/ab0f3e +Chevance M., Krumholz M. R., McLeod A. F., Ostriker E. C., Rosolowsky +E. W., Sternberg A., 2022, arXiv, arXiv:2203.09570 +Contreras Y., Schuller F., Urquhart J. S., Csengeri T., Wyrowski F., Beuther +H., Bontemps S., et al., 2013, A&A, 549, A45. doi:10.1051/0004- +6361/201220155 +Dale J. E., Bonnell I., 2011, MNRAS, 414, 321. doi:10.1111/j.1365- +2966.2011.18392.x +Dunham M. M., Crapsi A., Evans N. J., Bourke T. L., Huard T. L., Myers +P. C., Kauffmann J., 2008, ApJS, 179, 249. doi:10.1086/591085 +Davis C. J., Froebrich D., Stanke T., Megeath S. T., Kumar M. S. N., Adam- +son A., Eisl¨offel J., et al., 2009, A&A, 496, 153. doi:10.1051/0004- +6361:200811096 +Elia D., Strafella F., Dib S., Schneider N., Hennebelle P., Pezzuto S., Molinari +S., et al., 2018, MNRAS, 481, 509. doi:10.1093/mnras/sty2170 +Elia D., Molinari S., Schisano E., Soler J. D., Merello M., Russeil D., +Veneziani M., et al., 2022, arXiv, arXiv:2211.05573 +Foster J. B., Arce H. G., Kassis M., Sanhueza P., Jackson J. M., Finn S. C., +Offner S., et al., 2014, ApJ, 791, 108. doi:10.1088/0004-637X/791/2/108 +Giannetti A., Leurini S., Wyrowski F., Urquhart J., Csengeri T., Menten +K. M., K¨onig C., et al., 2017, A&A, 603, A33. doi:10.1051/0004- +6361/201630048 +Ginsburg A., Henkel C., Ao Y., Riquelme D., Kauffmann J., Pillai T., +Mills E. A. C., et al., 2016, A&A, 586, A50. doi:10.1051/0004- +6361/201526100 +Goodman A. A., Pineda J. E., Schnee S. L., 2009, ApJ, 692, 91. +doi:10.1088/0004-637X/692/1/91 +Grudi´c M. Y., Guszejnov D., Offner S. S. R., Rosen A. L., Raju A. N., +Faucher-Gigu`ere C.-A., Hopkins P. F., 2022, MNRAS, 512, 216. +doi:10.1093/mnras/stac526 +Guszejnov D., Grudi´c M. Y., Hopkins P. F., Offner S. S. R., Faucher-Gigu`ere +C.-A., 2020, MNRAS, 496, 5072. doi:10.1093/mnras/staa1883 +Guszejnov D., Grudi´c M. Y., Hopkins P. F., Offner S. S. R., Faucher-Gigu`ere +C.-A., 2021, MNRAS, 502, 3646. doi:10.1093/mnras/stab278 +Guo W., Chen X., Feng J., Sun L., Wang C., Su Y., Sun Y., et al., 2021, ApJ, +921, 23. doi:10.3847/1538-4357/ac15fe +Gutermuth R. A., Heyer M., 2015, AJ, 149, 64. doi:10.1088/0004- +6256/149/2/64 +Guzm´an A. E., Sanhueza P., Contreras Y., Smith H. A., Jackson J. M., +Hoq S., Rathborne J. M., 2015, ApJ, 815, 130. doi:10.1088/0004- +637X/815/2/130 +Hacar A., Clark S., Heitsch F., Kainulainen J., Panopoulou G., Seifried D., +Smith R., 2022, arXiv, arXiv:2203.09562 +Hennebelle P., Commerc¸on B., Lee Y.-N., Chabrier G., 2020, ApJ, 904, 194. +doi:10.3847/1538-4357/abbfab +Hennebelle P., Lebreuilly U., Colman T., Elia D., Fuller G., Leurini S., Nony +T., et al., 2022, arXiv, arXiv:2210.12475 +Issac N., Tej A., Liu T., Varricatt W., Vig S., Ishwara Chandra C. H., +Schultheis M., 2019, MNRAS, 485, 1775. doi:10.1093/mnras/stz466 +Krumholz M. R., Thompson T. A., 2012, ApJ, 760, 155. doi:10.1088/0004- +637X/760/2/155 +Kuhn M. A., de Souza R. S., Krone-Martins A., Castro-Ginard A., Ishida +E. E. O., Povich M. S., Hillenbrand L. A., et al., 2021, ApJS, 254, 33. +MNRAS 000, 1–15 (2021) + +14 +H.-L. Liu et al. +doi:10.3847/1538-4365/abe465 +Kumar M. S. N., Palmeirim P., Arzoumanian D., Inutsuka S. I., 2020, A&A, +642, A87. doi:10.1051/0004-6361/202038232 +Kumar M. S. N., Arzoumanian D., Men’shchikov A., Palmeirim P., Mat- +sumura M., Inutsuka S., 2022, A&A, 658, A114. doi:10.1051/0004- +6361/202140363 +Larson R. B., 2003, RPPh, 66, 1651. doi:10.1088/0034-4885/66/10/R03 +Lee K. I., Dunham M. M., Myers P. C., Arce H. G., Bourke T. L., Goodman +A. A., Jørgensen J. K., et al., 2016, ApJL, 820, L2. doi:10.3847/2041- +8205/820/1/L2 +Li S., Sanhueza P., Zhang Q., Nakamura F., Lu X., Wang J., Liu T., et al., +2020, ApJ, 903, 119. doi:10.3847/1538-4357/abb81f +Li S., Zhang Q., Liu H. B., Beuther H., Palau A., Girart J. M., Smith H., et +al., 2020, ApJ, 896, 110. doi:10.3847/1538-4357/ab84f1 +Li S., Zhang Q., Pillai T., Stephens I. W., Wang J., Li F., 2019, ApJ, 886, 130. +doi:10.3847/1538-4357/ab464e +Liu H. B., Quintana-Lacaci G., Wang K., Ho P. T. P., Li Z.-Y., Zhang Q., +Zhang Z.-Y., 2012, ApJ, 745, 61. doi:10.1088/0004-637X/745/1/61 +Liu H. B., Galv´an-Madrid R., Jim´enez-Serra I., Rom´an-Z´u˜niga C., Zhang Q., +Li Z., Chen H.-R., 2015, ApJ, 804, 37. doi:10.1088/0004-637X/804/1/37 +Liu H.-L., Sanhueza P., Liu T., Zavagno A., Tang X.-D., Wu Y., Zhang S., +2020, ApJ, 901, 31. doi:10.3847/1538-4357/abadfe +Liu H.-L., Liu T., Evans N. J., Wang K., Garay G., Qin S.-L., Li S., et al., +2021, MNRAS, 505, 2801. doi:10.1093/mnras/stab1352 +Liu H.-L., Tej A., Liu T., Issac N., Saha A., Goldsmith P. F., Wang J.-Z., et +al., 2022a, MNRAS, 510, 5009. doi:10.1093/mnras/stab2757 +Liu H.-L., Tej A., Liu T., Goldsmith P. F., Stutz A., Juvela M., Qin S.-L., et +al., 2022b, MNRAS, 511, 4480. doi:10.1093/mnras/stac378 +Liu T., Evans N. J., Kim K.-T., Goldsmith P. F., Liu S.-Y., Zhang Q., Tatem- +atsu K., et al., 2020a, MNRAS, 496, 2790. doi:10.1093/mnras/staa1577 +Liu T., Evans N. J., Kim K.-T., Goldsmith P. F., Liu S.-Y., Zhang Q., Tatem- +atsu K., et al., 2020b, MNRAS, 496, 2821. doi:10.1093/mnras/staa1501 +Longmore S. N., Kruijssen J. M. D., Bastian N., Bally J., Rath- +borne +J., +Testi +L., +Stolte +A., +et +al., +2014, +prpl.conf, +291. +doi:10.2458/azu uapress 9780816531240-ch013 +Louvet F., Hennebelle P., Men’shchikov A., Didelon P., Ntormousi E., Motte +F., 2021, A&A, 653, A157. doi:10.1051/0004-6361/202040053 +McKee C. F., Tan J. C., 2003, ApJ, 585, 850. doi:10.1086/346149 +Men’shchikov +A., +2021, +A&A, +649, +A89. +doi:10.1051/0004- +6361/202039913 +Molinari S., Swinyard B., Bally J., Barlow M., Bernard J.-P., Mar- +tin P., Moore T., et al., 2010, A&A, 518, L100. doi:10.1051/0004- +6361/201014659 +Morii K., Sanhueza P., Nakamura F., Jackson J. M., Li S., Beuther H., Zhang +Q., et al., 2021, ApJ, 923, 147. doi:10.3847/1538-4357/ac2365 +Motte F., Bontemps S., Csengeri T., Pouteau Y., Louvet F., Stutz A. M., +Cunningham N., et al., 2022, A&A, 662, A8. doi:10.1051/0004- +6361/202141677 +Motte +F., +Bontemps +S., +Louvet +F., +2018, +ARA&A, +56, +41. +doi:10.1146/annurev-astro-091916-055235 +Myers P. C., 2009, ApJ, 700, 1609. doi:10.1088/0004-637X/700/2/1609 +Offner S. S. R., Dunham M. M., Lee K. I., Arce H. G., Fielding D. B., 2016, +ApJL, 827, L11. doi:10.3847/2041-8205/827/1/L11 +Offner S. S. R., Chaban J., 2017, ApJ, 847, 104. doi:10.3847/1538- +4357/aa8996 +Offner S. S. R., Taylor J., Markey C., Chen H. H.-H., Pineda J. E., +Goodman A. A., Burkert A., et al., 2022, MNRAS, 517, 885. +doi:10.1093/mnras/stac2734 +Ossenkopf V., Henning T., 1994, A&A, 291, 943 +Padoan P., Pan L., Juvela M., Haugbølle T., Nordlund ˚A., 2020, ApJ, 900, +82. doi:10.3847/1538-4357/abaa47 +Peretto N., Fuller G. A., Duarte-Cabral A., Avison A., Hennebelle P., Pineda +J. E., Andr´e P., et al., 2013, A&A, 555, A112. doi:10.1051/0004- +6361/201321318 +Ragan S., Henning T., Krause O., Pitann J., Beuther H., Linz H., Tackenberg +J., et al., 2012, A&A, 547, A49. doi:10.1051/0004-6361/201219232 +Rosolowsky E. W., Pineda J. E., Kauffmann J., Goodman A. A., 2008, ApJ, +679, 1338. doi:10.1086/587685 +Sabatini G., Bovino S., Sanhueza P., Morii K., Li S., Redaelli E., Zhang Q., +et al., 2022, ApJ, 936, 80. doi:10.3847/1538-4357/ac83aa +Sanhueza P., Garay G., Bronfman L., Mardones D., May J., Saito M., 2010, +ApJ, 715, 18. doi:10.1088/0004-637X/715/1/18 +Sanhueza P., Jackson J. M., Zhang Q., Guzm´an A. E., Lu X., Stephens I. W., +Wang K., et al., 2017, ApJ, 841, 97. doi:10.3847/1538-4357/aa6ff8 +Sanhueza P., Contreras Y., Wu B., Jackson J. M., Guzm´an A. E., Zhang Q., +Li S., et al., 2019, ApJ, 886, 102. doi:10.3847/1538-4357/ab45e9 +Sanhueza P., Girart J. M., Padovani M., Galli D., Hull C. L. H., Zhang Q., +Cortes P., et al., 2021, ApJL, 915, L10. doi:10.3847/2041-8213/ac081c +Saha A., Tej A., Liu H.-L., Liu T., Issac N., Lee C. W., Garay G., et al., 2022, +MNRAS, 516, 1983. doi:10.1093/mnras/stac2353 +Sakai T., Sakai N., Foster J. B., Sanhueza P., Jackson J. M., Kassis M., Furuya +K., et al., 2013, ApJL, 775, L31. doi:10.1088/2041-8205/775/1/L31 +Sakai T., Sanhueza P., Furuya K., Tatematsu K., Li S., Aikawa Y., Lu X., et +al., 2022, ApJ, 925, 144. doi:10.3847/1538-4357/ac3d2e +Schneider N., Csengeri T., Hennemann M., Motte F., Didelon P., Feder- +rath C., Bontemps S., et al., 2012, A&A, 540, L11. doi:10.1051/0004- +6361/201118566 +Schneider N., Simon R., Guevara C., Buchbender C., Higgins R. D., Okada +Y., Stutzki J., et al., 2020, PASP, 132, 104301. doi:10.1088/1538- +3873/aba840 +Schuller F., Menten K. M., Contreras Y., Wyrowski F., Schilke P., Bronf- +man L., Henning T., et al., 2009, A&A, 504, 415. doi:10.1051/0004- +6361/200811568 +Stephens I. W., Dunham M. M., Myers P. C., Pokhrel R., Sadavoy S. I., +Vorobyov E. I., Tobin J. J., et al., 2017, ApJ, 846, 16. doi:10.3847/1538- +4357/aa8262 +Stutz A. M., Gould A., 2016, A&A, 590, A2. doi:10.1051/0004- +6361/201527979 +Trevi˜no-Morales S. P., Fuente A., S´anchez-Monge ´A., Kainulainen J., +Didelon P., Suri S., Schneider N., et al., 2019, A&A, 629, A81. +doi:10.1051/0004-6361/201935260 +Tafoya D., Sanhueza P., Zhang Q., Li S., Guzm´an A. E., Silva A., de la Fuente +E., et al., 2021, ApJ, 913, 131. doi:10.3847/1538-4357/abf5da +Tatematsu K., Ohashi S., Sanhueza P., Nguyen Luong Q., Umemoto T., +Mizuno N., 2016, PASJ, 68, 24. doi:10.1093/pasj/psw002 +Thomasson B., Joncour I., Moraux E., Crespelle C., Motte F., Pouteau Y., +Nony T., 2022, A&A, 665, A119. doi:10.1051/0004-6361/202243275 +Urquhart J. S., Moore T. J. T., Csengeri T., Wyrowski F., Schuller F., +Hoare M. G., Lumsden S. L., et al., 2014, MNRAS, 443, 1555. +doi:10.1093/mnras/stu1207 +V´azquez-Semadeni +E., +Palau +A., +Ballesteros-Paredes +J., +G´omez +G. +C., +Zamora-Avil´es +M., +2019, +MNRAS, +490, +3061. +doi:10.1093/mnras/stz2736 +Verliat A., Hennebelle P., Gonz´alez M., Lee Y.-N., Geen S., 2022, A&A, 663, +A6. doi:10.1051/0004-6361/202141765 +Wang +P., +Li +Z.-Y., +Abel +T., +Nakamura +F., +2010, +ApJ, +709, +27. +doi:10.1088/0004-637X/709/1/27 +Wang K., Zhang Q., Wu Y., Zhang H., 2011, ApJ, 735, 64. doi:10.1088/0004- +637X/735/1/64 +Wang K., Zhang Q., Testi L., van der Tak F., Wu Y., Zhang H., Pillai T., et +al., 2014, MNRAS, 439, 3275. doi:10.1093/mnras/stu127 +Williams +J. +P., +de +Geus +E. +J., +Blitz +L., +1994, +ApJ, +428, +693. +doi:10.1086/174279 +Williams G. M., Peretto N., Avison A., Duarte-Cabral A., Fuller G. A., 2018, +A&A, 613, A11. doi:10.1051/0004-6361/201731587 +Yuan J., Li J.-Z., Wu Y., Ellingsen S. P., Henkel C., Wang K., Liu T., et al., +2018, ApJ, 852, 12. doi:10.3847/1538-4357/aa9d40 +Yuan L., Yang J., Du F., Liu X., Zhang S., Lin Z., Sun J., et al., 2021, ApJS, +257, 51. doi:10.3847/1538-4365/ac242a +Zhang Q., Wang Y., Pillai T., Rathborne J., 2009, ApJ, 696, 268. +doi:10.1088/0004-637X/696/1/268 +Zhou +J.-W., +Liu +T., +Evans +N. +J., +Garay +G., +Goldsmith +P. +F., +G´omez G. C., V´azquez-Semadeni E., et al., 2022, MNRAS.tmp. +doi:10.1093/mnras/stac1735 +MNRAS 000, 1–15 (2021) + +High-mass star formation in HFS cloud +15 +APPENDIX A: COMPLEMENTARY FIGURES +Author affiliations: +1School of physics and astronomy, Yunnan University, Kunming, +650091, PR China +2Indian Institute of Space Science and Technology, Thiruvanantha- +puram 695 547, Kerala, India +3Shanghai Astronomical Observatory, Chinese Academy of Sci- +ences, 80 Nandan Road, Shanghai 200030, Peoples Republic of +China +4Key Laboratory for Research in Galaxies and Cosmology, Shang- +hai Astronomical Observatory, Chinese Academy of Sciences, 80 +Nandan Road, Shanghai 200030, Peoples Republic of China +5National Astronomical Observatory of Japan, National Institutes +of Natural Sciences, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan +6Department of Astronomical Science, The Graduate University +for Advanced Studies, SOKENDAI, 2-21-1 Osawa, Mitaka, Tokyo +181-8588, Japan +7Yunnan Observatories, Chinese Academy of Sciences, 396 Yang- +fangwang, Guandu District, Kunming, 650216, China +8Chinese Academy of Sciences South America Center for Astron- +omy, National Astronomical Observatories, CAS, Beijing 100101, +China +9Departamento de Astronom´ıa, Universidad de Chile, Casilla 36-D, +Santiago, Chile +10Jet Propulsion Laboratory, California Institute of Technology, +4800 Oak Grove Drive, Pasadena, CA 91109, USA +11Department of Astronomy, Graduate School of Science, The +University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, +Japan +12Max Planck Institute for Astronomy, Knigstuhl 17, D-69117 +Heidelberg, Germany +13Departamento de Astronom´ıa, Universidad de Concepci´on, Av. +Esteban Iturra s/n, Distrito Universitario, 160-C, Chile +14Max-Planck-Institute for Astronomy, K¨onigstuhl 17, 69117 +Heidelberg, Germany +15Kavli Institute for Astronomy and Astrophysics, Peking Univer- +sity, 5 Yiheyuan Road, Haidian District, Beijing 100871, People’s +Republic of China +16Department of Astronomy, Peking University, 100871, Beijing, +People’s Republic of China +17Indian Institute of Astrophysics, Koramangala II Block, Banga- +lore 560 034, India +18Satyendra Nath Bose National Centre for Basic Sciences, Block- +JD, Sector-III, Salt Lake, Kolkata-700 106 +19E¨otv¨os Lor´and University, Department of Astronomy, P´azm´any +P´eter s´et´any 1/A, H-1117, Budapest, Hungary +20Physical Research Laboratory, Navrangpura, Ahmedabad380 +009, India +21National Astronomical Observatories, Chinese Academy of +Sciences, Beijing 100101, China +22Korea Astronomy and Space Science Institute, 776 Daedeok- +daero, Yuseong-gu, Daejeon 34055, Republic of Korea +23University of Science and Technology, Korea (UST), 217 +Gajeong-ro, Yuseong-gu, Daejeon 34113, Republic of Korea +24School of Physics and Astronomy, Sun Yat-sen University, 2 +Daxue Road, Zhuhai, Guangdong, 519082, People’s Republic of +China +25SOFIA Science Centre, USRA, NASA Ames Research Centre, +MS-12, N232, Moffett Field, CA 94035, USA +MNRAS 000, 1–15 (2021) + +16 +H.-L. Liu et al. +18h17m28s +26s +24s +22s +20s +-16°24'00" +30" +25'00" +30" +26'00" +RA (J2000) +Dec (J2000) +8 m +HFS2 / G014.492-00.139 +RA: 18:17:23.21 +Dec: -16:25:04.08 +0.5pc +18h43m36s +32s +28s +24s +20s +-4°10'00" +11'00" +12'00" +13'00" +14'00" +RA (J2000) +Dec (J2000) +8 m +HFS3 / G028.273-00.167 +RA: 18:43:28.42 +Dec: -4:11:57.12 +0.5pc +16h11m39s +36s +33s +30s +-51°34'00" +30" +35'00" +30" +RA (J2000) +Dec (J2000) +8 m +HFS4 / G331.372-00.116 +RA: 16:11:33.41 +Dec: -51:34:43.68 +0.5pc +16h48m34s +32s +30s +28s +-45°10'20" +40" +11'00" +20" +40" +RA (J2000) +Dec (J2000) +8 m +HFS5 / G340.222-00.167 +RA: 16:48:30.74 +Dec: -45:11:04.56 +0.5pc +16h48m33s +30s +27s +24s +-45°09'00" +30" +10'00" +30" +RA (J2000) +Dec (J2000) +8 m +HFS6 / G340.232-00.146 +RA: 16:48:27.46 +Dec: -45:09:48.24 +0.5pc +16h51m18s +15s +12s +09s +-44°30'30" +31'00" +30" +32'00" +30" +RA (J2000) +Dec (J2000) +8 m +HFS7 / G341.039-00.114 +RA: 16:51:14.02 +Dec: -44:31:23.16 +0.5pc +17h01m04s +00s +00m56s +52s +-42°47'00" +30" +48'00" +30" +49'00" +30" +RA (J2000) +Dec (J2000) +8 m +HFS8 / G343.489-00.416 +RA: 17:00:59.42 +Dec: -42:48:00.36 +0.5pc +15h43m25s +20s +15s +10s +-54°05'30" +06'00" +30" +07'00" +30" +08'00" +RA (J2000) +Dec (J2000) +8 m +HFS10 / I15394-5358 +RA: 15:43:18.84 +Dec: -54:06:54.36 +0.5pc +15h55m54s +48s +42s +36s +30s +-52°41'00" +42'00" +43'00" +44'00" +45'00" +RA (J2000) +Dec (J2000) +8 m +HFS11 / I15520-5234 +RA: 15:55:42.05 +Dec: -52:42:39.24 +0.5pc +16h31m06s +00s +30m54s +48s +-48°42'00" +43'00" +44'00" +45'00" +RA (J2000) +Dec (J2000) +8 m +HFS12 / I16272-4837 +RA: 16:30:56.16 +Dec: -48:43:34.68 +0.5pc +16h39m00s +38m54s +48s +42s +36s +-47°28'00" +29'00" +30'00" +31'00" +RA (J2000) +Dec (J2000) +8 m +HFS13 / I16351-4722 +RA: 16:38:47.66 +Dec: -47:29:24.72 +0.5pc +16h46m15s +10s +05s +00s +-45°35'00" +36'00" +37'00" +RA (J2000) +Dec (J2000) +8 m +HFS14 / I16424-4531 +RA: 16:46:06.84 +Dec: -45:35:50.64 +0.5pc +17h05m20s +15s +10s +05s +-41°27'00" +28'00" +29'00" +30'00" +RA (J2000) +Dec (J2000) +8 m +HFS15 / I17016-4124 +RA: 17:05:11.54 +Dec: -41:28:30.00 +0.5pc +17h26m48s +42s +36s +30s +24s +-36°06'00" +08'00" +10'00" +RA (J2000) +Dec (J2000) +8 m +HFS16 / I17233-3606 +RA: 17:26:37.27 +Dec: -36:07:40.08 +0.5pc +18h53m22s +20s +18s +16s +14s +1°26'30" +00" +25'30" +00" +24'30" +RA (J2000) +Dec (J2000) +8 m +HFS17 / I18507+0121 +RA: 18:53:18.43 +Dec: +1:25:19.15 +0.5pc +Figure A1. Same as Fig. 1 but for the remaining 15 HFSs. +MNRAS 000, 1–15 (2021) + diff --git a/LdE1T4oBgHgl3EQfZAQe/content/tmp_files/load_file.txt b/LdE1T4oBgHgl3EQfZAQe/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..9de51136fef4e9a56bca52dbdb77f4f48ae87276 --- /dev/null +++ b/LdE1T4oBgHgl3EQfZAQe/content/tmp_files/load_file.txt @@ -0,0 +1,2881 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf,len=2880 +page_content='MNRAS 000, 1–15 (2021) Preprint 10 January 2023 Compiled using MNRAS LATEX style file v3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 Evidence of high-mass star formation through multi-scale mass accretion in hub-filament-system clouds Hong-Li Liu,⋆1 Anandmayee Tej,⋆2 Tie Liu,⋆3,4 Patricio Sanhueza,5,6 Shengli Qin,1 Jinhua He,7,8,9 Paul F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Goldsmith,10 Guido Garay,9 Sirong Pan,1 Kaho Morii,5,11 Shanghuo Li,12, Amelia Stutz,13,14 Ken’ichi Tatematsu,5 Feng-Wei Xu,15,16 Leonardo Bronfman,9 Anindya Saha,2 Namitha Issac,17 Tapas Baug,18 L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Viktor Toth,19 Lokesh Dewangan,20 Ke Wang,15,16 Jianwen Zhou,21 Chang Won Lee,22,23 Dongting Yang,1 Anxu Luo,1 Xianjin Shen,1 Yong Zhang,24 Yue-Fang Wu,15,16 Zhiyuan Ren,21 Xun-Chuan Liu,3 Archana Soam,25 Siju Zhang,15,16 Qiu-Yi Luo,3 Affiliations are listed at the end of the paper Accepted 2023 January 3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Received 2022 December 6;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' in original form 2022 September 13 ABSTRACT We present a statistical study of a sample of 17 hub-filament-system (HFS) clouds of high-mass star formation using high- angular resolution (∼ 1–2′′) ALMA 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 mm and 3 mm continuum data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The sample includes 8 infrared (IR)-dark and 9 IR- bright types, which correspond to an evolutionary sequence from the IR-dark to IR-bright stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The central massive clumps and their associated most massive cores are observed to follow a trend of increasing mass (M) and mass surface density (Σ) with evolution from IR-dark to IR-bright stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In addition, a mass-segregated cluster of young stellar objects (YSOs) are revealed in both IR-dark and IR-bright HFSs with massive YSOs located in the hub and the population of low-mass YSOs distributed over larger areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Moreover, outflow feedback in all HFSs are found to escape preferentially through the inter-filamentary diffuse cavities, suggesting that outflows would render a limited effect on the disruption of the HFSs and ongoing high-mass star formation therein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' From the above observations, we suggest that high-mass star formation in the HFSs can be described by a multi-scale mass accretion/transfer scenario, from hub-composing filaments through clumps down to cores, that can naturally lead to a mass-segregated cluster of stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Key words: stars: formation – stars: massive;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' ISM: individual objects: hub filament system;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' ISM: clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 1 INTRODUCTION High-mass stars are fundamental components of the universe, sig- nificantly impacting a multitude of astrophysical processes, for in- stance, the structure and evolution of the universe and its con- stituents (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Larson 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Understanding how high-mass stars form has therefore long been an active area of astrophysical research (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Motte, Bontemps, & Louvet 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' It is generally accepted that high-mass stars form in clusters probably as a result of the hi- erarchical, multi-scale fragmentation process from clouds, through filaments, clumps and cores, down to seeds of star formation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2011, 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Beuther et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Yuan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' V´azquez-Semadeni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2019, 2020b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Padoan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022a,b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Hacar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Chevance et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Under this paradigm, filaments as a “conveyor belt” play a critical role in transporting gas material between the scales above and below (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Longmore et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' V´azquez-Semadeni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Padoan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Indeed, filaments have been observed to be ubiquitous in the inter- stellar medium (ISM), and the sites of star formation in both nearby ⋆ E-mail: hongliliu2012@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='com;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' tej@iist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='in;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' liutie@shao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='cn low-mass and distant high-mass star-forming clouds (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Andr´e et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2010, 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Molinari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Stutz & Gould 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Guo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Yuan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Crisscrossing filaments result in a special web that can comprise of three or more filaments converging toward a central web node.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Defined as hub-filament systems (HFSs), these web networks are considered as a unique category of filaments for star formation, especially for high-mass star formation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Myers 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In the definition of HFS, the web node is defined as the hub while the associated individual filaments are defined as the hub-composing filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In general, the central hub has a lower aspect ratio but a higher column density, which are in contrast to the high aspect ratio and low column density observed in the hub-composing filaments (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Myers 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The hierarchical density structure discussed above can promote high-mass star formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This is supported by several observational studies that include both single dish and interferometric observations from the far-infrared (IR) to millimeter regime (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Schneider et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Peretto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Williams et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Yuan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Issac et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Anderson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Beltr´an et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022a,b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Saha et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Thomasson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' These studies reveal that young massive stellar clusters appear in HFSs with the high-mass stars being preferentially formed in the hubs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' © 2021 The Authors arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='03144v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='GA] 9 Jan 2023 2 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Longitudinal gas flows along the hub-composing filaments, which are observed in several HFSs to converge toward the hub at typical flow rates of ∼ 10−4–10−3 M⊙ yr−1, have been demonstrated to account for the required mass accretion (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Yuan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Trevi˜no-Morales et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The above scenario advocates for further detailed observational studies of HFSs from the perspective of high-mass star forma- tion and for the development of theoretical models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' For instance, the latest-generation models such as “global hierarchical collapse” (GHC, V´azquez-Semadeni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2019) and “inertial-inflow” (I2, Padoan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020), which in terms of the accretion process could be complementary to the two proposed competing theories of “tur- bulent core accretion” (McKee & Tan 2003) and “competitive ac- cretion” (Bonnell et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The merits of these latest-generation models can be attributed to the envisioned multi-scale gas accretion, from clouds to the seeds of star formation, which was proposed in earlier times as “clump-fed” accretion in simulations of Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2010), but not fully developed to the cloud scales due to the compu- tation limitation at that time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In addition, the HFSs are often repro- duced to be a common signature in the multi-scale accretion models as the preferential system of cluster and high-mass star formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' However, the major driver of multi-scale gas accretion (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', gravity, and/or turbulence) is predicted to be different in different models (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This is inferred from our previous ALMA observations, at ∼ 2′′ resolution, toward a well-studied, high-mass star-forming filamentary IRDC, G034.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='43+00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='24 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Sakai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Foster et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020, G34 hereafter).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' G34 can be regarded as an HFS with the hub located at the MM1 clump (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 1 of Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022a,b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Our investiga- tions have revealed multi-scale accretion process from cloud down to the seeds of star formation and the scale-dependent nature of gas kinematics of the multi-scale, hierarchical density structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Inter- preting our results in the framework of both GHC and I2 models, we conclude that the scale-dependent combined effect of turbulence and gravity is essential to explain the multi-scale, dynamical accre- tion process responsible for high-mass star formation in G34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In this paper, we aim to carry out a statistical study of a sample of 17 high-mass star forming HFSs using high-angular resolution (∼1–2 ′′) ALMA continuum data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The sample was selected partic- ularly to contain two different infrared (IR) characteristics (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 8 IR-dark and 9 IR-bright objects) since these two IR types can rep- resent two different evolutionary stages (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The purpose of this study is to gain insights into high-mass star formation sce- narios in HFS clouds by analysing the hierarchical structures of the HFSs as a function of evolution of high-mass star formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The pa- per is organised as follows: Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2 briefly describes the selection of the HFS sample and the ALMA data used, Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3 presents analysis on the hierarchical structures of the HFSs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', clouds, clumps, and cores), star formation therein, and the effect of outflow feedback on star formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 4 discusses the multi-scale accretion scenario, from the core through clump up to the cloud scales, and Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 5 gives a comprehensive summary of the results obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2 SAMPLE AND ALMA DATA 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 Sample The sample investigated here consists of 17 HFS clouds selected from the ASHES (The ALMA Survey of 70 µm Dark High-mass Clumps in Early Stages;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Saba- tini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022) and the ATOMS (ALMA Three-millimeter Obser- vations of Massive Star-forming regions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2020a,b, 2021)) surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The selection is based on their morphological appearance in the Spitzer 8 µm image (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The selected HFS cloud is re- quired to be globally seen as an HFS morphology in 8 µm emission with at least three hub-composing filaments intersecting at the cen- tral hub (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The hub-composing filaments appear as elon- gated dark lanes against bright 8 µm background emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' With the matching angular resolution (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2′′) as that of the ALMA data, the Spitzer image facilitates the ALMA analysis of the identified HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The selected HFSs are classified into 8 IR-dark and 9 IR-bright HFS clouds based on the lack or presence of IR emission in the cen- tral hubs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The IR-dark sample (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', HFSs 1–8) is from the ASHES survey where the hubs are identified as IR-dark clumps from 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 to 70 µm (Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In contrast, the hubs of the IR- bright HFSs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', HFSs 9–17), selected from the ATOMS survey, are bright in the same IR regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This, in essence, is a reflection of the bolometric luminosity (Lbol) of the embedded young stellar objects (YSOs) in the hubs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Making a simple assumption, the Lbol of YSOs in these hubs is assumed to approximately represent that of their host HFSs (see Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' While the absence of compact IR emission can qualify the central hubs of IR-dark HFSs as prestellar candidates, being 70 µm dark does not always imply absolute lack of star forma- tion (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2019, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Morii et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Tafoya et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Sakai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Hence, the lack of YSOs here could also indicate a relatively quiescent star formation stage with very low bolomet- ric luminosities (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Lbol ≲ 300 L⊙, see Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' On the other hand, the central hubs of the IR-bright HFSs have high-luminosity (Lbol ≳ 104 L⊙, see Table 1) IRAS sources typical of high-mass stars, thus suggesting an active star formation stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Interestingly, even with the relatively limited sample of HFSs investigated in this study strikingly different regimes of Lbol/Mclump ratios are seen for the IR-dark and IR-bright HFSs (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This lends strong support to the inference that two different star-formation stages are probed with these two IR types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The basic parameters (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', source name, distance, and luminos- ity) of the selected sample are listed in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' They have a median distance of ∼ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 kpc in a range of ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3–5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 kpc with the IR-dark HFSs (∼ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 kpc) being on average around 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 times farther than the IR-bright ones (∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 kpc).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' It is worth noting that the 9 IR-bright HFSs selected here have been reported by Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2022) as part of a statistical study to identify and study HFSs in a large sample of 146 active massive protoclusters based on the H13CO+ (1–0) line data from the same ATOMS survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Among the sample studied by Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2022), these 9 IR-bright HFSs stand out in terms of the 8 µm appearance of their hub-composing filaments as elongated dark lanes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Figure 1 presents an example of the large-scale appearance of the selected 17 HFSs studied here in the Spitzer 8 µm image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Overlaid in gray contours on the image is ATLASGAL 870 µm continuum representative of cold, dense dust thermal emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The size of the images was adjusted to recover the complete presence of the global HFS appearance in 8 µm emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' As shown in the figure, the global HFS appearance can be identified for all 17 HFS clouds with the hub-composing filaments intersecting at the centrally located hub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The hub-composing filaments seen as elongated dark lanes at 8 µm have associated 870 µm dust emission representative of cold and dense material, indicating that the filaments are essentially high den- sity structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 ALMA data We made use of the combined 12m+7m continuum data from ASHES (project IDs: 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='01539.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='S, PI: Patricio Sanhueza), and MNRAS 000, 1–15 (2021) High-mass star formation in HFS cloud 3 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Images showing examples of the IR-dark (left) and bright (right) HFS clouds at Spitzer 8 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The contours represent 870 µm dust continuum from the ATLASGAL survey (Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The solid circles represent the compact dust clumps (Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The dashed loop/circle demarcates the central subcloud field covered by our ALMA observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The dashed curves identify the filamentary structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 µm beam (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2′′) are shown at the bottom right-hand corner of the corresponding panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The image size for each HFS is determined individually to recover the full view of its HFS morphology at 8 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Parameters of the HFSs and their central clumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' HFS cloud Alias RA DEC d Lbol Tdust F int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 870µm Mclump Σclump ID J2000 J2000 kpc log(L⊙) K Jy M⊙ g cm−2 1 G010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='991-00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='082 18:10:06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='58 19:27:46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='44 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='94 355 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='38 2 G014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='492-00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='139 18:17:22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='08 16:24:59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='40 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='89 685 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='73 3 G028.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='273-00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='167 18:43:31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='27 4:13:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='48 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='05 365 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='39 4 G331.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='372-00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='116 16:11:34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='08 51:34:56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='28 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='90 266 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='28 5 G340.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='222-00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='167 16:48:30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='74 45:11:04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='56 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='07 155 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='17 6 G340.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='232-00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='146 16:48:27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='46 45:09:48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='24 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16 179 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='19 7 G341.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='039-00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='114 16:51:14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='21 44:31:24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='24 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='21 153 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16 8 G343.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='489-00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='416 17:01:01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='34 42:48:07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='92 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='04 156 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='17 9 I13484-6100 13:51:58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='51 61:15:42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='84 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='10 600 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='64 10 I15394-5358 15:43:16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='46 54:07:15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='24 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='69 482 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='51 11 I15520-5234 15:55:48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='62 52:43:05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='88 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='82 733 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='78 12 I16272-4837 16:30:59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='11 48:43:53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='40 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='64 748 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='80 13 I16351-4722 16:38:50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='69 47:27:58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='68 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='43 649 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='69 14 I16424-4531 16:46:06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='36 45:36:44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='64 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='70 153 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16 15 I17016-4124 17:05:11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='18 41:29:05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='28 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16 975 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='04 16 I17233-3606 17:26:42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='74 36:09:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='33 201 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='21 17 I18507+0121 18:53:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='12 +1:25:24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='24 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='34 882 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='94 Note: The distance d of the HFSs comes from Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2019) for HFSs 1–8, and Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2021) for HFSs 9–17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The bolometric luminosity Lbol of the HFSs is approximately represented by that of their centrally located young stellar objects (YSOs, Bronfman, Nyman, & May 1996;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Contreras et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020a,b, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' ATOMS (project ID: 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='00685.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='S;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' PI: Tie Liu) surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Detailed discussion on the scientific goals, observing set-ups, and data reduc- tion can be found in Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2019);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2020a,b, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Briefly, the two surveys observed the central area of ra- dius ∼ 31–39′′ of our selected HFSs (see the dashed loop in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 1) in different observing modes at different wavelengths, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 mm mosaic mode for ASHES, and 3 mm pointing observing mode for ATOMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In addition, the synthesized beams of the com- bined 12m+7m continuum data of the two surveys are different with ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2′′ for ASHES and ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0′′ for ATOMS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' However, the two sur- veys have similar field of views (FoVs, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', ∼ 62′′ for ASHES and 78′′ for ATOMS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Given their typical distances (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1), the IR-dark and bright HFSs selected from the respective ASHES, and ATOMS surveys have very close linear-scale FoVs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 pc and ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 pc, respectively).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This rather close agreement of FoVs ensures detailed high-resolution analysis (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', for cores) over al- most the same spatial scales for most of the HFSs studied here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The ASHES and ATOMS surveys have a maximum angular recoverable MNRAS 000, 1–15 (2021) HFS9/I13484-6100 8μm 61°12\'00" RA: 13:51:57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='86 Dec: -61:14:01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='68 13\'00" Dec (J2000) 14\'00" 15\'00" 16\'00" 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc/ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 13h52m10s s00 51m50s 40s RA (J2000)HFS1/G010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='991-00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content="082 19°26'30' 8μm RA:18:10:06." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='79 Dec: -19:27:B4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='56 27\'00" Dec (J2000) 30" 28\'00" 30" 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc 18h10m10s 08s 06s 04s 02s RA (J2000)4 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' scale of 19′′ and 60′′, respectively, for the combined data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Note that the different angular resolutions and maximum recoverable scales may lead to some observation biases to the properties of cores (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', mass), which will be discussed in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In addition, the typ- ical sensitivities of the combined continuum data for ASHES and ATOMS are ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 mJy beam−1 (Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2019) at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 mm and ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 mJy beam−1 at 3 mm (Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022a), respectively, which correspond to a mass sensitivity of ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='04 M⊙ (for a temper- ature of 15 K typical of IR-dark cases), and ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 M⊙ (for 25 K typ- ical of IR-bright cases), respectively, at a typical distance of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 kpc (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 for mass calculation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3 RESULTS AND ANALYSIS 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 Clumps in the HFSs Clumps are one of the characteristic hierarchical structures of the HFS clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 1, one can see that each HFS has a domi- nant central clump.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Generally, such density structures can be identi- fied using several widely-used algorithms, such as Dendrogram and CASA-imfit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' However, the use of these algorithms is limited by the intensity contrast of the clumps with respect to their natal clouds es- pecially for the IR-dark HFSs studied here where the contrast is low (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In these cases, the extracted clumps tend to have a large aspect ratio of > 3 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', ratio of the major to minor axis) indica- tive of more than one entity within them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' To avoid inaccurate clump identification for these low-contrast cases and to maintain unifor- mity, we define a circular aperture to enclose the enhanced 870 µm emission in the central area of both IR-dark and bright HFSs anal- ysed here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' From a careful scrutiny of the 870 µm maps of the entire sample, an optimum aperture with radius 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='25 pc is found suitable to encompass most of the 870 µm emission (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Hence, we consider this as the radius of the clump, Rclump.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Given this defini- tion, the integrated flux (F int 870µm) of the central clumps in all HFSs were extracted from the ATLASGAL 870 µm image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In addition, we retrieved the dust temperature (Tdust) of the clumps from San- hueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2019) for those in the IR-dark HFSs and from Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2020a) for those in the IR-bright HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' With the above parameters, the clump mass (Mclump) was computed following Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' B1–B2 of Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In the computation, we assumed the gas-to-dust mass ratio to be Rgd = 100, and the dust opacity per gram of dust to be k870µm = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='78 cm2 g−1, which corresponds to the opacity of dust grains with thin ice mantles at gas densities of 106 cm−3 (Os- senkopf & Henning 1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The mass surface density (Σclump) of the clumps was derived from Σclump = Mclump/(πR2 clump).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The derived parameters are listed in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' According to Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2017, 2019), the uncertainty of both Mclump and Σclump could be about 50%, which accounts for the combined uncertainties from k870µm (∼ 30%), Rgd (∼ 20%), Td (∼ 20%), and the kinematic distance (∼ 10%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The central clumps have a median Mclump of ∼ 223 M⊙ in a range of [153, 685] M⊙ in the IR-dark HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' For the IR-bright HFSs, the median Mclump is ∼649 M⊙ in a range of [153, 975] M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Σclump has a median value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='24 g cm−2 in a range of [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='73] g cm−2 in the IR-dark HFSs, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='69 g cm−2 in a range of [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='04] g cm−2 in the IR-bright HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Overall, the estimated Σclump values in all HFSs studied here satisfy the empirical high- mass star formation threshold of Σcrit ⩾ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='05 g cm−2, which was derived from the mass-size relationship established using the AT- LASGAL massive clumps containing high-mass star-forming signa- tures (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', methanol masers, and HII regions, Urquhart et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This provides evidence that the central clumps in both IR-dark and IR-bright HFSs are dense enough to form high-mass stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Evidence of high-mass star formation in the IR-dark HFSs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', HFSs 1–8) has been suggested in Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2019), while the same infer- ence in the IR-bright HFSs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', HFSs 9–17) is strengthened by their associated high luminosities of Lbol ≳ 104 L⊙ (see Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' To quantitatively describe the evolutionary stage of clumps that can represent the stage of their natal HFSs in terms of high-mass star formation, we consider the bolometric luminosity to mass ra- tio Lbol/Mclump, where the bolometric luminosity of each clump, Lbol, can be found in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This is approximately taken to be the luminosity of their centrally located YSOs (Bronfman, Nyman, & May 1996;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Contreras et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020a,b, 2021) This ratio is independent of distance, and has been widely used as an indicator of the evolutionary stage of clumps (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Guzm´an et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The clumps in IR-dark and bright HFSs have a median Lbol/Mclump value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='14 L⊙/M⊙ in a range of [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='04, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='46] L⊙/M⊙, and a median value of 105 L⊙/M⊙ in a range of [3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='58, 204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='62] L⊙/M⊙, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The ratio Lbol/Mclump has been used as a diagnostic tool to probe the evolutionary stages of ob- served clumps (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Urquhart et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Giannetti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Elia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Based on the results discussed in these papers, values of Lbol/Mclump ≲ 2 have been associated with a very early evolution- ary phase of mass accretion and possibly the beginning of protostel- lar activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Whereas, ratios between 2–40 are shown to represent a later evolutionary phase where the protostar grows in mass with continuing accretion reaching the zero age main sequence around Lbol/Mclump ∼ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Beyond a ratio of ≳ 40, onset of radio emission with detection of hypercompact and UCHII regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This strongly supports our conjecture that the ensemble of 8 IR-dark HFSs are at an earlier stage of high-mass star formation than that of the 9 IR-bright HFSs (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Following this evolution, an over- all increasing trend of both Mclump and Σclump can be found from the IR-dark (223 M⊙ and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='24 g cm−2) to IR-bright (649 M⊙ and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='69 g cm−2) stage of HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 Cores in the HFSs 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 Core identification The high-resolution (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2′′–2′′) ALMA continuum data, that corre- spond to linear scales 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='02 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='03 pc at the typical distances of the IR-dark and bright HFSs, respectively, enable the identification of compact cores where stars could form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A total of 224 compact cores in the 8 IR-dark HFSs have already been identified from ASHES 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 mm continuum by Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Slightly different ap- proaches have been implemented in Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2019) and Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2021) to identify compact cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' While the former study used the Dendrogram algorithm, the later used a two-step process in which the initial identification was carried out using Dendrogram then followed by CASA–imfit to estimate the parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Examining the performance of both schemes (especially for the low-mass cores in the IR-dark HFSs) and to maintain uniformity, we use Dendro- gram alone to extract cores in the 9 IR-bright HFSs from ATOMS 3 mm, combined 12m+7m continuum data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' It is worth mentioning here that there are a suite of clump/core identification algorithms available (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Clumpfind by Williams, de Geus, & Blitz 1994;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' getsf by Men’shchikov 2021) and Dendrogram is one such robust algo- rithm widely used in similar studies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Rosolowsky et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Ginsburg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Offner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' While a comparative study, which is beyond the focus of this paper, would help highlight the MNRAS 000, 1–15 (2021) High-mass star formation in HFS cloud 5 Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Parameters of cores in HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' HFS cloud Core ID RA DEC Rcore Rcore F int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' cont Mcore Σcore Assoc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' J2000 J2000 ′′ AU mJy M⊙ g cm−2 HFS9 ALMA1 13:51:58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='35 61:15:41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='53 8242 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='63 289.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='07 1,2 HFS9 ALMA2 13:51:55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='31 61:16:05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='57 8467 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='40 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='69 0 HFS9 ALMA3 13:52:00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='74 61:15:53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='89 10190 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='70 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='66 0 HFS9 ALMA4 13:51:57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='10 61:15:51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='69 9143 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='66 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='81 4 HFS9 ALMA5 13:51:58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='09 61:15:38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='79 9639 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='43 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='53 0 HFS9 ALMA6 13:51:58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='58 61:15:33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='98 5280 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='94 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='53 4 HFS9 ALMA7 13:51:57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='87 61:15:31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='99 5323 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='86 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='46 4 HFS9 ALMA8 13:52:01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='76 61:15:25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16 6267 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='86 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='69 0 HFS9 ALMA9 13:51:57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='56 61:16:06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='71 3851 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='86 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='84 4 HFS9 ALMA10 13:52:03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='09 61:15:53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='69 3700 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='84 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='89 0 HFS9 ALMA11 13:51:58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='29 61:15:45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='57 8496 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='93 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='39 4 HFS9 ALMA12 13:51:59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='32 61:15:41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='64 8839 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='79 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='52 4 HFS10 ALMA1 15:43:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='94 54:07:35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='08 1962 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='69 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='71 2,4 HFS10 ALMA2 15:43:16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='62 54:07:14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='80 5095 254.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='36 147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='12 2,4 HFS10 ALMA3 15:43:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='36 54:07:34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='87 5213 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='49 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='06 0 HFS10 ALMA4 15:43:14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='23 54:07:27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='13 2059 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='68 0 HFS10 ALMA5 15:43:16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='91 54:07:22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='83 6973 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='55 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='26 0 HFS10 ALMA6 15:43:16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='07 54:07:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='13 3884 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='80 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='41 0 HFS10 ALMA7 15:43:17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='15 54:07:07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='51 2739 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='58 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='57 0 HFS10 ALMA8 15:43:16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='96 54:06:59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='14 2082 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='94 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='12 0 HFS10 ALMA9 15:43:15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='76 54:07:22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='42 2577 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='81 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='45 0 HFS10 ALMA10 15:43:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='49 54:07:17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='70 1277 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='64 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='64 0 HFS11 ALMA1 15:55:48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='46 52:43:07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16 5723 190.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='43 234.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='27 1,3 HFS11 ALMA2 15:55:46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='39 52:43:23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='07 2838 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='30 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='89 4 HFS11 ALMA3 15:55:47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='93 52:43:13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='53 6693 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='84 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='56 0 HFS11 ALMA4 15:55:48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='99 52:43:12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='02 2714 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='26 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='38 0 HFS11 ALMA5 15:55:48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='87 52:43:02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='43 6430 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='63 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='41 0 HFS11 ALMA6 15:55:46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='18 52:43:00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='67 1774 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='14 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='58 0 HFS12 ALMA1 16:30:58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='82 48:43:53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='58 4601 156.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='58 234.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='30 1,2 HFS12 ALMA2 16:30:58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='61 48:43:57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='44 7128 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='75 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='40 0 HFS12 ALMA3 16:30:59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='26 48:43:53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='45 4219 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='41 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='57 0 HFS12 ALMA4 16:30:57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='17 48:43:54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='18 3449 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='81 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='64 0 HFS12 ALMA5 16:30:57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='37 48:43:39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='29 6685 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='57 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='14 2,4 HFS12 ALMA6 16:31:01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='53 48:44:05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='73 2128 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='84 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='79 0 HFS12 ALMA7 16:30:59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='32 48:43:51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='84 2439 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='19 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='85 0 HFS13 ALMA1 16:38:50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='55 47:28:01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='34 7078 179.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='71 287.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='24 1,3 HFS13 ALMA2 16:38:51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='68 47:28:20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='71 2155 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='47 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='43 4 HFS13 ALMA3 16:38:51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='24 47:28:13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='13 3410 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='56 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='78 4 HFS13 ALMA4 16:38:50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='06 47:28:04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='25 9812 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='91 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='56 4 HFS13 ALMA5 16:38:49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='70 47:27:55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='82 2485 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='50 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='83 4 HFS13 ALMA6 16:38:50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='61 47:27:52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='45 4377 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='73 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='88 0 HFS13 ALMA7 16:38:51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='42 47:27:48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='24 3750 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='02 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='65 4 HFS13 ALMA8 16:38:51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='77 47:28:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='81 2432 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='20 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='92 4 HFS13 ALMA9 16:38:53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='98 47:28:02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='66 2000 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='03 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16 0 HFS13 ALMA10 16:38:51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='60 47:27:56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='79 2397 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='21 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='95 4 HFS13 ALMA11 16:38:50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='28 47:27:47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='83 2504 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='47 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='06 0 HFS14 ALMA1 16:46:06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='08 45:36:43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='76 4625 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='41 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='56 1,2 HFS14 ALMA2 16:46:07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='30 45:36:40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16 3053 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='53 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='62 4 HFS14 ALMA3 16:46:06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='88 45:36:52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='15 5639 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='07 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='87 4 HFS14 ALMA4 16:46:04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='59 45:36:53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='09 2877 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='99 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='41 0 HFS14 ALMA5 16:46:05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='99 45:36:51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='75 1966 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='63 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='45 4 HFS14 ALMA6 16:46:05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='72 45:36:48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='99 2611 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='82 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='92 4 HFS14 ALMA7 16:46:05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='04 45:36:47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='78 2059 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='52 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='42 4 HFS14 ALMA8 16:46:07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='65 45:36:39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='36 3573 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='38 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='64 0 HFS14 ALMA9 16:46:08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='43 45:36:36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='83 2181 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='54 0 HFS14 ALMA10 16:46:06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='55 45:36:39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16 8309 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='35 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='27 4 HFS15 ALMA1 17:05:11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='15 41:29:07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='74 2380 271.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='70 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='69 3,4 HFS15 ALMA2 17:05:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='23 41:29:33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='07 1467 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='24 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='73 0 HFS15 ALMA3 17:05:09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='52 41:29:06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='85 1167 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='58 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='55 0 HFS15 ALMA4 17:05:11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='84 41:29:01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='95 1300 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='38 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='97 0 HFS15 ALMA5 17:05:09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='57 41:28:57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='99 1351 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='62 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='87 0 HFS15 ALMA6 17:05:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='92 41:28:47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='71 2340 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='29 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='43 0 HFS15 ALMA7 17:05:09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='40 41:29:28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='79 1078 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='47 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='59 0 HFS15 ALMA8 17:05:12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='17 41:29:08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='80 1089 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='79 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='76 0 HFS16 ALMA1 17:26:42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='56 36:09:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='15 2885 623.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='10 196.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='75 1,3 HFS16 ALMA2 17:26:43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='61 36:09:17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='50 2002 207.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='04 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='03 4 HFS16 ALMA3 17:26:42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='96 36:09:40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='74 985 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='98 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='74 4 HFS16 ALMA4 17:26:40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='26 36:09:36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='20 1611 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='06 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='74 0 HFS16 ALMA5 17:26:45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='12 36:09:19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='71 948 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='38 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='35 0 HFS16 ALMA6 17:26:42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='95 36:09:13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='28 3054 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='69 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='03 2,4 HFS16 ALMA7 17:26:43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='59 36:09:09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='07 1436 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='35 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='47 4 HFS16 ALMA8 17:26:42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='12 36:09:20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='12 1500 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='18 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='05 0 HFS16 ALMA9 17:26:43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='38 36:09:19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='83 2449 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='63 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='47 0 HFS17 ALMA1 18:53:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='64 +1:24:46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='03 3801 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='84 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16 3,4 HFS17 ALMA2 18:53:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='07 +1:25:25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='88 6952 158.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='09 379.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='23 1,2 HFS17 ALMA3 18:53:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='41 +1:24:54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='23 4559 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='00 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='27 4 HFS17 ALMA4 18:53:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='33 +1:25:13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='90 3338 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='41 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='69 4 HFS17 ALMA5 18:53:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='53 +1:25:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='87 3220 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='02 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='29 4 HFS17 ALMA6 18:53:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='23 +1:25:19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='08 7680 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='84 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='44 2,4 HFS17 ALMA7 18:53:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='07 +1:25:30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='15 7958 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='11 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='55 0 HFS17 ALMA8 18:53:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='66 +1:25:27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='13 4193 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='00 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='93 4 HFS17 ALMA9 18:53:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='51 +1:25:37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='11 7801 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='06 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='79 0 HFS17 ALMA10 18:53:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='75 +1:26:00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='03 3824 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='05 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='35 4 HFS17 ALMA11 18:53:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='72 +1:24:44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='15 4248 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='26 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='85 0 HFS17 ALMA12 18:53:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='43 +1:24:46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='37 5070 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='12 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='56 0 HFS17 ALMA13 18:53:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='34 +1:25:09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='15 4269 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='48 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='92 0 Note: This table includes only the parameters of cores in the nine IR-bright HFSs, while the same parameters of the cores in the eight IR-dark HFSs are referred to tables 3, and 4 of Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' F int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' cont represents the integrated 3 mm continuum flux of the cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Core association ranges from 0 to 4, where 0 = prestellar candidate, 1 = molecular outflow, 2 = hot core, 3 = compact HII region, and 4 = point-like 8/24 µm object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' MNRAS 000, 1–15 (2021) 6 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 103 104 Rcore [AU] 10 2 10 1 100 101 102 103 Mcore [M ] (a1) IR-dark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 d [kpc] 103 104 Rcore [AU] 10 2 10 1 100 101 102 103 Mcore [M ] (a2) IR-bright 2 3 4 5 d [kpc] IR dark IR bright Cores in the HFSs 1 0 1 2 log(Mcore) [M ] (a3) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='33 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='74 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='59 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='44 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='89 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='06 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='27 103 104 Rcore [AU] 10 1 100 101 102 core [g cm 2] (b1) IR-dark 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 d [kpc] 103 104 Rcore [AU] 10 1 100 101 102 core [g cm 2] (b2) IR-bright 2 3 4 5 d [kpc] IR dark IR bright Cores in the HFSs 2 1 0 1 2 log( core) [g cm 2] (b3) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='96 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='34 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='68 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='77 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='68 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='66 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='54 Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Panels (a1–a3): mass (Mcore) distribution of cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Panels a1, and a2 show the Mcore distribution against the radius of cores located in the IR-dark, and IR-bright HFSs, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The colors of dots in both panels represent the distances of the cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Panel a3 displays a box-whisker plot summarising the Mcore distribution of the cores in the two IR types of HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Panels (b1–b3): same as Panels (a1–a3) but for the mass surface density (Σcore) distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In the box-whisker plots, the numbers associated with the boxes from the top to bottom represent the upper quartile, median (inside the box), and lower quartile, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The red crosses indicate the outliers outside 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 times the interquartile range either above the upper quartile or below the lower quartile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 101 102 103 Mcore, 12m + 7m [M ] 101 102 103 Mcore, 12m [M ] Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Comparison between determinations of the masses of the mas- sive cores from the nine IR-bright HFSs, each having one clump.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The core masses were derived first from the ATOMS 12m data alone, and second the combined 12m+7m data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The dashed line indicates equal mass from each set of observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' nuances of each, the overall interpretation based on the retrieved pa- rameters would remain the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Following Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2019), an intensity threshold of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 σ, a step of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 σ (the rms noise of the continuum data, see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2), and a minimum number of pixels equal to those contained in each synthesized beam (half of the beam considered in Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2019) were used as input parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The algorithm identifies the small structures, called ”leaves”, which cannot further break up into smaller structures, and are thus defined here as cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Finally, cores with integrated flux densities less than 4 σ were excluded to avoid spurious identification, where 4 σ was determined from the corre- sponding negative level (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', −4 σ) within which the interferometric sidelobe effects cannot be ruled out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A total of 86 compact cores are obtained in the 9 IR-bright HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The parameters retrieved from the Dendrogram analysis are listed in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' These include the core coordinates, radius (Rcore), and integrated flux (F int cont).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The same parameters for the compact cores in the 8 IR-dark HFSs are referred to Tables 3 and 4 of Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The number of the cores in the IR-bright HFSs found in this study is about four times greater than that reported in Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2021) for the same regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Apart from the slightly different parameter used, a possible reason is the use of the higher resolution 12m data for core extraction in Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2021) as opposed to the combined 12m+7m data used here, which will be discussed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Similar differences were noted by Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2019) where inclusion of more ex- tended emission with the 7m array leads to detection of 20% greater number of cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 Star-forming nature of cores The star-forming activity in cores can be inferred from YSO sig- natures such as outflows, hot cores, compact HII regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2020) provided the catalogues of CO and SiO outflows associated with the cores in the IR-dark HFSs while the association of hot cores and HII regions with the cores in the IR-bright HFSs are tabulated in Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2021), who complied these based on the detection of rich complex organic molecular lines, and H40α line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Presence of point- like 24 µm or slightly extended but compact 8 µm sources, which are likely to be candidate YSOs and hence could be considered as signposts of star formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' These associations are listed in the last column of Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In total, 112 out of 310 cores are protostellar ones associated with one or more star-forming signatures (see above).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The remaining 198 cores without any of these signatures are treated here as prestellar candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 Derived parameters of cores From the parameters (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', radius Rcore, and integrated flux F int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' cont.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=') of the cores derived from the Dendrogram analysis discussed in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1, other parameters such as mass and mass surface den- sities can be estimated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Cores without detectable star-forming sig- natures are roughly assigned the temperature of their natal clumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' For cores with associated star-forming signatures, the temperature MNRAS 000, 1–15 (2021) High-mass star formation in HFS cloud 7 was assumed to be 50 K for those associated with outflows (San- hueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2019), and 100 K for those associated either with hot cores or compact HII regions (Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The mass (Mcore) and mass surface density (Σcore) parameters of the cores were cal- culated following the same approach outlined in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1, where the dust opacities per gram of dust were adjusted to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9 cm2 g−1 for 1 mm and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 cm2 g−1 for 3 mm according to Ossenkopf & Henning (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The uncertainties of Mcore and Σcore are around ∼ 50% (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The derived physical parameters are listed in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' It is worth noting that for those five cores associated with compact HII regions (see Table 2) that lie in five of nine IR-bright HFSs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', HFSs 11, 13, 15, 16, 17), the continuum flux of cores would have contribution from both dust thermal emission and free-free emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The values tabulated have been subtracted for the free-free emission component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' To estimate the contribution of free-free emission, we used the H40α hydrogen recombination line observations under the assumption of local thermodynamical equilibrium and optically thin emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The free-free emission intensity was estimated via the fol- lowing relation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Motte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022): Sff = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='43 × 10−4SRRL[ ν GHz]−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1[Te K ]1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='15(1 + NHe NH )−1, (1) where SRRL is the integrated intensity of H40α over its velocity extent;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' ν = 99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 GHz is the rest frequency of H40α observed in the ATOMS data;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' and we assume the electron temperature of Te = 6000 K as well as a relative abundance of helium to hydrogen of NHe/NH = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='08.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' We assume an upper limit of Te = 6000 K to avoid over subtraction of free-free continuum for the small scale ex- tracted cores (Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The above estimated free-free emis- sion intensity was subsequently subtracted from the 3 mm contin- uum image to yield the dust continuum emission image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Figure 2 (a–b) show the distribution of Mcore and Σcore as a func- tion of Rcore for the cores in both IR-dark and bright HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The colors in dots in the figure indicate the distance distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The cores in both IR types of HFSs have a similar radius range of [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='9, 10]×103 AU, with an average radius ratio of ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 of cores in the IR-dark HFSs to those in the IR-bright HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' As suggested by Lou- vet et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2021, this can be understood since the similar typical spatial resolutions of the ALMA observations toward the two IR-type HFSs can yield the close derived sizes of the extracted cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Considering the median values of the mass and mass surface den- sity in the IR-bright HFSs (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='7 M⊙ and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 g cm−2) and the IR-dark HFSs (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 M⊙ and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 g cm−2), it is seen that the mass and mass surface density is higher by factors of 6 and 3, respectively in the IR-bright HFSs (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2 c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2 (a–b), this difference can be seen to be independent of the source distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Instead, it could be in part a result of the observation bias caused by the different maxi- mum recoverable scales (MRS) in the ASHES (∼ 20′′) and ATOMS (∼ 60′′) combined 12m+7m data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' As suggested in Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2019), the higher MRS of the ATOMS combined data could intrin- sically lead to higher fluxes and thus flux-derived parameters (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', mass and mass surface densities) of cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Different mass sensitiv- ity of the surveys could also contribute since in the higher sensitiv- ity ASHES data, more low-mass cores are detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' However, it is worth noting that this observation bias could not affect significantly the most massive cores (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', nine cores with the highest Mcore and Σcore values in panels a–b), as can be seen from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Hence, in the analysis that follows, we focus on the most massive cores in the IR-bright sample of HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3, we compare the masses esti- mated from the ATOMS 12m continuum data alone with a MRS of ∼ 18 ′′(similar to the MRS of the ASHES data) with that de- rived from the 12m+7m combined data having a MRS of ∼ 60′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' From this comparison, we estimate a nominal factor of ∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 on av- erage higher mass estimates for the cores extracted in the IR-bright HFSs using ATOMS 12m+7m data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' As is also seen in the figure, the most massive cores in the IR-bright HFSs can be clearly distin- guished from the majority of low mass cores in the distributions of both Mcore and Σcore (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2 a2 and b2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This trend could be ei- ther a consequence of the limited HFS sample investigated here or the evolutionary phase of the IR-bright HFSs, the latter being related to their preferred central location and sufficiently long accretion his- tory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Certainly, larger sample of such IR-dark and IR-bright HFSs are required to examine the above possibilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 YSOs in the HFSs Investigating the spatial distribution of associated YSOs helps in un- derstanding star formation in HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' From the 24 µm point source catalogue of the Galactic plane from Spitzer/MIPSGAL (Gutermuth & Heyer 2015), we searched for point sources associated with the HFS sample studied here, and obtained their 24 µm photometric fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Here, we have used different search areas depending on the spatial extent of the HFSs in the 8 µm image (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', image size in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 1, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5′–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In addition to the catalogued sources, we identified ten bright, point-like sources in the 24 µm MIPSGAL images that were not included in the MIPSGAL point source catalogue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' These were identified in the HFSs 9, 11, 13, 14, 15, 16, and 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' For these sources, the photometry was performed manually using appropriate circular annulus whose inner and outer radii can represent well the point-like source and its associated background.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Since the typical distance of the HFSs studied here is ∼ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 kpc, some of the 24 µm point sources obtained above could be fore- ground/background stars along the line of sight of the HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' To al- leviate this, we correlate the identified sources with Gaia EDR3 data within a radius of 2′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The parallax distances of the Gaia-matched sources were subsequently calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' As a rough approximation, we assume that the sources with distance estimates more than 10% of the nearest HFS’s distance are foreground/background stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' It is to be noted that only a few sources were filtered out as fore- ground/background stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Finally, 175 point sources that are likely associated with the HFSs studied here are retained for further anal- ysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Furthermore, we classify the identified YSOs cross-matching (within 2′′ radius) using the SPICY catalogue that compiles ∼ 120,000 Spitzer/IRAC candidate YSOs for the Inner Galactic Midplane (Kuhn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This catalogue contains five classes of YSOs, including Class I, Flat-spectrum, Class II, Class III, and “Un- certain” YSOs that cannot be placed in any of the above four classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Class I YSOs are highly embedded protostars with the bolometric lu- minosity dominated by a spherical infalling envelope;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Class II YSOs are young stars surrounded by a substantial accreting disk;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Class III YSOs are young stars with most of their disk mass being dissipated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Flat spectrum YSOs are those in between Class I and Class II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' From the above exercise, 122 of the 175 detected 24 µm sources are clas- sified as YSOs (29 and 93 in the IR-dark and IR-bright HFSs, re- spectively) and 53 as “unknown” sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' To confirm the nature of the “unknown” sources requires detailed investigation of the photo- metric information over multiple wavelengths, which is beyond the scope of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The YSO luminosity can be directly linked to the star-formation process, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', either low or high-mass star formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In previous studies, the 24 µm photometric flux of both low and high-mass pro- tostellar sources was found to correlate well with their bolometric luminosity (Lbol, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Dunham et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Ragan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Ap- MNRAS 000, 1–15 (2021) 8 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Statistical number of outflows in HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' HFS ID N (outflow lobes) Filament-aligned Filament-not-aligned (%) HFS1 5 2 3 (60 ) HFS2 10 0 10 (100) HFS3 3 0 3 (100) HFS4 7 1 6 (86 ) HFS5 – – – (– ) HFS6 2 0 2 (100) HFS7 13 1 12 (92 ) HFS8 3 0 3 (100) HFS9 2 0 2 (100) HFS10 2 0 2 (100) HFS11 1 0 1 (100) HFS12 2 0 2 (100) HFS13 2 0 2 (100) HFS14 2 0 2 (100) HFS15 2 1 1 (50 ) HFS16 2 0 2 (100) HFS17 7 1 6 (80 ) Note: The statistics was made from Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2020) and Baug et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022 (under preparation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' plying this empirical correlation, we estimated the luminosities of the 175 candidate YSOs from their 24 µm fluxes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Except for the one luminous YSO (Lbol ∼ 104 L⊙;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 6), the candidate YSOs in the IR-dark HFSs have low luminosities of Lbol < 103 L⊙ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Note that the location of the one luminous YSO is more than 1 pc from the central hub of HFS 3, and thus do not conflict with the classifica- tion of the host HFS as IR-dark type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In case of the IR-bright HFSs, the majority of the candidate YSOs are also found to have low lu- minosities though there are 12 high-luminosity sources found with Lbol ∼ [104, 105] L⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The presence of a significant population of high-luminosity YSOs in the IR-bright HFSs agrees well with their more evolved stage inferred earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 Effects of outflow feedback on star formation The final stellar mass depends not only on the initial mass reser- voir of the natal clump but also on the mass accretion from the hub- composing filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' However, several observational studies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Schneider et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020) and theoretical simulations have shown the profound influence of stellar and protostellar feedback processes like collimated jets and bipolar outflows (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Offner & Chaban 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Guszejnov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Verliat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022), and radiative heating (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bate 2009, 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Krumholz & Thompson 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Hennebelle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020, 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Grudi´c et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022) in inhibiting mass accretion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Hence, for the protostar to grow in mass requires the strong accretion inflow to be least impacted by the above feed- back processes in the early stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' As discussed in Dale & Bonnell (2011);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2020), ionizing radiation, stellar wind and ion- izing gas (HII regions) are found to channel out through pre-existing, inter-filamentary voids without dispelling the natal clump or inhibit- ing the mass inflow through filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In this study, we focus on the influence of outflows since these are pronounced in our HFSs sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The protostar’s spin, and hence the orientation of the outflows, is inherited from the core scale where the angular momentum is hi- erarchically transferred from the natal cloud through the filament onto the star-forming core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Given that the large-scale filamentary in- flow is either onto the short axes of the filament or along the long axis, the alignment of the outflows is expected to be either prefer- entially parallel or perpendicular to the filament.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Anathpindika & Whitworth (2008) found observational evidence that outflows are preferentially aligned perpendicular to the filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In compari- son, observational results presented by Davis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2009) and more recently by Stephens et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2017);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Baug et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2021) reveal no preferred outflow-filament orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Several other studies have shown that the rotation of the protostar could be independent of the parent filament (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Tatematsu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2016) or could evolve significantly during formation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Offner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The outflow-filament alignment has implication on the form- ing protocluster in HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' If the outflows run along the individual fil- aments, the filament-rooted longitudinal mass flows will be inhibited or halted which will significantly hinder the mass growth of young stars embedded in the central hubs (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' To understand the potential effect of outflows on star formation in the HFSs studied here, we compiled the parameters (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', position, and orientation) of the associated outflows from Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2020) and Baug et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' under preparation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2020) have catalogued the CO and SiO outflows of the 8 IR-dark HFSs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', HFSs 1–8) taken from the ASHES survey data at ∼ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 mm (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2), while Baug et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2022) provide the HCO+ outflows of the 9 IR-bright HFSs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', HFSs 9–17) taken from the ATOMS survey data at ∼ 3 mm (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' As indicated in Table 3, we obtain 60 outflow lobes for all the HFSs investigated here, where 38 and 22 outflow lobes are associated with the IR-dark and IR-bright HFSs, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Note that we have considered the individual lobes of outflows here instead of the entire outflow entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The location and orientation of the identified outflows are dis- played in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 4, where the red/blue arrows indicate the estimated orientation and extent of the red/blue-shifted lobes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' As evident from the figure, most of the outflows have spatial extents smaller than the dimension of the host HFS subclouds (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', the central dense re- gions covered by ALMA observations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This result indicates that the outflows might have not escaped the dense regions of the HFSs in early stages of star formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' However, this result may be an ob- servational consequence due to the lack of total power in the anal- ysis made in the ASHES and ATOMS surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' But, if the outflows can escape the dense regions of the HFSs, then their direction can be traced by extending the identified outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' These are shown as white arrows in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The statistics of the outflows and their orientation are tabulated in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' For HFS 5 there are no identifiable outflows while HFS 1 and 15 have 60 %, and 50% of filament-aligned outflows, respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Except for these three HFSs, all the other HFSs have the ma- jority of outflows (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', ⩾ 86%) not aligned with the individual fil- aments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' There are a couple of caveats in the above analysis which need to be highlighted here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Firstly, the outflow identifications in the two studies used here are probably incomplete due to the presence of multiple overlapping outflows which tend to occur in high-mass star formation regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Secondly, projection effects would also in- fluence the observed orientations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Last but not the least, one needs to study more number of HFSs-outflow systems to enable a more robust statistical investigation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Keeping the above caveats in mind, our results show that the observed outflows (1) do not preferentially align parallel or perpendicular to the filaments and (2) tend to be oriented toward the voids of the hub-composing filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This sug- gests that, similar to the effect of other feedback processes, outflows render a limited effect on filamentary mass inflow and thus on the mass growth of young stars being formed in the centrally located hubs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Moreover, the inference obtained above agrees with the quanti- tative analysis of the related energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' For the IR-dark HFSs, Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2020) found that the outflow-induced turbulence cannot sustain the internal turbulence of the natal clumps as the outflow energy rate is around two orders of magnitude less than the turbulent en- MNRAS 000, 1–15 (2021) High-mass star formation in HFS cloud 9 Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Zoom-in images of Spitzer 8 µm and 24 µm for the central regions of the IR-dark (in top row) and bright (in bottom row) HFS clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The contours represent 870 µm dust continuum from the ATLASGAL survey (Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The blue/red arrows are blue/red-shifted outflowing lobes identified by Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' They are purposely extended as white arrows for easy comparison of the relative orientation between the outflows and hub-composing filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The dashed loop delineates the central subcloud field covered by our ALMA observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The red circles indicate the cores identified from the ALMA continuum data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The dashed curves identify the filamentary structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 and 24 µm beams are shown at the bottom right-hand corner of the corresponding panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' ergy dissipation rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' These authors also infer the outflow energy to be much smaller than the gravitational energy of the clumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' For the more evolved IR-bright HFSs investigated here, three of which (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='., HFSs 11–13) were studied in terms of the outflow dynamics in Baug et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2021), they argued that the kinetic energy of outflows alone cannot balance the gravitational binding energy of the hosting clumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Taken together, these results indicate the limited effect of outflows on the destruction of their host HFSs in early stages and thus on the progress of star formation therein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' However, as men- tioned above, a larger sample and improved statistics on filament- outflow alignment is required to conclusively interpret simulations of outflow feedback (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Offner & Chaban 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Guszejnov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Verliat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022) in the context of HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' MNRAS 000, 1–15 (2021) HFS9/I13484-6100 8μm 24μm 61°15\'00" 8 8 Dec (J2000) 30" 12 12 1 10 3 16\'00" 9 2 30" 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1pc 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1pc .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 00s 51m56s 52s RA (J2000)HFS1 /G010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='991-0b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='082 8μm 24pm 19°27\'00" Dec (J2000) 30" 16 16 X224 224 302 28\'00" 25 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 19 13 13 1512 1 6 6 30" 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1pc 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1pc .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 18h10m10s 08s 06s 04s RA (J2000)10 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='00 offset [pc] 10 1 100 101 102 (b) ALMA cores in IR-bright HFSs 100 200 300 Mcore (M ) 10 1 100 101 102 core [g cm 2] (a) ALMA cores in IR-dark HFSs 10 20 30 Mcore (M ) Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Distribution of mass surface density of cores in the HFSs against distance from the HFS centre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The colors in circles reflect the mass distribu- tion of the cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Panels (a) and (b) display the cores in the IR-dark, and IR- bright HFSs, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In both panels, the protostellar cores are indicated in circles with inserted pluses while candidate starless cores are in empty circles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Circles with black dots inside are the centrally located most massive cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The vertical dotted lines indicate the average distance weighted by the mass surface density of cores, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16 pc in panel a, and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='04 pc in panel b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 4 DISCUSSION 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 Spatial distribution of cores and YSOs Cores in the HFSs Figure 5 shows the distribution of the mass surface density (Σcore) of the cores as a function of the distance from the centre of the host HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The centre is defined to be the position where the intensity of the 870 µm emission peaks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Circles with inserted plus symbols distinguish the protostellar cores from that of the candidate star- less ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The centrally located most massive core of each HFS has an additional dot symbol included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Further, the plotted circles are colour-coded to represent the core mass (Mcore) distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Sev- eral interesting trends can be deciphered from these plots and are discussed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The number of cores is more in the central region with only a sparse population seen beyond ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The massive and dense cores in the IR-dark HFSs are located within ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='25 pc, whereas, in IR-bright HFSs these are confined to the innermost region of ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='05 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' All nine centrally located most massive cores in IR-bright HFSs are forming high-mass stars as inferred from the associated high luminosities of > 104 L⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This supports the scenario that in HFSs, the central areas of hubs are preferential sites for high-mass star formation where mass accretion occurs from the hub-composing filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The ideal location of such cores in IR-dark HFSs also qualifies them as potential high-mass star-forming cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The steep gradient seen in the spatial distribution of the most mas- sive and dense cores towards the inner most region in IR-bright HFSs suggests a more centrally peaked clustering as opposed to the wider distribution observed in the IR-dark HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' That is, the spatial distri- bution of massive dense cores peaks at ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16 pc in IR-dark HFSs, but at ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='04 pc in IR-bright HFSs, as indicated in the dotted lines in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' These represent the average distance from the HFS centre weighted by the mass surface density over all the cores in each IR type of HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The wider distribution of massive cores in the IR-dark hubs is in good agreement with the results of Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' These authors propose that cores in IR-dark HFSs originate from hierarchical subclustering rather than from centrally peaked cluster- ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The observed difference in the two IR types could suggest trans- formation to a centrally peaked clustering following the evolution of the host HFSs from the IR-dark to IR-bright stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Scarcity of high-mass prestellar cores (of Mcore ⩾ 30 M⊙ over the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1 pc scale, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sanhueza et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2017, 2019), the progenitors of high-mass stars, is observed in our sample of IR-dark HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Here, none of the detected cores have masses greater than the threshold de- fined above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This allows us to conjecture that high-mass star forma- tion could involve a dynamical, continuous mass accretion with evo- lution, which will be discussed further in Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' If we consider the prestellar cores in the IR-bright sample, only 11 (∼ 13% of cores) have mass estimates greater than 30 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' For these to form high- mass stars, the same mass accretion process should ensue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' However, the starless or prestellar nature of those cores needs to be confirmed through future higher-resolution observations with a more sensitive outflow tracer (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', CO 1–0), YSOs in the HFS clouds Figure 6 presents the distribution of bolometric luminosity (Lbol) of candidate YSOs against the distance from the centre of the host HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In the IR-dark HFSs, the YSO’s luminosity distribution is nearly constant at a low luminosity level (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', ∼ 100 L⊙) typi- cal of low-mass protostars, regardless of the distance of the YSOs from the centre of the HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Only one YSO with Lbol ∼ 104 L⊙, that is typical of high-mass protostars, is found at distance > 1 pc from the centre of the host HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Furthermore, only two HFSs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', HFSs 6, and 8) have identified YSOs (one each) within the hub- clump (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', central clump in the hub) region and their luminosities are low (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Lbol ≲ 100 L⊙).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In the case of the IR-bright HFSs, except for the three YSOs having Lbol ∼ 103–104 L⊙ located in a distance range of [1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1] pc from the center of HFS 13, all of the YSOs show a decreasing trend in luminosity from high (≳ 104 L⊙) to low (< 100 L⊙) luminosity values with the distance from the centre of the host HFSs up to ∼ 2 pc, beyond which the YSOs display nearly constant low luminosity values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Note that given the not so high luminsities (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', < 104 L⊙) of the above mentioned three luminous YSOs far from the centre of the host HFS 13, we assume that they could represent a cluster of intermediate and/or low-mass young stars instead of high-mass protostars, which agrees with the apparent multiplicity of these three YSOs seen at 8 µm but not well resolved at 24 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In view of this, the observed decreas- ing trend suggests a luminosity/mass-segregated cluster formation picture in the IR-bright stage of HFSs, in which high-mass stars represented by high luminosities prefer to form in the central area of HFSs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', the hub-clump region), while low-mass stars repre- sented by low luminosities tend to form in the outskirts of HFSs up to several pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In addition, the number of high-luminosity YSOs of Lbol > 104 L⊙ found in IR-bright HFSs is larger (eleven;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' see star symbols in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 6b) compared to the IR-dark HFSs where only one are detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Moreover, almost each of the IR-bright HFSs has a corresponding high-luminosity YSO within the hub-clump region, in contrast to the absence of high-luminosity YSOs within the same region of the IR-dark HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The above distribution of YSOs pos- sibly implies an evolutionary sequence from a relatively quiescent, IR-dark phase to an active, IR-bright phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' MNRAS 000, 1–15 (2021) High-mass star formation in HFS cloud 11 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5 offset [pc] (b) (b) (b) (b) (b) (b) (b) (b) (b) HFS9 HFS10 HFS11 HFS12 HFS13 HFS14 HFS15 HFS16 HFS17 0 1 2 3 4 5 offset [pc] 0 2 4 6 log(Lbol) [L⊙] (a) (a) (a) (a) (a) (a) (a) HFS1 HFS2 HFS3 HFS4 HFS6 HFS7 HFS8 Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Luminosity of YSOs bright at 24 µm associated with the IR-dark (panel a) and IR-bright HFSs (panel b) as a function of the distance from the HFS centre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The dashed lines indicate the typical size of the centrally-located clump for all HFSs, as defined in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Stars having luminosity above 104 L⊙ are shown as star symbols as opposed to those having luminosity below 104 L⊙ shown as triangle symbols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 Multi-scale mass transfer and high-mass star formation Figure 7 presents the mass distribution of the central massive clumps of the HFSs (in panel a) and their embedded massive cores (in panel b) against the Lbol/Mclump ratio of the clumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The colors in circles in the figure represent the mass surface density of the sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Note that, for this analysis, we have only considered the most massive cores since 1) they are (potential) sites of high-mass star formation, and 2) their mass and surface density estimates are not significantly affected by the observation bias caused by the dif- ferent MRSs associated with the ASHES and ATOMS data (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' As shown in the figure, the IR-dark and IR-bright stages of HFSs can be well represented by the Lbol/Mclump ratios of the clumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The mass and mass surface density of the central clumps show a marginal increase of a factor of ∼ 3 (on average) from the IR-dark to IR-bright stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In comparison, for the embedded mas- sive cores, the estimated values of the above parameters are en- hanced by a factor of ∼ 24 (on average) from the IR-dark to IR- bright stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Additionally, as previously discussed (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1), high-mass protostars (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', with Lbol ≳ 104 L⊙) are only identi- fied in the IR-bright HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' These results suggest that sufficient mass accumulation from the large-scale, hub-composing filaments is re- quired for the central clumps in IR-dark HFSs to evolve to clumps with high-mass protostars in IR-bright HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This process would continue till the hub-composing filaments are completely dispersed by stellar feedback (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', stellar winds, and ionization).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Further, the associated massive cores accumulate the required mass from their natal clumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Thus, a multi-scale mass accretion/transfer scenario unfolds in HFSs, where the mass accretion/transfer proceeds from the large-scale hub-composing filaments, through clumps, down to cores where high-mass stars finally form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Consistent with the ob- served trend, the mass and mass surface density of the clumps, and cores should be higher in the IR-bright stage of HFSs since the ac- cretion timescales of these density structures are more extended in the more evolved stage as along as the large-scale hub-composing filaments contain sufficient gas material.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This multi-scale mass ac- cretion process has also been observed toward one of the HFSs stud- ied here (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', HFS 17) in Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' These authors reveal the presence of the multi-scale mass accretion flows, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', accretion from clumps onto cores, and that from cores to embedded protostars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The above results from a selected sub-sample of the ASHES and ATOMS surveys agree well with the filament to cluster (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', F2C) evolutionary sequence discussed in a recent statistical study by Kumar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Based on a large sample of ∼ 3700 candi- date HFSs using far-infrared Herschel dust continuum maps at 70– 500 µm from the Hi-Gal survey, these authors propose four stages involved in the formation of high-mass stars in the context of HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' These are: I) formation of individual dense filaments by mechanisms such as cloud-cloud collisions, and compression from local turbu- lence;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' II) flow driven filaments overlap wherein intra-filamentary matter in the HFS cloud combine to form a hub with density am- plification making them more conducive to star formation as com- pared to the filaments;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' III) formation of high-mass stars in the den- sity amplified hub where the generated gravitational potential differ- ence between the hub and the filaments can trigger and direct the filament-rooted longitudinal flows toward the centrally-located hub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' IV) formation of “classical” (optically visible) HII regions in the hub along with a small embedded cluster of stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In this stage, the radiation pressure and ionization feedback from the newly forming massive stars channel out of the hub through the inter-filamentary diffuse cavities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' These four stages, where a multi-scale mass accre- tion/transfer process can be expected from hub-composing filaments through clumps (hubs) to cores (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Stage II and III), finally lead to a mass-segregated embedded cluster with high-mass stars preferen- tially formed in the hub and low-mass stars in the hub-composing filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' From the observational study presented here, the IR-dark HFSs resemble Stage II, where the density-enhanced hub has formed and is in a relatively quiescent phase of star formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Presence of low- luminosity YSOs outside the hub-clump region implies onset of low- mass star formation in the HFS cloud and/or individual filaments while the longitudinal flows continue to feed matter to the central hub which are devoid of high-luminosity sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In comparison, the observational features seen in IR-bright HFSs are characteris- tic of Stage III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In this sample, in addition to a similar picture of low-mass star formation in the entire HFS cloud, a small, mass- segregated embedded cluster of YSOs (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 6b), in which high- luminosity YSOs (≳ 104 L⊙) typical of high-mass protostars are preferentially located in the hub-clump region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Interestingly, the ori- entation of outflows along the low density, inter-filamentary voids (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4) also gives clues for channelling out radiation pressure MNRAS 000, 1–15 (2021) 12 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 10 1 100 101 102 Lbol/Mclump [L /M ] 102 103 Mclump [M ] HFS14 HFS16 (a) IR-bright IR-dark 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='0 clump [g cm 2] 10 1 100 101 102 Lbol/Mclump [L /M ] 101 102 103 Mmax core [M ] (b) IR-bright IR-dark 20 40 60 core [g cm 2] Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Mass distribution of the central massive clumps (panel a) and their embedded most massive cores (panel b) in the two IR types of HFS against the the Lbol/Mclump ratio of the clumps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The color-coded circles reflect the mass surface density of the sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The Lbol/Mclump ratio of the clumps represent the evolutionary stage of high-mass star formation of the HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' and ionization feedback in the next evolutionary stage (IV) of the classical HII regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Recent studies of molecular clouds found evidence for multi-scale hierarchical fragmentation cascade (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', from clouds, through fila- ments, clumps and cores, down to protostars, see e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Elia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Thomasson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022) probably as a major vector of star formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In conjunction with the latest theoretical models such as GHC (V´azquez-Semadeni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2019) and I2 (Padoan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2020), there seems to be a general consensus which can favor high-mass star formation in HFSs through a multi-scale mass accretion/transfer process that finally can lead to a mass-segregated cluster of stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Notwithstanding the selection bias (see Sect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3), one may con- sider the observed distinct mass distribution of the central massive clumps and their most massive cores as an evidence for the above processes in play in HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Towards the above efforts and to put more robust constraints to theoretical models, companion papers (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Yang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022, in prep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=') are in the pipeline on high- resolution, multi-scale (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', from hub-composing filaments, clumps, to cores) kinematic and dynamical studies dedicated to the HFSs in- vestigated here using the spectral line data from the same surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' For example, the GHC and I2 models agree on gravity-driven mass– accretion on small scales (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', cores), however, they predict two dis- tinct drivers on larger scales for the multi-scale mass accretion pro- cess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The former strongly favors a gravity–driven hierarchical mass accretion while the latter advocates for a turbulence–driven mass in- flow/accretion, which can be disentangled with the multi-scale kine- matic and dynamical studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 5 SUMMARY AND CONCLUSIONS We have presented a statistical study of a sample of 17 high-mass star formation HFSs using high-angular resolution (∼ 1–2′′) ALMA 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 mm and 3 mm continuum data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The statistical results have helped shed light on the high-mass star formation scenario in HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Our main results can be summarised as follows: The 17 HFSs are selected from the target lists of the ASHES 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3 mm and ATOMS 3 mm surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' They are identifiable in the Spitzer 8 µm image with hub-composing filaments intersecting at the central hub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' All the hub-composing filaments appear as elon- gated dark lanes in 8 µm emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Based on the different IR types of the hubs, the HFSs are divided into 8 IR-dark and 9 IR-bright HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The IR-dark HFSs contain an IR-dark hub without detectable IR emission shortward of 70 µm, while the IR-bright HFSs have an IR-bright hub with high-mass protostars in the same wavelength regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The two IR types can represent an evolutionary sequence of high-mass star formation HFSs from the IR-dark to IR-bright stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The 17 central massive clumps are identified in their natal HFSs from the available ATLASGAL 870 µm continuum data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' In addition, 310 embedded cores are extracted from the ALMA continuum data, including 224 from the IR-dark HFSs, and 86 from the IR-bright HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The massive, dense cores in the two IR types of HFSs are pre- dominantly distributed in the central hub-clump region of HFSs of radius 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='25 pc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' For IR-dark HFSs, the cores peak within ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16 pc of the centre displaying a hierarchical sub-clustering mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This transforms to a centrally-peaked clustering mode in IR-bright HFSs where the cores peak within ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='04 pc of the centre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The central massive clumps and their associated most massive cores in HFSs show a trend of increasing mass and mass surface density with the evolution of HFSs from the IR-dark to IR-bright stage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This could be a natural result of the multi-scale mass accre- tion/transfer scenario in HFSs from the hub-composing filaments through clumps to cores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A total of 122 candidate YSOs associated with the 17 HFSs are retrieved from the combined catalogues of the archival Spitzer/MIPSGAL 24 µm point sources and the Spitzer/IRAC candi- date YSOs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Their stellar bolometric luminosities are estimated from the 24 µm flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' From the spatial distributions of YSOs in the HFSs, we find the picture of a mass-segregated cluster of YSOs in which high-luminosity YSOs typical of high-mass protostars are preferen- tially located in the central hub-clump region, and surrounded by a population of low-luminosity YSOs typical of low-mass protostars in the entire HFS cloud extending to several parsecs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' From qualitative analysis of the relative orientation between the outflow and hub-composing filaments in all the HFSs studied here, most of the outflows are found oriented toward the lower den- sity inter-filamentary cavities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This suggests that outflow feedback would have a limited effect on the disruption of the HFS clouds and ongoing star formation therein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' From the observed facts of the trend on multi-scales (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=',' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' clumps and cores) of increasing mass and mass surface density with evolu- tion from IR-dark to IR-bright stage,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' the mass-segregated cluster of YSOs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' and the preferential escape directions of outflow feedback,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' we conclude that high-mass star formation in the HFSs can be de- scribed by a multi-scale mass accretion/transfer scenario,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' from hub- MNRAS 000,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 1–15 (2021) High-mass star formation in HFS cloud 13 composing filaments through clumps down to cores,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' that can natu- rally lead to a mass-segregated cluster of stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' To reveal the detailed physics related to the multi-scale accretion scenario requires further investigations, which will be carried out in our future multi-scale kinematic and dynamical studies dedicated to the HFSs investigated here using the high-resolution spectral line data from both ATOMS and ASHES surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' ACKNOWLEDGEMENTS We thank the anonymous referee for comments and suggestions that greatly improved the quality of this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This work has been supported by the National Key R&D Program of China (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022YFA1603101).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu is supported by National Nat- ural Science Foundation of China (NSFC) through the grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='12103045.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu acknowledges the supports by NSFC through grants No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='12073061 and No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='12122307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' PS was partially supported by a Grant-in-Aid for Scientific Research (KAKENHI Number 22H01271) of the Japan Society for the Promotion of Science (JSPS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Qin is supported by NSFC under No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='12033005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' AS gratefully acknowledges support by the Fondecyt Regular (project code 1220610).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This research was carried out in part at the Jet Propulsion Laboratory, which is operated by the California Insti- tute of Technology under a contract with the National Aeronau- tics and Space Administration (80NM0018D0004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', AS and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' gratefully acknowledges support by the ANID BASAL projects ACE210002 and FB210003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' is supported by the Basic Sci- ence Research Program through the National Research Founda- tion of Korea (NRF) funded by the Ministry of Education, Sci- ence and Technology(NRF-2019R1A2C1010851), and by the Ko- rea Astronomy and Space Science Institute grant funded by the Ko- rea government (MSIT) (Project No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2022-1-840-05).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This work is supported by the international partnership program of Chinese Academy of Sciences through grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='114231KYSB20200009, and Shanghai Pujiang Program 20PJ1415500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This paper makes use of the following ALMA data: ADS/JAO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='ALMA#2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='00685.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='S and 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='01539.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' ALMA is a partnership of ESO (represent- ing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Re- public of Korea), in cooperation with the Republic of Chile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This research made use of astrodendro, a Python package to compute dendrograms of Astronomical data (http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' dendrograms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='org/).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' This research made use of Astropy, a community-developed core Python package for Astronomy (As- tropy Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' DATA AVAILABILITY The data underlying this article will be shared on reasonable request to the corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' REFERENCES Anderson M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Peretto N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Ragan S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Rigby A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Avison A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Duarte-Cabral A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Fuller G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2021, MNRAS, 508, 2964.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/stab2674 Andr´e P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Men’shchikov A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bontemps S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', K¨onyves V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Motte F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Schnei- der N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Didelon P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2010, A&A, 518, L102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004- 6361/201014666 Andr´e P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Arzoumanian D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', K¨onyves V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Shimajiri Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Palmeirim P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2019, A&A, 629, L4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004-6361/201935915 Anathpindika S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Whitworth A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2008, A&A, 487, 605.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004- 6361:200810308 Astropy Collaboration, Price-Whelan A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sip˝ocz B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', G¨unther H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Lim P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Crawford S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Conseil S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2018, AJ, 156, 123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-3881/aabc4f Bate M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2009, MNRAS, 392, 1363.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1365- 2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='14165.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='x Bate M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2012, MNRAS, 419, 3115.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1365- 2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='19955.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='x Baug T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wang K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wu Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Li D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Tang M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2021, MNRAS, 507, 4316.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/stab1902 Beltr´an M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Rivilla V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Kumar M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Cesaroni R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Galli D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022, A&A, 660, L4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004-6361/202243361 Beuther H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Mottram J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Ahmadi A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bosco F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Linz H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Henning T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Klaassen P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2018, A&A, 617, A100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004- 6361/201833021 Bonnell I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bate M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Clarke C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Pringle J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2001, MNRAS, 323, 785.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1046/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1365-8711.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='04270.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='x Bronfman L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Nyman L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', May J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 1996, A&AS, 115, 81 Chen H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wright M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Busquet G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Lin Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Olguin F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2019, ApJ, 875, 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4357/ab0f3e Chevance M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Krumholz M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', McLeod A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Ostriker E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Rosolowsky E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sternberg A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022, arXiv, arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='09570 Contreras Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Schuller F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Urquhart J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Csengeri T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wyrowski F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Beuther H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bontemps S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2013, A&A, 549, A45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004- 6361/201220155 Dale J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bonnell I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2011, MNRAS, 414, 321.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1365- 2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='18392.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='x Dunham M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Crapsi A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Evans N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bourke T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Huard T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Myers P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Kauffmann J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2008, ApJS, 179, 249.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1086/591085 Davis C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Froebrich D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Stanke T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Megeath S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Kumar M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Adam- son A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Eisl¨offel J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2009, A&A, 496, 153.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004- 6361:200811096 Elia D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Strafella F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Dib S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Schneider N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Hennebelle P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Pezzuto S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Molinari S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2018, MNRAS, 481, 509.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/sty2170 Elia D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Molinari S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Schisano E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Soler J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Merello M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Russeil D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Veneziani M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022, arXiv, arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='05573 Foster J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Arce H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Kassis M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sanhueza P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Jackson J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Finn S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Offner S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2014, ApJ, 791, 108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1088/0004-637X/791/2/108 Giannetti A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Leurini S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wyrowski F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Urquhart J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Csengeri T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Menten K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', K¨onig C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2017, A&A, 603, A33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004- 6361/201630048 Ginsburg A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Henkel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Ao Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Riquelme D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Kauffmann J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Pillai T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Mills E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2016, A&A, 586, A50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004- 6361/201526100 Goodman A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Pineda J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Schnee S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2009, ApJ, 692, 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1088/0004-637X/692/1/91 Grudi´c M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Guszejnov D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Offner S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Rosen A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Raju A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Faucher-Gigu`ere C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Hopkins P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022, MNRAS, 512, 216.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/stac526 Guszejnov D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Grudi´c M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Hopkins P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Offner S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Faucher-Gigu`ere C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2020, MNRAS, 496, 5072.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/staa1883 Guszejnov D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Grudi´c M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Hopkins P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Offner S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Faucher-Gigu`ere C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2021, MNRAS, 502, 3646.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/stab278 Guo W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Chen X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Feng J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sun L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wang C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Su Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sun Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2021, ApJ, 921, 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4357/ac15fe Gutermuth R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Heyer M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2015, AJ, 149, 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1088/0004- 6256/149/2/64 Guzm´an A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sanhueza P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Contreras Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Smith H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Jackson J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Hoq S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Rathborne J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2015, ApJ, 815, 130.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1088/0004- 637X/815/2/130 Hacar A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Clark S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Heitsch F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Kainulainen J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Panopoulou G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Seifried D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Smith R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022, arXiv, arXiv:2203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='09562 Hennebelle P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Commerc¸on B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Lee Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Chabrier G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2020, ApJ, 904, 194.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4357/abbfab Hennebelle P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Lebreuilly U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Colman T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Elia D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Fuller G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Leurini S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Nony T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022, arXiv, arXiv:2210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='12475 Issac N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Tej A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Varricatt W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Vig S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Ishwara Chandra C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Schultheis M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2019, MNRAS, 485, 1775.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/stz466 Krumholz M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Thompson T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2012, ApJ, 760, 155.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1088/0004- 637X/760/2/155 Kuhn M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', de Souza R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Krone-Martins A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Castro-Ginard A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Ishida E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Povich M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Hillenbrand L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2021, ApJS, 254, 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' MNRAS 000, 1–15 (2021) 14 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4365/abe465 Kumar M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Palmeirim P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Arzoumanian D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Inutsuka S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2020, A&A, 642, A87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004-6361/202038232 Kumar M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Arzoumanian D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Men’shchikov A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Palmeirim P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Mat- sumura M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Inutsuka S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022, A&A, 658, A114.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004- 6361/202140363 Larson R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2003, RPPh, 66, 1651.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1088/0034-4885/66/10/R03 Lee K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Dunham M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Myers P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Arce H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bourke T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Goodman A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Jørgensen J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2016, ApJL, 820, L2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/2041- 8205/820/1/L2 Li S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sanhueza P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Nakamura F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Lu X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wang J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2020, ApJ, 903, 119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4357/abb81f Li S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Beuther H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Palau A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Girart J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Smith H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2020, ApJ, 896, 110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4357/ab84f1 Li S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Pillai T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Stephens I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wang J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Li F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2019, ApJ, 886, 130.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4357/ab464e Liu H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Quintana-Lacaci G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wang K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Ho P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Li Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2012, ApJ, 745, 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1088/0004-637X/745/1/61 Liu H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Galv´an-Madrid R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Jim´enez-Serra I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Rom´an-Z´u˜niga C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Li Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Chen H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2015, ApJ, 804, 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1088/0004-637X/804/1/37 Liu H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sanhueza P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zavagno A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Tang X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wu Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2020, ApJ, 901, 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4357/abadfe Liu H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Evans N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wang K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Garay G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Qin S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Li S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2021, MNRAS, 505, 2801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/stab1352 Liu H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Tej A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Issac N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Saha A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Goldsmith P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wang J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022a, MNRAS, 510, 5009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/stab2757 Liu H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Tej A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Goldsmith P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Stutz A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Juvela M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Qin S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022b, MNRAS, 511, 4480.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/stac378 Liu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Evans N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Kim K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Goldsmith P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Tatem- atsu K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2020a, MNRAS, 496, 2790.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/staa1577 Liu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Evans N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Kim K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Goldsmith P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Tatem- atsu K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2020b, MNRAS, 496, 2821.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/staa1501 Longmore S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Kruijssen J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bastian N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bally J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Rath- borne J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Testi L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Stolte A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2014, prpl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='conf, 291.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='2458/azu uapress 9780816531240-ch013 Louvet F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Hennebelle P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Men’shchikov A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Didelon P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Ntormousi E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Motte F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2021, A&A, 653, A157.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004-6361/202040053 McKee C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Tan J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2003, ApJ, 585, 850.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1086/346149 Men’shchikov A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2021, A&A, 649, A89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004- 6361/202039913 Molinari S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Swinyard B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bally J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Barlow M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bernard J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Mar- tin P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Moore T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2010, A&A, 518, L100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004- 6361/201014659 Morii K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sanhueza P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Nakamura F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Jackson J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Li S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Beuther H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2021, ApJ, 923, 147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4357/ac2365 Motte F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bontemps S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Csengeri T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Pouteau Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Louvet F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Stutz A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Cunningham N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022, A&A, 662, A8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004- 6361/202141677 Motte F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bontemps S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Louvet F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2018, ARA&A, 56, 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1146/annurev-astro-091916-055235 Myers P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2009, ApJ, 700, 1609.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1088/0004-637X/700/2/1609 Offner S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Dunham M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Lee K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Arce H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Fielding D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2016, ApJL, 827, L11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/2041-8205/827/1/L11 Offner S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Chaban J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2017, ApJ, 847, 104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538- 4357/aa8996 Offner S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Taylor J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Markey C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Chen H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Pineda J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Goodman A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Burkert A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022, MNRAS, 517, 885.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/stac2734 Ossenkopf V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Henning T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 1994, A&A, 291, 943 Padoan P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Pan L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Juvela M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Haugbølle T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Nordlund ˚A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2020, ApJ, 900, 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4357/abaa47 Peretto N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Fuller G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Duarte-Cabral A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Avison A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Hennebelle P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Pineda J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Andr´e P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2013, A&A, 555, A112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004- 6361/201321318 Ragan S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Henning T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Krause O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Pitann J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Beuther H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Linz H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Tackenberg J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2012, A&A, 547, A49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004-6361/201219232 Rosolowsky E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Pineda J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Kauffmann J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Goodman A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2008, ApJ, 679, 1338.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1086/587685 Sabatini G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bovino S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sanhueza P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Morii K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Li S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Redaelli E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022, ApJ, 936, 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4357/ac83aa Sanhueza P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Garay G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bronfman L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Mardones D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', May J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Saito M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2010, ApJ, 715, 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1088/0004-637X/715/1/18 Sanhueza P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Jackson J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Guzm´an A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Lu X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Stephens I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wang K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2017, ApJ, 841, 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4357/aa6ff8 Sanhueza P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Contreras Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wu B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Jackson J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Guzm´an A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Li S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2019, ApJ, 886, 102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4357/ab45e9 Sanhueza P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Girart J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Padovani M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Galli D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Hull C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Cortes P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2021, ApJL, 915, L10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/2041-8213/ac081c Saha A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Tej A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Issac N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Lee C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Garay G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022, MNRAS, 516, 1983.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/stac2353 Sakai T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sakai N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Foster J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sanhueza P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Jackson J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Kassis M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Furuya K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2013, ApJL, 775, L31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1088/2041-8205/775/1/L31 Sakai T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sanhueza P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Furuya K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Tatematsu K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Li S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Aikawa Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Lu X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022, ApJ, 925, 144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4357/ac3d2e Schneider N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Csengeri T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Hennemann M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Motte F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Didelon P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Feder- rath C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bontemps S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2012, A&A, 540, L11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004- 6361/201118566 Schneider N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Simon R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Guevara C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Buchbender C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Higgins R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Okada Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Stutzki J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2020, PASP, 132, 104301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1088/1538- 3873/aba840 Schuller F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Menten K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Contreras Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wyrowski F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Schilke P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Bronf- man L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Henning T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2009, A&A, 504, 415.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004- 6361/200811568 Stephens I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Dunham M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Myers P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Pokhrel R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sadavoy S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Vorobyov E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Tobin J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2017, ApJ, 846, 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538- 4357/aa8262 Stutz A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Gould A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2016, A&A, 590, A2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004- 6361/201527979 Trevi˜no-Morales S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Fuente A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', S´anchez-Monge ´A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Kainulainen J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Didelon P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Suri S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Schneider N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2019, A&A, 629, A81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004-6361/201935260 Tafoya D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sanhueza P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Li S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Guzm´an A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Silva A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', de la Fuente E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2021, ApJ, 913, 131.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4357/abf5da Tatematsu K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Ohashi S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sanhueza P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Nguyen Luong Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Umemoto T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Mizuno N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2016, PASJ, 68, 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/pasj/psw002 Thomasson B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Joncour I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Moraux E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Crespelle C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Motte F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Pouteau Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Nony T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022, A&A, 665, A119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004-6361/202243275 Urquhart J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Moore T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Csengeri T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wyrowski F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Schuller F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Hoare M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Lumsden S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2014, MNRAS, 443, 1555.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/stu1207 V´azquez-Semadeni E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Palau A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Ballesteros-Paredes J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', G´omez G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zamora-Avil´es M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2019, MNRAS, 490, 3061.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/stz2736 Verliat A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Hennebelle P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Gonz´alez M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Lee Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Geen S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022, A&A, 663, A6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004-6361/202141765 Wang P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Li Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Abel T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Nakamura F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2010, ApJ, 709, 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1088/0004-637X/709/1/27 Wang K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wu Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2011, ApJ, 735, 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1088/0004- 637X/735/1/64 Wang K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Testi L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', van der Tak F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wu Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Pillai T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2014, MNRAS, 439, 3275.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/stu127 Williams J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', de Geus E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Blitz L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 1994, ApJ, 428, 693.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1086/174279 Williams G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Peretto N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Avison A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Duarte-Cabral A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Fuller G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2018, A&A, 613, A11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1051/0004-6361/201731587 Yuan J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Li J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wu Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Ellingsen S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Henkel C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wang K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2018, ApJ, 852, 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4357/aa9d40 Yuan L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Yang J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Du F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Zhang S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Lin Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Sun J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2021, ApJS, 257, 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='3847/1538-4365/ac242a Zhang Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Wang Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Pillai T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Rathborne J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2009, ApJ, 696, 268.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1088/0004-637X/696/1/268 Zhou J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Liu T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Evans N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Garay G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', Goldsmith P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', G´omez G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', V´azquez-Semadeni E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=', 2022, MNRAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='tmp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='1093/mnras/stac1735 MNRAS 000,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 1–15 (2021) High-mass star formation in HFS cloud 15 APPENDIX A: COMPLEMENTARY FIGURES Author affiliations: 1School of physics and astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Yunnan University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Kunming,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 650091,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' PR China 2Indian Institute of Space Science and Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Thiruvanantha- puram 695 547,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Kerala,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' India 3Shanghai Astronomical Observatory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Chinese Academy of Sci- ences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 80 Nandan Road,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Shanghai 200030,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Peoples Republic of China 4Key Laboratory for Research in Galaxies and Cosmology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Shang- hai Astronomical Observatory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Chinese Academy of Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 80 Nandan Road,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Shanghai 200030,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Peoples Republic of China 5National Astronomical Observatory of Japan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' National Institutes of Natural Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2-21-1 Osawa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Mitaka,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Tokyo 181-8588,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Japan 6Department of Astronomical Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The Graduate University for Advanced Studies,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' SOKENDAI,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2-21-1 Osawa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Mitaka,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Tokyo 181-8588,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Japan 7Yunnan Observatories,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Chinese Academy of Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 396 Yang- fangwang,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Guandu District,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Kunming,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 650216,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' China 8Chinese Academy of Sciences South America Center for Astron- omy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' National Astronomical Observatories,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' CAS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Beijing 100101,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' China 9Departamento de Astronom´ıa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Universidad de Chile,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Casilla 36-D,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Santiago,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Chile 10Jet Propulsion Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' California Institute of Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 4800 Oak Grove Drive,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Pasadena,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' CA 91109,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' USA 11Department of Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Graduate School of Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' The University of Tokyo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 7-3-1 Hongo,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Bunkyo-ku,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Tokyo 113-0033,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Japan 12Max Planck Institute for Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Knigstuhl 17,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' D-69117 Heidelberg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Germany 13Departamento de Astronom´ıa,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Universidad de Concepci´on,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Av.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Esteban Iturra s/n,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Distrito Universitario,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 160-C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Chile 14Max-Planck-Institute for Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' K¨onigstuhl 17,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 69117 Heidelberg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Germany 15Kavli Institute for Astronomy and Astrophysics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Peking Univer- sity,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 5 Yiheyuan Road,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Haidian District,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Beijing 100871,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' People’s Republic of China 16Department of Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Peking University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 100871,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Beijing,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' People’s Republic of China 17Indian Institute of Astrophysics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Koramangala II Block,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Banga- lore 560 034,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' India 18Satyendra Nath Bose National Centre for Basic Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Block- JD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Sector-III,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Salt Lake,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Kolkata-700 106 19E¨otv¨os Lor´and University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Department of Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' P´azm´any P´eter s´et´any 1/A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' H-1117,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Budapest,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Hungary 20Physical Research Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Navrangpura,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Ahmedabad380 009,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' India 21National Astronomical Observatories,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Chinese Academy of Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Beijing 100101,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' China 22Korea Astronomy and Space Science Institute,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 776 Daedeok- daero,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Yuseong-gu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Daejeon 34055,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Republic of Korea 23University of Science and Technology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Korea (UST),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 217 Gajeong-ro,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Yuseong-gu,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Daejeon 34113,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Republic of Korea 24School of Physics and Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Sun Yat-sen University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 2 Daxue Road,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Zhuhai,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Guangdong,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 519082,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' People’s Republic of China 25SOFIA Science Centre,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' USRA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' NASA Ames Research Centre,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' MS-12,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' N232,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Moffett Field,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' CA 94035,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' USA MNRAS 000,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 1–15 (2021) 16 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 18h17m28s 26s 24s 22s 20s 16°24\'00" 30" 25\'00" 30" 26\'00" RA (J2000) Dec (J2000) 8 m HFS2 / G014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='492-00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='139 RA: 18:17:23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='21 Dec: -16:25:04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc 18h43m36s 32s 28s 24s 20s 4°10\'00" 11\'00" 12\'00" 13\'00" 14\'00" RA (J2000) Dec (J2000) 8 m HFS3 / G028.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='273-00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='167 RA: 18:43:28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='42 Dec: -4:11:57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc 16h11m39s 36s 33s 30s 51°34\'00" 30" 35\'00" 30" RA (J2000) Dec (J2000) 8 m HFS4 / G331.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='372-00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='116 RA: 16:11:33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='41 Dec: -51:34:43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='68 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc 16h48m34s 32s 30s 28s 45°10\'20" 40" 11\'00" 20" 40" RA (J2000) Dec (J2000) 8 m HFS5 / G340.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='222-00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='167 RA: 16:48:30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='74 Dec: -45:11:04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='56 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc 16h48m33s 30s 27s 24s 45°09\'00" 30" 10\'00" 30" RA (J2000) Dec (J2000) 8 m HFS6 / G340.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='232-00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='146 RA: 16:48:27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='46 Dec: -45:09:48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc 16h51m18s 15s 12s 09s 44°30\'30" 31\'00" 30" 32\'00" 30" RA (J2000) Dec (J2000) 8 m HFS7 / G341.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='039-00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='114 RA: 16:51:14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='02 Dec: -44:31:23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc 17h01m04s 00s 00m56s 52s 42°47\'00" 30" 48\'00" 30" 49\'00" 30" RA (J2000) Dec (J2000) 8 m HFS8 / G343.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='489-00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='416 RA: 17:00:59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='42 Dec: -42:48:00.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc 15h43m25s 20s 15s 10s 54°05\'30" 06\'00" 30" 07\'00" 30" 08\'00" RA (J2000) Dec (J2000) 8 m HFS10 / I15394-5358 RA: 15:43:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='84 Dec: -54:06:54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='36 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc 15h55m54s 48s 42s 36s 30s 52°41\'00" 42\'00" 43\'00" 44\'00" 45\'00" RA (J2000) Dec (J2000) 8 m HFS11 / I15520-5234 RA: 15:55:42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='05 Dec: -52:42:39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc 16h31m06s 00s 30m54s 48s 48°42\'00" 43\'00" 44\'00" 45\'00" RA (J2000) Dec (J2000) 8 m HFS12 / I16272-4837 RA: 16:30:56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='16 Dec: -48:43:34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='68 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc 16h39m00s 38m54s 48s 42s 36s 47°28\'00" 29\'00" 30\'00" 31\'00" RA (J2000) Dec (J2000) 8 m HFS13 / I16351-4722 RA: 16:38:47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='66 Dec: -47:29:24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='72 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc 16h46m15s 10s 05s 00s 45°35\'00" 36\'00" 37\'00" RA (J2000) Dec (J2000) 8 m HFS14 / I16424-4531 RA: 16:46:06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='84 Dec: -45:35:50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='64 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc 17h05m20s 15s 10s 05s 41°27\'00" 28\'00" 29\'00" 30\'00" RA (J2000) Dec (J2000) 8 m HFS15 / I17016-4124 RA: 17:05:11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='54 Dec: -41:28:30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc 17h26m48s 42s 36s 30s 24s 36°06\'00" 08\'00" 10\'00" RA (J2000) Dec (J2000) 8 m HFS16 / I17233-3606 RA: 17:26:37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='27 Dec: -36:07:40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc 18h53m22s 20s 18s 16s 14s 1°26\'30" 00" 25\'30" 00" 24\'30" RA (J2000) Dec (J2000) 8 m HFS17 / I18507+0121 RA: 18:53:18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='43 Dec: +1:25:19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content='5pc Figure A1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' Same as Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' 1 but for the remaining 15 HFSs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} +page_content=' MNRAS 000, 1–15 (2021)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/LdE1T4oBgHgl3EQfZAQe/content/2301.03144v1.pdf'} diff --git a/MdE2T4oBgHgl3EQfBQZc/content/2301.03600v1.pdf b/MdE2T4oBgHgl3EQfBQZc/content/2301.03600v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ffdba37470af85a200a348f41728923751001fb9 --- /dev/null +++ b/MdE2T4oBgHgl3EQfBQZc/content/2301.03600v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:901d3b912baef1724906a106b982fb550235be985cfcf273d026cd96b5100957 +size 3358782 diff --git a/NNFRT4oBgHgl3EQfGTcp/content/2301.13484v1.pdf b/NNFRT4oBgHgl3EQfGTcp/content/2301.13484v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d591c30d1791f80a89406d370e47518c21622f01 --- /dev/null +++ b/NNFRT4oBgHgl3EQfGTcp/content/2301.13484v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e53821ae292c31df842c30e09326c67dc59e92d993e309116856b2c07b7bfe7e +size 2259912 diff --git a/NNFRT4oBgHgl3EQfGTcp/vector_store/index.faiss b/NNFRT4oBgHgl3EQfGTcp/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..7c2be04ec697e6e9851ee273277635e592e156a8 --- /dev/null +++ b/NNFRT4oBgHgl3EQfGTcp/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ff4352e112ae450e0efdf5ac4d230e6d27aa66276a4fe6889a2cdf2bb9ca132b +size 10551341 diff --git a/NNFRT4oBgHgl3EQfGTcp/vector_store/index.pkl b/NNFRT4oBgHgl3EQfGTcp/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..525361ba35ce62f7410397f1e0d5d0928aa8a2f3 --- /dev/null +++ b/NNFRT4oBgHgl3EQfGTcp/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cfb3de4819d8c60f1abe99fbd74277fdd8315f3e86cea75199b11da4da53337e +size 312503 diff --git a/NtE3T4oBgHgl3EQfwwva/vector_store/index.pkl b/NtE3T4oBgHgl3EQfwwva/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..d9d9656056a4eb2df65a250eff66456bd955ed89 --- /dev/null +++ b/NtE3T4oBgHgl3EQfwwva/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:83a9cf263ce9ac51f24963b3b8a376105525ad376a19dd3866590773819a0852 +size 273708 diff --git a/Plough Knowledge Ocean Intro/content/tmp_files/load_file.txt b/Plough Knowledge Ocean Intro/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..52d03584a8b660a355c179077088a27a6099abfa --- /dev/null +++ b/Plough Knowledge Ocean Intro/content/tmp_files/load_file.txt @@ -0,0 +1,1782 @@ +filepath=D:\projects\langchain-ChatGLM-master\knowledge_base\Plough Knowledge Ocean Intro\content\北斗知海系统用户指南.pdf,len=890 +page_content='1 / 29 ⼀、系统整体介绍 1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 背景 “笃志问题求解，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='贯通古今中外”，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='北⽃知海系统(Plough Knowledge Ocean，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='aka,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' PKO) 旨在建⽴全球最⼤的综合知识库，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以跨语⾔、多学科、可计算和⾃增殖的知识计算为研究主 题，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以“⼤”、“动”、“亮”落地场景为应⽤特⾊，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以⼈机协同的HAO智能为技术抓⼿，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='集成深 度学习与图谱构建，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='开拓数据和知识双轮驱动。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以知识碎⽚化问题为切⼊点，利⽤“表示演 化 多源融合 知识导航”的解决思路，实现多源海量数据到知识的“量 质 序”的转化。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ⽬标 北⽃知海系统旨在建⽴⼀个以问题求解为驱动、跨学科、多场景、可计算、可增值的动 态知识库，集成深度学习与图谱构建，开拓数据和知识的双轮驱动研究。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过研究以下四个 科学问题：①异构⾃治的多源知识获取，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='②跨学科多媒体知识的表示、评估和融合，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='③多重 知识推理和计算，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='④类⼈智能技术的⼈机协同，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在以下⼋项关键技术上寻求突破：①数字⼈ 设计技术，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='②多维信息感知、交互与融合，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='③⼤规模知识图谱构建，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='④跨媒体智能分析与理 解，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⑤多重关系联想与复合知识索引，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⑥⼈机交互和双向双轮驱动，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⑦开放环境下的持续学 习，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⑧⾃然⼈、数字⼈、机器⼈在物理空间和数字空间的全息融合。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在技术上达到国际领先 ⽔平，并在智能教育、智慧药物、以及服务机器⼈等场景进⾏落地应⽤。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 应⽤场景 北⽃知海系统依托全⽹数据和知识，期待在智慧医疗、智慧教育、智慧⾦融、以及智慧 机器⼈等众多垂直领域（⻅图1）发挥重要作⽤。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 北⽃知海系统⽤户指南 2 / 29 图1：垂直领域应⽤场景 在智慧医疗领域中，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过使⽤机器学习和⼈⼯智能技术，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='构建药物数据库，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='对蛋⽩、分 ⼦等数据的联合分析，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='识别疾病机理，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='并进⼀步分析分⼦成药性质，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='将知识可⽤于分⼦筛 选。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='同时，通过联邦学习平台利⽤多⽅数据，探索分⼦数据的群体效能，进⼀步加速药物发 现。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 在智慧教育领域，通过使⽤虚拟现实和增强现实技术，提供有趣且有效的学习⽅式。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通 过互动问答，掌握学⽣学习状况，提供个性化定制学习路径推荐。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='帮助学⽣更好地理解课程 内容，更好地掌握知识点，并为学⽣提供实践机会，以增强学⽣的实践能⼒。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 在智慧⾦融领域，通过使⽤⼤数据技术和区块链技术，帮助⾦融机构更好地管理⻛险， 提⾼⾦融服务的效率。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='帮助⾦融机构分析客户的信⽤⻛险，提供个性化的⾦融产品和服务， 并帮助⾦融机构更好地管理⾦融交易。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 在智慧机器⼈领域，通过使⽤机器学习和⼈⼯智能技术，使机器⼈能够更好地理解⼈类 语⾔，与⼈类进⾏更有效的沟通。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='利⽤家居云脑技术，应⽤于智慧家居⾏业。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 系统模块 智慧 智慧 教育 金融 智慧 智慧 应用场景 医疗 机器人3 / 29 整个系统依托北⽃知海知识库，包含了①⽹站⾸⻚、②示范应⽤、③管理后台三⼤模块 （⻅图2）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⽹站⾸⻚是北⽃知海系统的⻔户，向⽤户全⾯展示北⽃知海系统的整体内容；' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='示 范应⽤是依托知识库研发的各类应⽤，⽤于解决各类垂直领域的具体问题；' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='管理后台是北⽃ 知海系统的基座，⽤于管理系统的各类基础数据，例如⽤户、权限、⽇志等等。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图2：北⽃知海系统三⼤模块 ⼆、⽹站⾸⻚介绍 北斗知海系统 网站首 示范 管理 页 应用 后台4 / 29 ⽹站⾸⻚是北⽃知海的⻔户，向⽤户全⾯宣传和展示系统的整体框架。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='可以通过链接 “ https://ko.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='zhejianglab.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='com” 进⼊北⽃知海系统的⾸⻚，其中⻚⾯顶部导航栏列出了⽹站的 各个主要⻚⾯（如图3所示）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='每个⻚⾯同时具有相同的底部内容，⽤于展示相应的⽹站信息 （如图4所示）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图3：北⽃知海⾸⻚顶部导航栏 图4：⻚⾯底部内容 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ⽹站⾸⻚ 点击顶部“⽹站⾸⻚”进⼊，该⻚⾯包含了⾸⻚图⽚、知海规模、知海定义、示范应⽤、 发展成就。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⾸⻚图⽚是对北⽃知海系统的形象化描述，上有北⽃七星，下有⽆边⼤海（⻅图 5）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图5：⾸⻚图⽚ 知海规模给出了当前知海系统所达到的规模，列出了条⽬、关系、⼀层科⽬、和⼆层科 ⽬的最新统计数（⻅图6）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='KO 知识海洋 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='网站首页 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知海萃取 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知识问答 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='示范应用 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='一站式管理平台 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='发展成就 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='联系我们 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='连通、综合、 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='容纳、制衡 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='演化的知识海 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='洋友情链接： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之江实验室华谱系统合工大 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='公司网站 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='加入知海 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='服务协议 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='隐私协议 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='中心名称：之江实验空知识工程研究中心 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='中心邮箱：ke@zhejianglab.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='com ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='版本号：20230620 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Copyright2022 2023由之江实验室提供技术支持All RightsReserved本系统服务的范围及用途均适用于并遵循中华人民共和国法律和相关法规连通、综合、 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='容纳、制衡 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='演化的知识海 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='洋当前规模 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='485,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='311,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='385 317,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='319,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='224 128 1,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='139 条目 关系 一层科目 二层科目 数据来源：中华谱 知海5 / 29 图6：知海规模 知海定义为吴信东院⼠对北⽃知海项⽬的精准定义（⻅图7）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图7：知海定义 示范应⽤为依托北⽃知海平台开发的各类垂直领域应⽤（⻅图8）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='此处展示热度排名前 三的应⽤，需要查看更多应⽤可以进⼊“示范应⽤”⻚⾯查看详情。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='点击每段⽂字后的“更多” 可以进⼊应⽤介绍⻚⾯，点击“查看详情 ”可直接进⼊相应的应⽤⻚⾯。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图8：示范应⽤ 发展成就为北⽃知海平台及知识⼯程研究中⼼发展过程中的重要事件。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='重点选取每个时 期的代表性事件，需要查看完整发展过程，可在”发展成就“⻚⾯查看。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 同时，⻚⾯下⽅有分 ⻚控件，可通过点击左右按钮和数字按钮的⽅式灵活选择，查看不同时期的事件 （⻅图 9）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 关于知海 一片连通、综合、容纳、制衡、演化的知识海洋 笃志问题求解，贯通古今中外。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知海KO（KnowledgeOcean）含有全球最大的综 合知识库，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以跨语言、多学科、可计算和自增殖的知识计算为研究主题 以"大"、“动"、“亮"落地场景为应用特色，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以人机协同的HAO智能为技术抓手，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='集 成深度学习与图谱构建，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='开拓数据和知识双轮驱动。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 吴信东2022年10月19日示范应用 家具云脑 智慧制药 工资QA 项目旨在构建满足智能家居应 现代药物研发流程具有典型的 在北斗知海的图数据库中，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知 用的云脑平台，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过引入之江 长周期、高风险以及高投资的 识工程中心导入了大学和公司 北斗综合性知识库、HAO推理 特点，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='究其原因，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='是因为我们 的职员工资数据，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='构建了人 机、以及数据挖掘、自然语言 当前的药物研发流程十分依赖 员、岗位、部门和薪资等实 处理、强化学习、搜索推荐、 生物实验。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='针对某个疾病.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='.更 体，年份等属性，以及雇佣、 规划监测.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='.更多 多 隶属等关系.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='.更多 查看详情 查看详情 查看详情6 / 29 图9：发展成就 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 知海萃取 知识⼯程中⼼⾯向科学前沿和国家重⼤需求，以知识⼯程为核⼼，兼顾多学科交叉，开 展基础理论、算法模型以及落地应⽤等⽅⾯的研究。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在知识抽取、知识管理、模型训练与推 理⽅⾯有⼀定的积累与优势。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 知识⼯程中⼼结合之江实验室在基因、制药、天⽂、材料等领域的积累与⽂献抽取需 求，拟构造基于国内外开源⼤语⾔模型的【国产⽂献抽取⼤模型】。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 基于⼤模型的科学⽂献抽取调研评测报告 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 基于⼤模型的科学⽂献领域垂直数据集与评测平台 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 国产科学⽂献抽取⼤模型 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 知识问答 知识问答模块主要使⽤⽣成式语⾔⼤模型来进⾏⽂档问答（QA）的任务。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='与传统的⽂档 问答系统相⽐，这种⽅法的优点在于可以利⽤⽣成式语⾔⼤模型强⼤的⽣成能⼒来产⽣更为 准确、详细的答案。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在此过程中，⼤模型通过阅读相关⽂档并提取问题所需的信息来寻找答 案。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='这种⽅法不仅可以提⾼QA的准确性，还可以提⾼系统的可扩展性和适应性。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='发展成就 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='第十届吴文俊人工智能技术发明奖一等奖 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知识图讯 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='A智创十年赋能未来 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='吴信东等斩获吴 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='《知识图谱》由 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之江实验室知识 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='文俊人工智能科 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='科学出版社出版 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工程研究中心成 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='学技术奖技术发 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='发行 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='立 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='明一等奖 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2021年4月10日 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2022年7月 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2023年2月9日《 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='4 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='5 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='6 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='10 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='》7 / 29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过上传PDF⽂件到知识问答模块，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='就能实现和PDF跨语⾔对话，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='并根据PDF内容回答 提问。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='即通过知识问答模块能够实现和PDF聊天。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='跨语⾔是指如果PDF是英⽂，你可以输⼊ 中⽂和它对话，反之亦然。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⽽该应⽤的核⼼⽅法就是基于OpenAI的 Chat API，给PDF的每⼀ 段创建语义索引，然后使⽤关联最密切的段落去提示 (Prompt) Chat API。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 知识问答可以帮助⽤户更好地学习。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⽆论是课本、讲义还是演示⽂稿，都可以轻松理 解。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⽆需再花费数⼩时翻阅研究论⽂和学术⽂章，让⽤户更有效地⽀持学术成⻓。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过知识 问答，⽤户可以轻松地解锁⽆尽知识。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='从历史⽂档到诗歌、⽂学作品，⽆论是什么语⾔，知 识问答都能理解并⽤喜欢的语⾔回复。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='让好奇⼼得到满⾜，拓宽视野，这个⼯具能回答任何 来⾃PDF⽂件的问题。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 示范应⽤ 在“示范应⽤”⻚⾯点击“更多”（⻅图10）后会展示每个示范应⽤的详情信息。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图10: 点击“更多”进⼊示范应⽤的详情⻚⾯ 以⼯资QA为例，当点击“更多"按钮，相关的详细信息将会进⼀步呈现（⻅图11）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 示范应用 家具云脑 智慧制药 工资QA 项目旨在构建满足智能家居应 现代药物研发流程具有典型的 在北斗知海的图数据库中，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知 用的云脑平台，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过引入之江 长周期、高风险以及高投资的 识工程中心导入了大学和公司 北斗综合性知识库、HAO推理 特点，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='究其原因，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='是因为我们 的职员工资数据，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='构建了人 机、以及数据挖掘、自然语言 当前的药物研发流程十分依赖 员、岗位、部门和薪资等实 处理、强化学习、搜索推荐、 生物实验。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='针对某个疾病.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='.更 体，年份等属性，以及雇佣、 规划监测.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='.更多 多 隶属等关系.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='.更多 查看详情 查看详情 查看详情8 / 29 图11：⼯资QA更多信息 当点击”⼯资QA“的”查看详情“时，⽤户登录注册界⾯会展现，提示⽤户需要注册后登 录使⽤该功能（⻅图12）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图12：点击”查看详情“后的登录界⾯ 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='5.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ⼀站式管理平台 工资QA 在北斗知海的图数据库中，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知识工程中心导入了大学和公司的职员工资数据，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='构建了人员、岗位、部门和新资等实体，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='年份等属性，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以及 雇佣、隶属等关系，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='形成了完整的工资知识图谱数据结构。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过知识推理和自然语言处理技术，可以实现工资的查询、统计、多步推理，以及 预测、规划分配等场景的响应。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='系统具有流畅的自然语言对话形式问答界面，以及工资查询，图谱展示和数据分析的功能，且具有与北斗知海 进行通用知识库与专有知识库的数据交互和知识萃取的功能。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工资问答示范系统全面展现了北斗知海在工资场景知识工程的综合应用。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之江实验室 ZHEJIANG LAB 登录 8账号 请输入账号 邑 密码 请输入密码 立即登录 没有账号？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 8立即注册9 / 29 点击“⼀站式管理平台”或链接“https://ko.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='zhejianglab.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='com/ADMIN”，进⼊管理后台⻚⾯ （⻅图13）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图13：⼀站式管理平台登录 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 发展成就 点击“发展成就”或链接“ https://ko.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='zhejianglab.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='com/news.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='html”进⼊“发展成就”⻚⾯， 北⽃知海平台及知识⼯程研究中⼼发展过程中的重要事件按照时间倒序的⽅式逐⼀呈现（⻅ 图14）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' R admin 请输入验证码 KO一站式服务管理平台 账号密码短结登录用户注期10 / 29 图14：发展成就 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='7.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 联系我们 点击“联系我们”或链接“ https://ko.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='zhejianglab.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='com/contact.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='html”进⼊"联系我们"⻚⾯ （⻅图15）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知识⼯程研究中⼼正处于发展前期，需要各类⼈才的加⼊。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='同时，依托北⽃知 海，定有⼴⼤作为，我们也寻求更多的合作。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='网站首页 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知海萃取 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知识问答 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='示范应用 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='一站式管理平台 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='发展成就 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之江沙龙：大模型时代的知识工程 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='大模型时代的知识工程大模型时代的知识工程大模型时代的知识工程大模型时代 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='的知识工程大模型时代的知识工程大模型时代的知识工程 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2023年4月24日 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之江学本护亮 ） ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='大模型时代的知识工程 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='圆桌论坛 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之江实验室知识工程研究中心成立 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之江实验室知识工程研究中心成立之江实验室知识工程研究中心成立之江实验室 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知识工程研究中心成立之江实验室知识工程研究中心成立之江实验室知识工程研 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='究中心成立之江实验室知识工程研究中心成立 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2023年2月9日 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='《知识图谱》由科学出版社出版发行 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='这部专著系统介绍了知识图谱的概念、发展历程、技术体系、前沿技术与应用实 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='践。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在基础知识方面，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='本书囊括了知识图谱从源数据到产生决策的全生命周期的 N 各个环节，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='分析了数据图谱和知识图谱的核心区别，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='介绍了图谱构建和知识表 机协 识11 / 29 图15：联系我们 三、示范应⽤介绍 北⽃知海系统具有⼴泛的示范应⽤价值，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='应⽤范围可涵盖交通、通信、能源、医疗、环 保等多个⽅⾯，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='有望在这些领域取得了卓越的成果。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='例如，在交通领域，该系统的智能交通 管理系统可以实现城市交通的智能化和⾼效化，提⾼交通运输效率，减少交通事故的发⽣；' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 在通信领域，该系统的⾼速⽹络技术可以实现⾼速、稳定、安全的数据传输，满⾜⼈们对于 信息交流和共享的需求；' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在能源领域，该系统的能源管理系统可以实现对能源的精细管理和 有效利⽤，提⾼能源利⽤效率，降低能源消耗成本；' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在医疗领域，该系统的智能医疗系统可 以实现医疗资源的优化分配和管理，提⾼医疗服务的质量和效率；' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在环保领域，该系统的环 境监测系统可以实现对环境污染的实时监测和预警，提⾼环境保护的效果和⽔平。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='综上所 述，该系统的⼴泛应⽤和卓越成果为社会进步和发展做出了重要贡献。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ⼯资问答 欢迎您的咨询和加入 寻求合作，知识工程研究中心欢迎各类人才的加入 contact us 联系我们 e 邮箱：bigke2016@gmail.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='com 地址：杭州市之江实验室12 / 29 在北⽃知海的图数据库中，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知识⼯程中⼼导⼊了⼤学和公司的职员⼯资数据，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='构建了⼈ 员、岗位、部⻔和薪资等实体，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='年份等属性，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以及雇佣、⾪属等关系，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='形成了完整的⼯资知 识图谱数据结构。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过知识推理和⾃然语⾔处理技术，可以实现⼯资的查询、统计、多步推 理，以及预测、规划分配等场景的响应。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='系统具有流畅的⾃然语⾔对话形式问答界⾯，以及 ⼯资查询，图谱展示和数据分析的功能，且具有与北⽃知海进⾏通⽤知识库与专有知识库的 数据交互和知识萃取的功能。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⼯资问答示范系统全⾯展现了北⽃知海在⼯资场景知识⼯程的 综合应⽤。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ⼯资问答系统是⼀个完整的知识⼯程应⽤，是⼀个基于知识图谱的对话问答系统，系统 架构如图16所示。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图16： ⼯资问答系统架构 在系统架构上从底⾄上分为四层：⼯程底座，数据层，应⽤实现层和业务层。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ⼯程底座，包含了对接管理后台的⽤户注册，登录，权限控制和应⽤调度功能。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 数据层，包含了图数据库Neo4j，以及从外部知海系统和⽂件等进⾏知识萃取的功能 模块。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 应⽤实现层，主要通过两条技术路径实现⾃然语⾔的问答解析，基于Cypher语⾔的知 识推理，以及答案内容的⽣成：⼀是KBQA，⼆是语⾔⼤模型。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='封装在后端NLP Python⼯程中，以接⼝⽅式与数据层和业务层通信。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 业务层，包含了Web应⽤实现的⼏个模块，主要包含⼯资问答、我的⼯资、图谱展 示、数据分析⼏个⻚⾯和功能。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 工资间管蒙练架构 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工资问答 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工资查询 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图谱展示 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='数据分析 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='QA 问答引擎 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Cypher查询推理 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='语言大模型内容生成 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='NLP Python工程 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工资文件(UMV) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='导入 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='数据库 Neo4J ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='萃取 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知海 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工程底座用户登录，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='权限，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='APP调度13 / 29 以下将根据系统功能分为 注册登录、数据模型、⼯资问答、我的⼯资、图谱展示、数据 分析⼏个模块介绍⼯资问答系统。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 注册登录 注册模块完成⽤户注册到系统中的操作，需要提供⼿机号来验证身份。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='注册成功的⽤户 才可以使⽤系统的功能。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⾸次访问⽹⻚会⾃动跳转到登录⻚⾯，在登录⻚⾯中点击“⽴即注 册”进⼊注册⻚⾯。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⽤户填写注册⻚⾯所需要登记的信息，点击“⽴即注册”按钮提交信息 （⻅图17），然后点击“⽴即登⼊”转到登录⻚⾯进⾏登录（⻅图18）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图17：注册⻚⾯ ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='注册 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之江实验室 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='ZHEJIANG LAB ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='8账号 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入账号 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='手机号 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入手机号 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='验证码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入验证码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='密码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入密码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='密码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请再次输入密码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='立即注册 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='没有账号?' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 8立即登入14 / 29 图18：登录⻚⾯ 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2 数据模型 ⼯资的数据模型，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='包括person（⼈员）、salary（⼯资）、position（职位）和 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='department（部⻔）四种节点和 earn（赚钱）、 employ（雇佣）、pricing（价值）和in ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='（属于）四种关系，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='person中包含name（姓名）属性，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='salary中包含year（年份）和salary （⼯资）属性，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='position中包含year（年份）和position（职位）属性，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='department中包含 year（年份）和department（部⻔）属性（⻅图19）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 之江实验室 ZHEJIANG LAB 登录 8账号 请输入账号 密码 请输入密码 立即登录 没有账号?' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 8立即注册15 / 29 图19：⼯资数据模型 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3 ⼯资问答 ⼯资问答以⼯资知识图谱为基础，采⽤基于知识图谱的问答框架（⻅图20）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='该框架以 ⾃然语⾔问句为输⼊，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过问句分类将输⼊⽂本分到预设的问题类别下、然后通过问句解析 模块将不同类别下的问句进⾏实体识别与抽取，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之后通过查询语句转化模块将⾃然语⾔问句 转换为对应的查询语⾔在⼯资知识图谱中进⾏相应的查询，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之后调⽤相应类别问题下的统 计、计算、预测等任务模块执⾏，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='最后根据分类类别与获取到的执⾏结果进⾏回答语句组 装，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='进⾏答复。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='department ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='person ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='property: ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='year ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='in ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='property : ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='department ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='property:name ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='node ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='employ ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='earn ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='node ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='salary ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='property: year ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='property: position ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='property: year ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='position ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='pricing ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='property: salary ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='node ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='node16 / 29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图20：⼯资问答技术框架 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⼯资KBQA问题列表 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以下是⼯资KBQA问题列表：这些问题通过⼈名、时间、职位、部⻔、薪资四个维度的 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='组合可以实现，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='例如： a.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 个⼈某年的⼯资、职位、部⻔查询 b.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 某个职位或者部⻔的平均薪资计算 c.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 个⼈所在职级、职位上的薪资⽔平统计 d.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 个⼈在某年的薪资是否能够达到同职级、部⻔的平均⽔平的计算⽐较 图21展示了⼀些基于上述组合的示例问题。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=" question_1 = '我是Davis,Wendy Sue，我2014年的⼯资是多少？" metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='\' question_2 = "请问职级为Professor的⼈，2015年平均⼯资是多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='" question_3 = "我是Davis,Wendy Sue，我所在的职级年薪⼤于50000的⼈有多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='" question_4 = "请问Davis,Wendy Sue的2015年的⼯资是否达到同级别的平均⽔平？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='" question_5 = \'我是Davis,Wendy Sue，我2014年所在的部门是什么？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⼯资是多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content="' question_6 = '请问部门为Computer Science的⼈，2015年平均⼯资是多少？" metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content="' question_7 = '我是Davis,Wendy Sue，我所在的部门年薪⼤于50000的⼈有多少？" metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='\' question_8 = "请问Davis,Wendy Sue的2015年的⼯资是否达到同部门的平均⽔平？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='" ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='4 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='5 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='6 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='7 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='8 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='9 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='10 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='组件 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='自然问句 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='细节 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='question ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Ruler ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='问句分类 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Word ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='classifier ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WordKB ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Expansion ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='question ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Ruler ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='问句解析 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Dependency ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='parser ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WordKB ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Parser ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='查询语句 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='slot ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='cypher ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='search_sqler ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='转换 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='filling ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='pattern ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='结果返回 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工资知识图谱 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='基于知识图谱的问答框架17 / 29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图21：示例问题 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图22（a d）以系统截图⽅式展示了⼀些问答实例 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图22（a）：问答实例1 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图22（b）：问答实例2 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='10 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2023 06 13 15:17:46 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='我是Ades,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Steven，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 我2014年的工资是多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 13 15:17:46 您好，Ades,Steven的2014年的工资为40000。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 1315:18:06 请问职级为Professor的人，2015年平均工资是多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 1315:18:06 您好，职级为Professor的人2015年的平均工资为121385我是Davis,WendySue，我所在的职级年薪大于50000的人有多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 13 15:18:20 您好，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WendySue所在的职级为Professor，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='年薪大于50000的人有818位 2023 06 13 15:18:35 请问DavisWendySue的2015年的工资是否达到同级别的平均水平？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 1315:18:35 您好，能够达到！' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 1315:18:35 因为Davis,WendySue在2015年所在的职级为Professor，年薪是160635，该年这个职级的平均工资是121385 所以能够达到！' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='18 / 29 图22（c）：问答实例3 图22（d）：问答实例4 ⼯资规划和预测 ⼯资预测问题：输⼊相关的⼯资预测问题，得到系统答复。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='答复中会包含⼯资预测的计 算逻辑，并⽤平滑曲线图展示历史⼯资信息。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='例如⽤户可以问，”Abaied, Jamie L.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在2024年 ⼯资预计达到多少”，后台算法会根据被询问者的历史⼯资特征对未来⼯资情况进⾏预测（⻅ 图23）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 1315:20:39 我是Davis,WendySue，我2014年所在的部门是什么？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工资是多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 1315:20:39 您好，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Davis，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WendySue所在的部门是：PhysicalCulture，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在2014年的工资为153000 2023 06 1315:20:53 请问部门为ComputerScience的人，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2015年平均工资是多少?' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='我是Davis,WendySue，我所在的部门年薪大于50000的人有多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 13 15:21:04 您好，Davis，WendySue所在的部门为PhysicalCulture，年薪大于50000的人有1624位。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 13 15:21:20 请问Davis,WendySue的2015年的工资是否达到同部门的平均水平？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 13 15:21:20 您好，能够达到！' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 13 15:21:20 因为Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WendySue在2015年所在的部门为PhysicalCulture，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='年薪是160635，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='该年这个部门的平均工资是 67486，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='所以能够达到！' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='19 / 29 图23：⼯资预测问答示例 另⼀种常⻅的场景是，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⽤户希望知道在给定薪酬总包的情况下，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='如何分配给各位在职员 ⼯，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='则可以提问：“假设2024年薪酬总包是288,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000元，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='建议分配给Zimakas,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' Nilgun T.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='的 数额是多少？”' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 算法根据被询问者的个⼈⼯资变化情况、所在职位的历年平均⼯资的变化趋势、薪酬总 包三⽅⾯因素，综合考量给出薪酬分配的建议值。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='具体来说，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='系统⾸先根据所在职位的历年 平均⼯资的变化趋势，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='预测出该职位的⼯资⽔位，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='然后通过⽐较被询问者与同岗职⼯之间历 年⼯资变化情况，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='判断个体竞争⼒，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='最后结合⽤户给出的薪酬总包⼤⼩，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='计算分配给个体的 份额（⻅图24）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 此外，我们根据历年⼯资变化趋势，预测出2023年的薪酬总包⼤约为289,000,000元， 因此，⽤户在输⼊薪酬分配问题时，在此数值附近，所得到的答复会更符合实际。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 预测ABAIEDJAMIEL在2024年的工资。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 061417:23:05 ABAIED，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='JAMIEL最近一次职务变动是从ASSISTANTPROFESSOR成为ASSISTANTPROFESSOR，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='根据担任 ASSISTANTPROFESSOR期间工资年均增长率0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0252预测其2024年工资为88927.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='43。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 100,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 80,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 60,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 40,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 20,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 2016 2011 2018 2019 2020 202 2014 2015 2022假设2024年薪酬总包是288000000元，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='分配给Zimakas,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='NilgunT.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='的数额是多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 062609:47:00 ZIMAKAS,NILGUNT当前职位为ASSISTANTPROFESSOR（COM)，根据该职位平均新酬变化趋势，以及 ZIMAKAS.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='NILGUNT个人工资变化趋势，预测2024年在薪酬总包288000000.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0元中的分配数额为17694.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 18,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 15,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 12,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 9,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 6,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 3,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 0 2013 2014 2015 2016 2017 2018 2019 2020 202120 / 29 图24：⼯资总包分配示例 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='4 我的⼯资查询 进⼊”我的⼯资”⻚⾯，输⼊姓名、时间、⼯资范围，即可点击“搜索”按钮查询对应的⼯ 资信息，具体查询到的⼯资信息以列表形式展示（⻅图25）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图25：⼯资查询结果 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='5 图谱展示 进⼊图谱展示，输⼊姓名，开始时间，结束时间，查询范围相关搜索条件，即可查询相 关⼈员的⼯资的知识图谱（图26）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 之江实验室 ZHEJIANG LAB admin 工资问答 我的工资 工资图谱 数据分析 姓名 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Wendy Sue 开始时间 2000 结束时间 2028 查询范围 0 8000000 搜索 重置 工资明细 姓名 职位 年份 应发工资 实发工资 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WendySue Professor 2013 112500 112500 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Wendy Sue Professor 2014 153000 153000 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WendySue Professor 2015 160635 160635 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Wendy Sue Professor (COM) 2017 177067 177067 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Wendy Sue Professor(COM) 2018 185902 185902 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Wendy Sue Professor (COM) 2019 191479 191479 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WendySue Professor (COM) 2020 181905 181905 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WendySue ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Professor (COM) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2021 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='193394 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='193394 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='京公网安备10000001000001号京ICP证010101号互联网新闻信息服务许可证11110110001网络文化经营许可证：京网文【2023】1011 001号21 / 29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图26：图谱查询结果 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='6 数据分析 ⼯资总数以指标卡形式展现总发放⼯资和总⼈⼒成本（⻅图27）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图27：⼯资总数 根据部⻔和职位，以折线图统计呈现历年平均⼯资⾛势（⻅图28）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 工资问答 我的工资 工资图谱 数据分析 筛选条件 图谱展示 姓名 Abair,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Shirley Sam ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='开始时间 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='菌 2002 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='eneralist(2014) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='结束时间 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='菌 2022 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='fice/Prgm SuF ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='(Pport (ariperalist(2017) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Office/Prgm Su ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2017) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='查询范围 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='11 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Abal ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='earn ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='ean ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='24637 (2013) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='salar:27480 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2018) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='查询范围 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='11111111111 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Mojdu ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='earn ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Office/Prgm SupportGeneralist(213) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Office/Prgm Support G ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Generalist(2018) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='28219 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2019 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='搜索 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='重置 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Office/Prgm Support Genera ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='t(2019) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='京公网安备10000001000001号京ICP证010101号互联网新闻信息服务许可证11110110001网络文化经营许可证：京网文【2023】1011 001号之江实验室 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='ZHEJIANG LAB ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='admin ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工资问答 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='我的工资 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工资图谱 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='数据分析 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='今年总发放工资 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='今年总人力成本 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='$283,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='860,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='487.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='00 ￥ 28,425.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='00 相比去年 7.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='03% ↑ 相比去年 20% ↑22 / 29 图28：平均⼯资 其中，可由下拉选择框筛选部⻔和职位（⻅图29）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图29：筛选部⻔职位 平均工资 请选择 开始日期 至 结束日期 搜索 150,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 120,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 90,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 60,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 30,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 平均工资 请选择 开始日期 至 结束日期 搜索 80,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 100 % 70,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 90 % 80 % 60,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 70 % 50,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 60 % 40,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 50 % 30,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 40 % 30 % 20,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 20 % 10,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='10 % ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0 % ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='201 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='201 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='019 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2020 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='202平均工资 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请选择 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='菌 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='开始日期 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='至 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='结束日期 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='搜索 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='部门 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='> ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Mathematics Department ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='150,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 职位 Biomedical Sciences 120,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 Business Administration Department Mechanical Engineering 90,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 Philosophy 60,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 30,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 0 2013 2014 2015 2016 2017 2018 2019 2020 2021 202223 / 29 根据部⻔⼯资排⾏，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='显示Top 7的部⻔⾦额（⻅图30）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图30：部⻔⼯资排⾏ 岗位⼯资排⾏⻅图31。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 部门工资排行 季度 月度 排名 部门 较上月 金额 0 Politics 0+ 83578.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='9 2 Economics 0+ 80637 B Nutrition 21 + 75624.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='75 4 English 74971.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='73 5 Entrepreneurship 3 74376.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='91 latin american 6 4 74331.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content="04 studies Women's and 7 56 + 74263." metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='52 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Gender Studies24 / 29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图31：岗位⼯资排⾏ ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='岗位工资排行 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='季度 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='月度 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='排名 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='部门 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='较上月 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='金额 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='President ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='+ 0 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='484800 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='日 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Senior Vice ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0+ ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='367200 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Pres/Provost ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Athletic Head ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='325913 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Coach Sr ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='4 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Director-Faculty ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='307120 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='5 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content="Vice Pres & Gen'l " metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='300000 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Counsel ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='VP of Finance & ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='6 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Administration ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='t 0 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='290700 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='7 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Dean ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='287994.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='7325 / 29 ⼈员构成⽤来显示各职位⼈员构成⽐例（⻅图32）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图32：⼈⼯构成 问答词云统计显示⼯资问答历史记录的⽂本内容构成的词云，可以展示⾼频问答关键词 （⻅图33）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 人员构成 6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='82% 6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='75% 6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='44% 6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='41% 56.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='96% 4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='41% 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='32% 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1% 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='92% 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='87% ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Assistant Professor (COM) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Prote ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='ssor ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Office/Prgm Support Generalist ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Associate Professor ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Assistant Professor ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Administrative Professional ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Associate Professor (COM) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Custodial Maintenance Worker ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Lecturer ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='其他26 / 29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图33：问答词云 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='四、管理后台介绍 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='管理后台是北⽃知海系统的基座，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⽤于管理系统的各类基础数据，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='例如⽤户、权限、⽇ 志等等。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 登录注册 点击链接“https://ko.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='zhejianglab.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='com/ADMIN/#/login”进⼊管理后台的登录⻚⾯（⻅图 34）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 人员构成 吴信东 之江实验室 工资27 / 29 图34：后台管理系统登录⻚⾯ 当前系统⽀持通过⼿机号加密码的⽅式登录，输⼊正确的⼿机号和密码，点击登录按 钮，即可进⼊系统。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='点击“⽤户注册”进⼊注册⻚⾯（⻅图35）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图35：后台管理系统⽤户注册⻚⾯ 通过输⼊⽤户名、密码和⼿机号码注册⼀个新⽤户，在录⼊⽤户名和⼿机号码时会实时 验证是否存在相同⽤户名或⼿机号码，如果已存在，则会在输⼊框下红字提醒。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='输⼊正确的 ⼿机号和密码后，登⼊系统⾸⻚。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ⽤户管理 如果前登录⽤户具有“⽤户管理”⻚⾯的访问权限，可以点击权限管理-⽤户管理，进⼊“⽤ 户管理”⻚⾯（⻅图36）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='8请编入手机号码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='斗加海 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入于机号码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请验入度码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入座码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='登示 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='KO一站式服务管理平台 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='手机号密码用户注前8请输入用户名 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='输入用户名 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='合请能入密码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='清输入密码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='臣请输入手机号码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='清输入丁机号 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='KO一站式服务管理平台 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='手机号密码用户注带28 / 29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图36：⽤户管理⻚⾯ ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在该⻚⾯可对⽤户进⾏查询、添加、导⼊、导出、分⻚浏览等操作。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='例如，点击添加按 钮，弹出新增⽤户弹窗，可为新⽤户设置⽤户名、密码、部⻔、⼿机号、⻆⾊、岗位、状态 信息。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='点击保存，新⽤户保存到系统（⻅图37）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图37：新增⽤户 4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ⽇志管理 如果当前登录⽤户具有“⽇志管理”⻚⾯的访问权限，可点击系统管理 ⽇志管理，进⼊ “⽇志管理”⻚⾯。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='可对⽇志进⾏搜索、导出、查看、删除操作。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='每⼀条⽇志包含了类型、标 题、IP、请求⽅式、客户端、请求时间、创建时间、异常⽇志等详细信息，便于管理者查看 （⻅图38）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='用户名： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入用户名 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Q接索 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='仓清空 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='± ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='导入 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='+ ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='导出 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Q ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='序号 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='用户名 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='手机号 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='角色 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='部门 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='岗位 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='状态 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='创建时间 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='操作 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='admi ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='131155522 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='普递用户 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正常 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='20-90-E202 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='编抗白 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='制除 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='aa ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='普道用户 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正常 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='L-50-E202 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='C ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='编排 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='副除 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='m ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='zhang2 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='普递用户 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='[正路 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0E-50-E202 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='编辑 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='除 4 zhang1 1350000 普通用户 正常 0-50-E202 C ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='编辑 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='副除 zhang 1350000 正常 0E-0-E202 编辑 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='除 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='6 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='orybuswonb ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='13434563458 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='普通用户 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='行政中心 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='员 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正常 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='SL-50-E202 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='jack ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='15837570607 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='普递用户 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='研发中心 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='co ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正常 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='SL-S0-EZ02 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='8 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='newuseri ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='13445674567 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='普递用户 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='运营中心 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='员工 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正路 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='LL-S0-E202 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='9 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='zheshixinde ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='13412341234 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='普运用户 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正若 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0L-50-E202 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='C编辑 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='除 10 testuser 18168789253 普退用户 正常 0L-50-E202 11 newuser 普题用户 正路 0L-50-E202 E 编辑 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='白 副除 12 Sunshanvin 17712341234 普通用户 研发中心 员 正常 2023-04-26 L 排 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='除 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='test1 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='13365874125 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='普通用户 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='行政中心 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='童事长 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正常 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='12-80-202 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='14 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='admin ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='管理员 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='总经办 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='员 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正路 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='02-P0-8102 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='共14条 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='20条/顶 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='前往新增 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='× ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='*用户名： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入用户名 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入用户名 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='密码： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入密码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入密码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='*所属部门： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请选择所属部门 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='*手机号： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入手机号 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='*角色： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请选择角色 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='*岗位： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请选择岗位 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='*状态： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正常 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='锁定 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='④保存 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='取消29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='/ ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图38：⽇志管理⻚⾯ ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='类型：请选择类型 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='IP地址 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入IP地址 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='创建时间 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='开始 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='结束 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Q搜索 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='自清空 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='￥导出 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='鲁 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='类型 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='标题 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='IP地址 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请求方式 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='客户端 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请求时 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='间 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='创建时间 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='操作 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正常 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='登录成功 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='POST ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='166 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2023 06 13 15:11 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='直看白制际 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正常 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='登录成功 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1,40.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='253 POST 197 3 异常 婴录失败 10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='11,40.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='253 POST 164 2023 06 13 15:07 4 正常 退出威功 127.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 DELETE pig @查看 白副除 5 正常 登录成功 POST 1144 6 异常 登录失败 127.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 POST 364 PEPL EL 90 E202 7 异常 登录失敷 POST 9435 查看白删际 8 正常 退出成功 127.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 DELETE pig 查看 白副除 9 正常 录减功 127.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 POST 480 10 正常 登录成功 10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='140.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='4 POST 138 9 01 E1 90 EZ02 @查看 白制脉 11 正常 登录成功 0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 POST 398 05 01 E1 90 E202 12 正常 登录成功 10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='11.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='40.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='4 POST 148 PE60 E1 90 EZ02 查看 白删际 13 正常 曼录成功 10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1,40.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='62 POST 147 @查看 白剧除 14 正常 登录成功 POST 131 2023 06 13 08:05 15 正常 登录威功 10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='11.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='40.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='62 POST 137 16 正常 登录成功 10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1,40.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='253 POST 144 EL 21 90 E202 17 正常 0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='11.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='404 POSt' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +filepath=D:\projects\langchain-ChatGLM-master\knowledge_base\Plough Knowledge Ocean Intro\content\北斗知海系统用户指南.pdf,len=890 +page_content='1 / 29 ⼀、系统整体介绍 1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 背景 “笃志问题求解，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='贯通古今中外”，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='北⽃知海系统(Plough Knowledge Ocean，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='aka,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' PKO) 旨在建⽴全球最⼤的综合知识库，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以跨语⾔、多学科、可计算和⾃增殖的知识计算为研究主 题，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以“⼤”、“动”、“亮”落地场景为应⽤特⾊，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以⼈机协同的HAO智能为技术抓⼿，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='集成深 度学习与图谱构建，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='开拓数据和知识双轮驱动。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以知识碎⽚化问题为切⼊点，利⽤“表示演 化 多源融合 知识导航”的解决思路，实现多源海量数据到知识的“量 质 序”的转化。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ⽬标 北⽃知海系统旨在建⽴⼀个以问题求解为驱动、跨学科、多场景、可计算、可增值的动 态知识库，集成深度学习与图谱构建，开拓数据和知识的双轮驱动研究。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过研究以下四个 科学问题：①异构⾃治的多源知识获取，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='②跨学科多媒体知识的表示、评估和融合，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='③多重 知识推理和计算，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='④类⼈智能技术的⼈机协同，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在以下⼋项关键技术上寻求突破：①数字⼈ 设计技术，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='②多维信息感知、交互与融合，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='③⼤规模知识图谱构建，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='④跨媒体智能分析与理 解，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⑤多重关系联想与复合知识索引，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⑥⼈机交互和双向双轮驱动，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⑦开放环境下的持续学 习，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⑧⾃然⼈、数字⼈、机器⼈在物理空间和数字空间的全息融合。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在技术上达到国际领先 ⽔平，并在智能教育、智慧药物、以及服务机器⼈等场景进⾏落地应⽤。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 应⽤场景 北⽃知海系统依托全⽹数据和知识，期待在智慧医疗、智慧教育、智慧⾦融、以及智慧 机器⼈等众多垂直领域（⻅图1）发挥重要作⽤。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 北⽃知海系统⽤户指南 2 / 29 图1：垂直领域应⽤场景 在智慧医疗领域中，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过使⽤机器学习和⼈⼯智能技术，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='构建药物数据库，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='对蛋⽩、分 ⼦等数据的联合分析，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='识别疾病机理，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='并进⼀步分析分⼦成药性质，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='将知识可⽤于分⼦筛 选。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='同时，通过联邦学习平台利⽤多⽅数据，探索分⼦数据的群体效能，进⼀步加速药物发 现。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 在智慧教育领域，通过使⽤虚拟现实和增强现实技术，提供有趣且有效的学习⽅式。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通 过互动问答，掌握学⽣学习状况，提供个性化定制学习路径推荐。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='帮助学⽣更好地理解课程 内容，更好地掌握知识点，并为学⽣提供实践机会，以增强学⽣的实践能⼒。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 在智慧⾦融领域，通过使⽤⼤数据技术和区块链技术，帮助⾦融机构更好地管理⻛险， 提⾼⾦融服务的效率。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='帮助⾦融机构分析客户的信⽤⻛险，提供个性化的⾦融产品和服务， 并帮助⾦融机构更好地管理⾦融交易。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 在智慧机器⼈领域，通过使⽤机器学习和⼈⼯智能技术，使机器⼈能够更好地理解⼈类 语⾔，与⼈类进⾏更有效的沟通。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='利⽤家居云脑技术，应⽤于智慧家居⾏业。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 系统模块 智慧 智慧 教育 金融 智慧 智慧 应用场景 医疗 机器人3 / 29 整个系统依托北⽃知海知识库，包含了①⽹站⾸⻚、②示范应⽤、③管理后台三⼤模块 （⻅图2）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⽹站⾸⻚是北⽃知海系统的⻔户，向⽤户全⾯展示北⽃知海系统的整体内容；' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='示 范应⽤是依托知识库研发的各类应⽤，⽤于解决各类垂直领域的具体问题；' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='管理后台是北⽃ 知海系统的基座，⽤于管理系统的各类基础数据，例如⽤户、权限、⽇志等等。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图2：北⽃知海系统三⼤模块 ⼆、⽹站⾸⻚介绍 北斗知海系统 网站首 示范 管理 页 应用 后台4 / 29 ⽹站⾸⻚是北⽃知海的⻔户，向⽤户全⾯宣传和展示系统的整体框架。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='可以通过链接 “ https://ko.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='zhejianglab.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='com” 进⼊北⽃知海系统的⾸⻚，其中⻚⾯顶部导航栏列出了⽹站的 各个主要⻚⾯（如图3所示）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='每个⻚⾯同时具有相同的底部内容，⽤于展示相应的⽹站信息 （如图4所示）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图3：北⽃知海⾸⻚顶部导航栏 图4：⻚⾯底部内容 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ⽹站⾸⻚ 点击顶部“⽹站⾸⻚”进⼊，该⻚⾯包含了⾸⻚图⽚、知海规模、知海定义、示范应⽤、 发展成就。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⾸⻚图⽚是对北⽃知海系统的形象化描述，上有北⽃七星，下有⽆边⼤海（⻅图 5）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图5：⾸⻚图⽚ 知海规模给出了当前知海系统所达到的规模，列出了条⽬、关系、⼀层科⽬、和⼆层科 ⽬的最新统计数（⻅图6）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='KO 知识海洋 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='网站首页 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知海萃取 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知识问答 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='示范应用 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='一站式管理平台 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='发展成就 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='联系我们 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='连通、综合、 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='容纳、制衡 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='演化的知识海 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='洋友情链接： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之江实验室华谱系统合工大 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='公司网站 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='加入知海 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='服务协议 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='隐私协议 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='中心名称：之江实验空知识工程研究中心 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='中心邮箱：ke@zhejianglab.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='com ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='版本号：20230620 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Copyright2022 2023由之江实验室提供技术支持All RightsReserved本系统服务的范围及用途均适用于并遵循中华人民共和国法律和相关法规连通、综合、 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='容纳、制衡 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='演化的知识海 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='洋当前规模 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='485,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='311,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='385 317,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='319,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='224 128 1,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='139 条目 关系 一层科目 二层科目 数据来源：中华谱 知海5 / 29 图6：知海规模 知海定义为吴信东院⼠对北⽃知海项⽬的精准定义（⻅图7）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图7：知海定义 示范应⽤为依托北⽃知海平台开发的各类垂直领域应⽤（⻅图8）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='此处展示热度排名前 三的应⽤，需要查看更多应⽤可以进⼊“示范应⽤”⻚⾯查看详情。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='点击每段⽂字后的“更多” 可以进⼊应⽤介绍⻚⾯，点击“查看详情 ”可直接进⼊相应的应⽤⻚⾯。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图8：示范应⽤ 发展成就为北⽃知海平台及知识⼯程研究中⼼发展过程中的重要事件。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='重点选取每个时 期的代表性事件，需要查看完整发展过程，可在”发展成就“⻚⾯查看。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 同时，⻚⾯下⽅有分 ⻚控件，可通过点击左右按钮和数字按钮的⽅式灵活选择，查看不同时期的事件 （⻅图 9）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 关于知海 一片连通、综合、容纳、制衡、演化的知识海洋 笃志问题求解，贯通古今中外。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知海KO（KnowledgeOcean）含有全球最大的综 合知识库，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以跨语言、多学科、可计算和自增殖的知识计算为研究主题 以"大"、“动"、“亮"落地场景为应用特色，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以人机协同的HAO智能为技术抓手，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='集 成深度学习与图谱构建，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='开拓数据和知识双轮驱动。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 吴信东2022年10月19日示范应用 家具云脑 智慧制药 工资QA 项目旨在构建满足智能家居应 现代药物研发流程具有典型的 在北斗知海的图数据库中，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知 用的云脑平台，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过引入之江 长周期、高风险以及高投资的 识工程中心导入了大学和公司 北斗综合性知识库、HAO推理 特点，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='究其原因，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='是因为我们 的职员工资数据，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='构建了人 机、以及数据挖掘、自然语言 当前的药物研发流程十分依赖 员、岗位、部门和薪资等实 处理、强化学习、搜索推荐、 生物实验。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='针对某个疾病.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='.更 体，年份等属性，以及雇佣、 规划监测.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='.更多 多 隶属等关系.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='.更多 查看详情 查看详情 查看详情6 / 29 图9：发展成就 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 知海萃取 知识⼯程中⼼⾯向科学前沿和国家重⼤需求，以知识⼯程为核⼼，兼顾多学科交叉，开 展基础理论、算法模型以及落地应⽤等⽅⾯的研究。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在知识抽取、知识管理、模型训练与推 理⽅⾯有⼀定的积累与优势。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 知识⼯程中⼼结合之江实验室在基因、制药、天⽂、材料等领域的积累与⽂献抽取需 求，拟构造基于国内外开源⼤语⾔模型的【国产⽂献抽取⼤模型】。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 基于⼤模型的科学⽂献抽取调研评测报告 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 基于⼤模型的科学⽂献领域垂直数据集与评测平台 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 国产科学⽂献抽取⼤模型 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 知识问答 知识问答模块主要使⽤⽣成式语⾔⼤模型来进⾏⽂档问答（QA）的任务。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='与传统的⽂档 问答系统相⽐，这种⽅法的优点在于可以利⽤⽣成式语⾔⼤模型强⼤的⽣成能⼒来产⽣更为 准确、详细的答案。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在此过程中，⼤模型通过阅读相关⽂档并提取问题所需的信息来寻找答 案。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='这种⽅法不仅可以提⾼QA的准确性，还可以提⾼系统的可扩展性和适应性。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='发展成就 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='第十届吴文俊人工智能技术发明奖一等奖 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知识图讯 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='A智创十年赋能未来 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='吴信东等斩获吴 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='《知识图谱》由 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之江实验室知识 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='文俊人工智能科 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='科学出版社出版 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工程研究中心成 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='学技术奖技术发 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='发行 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='立 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='明一等奖 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2021年4月10日 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2022年7月 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2023年2月9日《 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='4 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='5 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='6 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='10 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='》7 / 29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过上传PDF⽂件到知识问答模块，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='就能实现和PDF跨语⾔对话，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='并根据PDF内容回答 提问。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='即通过知识问答模块能够实现和PDF聊天。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='跨语⾔是指如果PDF是英⽂，你可以输⼊ 中⽂和它对话，反之亦然。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⽽该应⽤的核⼼⽅法就是基于OpenAI的 Chat API，给PDF的每⼀ 段创建语义索引，然后使⽤关联最密切的段落去提示 (Prompt) Chat API。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 知识问答可以帮助⽤户更好地学习。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⽆论是课本、讲义还是演示⽂稿，都可以轻松理 解。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⽆需再花费数⼩时翻阅研究论⽂和学术⽂章，让⽤户更有效地⽀持学术成⻓。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过知识 问答，⽤户可以轻松地解锁⽆尽知识。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='从历史⽂档到诗歌、⽂学作品，⽆论是什么语⾔，知 识问答都能理解并⽤喜欢的语⾔回复。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='让好奇⼼得到满⾜，拓宽视野，这个⼯具能回答任何 来⾃PDF⽂件的问题。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 示范应⽤ 在“示范应⽤”⻚⾯点击“更多”（⻅图10）后会展示每个示范应⽤的详情信息。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图10: 点击“更多”进⼊示范应⽤的详情⻚⾯ 以⼯资QA为例，当点击“更多"按钮，相关的详细信息将会进⼀步呈现（⻅图11）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 示范应用 家具云脑 智慧制药 工资QA 项目旨在构建满足智能家居应 现代药物研发流程具有典型的 在北斗知海的图数据库中，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知 用的云脑平台，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过引入之江 长周期、高风险以及高投资的 识工程中心导入了大学和公司 北斗综合性知识库、HAO推理 特点，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='究其原因，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='是因为我们 的职员工资数据，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='构建了人 机、以及数据挖掘、自然语言 当前的药物研发流程十分依赖 员、岗位、部门和薪资等实 处理、强化学习、搜索推荐、 生物实验。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='针对某个疾病.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='.更 体，年份等属性，以及雇佣、 规划监测.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='.更多 多 隶属等关系.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='.更多 查看详情 查看详情 查看详情8 / 29 图11：⼯资QA更多信息 当点击”⼯资QA“的”查看详情“时，⽤户登录注册界⾯会展现，提示⽤户需要注册后登 录使⽤该功能（⻅图12）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图12：点击”查看详情“后的登录界⾯ 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='5.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ⼀站式管理平台 工资QA 在北斗知海的图数据库中，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知识工程中心导入了大学和公司的职员工资数据，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='构建了人员、岗位、部门和新资等实体，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='年份等属性，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以及 雇佣、隶属等关系，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='形成了完整的工资知识图谱数据结构。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过知识推理和自然语言处理技术，可以实现工资的查询、统计、多步推理，以及 预测、规划分配等场景的响应。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='系统具有流畅的自然语言对话形式问答界面，以及工资查询，图谱展示和数据分析的功能，且具有与北斗知海 进行通用知识库与专有知识库的数据交互和知识萃取的功能。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工资问答示范系统全面展现了北斗知海在工资场景知识工程的综合应用。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之江实验室 ZHEJIANG LAB 登录 8账号 请输入账号 邑 密码 请输入密码 立即登录 没有账号？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 8立即注册9 / 29 点击“⼀站式管理平台”或链接“https://ko.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='zhejianglab.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='com/ADMIN”，进⼊管理后台⻚⾯ （⻅图13）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图13：⼀站式管理平台登录 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 发展成就 点击“发展成就”或链接“ https://ko.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='zhejianglab.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='com/news.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='html”进⼊“发展成就”⻚⾯， 北⽃知海平台及知识⼯程研究中⼼发展过程中的重要事件按照时间倒序的⽅式逐⼀呈现（⻅ 图14）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' R admin 请输入验证码 KO一站式服务管理平台 账号密码短结登录用户注期10 / 29 图14：发展成就 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='7.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 联系我们 点击“联系我们”或链接“ https://ko.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='zhejianglab.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='com/contact.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='html”进⼊"联系我们"⻚⾯ （⻅图15）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知识⼯程研究中⼼正处于发展前期，需要各类⼈才的加⼊。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='同时，依托北⽃知 海，定有⼴⼤作为，我们也寻求更多的合作。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='网站首页 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知海萃取 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知识问答 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='示范应用 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='一站式管理平台 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='发展成就 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之江沙龙：大模型时代的知识工程 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='大模型时代的知识工程大模型时代的知识工程大模型时代的知识工程大模型时代 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='的知识工程大模型时代的知识工程大模型时代的知识工程 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2023年4月24日 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之江学本护亮 ） ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='大模型时代的知识工程 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='圆桌论坛 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之江实验室知识工程研究中心成立 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之江实验室知识工程研究中心成立之江实验室知识工程研究中心成立之江实验室 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知识工程研究中心成立之江实验室知识工程研究中心成立之江实验室知识工程研 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='究中心成立之江实验室知识工程研究中心成立 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2023年2月9日 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='《知识图谱》由科学出版社出版发行 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='这部专著系统介绍了知识图谱的概念、发展历程、技术体系、前沿技术与应用实 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='践。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在基础知识方面，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='本书囊括了知识图谱从源数据到产生决策的全生命周期的 N 各个环节，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='分析了数据图谱和知识图谱的核心区别，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='介绍了图谱构建和知识表 机协 识11 / 29 图15：联系我们 三、示范应⽤介绍 北⽃知海系统具有⼴泛的示范应⽤价值，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='应⽤范围可涵盖交通、通信、能源、医疗、环 保等多个⽅⾯，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='有望在这些领域取得了卓越的成果。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='例如，在交通领域，该系统的智能交通 管理系统可以实现城市交通的智能化和⾼效化，提⾼交通运输效率，减少交通事故的发⽣；' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 在通信领域，该系统的⾼速⽹络技术可以实现⾼速、稳定、安全的数据传输，满⾜⼈们对于 信息交流和共享的需求；' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在能源领域，该系统的能源管理系统可以实现对能源的精细管理和 有效利⽤，提⾼能源利⽤效率，降低能源消耗成本；' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在医疗领域，该系统的智能医疗系统可 以实现医疗资源的优化分配和管理，提⾼医疗服务的质量和效率；' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在环保领域，该系统的环 境监测系统可以实现对环境污染的实时监测和预警，提⾼环境保护的效果和⽔平。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='综上所 述，该系统的⼴泛应⽤和卓越成果为社会进步和发展做出了重要贡献。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ⼯资问答 欢迎您的咨询和加入 寻求合作，知识工程研究中心欢迎各类人才的加入 contact us 联系我们 e 邮箱：bigke2016@gmail.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='com 地址：杭州市之江实验室12 / 29 在北⽃知海的图数据库中，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知识⼯程中⼼导⼊了⼤学和公司的职员⼯资数据，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='构建了⼈ 员、岗位、部⻔和薪资等实体，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='年份等属性，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以及雇佣、⾪属等关系，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='形成了完整的⼯资知 识图谱数据结构。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过知识推理和⾃然语⾔处理技术，可以实现⼯资的查询、统计、多步推 理，以及预测、规划分配等场景的响应。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='系统具有流畅的⾃然语⾔对话形式问答界⾯，以及 ⼯资查询，图谱展示和数据分析的功能，且具有与北⽃知海进⾏通⽤知识库与专有知识库的 数据交互和知识萃取的功能。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⼯资问答示范系统全⾯展现了北⽃知海在⼯资场景知识⼯程的 综合应⽤。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ⼯资问答系统是⼀个完整的知识⼯程应⽤，是⼀个基于知识图谱的对话问答系统，系统 架构如图16所示。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图16： ⼯资问答系统架构 在系统架构上从底⾄上分为四层：⼯程底座，数据层，应⽤实现层和业务层。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ⼯程底座，包含了对接管理后台的⽤户注册，登录，权限控制和应⽤调度功能。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 数据层，包含了图数据库Neo4j，以及从外部知海系统和⽂件等进⾏知识萃取的功能 模块。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 应⽤实现层，主要通过两条技术路径实现⾃然语⾔的问答解析，基于Cypher语⾔的知 识推理，以及答案内容的⽣成：⼀是KBQA，⼆是语⾔⼤模型。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='封装在后端NLP Python⼯程中，以接⼝⽅式与数据层和业务层通信。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 业务层，包含了Web应⽤实现的⼏个模块，主要包含⼯资问答、我的⼯资、图谱展 示、数据分析⼏个⻚⾯和功能。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 工资间管蒙练架构 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工资问答 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工资查询 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图谱展示 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='数据分析 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='QA 问答引擎 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Cypher查询推理 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='语言大模型内容生成 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='NLP Python工程 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工资文件(UMV) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='导入 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='数据库 Neo4J ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='萃取 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='知海 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工程底座用户登录，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='权限，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='APP调度13 / 29 以下将根据系统功能分为 注册登录、数据模型、⼯资问答、我的⼯资、图谱展示、数据 分析⼏个模块介绍⼯资问答系统。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 注册登录 注册模块完成⽤户注册到系统中的操作，需要提供⼿机号来验证身份。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='注册成功的⽤户 才可以使⽤系统的功能。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⾸次访问⽹⻚会⾃动跳转到登录⻚⾯，在登录⻚⾯中点击“⽴即注 册”进⼊注册⻚⾯。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⽤户填写注册⻚⾯所需要登记的信息，点击“⽴即注册”按钮提交信息 （⻅图17），然后点击“⽴即登⼊”转到登录⻚⾯进⾏登录（⻅图18）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图17：注册⻚⾯ ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='注册 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之江实验室 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='ZHEJIANG LAB ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='8账号 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入账号 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='手机号 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入手机号 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='验证码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入验证码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='密码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入密码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='密码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请再次输入密码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='立即注册 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='没有账号?' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 8立即登入14 / 29 图18：登录⻚⾯ 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2 数据模型 ⼯资的数据模型，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='包括person（⼈员）、salary（⼯资）、position（职位）和 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='department（部⻔）四种节点和 earn（赚钱）、 employ（雇佣）、pricing（价值）和in ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='（属于）四种关系，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='person中包含name（姓名）属性，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='salary中包含year（年份）和salary （⼯资）属性，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='position中包含year（年份）和position（职位）属性，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='department中包含 year（年份）和department（部⻔）属性（⻅图19）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 之江实验室 ZHEJIANG LAB 登录 8账号 请输入账号 密码 请输入密码 立即登录 没有账号?' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 8立即注册15 / 29 图19：⼯资数据模型 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3 ⼯资问答 ⼯资问答以⼯资知识图谱为基础，采⽤基于知识图谱的问答框架（⻅图20）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='该框架以 ⾃然语⾔问句为输⼊，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='通过问句分类将输⼊⽂本分到预设的问题类别下、然后通过问句解析 模块将不同类别下的问句进⾏实体识别与抽取，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之后通过查询语句转化模块将⾃然语⾔问句 转换为对应的查询语⾔在⼯资知识图谱中进⾏相应的查询，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='之后调⽤相应类别问题下的统 计、计算、预测等任务模块执⾏，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='最后根据分类类别与获取到的执⾏结果进⾏回答语句组 装，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='进⾏答复。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='department ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='person ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='property: ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='year ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='in ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='property : ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='department ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='property:name ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='node ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='employ ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='earn ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='node ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='salary ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='property: year ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='property: position ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='property: year ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='position ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='pricing ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='property: salary ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='node ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='node16 / 29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图20：⼯资问答技术框架 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⼯资KBQA问题列表 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='以下是⼯资KBQA问题列表：这些问题通过⼈名、时间、职位、部⻔、薪资四个维度的 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='组合可以实现，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='例如： a.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 个⼈某年的⼯资、职位、部⻔查询 b.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 某个职位或者部⻔的平均薪资计算 c.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 个⼈所在职级、职位上的薪资⽔平统计 d.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 个⼈在某年的薪资是否能够达到同职级、部⻔的平均⽔平的计算⽐较 图21展示了⼀些基于上述组合的示例问题。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=" question_1 = '我是Davis,Wendy Sue，我2014年的⼯资是多少？" metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='\' question_2 = "请问职级为Professor的⼈，2015年平均⼯资是多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='" question_3 = "我是Davis,Wendy Sue，我所在的职级年薪⼤于50000的⼈有多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='" question_4 = "请问Davis,Wendy Sue的2015年的⼯资是否达到同级别的平均⽔平？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='" question_5 = \'我是Davis,Wendy Sue，我2014年所在的部门是什么？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⼯资是多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content="' question_6 = '请问部门为Computer Science的⼈，2015年平均⼯资是多少？" metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content="' question_7 = '我是Davis,Wendy Sue，我所在的部门年薪⼤于50000的⼈有多少？" metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='\' question_8 = "请问Davis,Wendy Sue的2015年的⼯资是否达到同部门的平均⽔平？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='" ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='4 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='5 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='6 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='7 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='8 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='9 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='10 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='组件 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='自然问句 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='细节 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='question ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Ruler ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='问句分类 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Word ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='classifier ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WordKB ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Expansion ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='question ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Ruler ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='问句解析 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Dependency ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='parser ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WordKB ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Parser ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='查询语句 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='slot ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='cypher ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='search_sqler ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='转换 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='filling ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='pattern ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='结果返回 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工资知识图谱 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='基于知识图谱的问答框架17 / 29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图21：示例问题 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图22（a d）以系统截图⽅式展示了⼀些问答实例 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图22（a）：问答实例1 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图22（b）：问答实例2 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='10 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2023 06 13 15:17:46 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='我是Ades,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Steven，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 我2014年的工资是多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 13 15:17:46 您好，Ades,Steven的2014年的工资为40000。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 1315:18:06 请问职级为Professor的人，2015年平均工资是多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 1315:18:06 您好，职级为Professor的人2015年的平均工资为121385我是Davis,WendySue，我所在的职级年薪大于50000的人有多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 13 15:18:20 您好，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WendySue所在的职级为Professor，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='年薪大于50000的人有818位 2023 06 13 15:18:35 请问DavisWendySue的2015年的工资是否达到同级别的平均水平？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 1315:18:35 您好，能够达到！' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 1315:18:35 因为Davis,WendySue在2015年所在的职级为Professor，年薪是160635，该年这个职级的平均工资是121385 所以能够达到！' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='18 / 29 图22（c）：问答实例3 图22（d）：问答实例4 ⼯资规划和预测 ⼯资预测问题：输⼊相关的⼯资预测问题，得到系统答复。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='答复中会包含⼯资预测的计 算逻辑，并⽤平滑曲线图展示历史⼯资信息。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='例如⽤户可以问，”Abaied, Jamie L.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在2024年 ⼯资预计达到多少”，后台算法会根据被询问者的历史⼯资特征对未来⼯资情况进⾏预测（⻅ 图23）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 1315:20:39 我是Davis,WendySue，我2014年所在的部门是什么？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工资是多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 1315:20:39 您好，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Davis，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WendySue所在的部门是：PhysicalCulture，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在2014年的工资为153000 2023 06 1315:20:53 请问部门为ComputerScience的人，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2015年平均工资是多少?' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='我是Davis,WendySue，我所在的部门年薪大于50000的人有多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 13 15:21:04 您好，Davis，WendySue所在的部门为PhysicalCulture，年薪大于50000的人有1624位。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 13 15:21:20 请问Davis,WendySue的2015年的工资是否达到同部门的平均水平？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 13 15:21:20 您好，能够达到！' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 06 13 15:21:20 因为Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WendySue在2015年所在的部门为PhysicalCulture，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='年薪是160635，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='该年这个部门的平均工资是 67486，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='所以能够达到！' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='19 / 29 图23：⼯资预测问答示例 另⼀种常⻅的场景是，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⽤户希望知道在给定薪酬总包的情况下，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='如何分配给各位在职员 ⼯，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='则可以提问：“假设2024年薪酬总包是288,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000元，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='建议分配给Zimakas,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' Nilgun T.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='的 数额是多少？”' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 算法根据被询问者的个⼈⼯资变化情况、所在职位的历年平均⼯资的变化趋势、薪酬总 包三⽅⾯因素，综合考量给出薪酬分配的建议值。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='具体来说，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='系统⾸先根据所在职位的历年 平均⼯资的变化趋势，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='预测出该职位的⼯资⽔位，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='然后通过⽐较被询问者与同岗职⼯之间历 年⼯资变化情况，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='判断个体竞争⼒，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='最后结合⽤户给出的薪酬总包⼤⼩，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='计算分配给个体的 份额（⻅图24）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 此外，我们根据历年⼯资变化趋势，预测出2023年的薪酬总包⼤约为289,000,000元， 因此，⽤户在输⼊薪酬分配问题时，在此数值附近，所得到的答复会更符合实际。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 预测ABAIEDJAMIEL在2024年的工资。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 061417:23:05 ABAIED，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='JAMIEL最近一次职务变动是从ASSISTANTPROFESSOR成为ASSISTANTPROFESSOR，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='根据担任 ASSISTANTPROFESSOR期间工资年均增长率0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0252预测其2024年工资为88927.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='43。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 100,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 80,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 60,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 40,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 20,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 2016 2011 2018 2019 2020 202 2014 2015 2022假设2024年薪酬总包是288000000元，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='分配给Zimakas,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='NilgunT.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='的数额是多少？' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 2023 062609:47:00 ZIMAKAS,NILGUNT当前职位为ASSISTANTPROFESSOR（COM)，根据该职位平均新酬变化趋势，以及 ZIMAKAS.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='NILGUNT个人工资变化趋势，预测2024年在薪酬总包288000000.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0元中的分配数额为17694.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 18,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 15,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 12,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 9,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 6,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 3,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 0 2013 2014 2015 2016 2017 2018 2019 2020 202120 / 29 图24：⼯资总包分配示例 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='4 我的⼯资查询 进⼊”我的⼯资”⻚⾯，输⼊姓名、时间、⼯资范围，即可点击“搜索”按钮查询对应的⼯ 资信息，具体查询到的⼯资信息以列表形式展示（⻅图25）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图25：⼯资查询结果 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='5 图谱展示 进⼊图谱展示，输⼊姓名，开始时间，结束时间，查询范围相关搜索条件，即可查询相 关⼈员的⼯资的知识图谱（图26）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 之江实验室 ZHEJIANG LAB admin 工资问答 我的工资 工资图谱 数据分析 姓名 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Wendy Sue 开始时间 2000 结束时间 2028 查询范围 0 8000000 搜索 重置 工资明细 姓名 职位 年份 应发工资 实发工资 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WendySue Professor 2013 112500 112500 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Wendy Sue Professor 2014 153000 153000 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WendySue Professor 2015 160635 160635 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Wendy Sue Professor (COM) 2017 177067 177067 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Wendy Sue Professor(COM) 2018 185902 185902 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Wendy Sue Professor (COM) 2019 191479 191479 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WendySue Professor (COM) 2020 181905 181905 Davis,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='WendySue ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Professor (COM) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2021 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='193394 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='193394 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='京公网安备10000001000001号京ICP证010101号互联网新闻信息服务许可证11110110001网络文化经营许可证：京网文【2023】1011 001号21 / 29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图26：图谱查询结果 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='6 数据分析 ⼯资总数以指标卡形式展现总发放⼯资和总⼈⼒成本（⻅图27）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图27：⼯资总数 根据部⻔和职位，以折线图统计呈现历年平均⼯资⾛势（⻅图28）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 工资问答 我的工资 工资图谱 数据分析 筛选条件 图谱展示 姓名 Abair,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Shirley Sam ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='开始时间 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='菌 2002 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='eneralist(2014) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='结束时间 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='菌 2022 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='fice/Prgm SuF ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='(Pport (ariperalist(2017) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Office/Prgm Su ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2017) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='查询范围 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='11 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Abal ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='earn ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='ean ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='24637 (2013) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='salar:27480 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2018) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='查询范围 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='11111111111 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Mojdu ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='earn ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Office/Prgm SupportGeneralist(213) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Office/Prgm Support G ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Generalist(2018) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='28219 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2019 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='搜索 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='重置 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Office/Prgm Support Genera ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='t(2019) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='京公网安备10000001000001号京ICP证010101号互联网新闻信息服务许可证11110110001网络文化经营许可证：京网文【2023】1011 001号之江实验室 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='ZHEJIANG LAB ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='admin ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工资问答 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='我的工资 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='工资图谱 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='数据分析 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='今年总发放工资 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='今年总人力成本 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='$283,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='860,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='487.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='00 ￥ 28,425.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='00 相比去年 7.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='03% ↑ 相比去年 20% ↑22 / 29 图28：平均⼯资 其中，可由下拉选择框筛选部⻔和职位（⻅图29）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图29：筛选部⻔职位 平均工资 请选择 开始日期 至 结束日期 搜索 150,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 120,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 90,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 60,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 30,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 平均工资 请选择 开始日期 至 结束日期 搜索 80,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 100 % 70,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 90 % 80 % 60,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 70 % 50,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 60 % 40,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 50 % 30,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 40 % 30 % 20,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 20 % 10,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='10 % ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0 % ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='201 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='201 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='019 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2020 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='202平均工资 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请选择 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='菌 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='开始日期 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='至 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='结束日期 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='搜索 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='部门 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='> ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Mathematics Department ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='150,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 职位 Biomedical Sciences 120,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 Business Administration Department Mechanical Engineering 90,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 Philosophy 60,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 30,' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='000 0 2013 2014 2015 2016 2017 2018 2019 2020 2021 202223 / 29 根据部⻔⼯资排⾏，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='显示Top 7的部⻔⾦额（⻅图30）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图30：部⻔⼯资排⾏ 岗位⼯资排⾏⻅图31。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 部门工资排行 季度 月度 排名 部门 较上月 金额 0 Politics 0+ 83578.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='9 2 Economics 0+ 80637 B Nutrition 21 + 75624.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='75 4 English 74971.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='73 5 Entrepreneurship 3 74376.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='91 latin american 6 4 74331.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content="04 studies Women's and 7 56 + 74263." metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='52 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Gender Studies24 / 29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图31：岗位⼯资排⾏ ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='岗位工资排行 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='季度 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='月度 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='排名 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='部门 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='较上月 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='金额 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='President ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='+ 0 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='484800 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='日 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Senior Vice ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0+ ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='367200 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Pres/Provost ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Athletic Head ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='325913 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Coach Sr ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='4 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Director-Faculty ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='307120 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='5 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content="Vice Pres & Gen'l " metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='300000 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Counsel ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='VP of Finance & ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='6 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Administration ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='t 0 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='290700 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='7 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Dean ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='287994.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='7325 / 29 ⼈员构成⽤来显示各职位⼈员构成⽐例（⻅图32）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图32：⼈⼯构成 问答词云统计显示⼯资问答历史记录的⽂本内容构成的词云，可以展示⾼频问答关键词 （⻅图33）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 人员构成 6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='82% 6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='75% 6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='44% 6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='41% 56.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='96% 4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='41% 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='32% 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1% 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='92% 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='87% ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Assistant Professor (COM) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Prote ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='ssor ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Office/Prgm Support Generalist ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Associate Professor ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Assistant Professor ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Administrative Professional ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Associate Professor (COM) ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Custodial Maintenance Worker ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Lecturer ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='其他26 / 29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图33：问答词云 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='四、管理后台介绍 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='管理后台是北⽃知海系统的基座，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='⽤于管理系统的各类基础数据，' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='例如⽤户、权限、⽇ 志等等。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 登录注册 点击链接“https://ko.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='zhejianglab.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='com/ADMIN/#/login”进⼊管理后台的登录⻚⾯（⻅图 34）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 人员构成 吴信东 之江实验室 工资27 / 29 图34：后台管理系统登录⻚⾯ 当前系统⽀持通过⼿机号加密码的⽅式登录，输⼊正确的⼿机号和密码，点击登录按 钮，即可进⼊系统。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='点击“⽤户注册”进⼊注册⻚⾯（⻅图35）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图35：后台管理系统⽤户注册⻚⾯ 通过输⼊⽤户名、密码和⼿机号码注册⼀个新⽤户，在录⼊⽤户名和⼿机号码时会实时 验证是否存在相同⽤户名或⼿机号码，如果已存在，则会在输⼊框下红字提醒。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='输⼊正确的 ⼿机号和密码后，登⼊系统⾸⻚。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ⽤户管理 如果前登录⽤户具有“⽤户管理”⻚⾯的访问权限，可以点击权限管理-⽤户管理，进⼊“⽤ 户管理”⻚⾯（⻅图36）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='8请编入手机号码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='斗加海 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入于机号码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请验入度码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入座码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='登示 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='KO一站式服务管理平台 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='手机号密码用户注前8请输入用户名 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='输入用户名 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='合请能入密码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='清输入密码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='臣请输入手机号码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='清输入丁机号 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='KO一站式服务管理平台 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='手机号密码用户注带28 / 29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图36：⽤户管理⻚⾯ ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='在该⻚⾯可对⽤户进⾏查询、添加、导⼊、导出、分⻚浏览等操作。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='例如，点击添加按 钮，弹出新增⽤户弹窗，可为新⽤户设置⽤户名、密码、部⻔、⼿机号、⻆⾊、岗位、状态 信息。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='点击保存，新⽤户保存到系统（⻅图37）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' 图37：新增⽤户 4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ⽇志管理 如果当前登录⽤户具有“⽇志管理”⻚⾯的访问权限，可点击系统管理 ⽇志管理，进⼊ “⽇志管理”⻚⾯。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='可对⽇志进⾏搜索、导出、查看、删除操作。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='每⼀条⽇志包含了类型、标 题、IP、请求⽅式、客户端、请求时间、创建时间、异常⽇志等详细信息，便于管理者查看 （⻅图38）。' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content=' ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='用户名： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入用户名 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Q接索 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='仓清空 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='± ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='导入 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='+ ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='导出 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Q ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='序号 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='用户名 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='手机号 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='角色 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='部门 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='岗位 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='状态 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='创建时间 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='操作 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='admi ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='131155522 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='普递用户 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正常 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='20-90-E202 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='编抗白 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='制除 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='aa ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='普道用户 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正常 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='L-50-E202 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='C ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='编排 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='副除 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='m ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='zhang2 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='普递用户 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='[正路 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0E-50-E202 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='编辑 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='除 4 zhang1 1350000 普通用户 正常 0-50-E202 C ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='编辑 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='副除 zhang 1350000 正常 0E-0-E202 编辑 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='除 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='6 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='orybuswonb ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='13434563458 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='普通用户 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='行政中心 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='员 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正常 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='SL-50-E202 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='jack ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='15837570607 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='普递用户 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='研发中心 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='co ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正常 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='SL-S0-EZ02 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='8 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='newuseri ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='13445674567 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='普递用户 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='运营中心 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='员工 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正路 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='LL-S0-E202 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='9 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='zheshixinde ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='13412341234 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='普运用户 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正若 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0L-50-E202 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='C编辑 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='除 10 testuser 18168789253 普退用户 正常 0L-50-E202 11 newuser 普题用户 正路 0L-50-E202 E 编辑 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='白 副除 12 Sunshanvin 17712341234 普通用户 研发中心 员 正常 2023-04-26 L 排 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='除 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='test1 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='13365874125 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='普通用户 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='行政中心 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='童事长 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正常 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='12-80-202 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='14 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='admin ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='管理员 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='总经办 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='员 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正路 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='02-P0-8102 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='共14条 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='20条/顶 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='前往新增 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='3 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='× ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='*用户名： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入用户名 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入用户名 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='密码： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入密码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入密码 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='*所属部门： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请选择所属部门 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='*手机号： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入手机号 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='*角色： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请选择角色 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='*岗位： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请选择岗位 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='*状态： ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正常 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='锁定 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='④保存 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='取消29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='/ ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='29 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='图38：⽇志管理⻚⾯ ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='类型：请选择类型 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='IP地址 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请输入IP地址 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='创建时间 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='开始 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='结束 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='Q搜索 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='自清空 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='￥导出 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='鲁 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='类型 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='标题 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='IP地址 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请求方式 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='客户端 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='请求时 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='间 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='创建时间 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='操作 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正常 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='登录成功 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='POST ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='166 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2023 06 13 15:11 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='直看白制际 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='2 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='正常 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='登录成功 ' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1,40.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='253 POST 197 3 异常 婴录失败 10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='11,40.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='253 POST 164 2023 06 13 15:07 4 正常 退出威功 127.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 DELETE pig @查看 白副除 5 正常 登录成功 POST 1144 6 异常 登录失败 127.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 POST 364 PEPL EL 90 E202 7 异常 登录失敷 POST 9435 查看白删际 8 正常 退出成功 127.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 DELETE pig 查看 白副除 9 正常 录减功 127.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 POST 480 10 正常 登录成功 10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='140.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='4 POST 138 9 01 E1 90 EZ02 @查看 白制脉 11 正常 登录成功 0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1 POST 398 05 01 E1 90 E202 12 正常 登录成功 10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='11.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='40.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='4 POST 148 PE60 E1 90 EZ02 查看 白删际 13 正常 曼录成功 10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1,40.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='62 POST 147 @查看 白剧除 14 正常 登录成功 POST 131 2023 06 13 08:05 15 正常 登录威功 10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='11.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='40.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='62 POST 137 16 正常 登录成功 10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='1,40.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='253 POST 144 EL 21 90 E202 17 正常 0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='11.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} +page_content='404 POSt' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\Plough Knowledge Ocean Intro\\content\\北斗知海系统用户指南.pdf'} diff --git "a/Plough Knowledge Ocean Intro/content/tmp_files/\345\214\227\346\226\227\347\237\245\346\265\267\347\263\273\347\273\237\347\224\250\346\210\267\346\214\207\345\215\227.pdf.txt" "b/Plough Knowledge Ocean Intro/content/tmp_files/\345\214\227\346\226\227\347\237\245\346\265\267\347\263\273\347\273\237\347\224\250\346\210\267\346\214\207\345\215\227.pdf.txt" new file mode 100644 index 0000000000000000000000000000000000000000..b3dcf353f04b4208e536c134106fa498e40d6f49 --- /dev/null +++ "b/Plough Knowledge Ocean Intro/content/tmp_files/\345\214\227\346\226\227\347\237\245\346\265\267\347\263\273\347\273\237\347\224\250\346\210\267\346\214\207\345\215\227.pdf.txt" @@ -0,0 +1,1280 @@ +1 / 29 +⼀、系统整体介绍 +1.1. +背景 + “笃志问题求解，贯通古今中外”，北⽃知海系统(Plough Knowledge Ocean，aka, PKO) +旨在建⽴全球最⼤的综合知识库，以跨语⾔、多学科、可计算和⾃增殖的知识计算为研究主 +题，以“⼤”、“动”、“亮”落地场景为应⽤特⾊，以⼈机协同的HAO智能为技术抓⼿，集成深 +度学习与图谱构建，开拓数据和知识双轮驱动。以知识碎⽚化问题为切⼊点，利⽤“表示演 +化-多源融合-知识导航”的解决思路，实现多源海量数据到知识的“量-质-序”的转化。 +1.2. +⽬标 + 北⽃知海系统旨在建⽴⼀个以问题求解为驱动、跨学科、多场景、可计算、可增值的动 +态知识库，集成深度学习与图谱构建，开拓数据和知识的双轮驱动研究。通过研究以下四个 +科学问题：①异构⾃治的多源知识获取，②跨学科多媒体知识的表示、评估和融合，③多重 +知识推理和计算，④类⼈智能技术的⼈机协同，在以下⼋项关键技术上寻求突破：①数字⼈ +设计技术，②多维信息感知、交互与融合，③⼤规模知识图谱构建，④跨媒体智能分析与理 +解，⑤多重关系联想与复合知识索引，⑥⼈机交互和双向双轮驱动，⑦开放环境下的持续学 +习，⑧⾃然⼈、数字⼈、机器⼈在物理空间和数字空间的全息融合。在技术上达到国际领先 +⽔平，并在智能教育、智慧药物、以及服务机器⼈等场景进⾏落地应⽤。 +1.3. +应⽤场景 + 北⽃知海系统依托全⽹数据和知识，期待在智慧医疗、智慧教育、智慧⾦融、以及智慧 +机器⼈等众多垂直领域（⻅图1）发挥重要作⽤。 +北⽃知海系统⽤户指南 + +2 / 29 +图1：垂直领域应⽤场景 + 在智慧医疗领域中，通过使⽤机器学习和⼈⼯智能技术，构建药物数据库，对蛋⽩、分 +⼦等数据的联合分析，识别疾病机理，并进⼀步分析分⼦成药性质，将知识可⽤于分⼦筛 +选。同时，通过联邦学习平台利⽤多⽅数据，探索分⼦数据的群体效能，进⼀步加速药物发 +现。 + 在智慧教育领域，通过使⽤虚拟现实和增强现实技术，提供有趣且有效的学习⽅式。通 +过互动问答，掌握学⽣学习状况，提供个性化定制学习路径推荐。帮助学⽣更好地理解课程 +内容，更好地掌握知识点，并为学⽣提供实践机会，以增强学⽣的实践能⼒。 + 在智慧⾦融领域，通过使⽤⼤数据技术和区块链技术，帮助⾦融机构更好地管理⻛险， +提⾼⾦融服务的效率。帮助⾦融机构分析客户的信⽤⻛险，提供个性化的⾦融产品和服务， +并帮助⾦融机构更好地管理⾦融交易。 + 在智慧机器⼈领域，通过使⽤机器学习和⼈⼯智能技术，使机器⼈能够更好地理解⼈类 +语⾔，与⼈类进⾏更有效的沟通。利⽤家居云脑技术，应⽤于智慧家居⾏业。 +1.4. +系统模块 + +智慧 +智慧 +教育 +金融 +智慧 +智慧 +应用场景 +医疗 +机器人3 / 29 + 整个系统依托北⽃知海知识库，包含了①⽹站⾸⻚、②示范应⽤、③管理后台三⼤模块 +（⻅图2）。⽹站⾸⻚是北⽃知海系统的⻔户，向⽤户全⾯展示北⽃知海系统的整体内容；示 +范应⽤是依托知识库研发的各类应⽤，⽤于解决各类垂直领域的具体问题；管理后台是北⽃ +知海系统的基座，⽤于管理系统的各类基础数据，例如⽤户、权限、⽇志等等。 +图2：北⽃知海系统三⼤模块 + +⼆、⽹站⾸⻚介绍 + +北斗知海系统 +网站首 +示范 +管理 +页 +应用 +后台4 / 29 + ⽹站⾸⻚是北⽃知海的⻔户，向⽤户全⾯宣传和展示系统的整体框架。可以通过链接 +“ https://ko.zhejianglab.com” 进⼊北⽃知海系统的⾸⻚，其中⻚⾯顶部导航栏列出了⽹站的 +各个主要⻚⾯（如图3所示）。每个⻚⾯同时具有相同的底部内容，⽤于展示相应的⽹站信息 +（如图4所示）。 +图3：北⽃知海⾸⻚顶部导航栏 +图4：⻚⾯底部内容 +2.1. +⽹站⾸⻚ + 点击顶部“⽹站⾸⻚”进⼊，该⻚⾯包含了⾸⻚图⽚、知海规模、知海定义、示范应⽤、 +发展成就。⾸⻚图⽚是对北⽃知海系统的形象化描述，上有北⽃七星，下有⽆边⼤海（⻅图 +5）。 +图5：⾸⻚图⽚ + + + + + + +知海规模给出了当前知海系统所达到的规模，列出了条⽬、关系、⼀层科⽬、和⼆层科 +⽬的最新统计数（⻅图6）。 + +KO 知识海洋 +网站首页 +知海萃取 +知识问答 +示范应用 +一站式管理平台 +发展成就 +联系我们 +连通、综合、 +容纳、制衡 +演化的知识海 +洋友情链接： +之江实验室华谱系统合工大 +公司网站 +加入知海 +服务协议 +隐私协议 +中心名称：之江实验空知识工程研究中心 +中心邮箱：ke@zhejianglab.com +版本号：20230620 +Copyright2022-2023由之江实验室提供技术支持All RightsReserved本系统服务的范围及用途均适用于并遵循中华人民共和国法律和相关法规连通、综合、 +容纳、制衡 +演化的知识海 +洋当前规模 +485,311,385 +317,319,224 +128 +1,139 +条目 +关系 +一层科目 +二层科目 +数据来源：中华谱-知海5 / 29 +图6：知海规模 + + + + + + + +知海定义为吴信东院⼠对北⽃知海项⽬的精准定义（⻅图7）。 +图7：知海定义 + + + + + + + +示范应⽤为依托北⽃知海平台开发的各类垂直领域应⽤（⻅图8）。此处展示热度排名前 +三的应⽤，需要查看更多应⽤可以进⼊“示范应⽤”⻚⾯查看详情。点击每段⽂字后的“更多” +可以进⼊应⽤介绍⻚⾯，点击“查看详情 ”可直接进⼊相应的应⽤⻚⾯。 +图8：示范应⽤ + + + + + + +发展成就为北⽃知海平台及知识⼯程研究中⼼发展过程中的重要事件。重点选取每个时 +期的代表性事件，需要查看完整发展过程，可在”发展成就“⻚⾯查看。 同时，⻚⾯下⽅有分 +⻚控件，可通过点击左右按钮和数字按钮的⽅式灵活选择，查看不同时期的事件 （⻅图 +9）。 + +关于知海 +一片连通、综合、容纳、制衡、演化的知识海洋 +笃志问题求解，贯通古今中外。知海KO（KnowledgeOcean）含有全球最大的综 +合知识库，以跨语言、多学科、可计算和自增殖的知识计算为研究主题 +以"大"、“动"、“亮"落地场景为应用特色，以人机协同的HAO智能为技术抓手，集 +成深度学习与图谱构建，开拓数据和知识双轮驱动。 +吴信东2022年10月19日示范应用 +家具云脑 +智慧制药 +工资QA +项目旨在构建满足智能家居应 +现代药物研发流程具有典型的 +在北斗知海的图数据库中，知 +用的云脑平台，通过引入之江 +长周期、高风险以及高投资的 +识工程中心导入了大学和公司 +北斗综合性知识库、HAO推理 +特点，究其原因，是因为我们 +的职员工资数据，构建了人 +机、以及数据挖掘、自然语言 +当前的药物研发流程十分依赖 +员、岗位、部门和薪资等实 +处理、强化学习、搜索推荐、 +生物实验。针对某个疾病..更 +体，年份等属性，以及雇佣、 +规划监测..更多 +多 +隶属等关系..更多 +查看详情 +查看详情 +查看详情6 / 29 +图9：发展成就 +2.2. +知海萃取 + 知识⼯程中⼼⾯向科学前沿和国家重⼤需求，以知识⼯程为核⼼，兼顾多学科交叉，开 +展基础理论、算法模型以及落地应⽤等⽅⾯的研究。在知识抽取、知识管理、模型训练与推 +理⽅⾯有⼀定的积累与优势。 + 知识⼯程中⼼结合之江实验室在基因、制药、天⽂、材料等领域的积累与⽂献抽取需 +求，拟构造基于国内外开源⼤语⾔模型的【国产⽂献抽取⼤模型】。 +1. 基于⼤模型的科学⽂献抽取调研评测报告 +2. 基于⼤模型的科学⽂献领域垂直数据集与评测平台 +3. 国产科学⽂献抽取⼤模型 +2.3. +知识问答 + 知识问答模块主要使⽤⽣成式语⾔⼤模型来进⾏⽂档问答（QA）的任务。与传统的⽂档 +问答系统相⽐，这种⽅法的优点在于可以利⽤⽣成式语⾔⼤模型强⼤的⽣成能⼒来产⽣更为 +准确、详细的答案。在此过程中，⼤模型通过阅读相关⽂档并提取问题所需的信息来寻找答 +案。这种⽅法不仅可以提⾼QA的准确性，还可以提⾼系统的可扩展性和适应性。 + +发展成就 +第十届吴文俊人工智能技术发明奖一等奖 +知识图讯 +A智创十年赋能未来 +吴信东等斩获吴 +《知识图谱》由 +之江实验室知识 +文俊人工智能科 +科学出版社出版 +工程研究中心成 +学技术奖技术发 +发行 +立 +明一等奖 +2021年4月10日 +2022年7月 +2023年2月9日《 +1 +2 +3 +4 +5 +6 +10 +》7 / 29 + 通过上传PDF⽂件到知识问答模块，就能实现和PDF跨语⾔对话，并根据PDF内容回答 +提问。即通过知识问答模块能够实现和PDF聊天。跨语⾔是指如果PDF是英⽂，你可以输⼊ +中⽂和它对话，反之亦然。⽽该应⽤的核⼼⽅法就是基于OpenAI的 Chat API，给PDF的每⼀ +段创建语义索引，然后使⽤关联最密切的段落去提示 (Prompt) Chat API。 + 知识问答可以帮助⽤户更好地学习。⽆论是课本、讲义还是演示⽂稿，都可以轻松理 +解。⽆需再花费数⼩时翻阅研究论⽂和学术⽂章，让⽤户更有效地⽀持学术成⻓。通过知识 +问答，⽤户可以轻松地解锁⽆尽知识。从历史⽂档到诗歌、⽂学作品，⽆论是什么语⾔，知 +识问答都能理解并⽤喜欢的语⾔回复。让好奇⼼得到满⾜，拓宽视野，这个⼯具能回答任何 +来⾃PDF⽂件的问题。 +2.4. +示范应⽤ + 在“示范应⽤”⻚⾯点击“更多”（⻅图10）后会展示每个示范应⽤的详情信息。 +图10: 点击“更多”进⼊示范应⽤的详情⻚⾯ + 以⼯资QA为例，当点击“更多"按钮，相关的详细信息将会进⼀步呈现（⻅图11）。 + +示范应用 +家具云脑 +智慧制药 +工资QA +项目旨在构建满足智能家居应 +现代药物研发流程具有典型的 +在北斗知海的图数据库中，知 +用的云脑平台，通过引入之江 +长周期、高风险以及高投资的 +识工程中心导入了大学和公司 +北斗综合性知识库、HAO推理 +特点，究其原因，是因为我们 +的职员工资数据，构建了人 +机、以及数据挖掘、自然语言 +当前的药物研发流程十分依赖 +员、岗位、部门和薪资等实 +处理、强化学习、搜索推荐、 +生物实验。针对某个疾病..更 +体，年份等属性，以及雇佣、 +规划监测..更多 +多 +隶属等关系..更多 +查看详情 +查看详情 +查看详情8 / 29 +图11：⼯资QA更多信息 + 当点击”⼯资QA“的”查看详情“时，⽤户登录注册界⾯会展现，提示⽤户需要注册后登 +录使⽤该功能（⻅图12）。 +图12：点击”查看详情“后的登录界⾯ +2.5. +⼀站式管理平台 + +工资QA +在北斗知海的图数据库中，知识工程中心导入了大学和公司的职员工资数据，构建了人员、岗位、部门和新资等实体，年份等属性，以及 +雇佣、隶属等关系，形成了完整的工资知识图谱数据结构。通过知识推理和自然语言处理技术，可以实现工资的查询、统计、多步推理，以及 +预测、规划分配等场景的响应。系统具有流畅的自然语言对话形式问答界面，以及工资查询，图谱展示和数据分析的功能，且具有与北斗知海 +进行通用知识库与专有知识库的数据交互和知识萃取的功能。工资问答示范系统全面展现了北斗知海在工资场景知识工程的综合应用。之江实验室 +ZHEJIANG LAB +登录 +8账号 +请输入账号 +邑 密码 +请输入密码 +立即登录 +没有账号？ +8立即注册9 / 29 + 点击“⼀站式管理平台”或链接“https://ko.zhejianglab.com/ADMIN”，进⼊管理后台⻚⾯ +（⻅图13）。 +图13：⼀站式管理平台登录 +2.6. +发展成就 + 点击“发展成就”或链接“ https://ko.zhejianglab.com/news.html”进⼊“发展成就”⻚⾯， +北⽃知海平台及知识⼯程研究中⼼发展过程中的重要事件按照时间倒序的⽅式逐⼀呈现（⻅ +图14）。 + +R admin +请输入验证码 +KO一站式服务管理平台 +账号密码短结登录用户注期10 / 29 +图14：发展成就 +2.7. +联系我们 + 点击“联系我们”或链接“ https://ko.zhejianglab.com/contact.html”进⼊"联系我们"⻚⾯ +（⻅图15）。知识⼯程研究中⼼正处于发展前期，需要各类⼈才的加⼊。同时，依托北⽃知 +海，定有⼴⼤作为，我们也寻求更多的合作。 + +网站首页 +知海萃取 +知识问答 +示范应用 +一站式管理平台 +发展成就 +之江沙龙：大模型时代的知识工程 +大模型时代的知识工程大模型时代的知识工程大模型时代的知识工程大模型时代 +的知识工程大模型时代的知识工程大模型时代的知识工程 +2023年4月24日 +之江学本护亮-） +大模型时代的知识工程 +圆桌论坛 +之江实验室知识工程研究中心成立 +之江实验室知识工程研究中心成立之江实验室知识工程研究中心成立之江实验室 +知识工程研究中心成立之江实验室知识工程研究中心成立之江实验室知识工程研 +究中心成立之江实验室知识工程研究中心成立 +2023年2月9日 +《知识图谱》由科学出版社出版发行 +这部专著系统介绍了知识图谱的概念、发展历程、技术体系、前沿技术与应用实 +践。在基础知识方面，本书囊括了知识图谱从源数据到产生决策的全生命周期的 +N +各个环节，分析了数据图谱和知识图谱的核心区别，介绍了图谱构建和知识表 +机协 +识11 / 29 +图15：联系我们 +三、示范应⽤介绍 + 北⽃知海系统具有⼴泛的示范应⽤价值，应⽤范围可涵盖交通、通信、能源、医疗、环 +保等多个⽅⾯，有望在这些领域取得了卓越的成果。例如，在交通领域，该系统的智能交通 +管理系统可以实现城市交通的智能化和⾼效化，提⾼交通运输效率，减少交通事故的发⽣； +在通信领域，该系统的⾼速⽹络技术可以实现⾼速、稳定、安全的数据传输，满⾜⼈们对于 +信息交流和共享的需求；在能源领域，该系统的能源管理系统可以实现对能源的精细管理和 +有效利⽤，提⾼能源利⽤效率，降低能源消耗成本；在医疗领域，该系统的智能医疗系统可 +以实现医疗资源的优化分配和管理，提⾼医疗服务的质量和效率；在环保领域，该系统的环 +境监测系统可以实现对环境污染的实时监测和预警，提⾼环境保护的效果和⽔平。综上所 +述，该系统的⼴泛应⽤和卓越成果为社会进步和发展做出了重要贡献。 +3.1. +⼯资问答 + +欢迎您的咨询和加入 +寻求合作，知识工程研究中心欢迎各类人才的加入 +contact us +联系我们 +e +邮箱：bigke2016@gmail.com +地址：杭州市之江实验室12 / 29 + 在北⽃知海的图数据库中，知识⼯程中⼼导⼊了⼤学和公司的职员⼯资数据，构建了⼈ +员、岗位、部⻔和薪资等实体，年份等属性，以及雇佣、⾪属等关系，形成了完整的⼯资知 +识图谱数据结构。通过知识推理和⾃然语⾔处理技术，可以实现⼯资的查询、统计、多步推 +理，以及预测、规划分配等场景的响应。系统具有流畅的⾃然语⾔对话形式问答界⾯，以及 +⼯资查询，图谱展示和数据分析的功能，且具有与北⽃知海进⾏通⽤知识库与专有知识库的 +数据交互和知识萃取的功能。⼯资问答示范系统全⾯展现了北⽃知海在⼯资场景知识⼯程的 +综合应⽤。 + ⼯资问答系统是⼀个完整的知识⼯程应⽤，是⼀个基于知识图谱的对话问答系统，系统 +架构如图16所示。 +图16： ⼯资问答系统架构 + 在系统架构上从底⾄上分为四层：⼯程底座，数据层，应⽤实现层和业务层。 +⼯程底座，包含了对接管理后台的⽤户注册，登录，权限控制和应⽤调度功能。 +数据层，包含了图数据库Neo4j，以及从外部知海系统和⽂件等进⾏知识萃取的功能 +模块。 +应⽤实现层，主要通过两条技术路径实现⾃然语⾔的问答解析，基于Cypher语⾔的知 +识推理，以及答案内容的⽣成：⼀是KBQA，⼆是语⾔⼤模型。封装在后端NLP +Python⼯程中，以接⼝⽅式与数据层和业务层通信。 +业务层，包含了Web应⽤实现的⼏个模块，主要包含⼯资问答、我的⼯资、图谱展 +示、数据分析⼏个⻚⾯和功能。 +○ +○ +○ +○ + +工资间管蒙练架构 +工资问答 +工资查询 +图谱展示 +数据分析 +QA 问答引擎 +Cypher查询推理 +语言大模型内容生成 +NLP Python工程 +工资文件(UMV) +导入 +数据库 Neo4J +萃取 +知海 +工程底座用户登录，权限，APP调度13 / 29 + 以下将根据系统功能分为 注册登录、数据模型、⼯资问答、我的⼯资、图谱展示、数据 +分析⼏个模块介绍⼯资问答系统。 +3.1.1 +注册登录 + 注册模块完成⽤户注册到系统中的操作，需要提供⼿机号来验证身份。注册成功的⽤户 +才可以使⽤系统的功能。⾸次访问⽹⻚会⾃动跳转到登录⻚⾯，在登录⻚⾯中点击“⽴即注 +册”进⼊注册⻚⾯。⽤户填写注册⻚⾯所需要登记的信息，点击“⽴即注册”按钮提交信息 +（⻅图17），然后点击“⽴即登⼊”转到登录⻚⾯进⾏登录（⻅图18）。 +图17：注册⻚⾯ + +注册 +之江实验室 +ZHEJIANG LAB +8账号 +请输入账号 +手机号 +请输入手机号 +验证码 +请输入验证码 +密码 +请输入密码 +密码 +请再次输入密码 +立即注册 +没有账号? +8立即登入14 / 29 +图18：登录⻚⾯ +3.1.2 +数据模型 + ⼯资的数据模型，包括person（⼈员）、salary（⼯资）、position（职位）和 +department（部⻔）四种节点和 earn（赚钱）、 employ（雇佣）、pricing（价值）和in +（属于）四种关系，person中包含name（姓名）属性，salary中包含year（年份）和salary +（⼯资）属性，position中包含year（年份）和position（职位）属性，department中包含 +year（年份）和department（部⻔）属性（⻅图19）。 + +之江实验室 +ZHEJIANG LAB +登录 +8账号 +请输入账号 +密码 +请输入密码 +立即登录 +没有账号? +8立即注册15 / 29 +图19：⼯资数据模型 +3.1.3 +⼯资问答 + ⼯资问答以⼯资知识图谱为基础，采⽤基于知识图谱的问答框架（⻅图20）。该框架以 +⾃然语⾔问句为输⼊，通过问句分类将输⼊⽂本分到预设的问题类别下、然后通过问句解析 +模块将不同类别下的问句进⾏实体识别与抽取，之后通过查询语句转化模块将⾃然语⾔问句 +转换为对应的查询语⾔在⼯资知识图谱中进⾏相应的查询，之后调⽤相应类别问题下的统 +计、计算、预测等任务模块执⾏，最后根据分类类别与获取到的执⾏结果进⾏回答语句组 +装，进⾏答复。 + +department +person +property: +year +in +property : +department +property:name +node +employ +earn +node +salary +property: year +property: position +property: year +position +pricing +property: salary +node +node16 / 29 +图20：⼯资问答技术框架 +⼯资KBQA问题列表 + + 以下是⼯资KBQA问题列表：这些问题通过⼈名、时间、职位、部⻔、薪资四个维度的 +组合可以实现，例如： +a. 个⼈某年的⼯资、职位、部⻔查询 +b. 某个职位或者部⻔的平均薪资计算 +c. 个⼈所在职级、职位上的薪资⽔平统计 +d. 个⼈在某年的薪资是否能够达到同职级、部⻔的平均⽔平的计算⽐较 + 图21展示了⼀些基于上述组合的示例问题。 +question_1 = '我是Davis,Wendy Sue，我2014年的⼯资是多少？' +question_2 = "请问职级为Professor的⼈，2015年平均⼯资是多少？" +question_3 = "我是Davis,Wendy Sue，我所在的职级年薪⼤于50000的⼈有多少？" +question_4 = "请问Davis,Wendy Sue的2015年的⼯资是否达到同级别的平均⽔平？" +question_5 = '我是Davis,Wendy Sue，我2014年所在的部门是什么？⼯资是多少？' +question_6 = '请问部门为Computer Science的⼈，2015年平均⼯资是多少？' +question_7 = '我是Davis,Wendy Sue，我所在的部门年薪⼤于50000的⼈有多少？' +question_8 = "请问Davis,Wendy Sue的2015年的⼯资是否达到同部门的平均⽔平？" +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 + +组件 +自然问句 +细节 +question +Ruler +问句分类 +Word +classifier +WordKB +Expansion +question +Ruler +问句解析 +Dependency +parser +WordKB +Parser +查询语句 +slot +cypher +search_sqler +转换 +filling +pattern +结果返回 +工资知识图谱 +基于知识图谱的问答框架17 / 29 +图21：示例问题 + 图22（a-d）以系统截图⽅式展示了⼀些问答实例 +图22（a）：问答实例1 +图22（b）：问答实例2 +10 + +2023-06-13 15:17:46 +我是Ades,Steven， +我2014年的工资是多少？ +2023-06-13 15:17:46 +您好，Ades,Steven的2014年的工资为40000。 +2023-06-1315:18:06 +请问职级为Professor的人，2015年平均工资是多少？ +2023-06-1315:18:06 +您好，职级为Professor的人2015年的平均工资为121385我是Davis,WendySue，我所在的职级年薪大于50000的人有多少？ +2023-06-13 15:18:20 +您好，Davis,WendySue所在的职级为Professor，年薪大于50000的人有818位 +2023-06-13 15:18:35 +请问DavisWendySue的2015年的工资是否达到同级别的平均水平？ +2023-06-1315:18:35 +您好，能够达到！ +2023-06-1315:18:35 +因为Davis,WendySue在2015年所在的职级为Professor，年薪是160635，该年这个职级的平均工资是121385 +所以能够达到！18 / 29 +图22（c）：问答实例3 +图22（d）：问答实例4 +⼯资规划和预测 + ⼯资预测问题：输⼊相关的⼯资预测问题，得到系统答复。答复中会包含⼯资预测的计 +算逻辑，并⽤平滑曲线图展示历史⼯资信息。例如⽤户可以问，”Abaied, Jamie L.在2024年 +⼯资预计达到多少”，后台算法会根据被询问者的历史⼯资特征对未来⼯资情况进⾏预测（⻅ +图23）。 + +2023-06-1315:20:39 +我是Davis,WendySue，我2014年所在的部门是什么？工资是多少？ +2023-06-1315:20:39 +您好，Davis，WendySue所在的部门是：PhysicalCulture，在2014年的工资为153000 +2023-06-1315:20:53 +请问部门为ComputerScience的人，2015年平均工资是多少?我是Davis,WendySue，我所在的部门年薪大于50000的人有多少？ +2023-06-13 15:21:04 +您好，Davis，WendySue所在的部门为PhysicalCulture，年薪大于50000的人有1624位。 +2023-06-13 15:21:20 +请问Davis,WendySue的2015年的工资是否达到同部门的平均水平？ +2023-06-13 15:21:20 +您好，能够达到！ +2023-06-13 15:21:20 +因为Davis,WendySue在2015年所在的部门为PhysicalCulture，年薪是160635，该年这个部门的平均工资是 +67486，所以能够达到！19 / 29 +图23：⼯资预测问答示例 + 另⼀种常⻅的场景是，⽤户希望知道在给定薪酬总包的情况下，如何分配给各位在职员 +⼯，则可以提问：“假设2024年薪酬总包是288,000,000元，建议分配给Zimakas, Nilgun T.的 +数额是多少？” + 算法根据被询问者的个⼈⼯资变化情况、所在职位的历年平均⼯资的变化趋势、薪酬总 +包三⽅⾯因素，综合考量给出薪酬分配的建议值。具体来说，系统⾸先根据所在职位的历年 +平均⼯资的变化趋势，预测出该职位的⼯资⽔位，然后通过⽐较被询问者与同岗职⼯之间历 +年⼯资变化情况，判断个体竞争⼒，最后结合⽤户给出的薪酬总包⼤⼩，计算分配给个体的 +份额（⻅图24）。 + 此外，我们根据历年⼯资变化趋势，预测出2023年的薪酬总包⼤约为289,000,000元， +因此，⽤户在输⼊薪酬分配问题时，在此数值附近，所得到的答复会更符合实际。 + +预测ABAIEDJAMIEL在2024年的工资。 +2023-061417:23:05 +ABAIED，JAMIEL最近一次职务变动是从ASSISTANTPROFESSOR成为ASSISTANTPROFESSOR，根据担任 +ASSISTANTPROFESSOR期间工资年均增长率0.0252预测其2024年工资为88927.43。 +100,000 +80,000 +60,000 +40,000 +20,000 +2016 +2011 +2018 +2019 +2020 +202 +2014 +2015 +2022假设2024年薪酬总包是288000000元，分配给Zimakas,NilgunT.的数额是多少？ +2023-062609:47:00 +ZIMAKAS,NILGUNT当前职位为ASSISTANTPROFESSOR（COM)，根据该职位平均新酬变化趋势，以及 +ZIMAKAS.NILGUNT个人工资变化趋势，预测2024年在薪酬总包288000000.0元中的分配数额为17694.3。 +18,000 +15,000 +12,000 +9,000 +6,000 +3,000 +0 +2013 +2014 +2015 +2016 +2017 +2018 +2019 +2020 +202120 / 29 +图24：⼯资总包分配示例 +3.1.4 +我的⼯资查询 + 进⼊”我的⼯资”⻚⾯，输⼊姓名、时间、⼯资范围，即可点击“搜索”按钮查询对应的⼯ +资信息，具体查询到的⼯资信息以列表形式展示（⻅图25）。 +图25：⼯资查询结果 +3.1.5 +图谱展示 + 进⼊图谱展示，输⼊姓名，开始时间，结束时间，查询范围相关搜索条件，即可查询相 +关⼈员的⼯资的知识图谱（图26）。 + +之江实验室 +ZHEJIANG LAB +admin +工资问答 +我的工资 +工资图谱 +数据分析 +姓名 +Davis,Wendy Sue +开始时间 +2000 +结束时间 +2028 +查询范围 +0 +8000000 +搜索 +重置 +工资明细 +姓名 +职位 +年份 +应发工资 +实发工资 +Davis,WendySue +Professor +2013 +112500 +112500 +Davis,Wendy Sue +Professor +2014 +153000 +153000 +Davis,WendySue +Professor +2015 +160635 +160635 +Davis,Wendy Sue +Professor (COM) +2017 +177067 +177067 +Davis,Wendy Sue +Professor(COM) +2018 +185902 +185902 +Davis,Wendy Sue +Professor (COM) +2019 +191479 +191479 +Davis,WendySue +Professor (COM) +2020 +181905 +181905 +Davis,WendySue +Professor (COM) +2021 +193394 +193394 +京公网安备10000001000001号京ICP证010101号互联网新闻信息服务许可证11110110001网络文化经营许可证：京网文【2023】1011-001号21 / 29 +图26：图谱查询结果 +3.1.6 +数据分析 + + + + + + + ⼯资总数以指标卡形式展现总发放⼯资和总⼈⼒成本（⻅图27）。 +图27：⼯资总数 + + + + + + + +根据部⻔和职位，以折线图统计呈现历年平均⼯资⾛势（⻅图28）。 + +工资问答 +我的工资 +工资图谱 +数据分析 +筛选条件 +图谱展示 +姓名 +Abair,Shirley Sam +开始时间 +菌 2002 +eneralist(2014) +结束时间 +菌 2022 +fice/Prgm SuF +(Pport (ariperalist(2017) +Office/Prgm Su +2017) +查询范围 +11 +Abal +earn +ean +24637 (2013) +salar:27480 +2018) +查询范围 +11111111111 +Mojdu +earn +Office/Prgm SupportGeneralist(213) +Office/Prgm Support G +Generalist(2018) +28219 +2019 +搜索 +重置 +Office/Prgm Support Genera +t(2019) +京公网安备10000001000001号京ICP证010101号互联网新闻信息服务许可证11110110001网络文化经营许可证：京网文【2023】1011-001号之江实验室 +ZHEJIANG LAB +admin +工资问答 +我的工资 +工资图谱 +数据分析 +今年总发放工资 +今年总人力成本 +$283,860,487.00 +￥ 28,425.00 +相比去年 +7.03% ↑ +相比去年 +20% ↑22 / 29 + 图28：平均⼯资 + 其中，可由下拉选择框筛选部⻔和职位（⻅图29）。 +图29：筛选部⻔职位 + +平均工资 +请选择 +开始日期 +至 +结束日期 +搜索 +150,000 +120,000 +90,000 +60,000 +30,000 +平均工资 +请选择 +开始日期 +至 +结束日期 +搜索 +80,000 +100 % +70,000 +90 % +80 % +60,000 +70 % +50,000 +60 % +40,000 +50 % +30,000 +40 % +30 % +20,000 +20 % +10,000 +10 % + 0 % +201 +201 +019 +2020 +202平均工资 +请选择 +菌 +开始日期 +至 +结束日期 +搜索 +部门 +> +Mathematics Department +150,000 +职位 +Biomedical Sciences +120,000 +Business Administration Department +Mechanical Engineering +90,000 +Philosophy +60,000 +30,000 +0 +2013 +2014 +2015 +2016 +2017 +2018 +2019 +2020 +2021 +202223 / 29 + + + + + + + +根据部⻔⼯资排⾏，显示Top 7的部⻔⾦额（⻅图30）。 +图30：部⻔⼯资排⾏ + 岗位⼯资排⾏⻅图31。 + +部门工资排行 +季度 +月度 +排名 +部门 +较上月 +金额 +0 +Politics +0+ +83578.9 +2 +Economics +0+ +80637 +B +Nutrition +21 + +75624.75 +4 +English +74971.73 +5 +Entrepreneurship +3 +74376.91 +latin american +6 +4 +74331.04 +studies +Women's and +7 +56 + +74263.52 +Gender Studies24 / 29 +图31：岗位⼯资排⾏ + +·岗位工资排行 +季度 +月度 +排名 +部门 +较上月 +金额 +0 +President ++ 0 +484800 +日 +Senior Vice +0+ +367200 +Pres/Provost +Athletic Head +325913 +Coach Sr +4 +Director-Faculty +1 +307120 +5 +Vice Pres & Gen'l +300000 +Counsel +VP of Finance & +6 +Administration +t 0 +290700 +7 +Dean +287994.7325 / 29 + ⼈员构成⽤来显示各职位⼈员构成⽐例（⻅图32）。 +图32：⼈⼯构成 + + + + + + + 问答词云统计显示⼯资问答历史记录的⽂本内容构成的词云，可以展示⾼频问答关键词 +（⻅图33）。 + +人员构成 +6.82% +6.75% +6.44% +6.41% +56.96% +4.41% +3.32% +3.1% +2.92% +2.87% +Assistant Professor (COM) +Prote +ssor +Office/Prgm Support Generalist +Associate Professor +Assistant Professor +Administrative Professional +Associate Professor (COM) +Custodial Maintenance Worker +Lecturer +其他26 / 29 +图33：问答词云 +四、管理后台介绍 + 管理后台是北⽃知海系统的基座，⽤于管理系统的各类基础数据，例如⽤户、权限、⽇ +志等等。 +4.1. +登录注册 + 点击链接“https://ko.zhejianglab.com/ADMIN/#/login”进⼊管理后台的登录⻚⾯（⻅图 +34）。 + +·人员构成 +吴信东 +之江实验室 +工资27 / 29 +图34：后台管理系统登录⻚⾯ + 当前系统⽀持通过⼿机号加密码的⽅式登录，输⼊正确的⼿机号和密码，点击登录按 +钮，即可进⼊系统。点击“⽤户注册”进⼊注册⻚⾯（⻅图35）。 +图35：后台管理系统⽤户注册⻚⾯ + 通过输⼊⽤户名、密码和⼿机号码注册⼀个新⽤户，在录⼊⽤户名和⼿机号码时会实时 +验证是否存在相同⽤户名或⼿机号码，如果已存在，则会在输⼊框下红字提醒。输⼊正确的 +⼿机号和密码后，登⼊系统⾸⻚。 +4.2. +⽤户管理 + 如果前登录⽤户具有“⽤户管理”⻚⾯的访问权限，可以点击权限管理-⽤户管理，进⼊“⽤ +户管理”⻚⾯（⻅图36）。 + +8请编入手机号码 +斗加海 +请输入于机号码 +请验入度码 +请输入座码 +登示 +KO一站式服务管理平台 +手机号密码用户注前8请输入用户名 +输入用户名 +合请能入密码 +清输入密码 +臣请输入手机号码 +清输入丁机号 +KO一站式服务管理平台 +手机号密码用户注带28 / 29 +图36：⽤户管理⻚⾯ + 在该⻚⾯可对⽤户进⾏查询、添加、导⼊、导出、分⻚浏览等操作。例如，点击添加按 +钮，弹出新增⽤户弹窗，可为新⽤户设置⽤户名、密码、部⻔、⼿机号、⻆⾊、岗位、状态 +信息。点击保存，新⽤户保存到系统（⻅图37）。 +图37：新增⽤户 +4.3. +⽇志管理 + 如果当前登录⽤户具有“⽇志管理”⻚⾯的访问权限，可点击系统管理-⽇志管理，进⼊ +“⽇志管理”⻚⾯。可对⽇志进⾏搜索、导出、查看、删除操作。每⼀条⽇志包含了类型、标 +题、IP、请求⽅式、客户端、请求时间、创建时间、异常⽇志等详细信息，便于管理者查看 +（⻅图38）。 + +用户名： +请输入用户名 +Q接索 +仓清空 +± 导入 ++ 导出 +Q +序号 +用户名 +手机号 +角色 +部门 +岗位 +状态 +创建时间 +操作 +1 +admi +131155522 +普递用户 +正常 +20-90-E202 + 编抗白 制除 +2 +aa +普道用户 +正常 +L-50-E202 +C 编排 副除 +m +zhang2 +普递用户 +[正路 +0E-50-E202 + 编辑 除 +4 +zhang1 +1350000 +普通用户 +正常 +0-50-E202 +C 编辑 副除 +zhang +1350000 +正常 +0E-0-E202 + 编辑 除 +6 +orybuswonb +13434563458 +普通用户 +行政中心 +员 +正常 +SL-50-E202 + jack +15837570607 +普递用户 +研发中心 +co +正常 +SL-S0-EZ02 +8 +newuseri +13445674567 +普递用户 +运营中心 +员工 +正路 +LL-S0-E202 +9 +zheshixinde +13412341234 +普运用户 +正若 +0L-50-E202 +C编辑 除 +10 +testuser +18168789253 +普退用户 +正常 +0L-50-E202 +11 +newuser +普题用户 +正路 +0L-50-E202 +E 编辑 白 副除 +12 + Sunshanvin +17712341234 +普通用户 +研发中心 +员 +正常 +2023-04-26 +L 排 除 +test1 +13365874125 +普通用户 +行政中心 +童事长 +正常 +12-80-202 +14 +admin +管理员 +总经办 +员 +正路 +02-P0-8102 +共14条 +20条/顶 +前往新增 +3 × +*用户名： +请输入用户名 +请输入用户名 +密码： +请输入密码 +请输入密码 +*所属部门： +请选择所属部门 +*手机号： +请输入手机号 +*角色： +请选择角色 +*岗位： +请选择岗位 +*状态： + 正常 +锁定 +④保存 +取消29 / 29 +图38：⽇志管理⻚⾯ + +类型：请选择类型 +IP地址 +请输入IP地址 +创建时间 +开始 +结束 +Q搜索 +自清空 +￥导出 +鲁 +类型 +标题 +IP地址 +请求方式 +客户端 +请求时 +间 +创建时间 +操作 +1 +正常 +登录成功 +POST +166 +2023-06-13 15:11 +直看白制际 +2 +正常 +登录成功 +10.1,40.253 +POST +197 +3 +异常 +婴录失败 +10.11,40.253 +POST +164 +2023-06-13 15:07 +4 +正常 +退出威功 +127.0.0.1 +DELETE +pig +@查看 白副除 +5 +正常 +登录成功 +POST +1144 +6 +异常 +登录失败 +127.0.0.1 +POST +364 +PEPL EL-90-E202 +7 +异常 +登录失敷 +POST +9435 +查看白删际 +8 +正常 +退出成功 +127.0.0.1 +DELETE +pig +查看 白副除 +9 +正常 +录减功 +127.0.0.1 +POST + 480 +10 +正常 +登录成功 +10.140.4 +POST +138 +9-01 E1-90-EZ02 +@查看 白制脉 +11 +正常 +登录成功 +0.0.0.0.0.0.0.1 +POST +398 +05-01 E1-90-E202 +12 +正常 +登录成功 +10.11.40.4 +POST +148 +PE60 E1-90-EZ02 +查看 白删际 +13 +正常 +曼录成功 +10.1,40.62 +POST +147 +@查看 白剧除 +14 +正常 +登录成功 +POST +131 +2023-06-13 08:05 +15 +正常 +登录威功 +10.11.40.62 +POST +137 +16 +正常 +登录成功 +10.1,40.253 +POST +144 +EL 21-90-E202 +17 +正常 +0.11.404 +POSt \ No newline at end of file diff --git a/R9E3T4oBgHgl3EQfDQnp/content/tmp_files/2301.04286v1.pdf.txt b/R9E3T4oBgHgl3EQfDQnp/content/tmp_files/2301.04286v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..43d0381c38633ada0f10be2e43e3286ba4e393a8 --- /dev/null +++ b/R9E3T4oBgHgl3EQfDQnp/content/tmp_files/2301.04286v1.pdf.txt @@ -0,0 +1,789 @@ +arXiv:2301.04286v1 [astro-ph.SR] 11 Jan 2023 +Manuscript for Revista Mexicana de Astronom´ıa y Astrof´ısica (2007) +REVISITING FS AURIGAE AND ITS TRIPLE CATACLYSMIC +VARIABLE SYSTEM HYPOTHESIS +Carlos E. Chavez,1 Andres Aviles,1 Nikolaos Georgakarakos,2 Cesar Ramos,3,5 +Hector Aceves,4 Gagik Tovmassian,4 Sergey Zharikov,4 +Draft version: January 12, 2023 +RESUMEN +Una variabilidad de muy larga duraci´on (VLPP), con un periodo de 875 d´ıas, fue +observado en la curva de luz de FS Aur en 2011. El periodo fue calculado con 6 +ciclos. Reexaminamos el periodo con nuevas observaciones de los pasados 5 a˜nos. +Un total de 18 a˜nos de observaciones confirman la hip´otesis de un tercer cuerpo +perturbando de manera secular la variable catacl´ısmica (VC). Mejoras al modelo +como ´orbitas exc´entricas e inclinadas para el tercer cuerpo y una correcci´on post– +Newtoniana para la binaria son consideradas. Confirmamos el VLPP de FS Aur y +encontramos el nuevo periodo de 857 ± 78 d´ıas. Las perturbaciones seculares son +m´as eficientes cuando la masa del tercer cuerpo es M3 ≈ 29MJ, menor a M3 ≈ 50MJ +reportado en 2011. Estimamos el efecto del tercer cuerpo en la tasa de transferencia +de masa y del brillo del sistema. Consideramos otras explicaciones para el VLPP. +Estos nuevos datos y an´alisis apoyan la hip´otesis de una VC triple para FS Aur. +ABSTRACT +A very long term variability (VLPP), with period of 875 days, was observed in the +long-term light curve of FS Aurigae (FS Aur) in 2011. This periodicity was cal- +culated on 6 cycles. We re–examine the periodicity with new observations over of +the past 5 yrs. A total of 18 yrs of observations confirm the hypothesis of a third +body perturbing in a secular way the cataclysmic variable (CV). Improvements to +the model such as eccentric and inclined orbits for the third body and a binary post– +Newtonian correction are considered. We confirm the VLPP of FS Aur and find the +new period of 857 ± 78 days. The secular perturbations are most efficient when the +mass of the third body is M3 ≈ 29 MJ, much less than the 50 MJ reported in 2011. +We estimate the effect of the third body on the mass transfer rate and the brightness +of the system. We consider alternative scenarios for the VLPP. The new data and +analysis supports the hypothesis that FS Aur is a CV in a triple system. +Key Words: Stars: binaries (including multiple) — Stars: individual (FS Aur) — +Stars: novae, cataclysmic variables +1. INTRODUCTION +FS Aur is a Cataclysmic Variable (CV) that shows a wide range of light periodic +signals. It has a short orbital period of just 85.7 min (Thorstensen et al. 1996), a long +1FIME-UANL. M´exico. +2New York University Abu Dhabi, UAE. +3FCFM-UANL. M´exico +4IA-UNAM, Ensenada. M´exico +5CINVESTAV, Ciudad de M´exico. M´exico +1 + +2 +CHAVEZ ET AL. +photometric period of 205.5 min (Tovmassian et al. 2003) and a long spectroscopic +period of 147 min (Tovmassian et al. 2007). The latter two periods are attributed to +the precession of a fast rotating magnetic white dwarf and its beat with the orbital +period, respectively (see Table 1 for details). All these frequencies were discussed +in more detail in Chavez et al. (2012, hereafter CH2012). In that paper we showed +the presence of a very long photometric period (VLPP) modulation observed in the +long-term FS Aur light curve, with a 2–mag amplitude and a period around 900 days. +We argued that the origin of such modulation could be a third substellar-body (25 to +65 times Jupiter’s mass) that perturbs the eccentricity of the inner binary star system. +This triple–system hypothesis provided an explanation for the VLPP, and it was +also suggested that it might give a plausible answer for other observed peculiarities +of FS Aur. More importantly is perhaps the fact that it offers a new possibility for +detecting planets in accretion disk environments, where other methods fail. +There are other binary systems claimed to have a third object in a close orbit. +LX Ser possess an extra component of 7.5 times the mass of Jupiter that explains +a sinusoidal oscillation observed in the O – C diagram with a period of 22.8 years +(Li et al. 2016). Another example is V893 Scorpi where observed variations of the +eclipse period of 10.2 years are interpreted as a light travel time effect caused by the +presence of a giant planet with 9.5 times the mass of Jupiter (Bruch 2014). Finally +DP Leonis (Beuermann et al. 2011), HW Vir (Lee et al. 2009), NN Ser (Beuermann +et al. 2010), NY Virginis (Qian et al. 2012a), RR Caeli (Qian et al. 2012b) and +KIC 5095269 (Getley et al. 2017) are part of this small group of post-CE binaries +suspected to possess planets. +The purpose of this paper is to make use of 5 more years of observations of FS +Aurigae to see whether the VLPP signal reported in CH2012 is stronger or, on the +contrary, is disappearing. We also want to model the hierarchical triple hypothesis +in a more realistic manner by including eccentric and inclined orbits and also first +order post–Newtonian correction, that is a first order general relativity correction. +Then studying the effect these complications have on the range of possible values +on mass and semi–major axis that may explain the VLPP by secular perturbations +on the Cataclysmic Variable. This paper is organized as follows. In §2, we review +observational data of FS Aur in search of the very long photometric period (VLPP). +In §3.1 we revisit the initial conditions used in our previous research and more recent +and more accurate parameters for our system are indicated. In §3.2 we examine the +scenario where the perturber moves on a circular and coplanar orbit, whose period is +much shorter than the long period, and yet produces a binary eccentricity variation +with the latter period by secular perturbations. In §3.3 we extend this to eccentric and +inclined orbits. The range and properties of the allowed solutions are shown. In §3.4 +we check if the VLPP could be explained as a consequence of the precession effect of +the orbit due to first order general relativity corrections. In §3.5 we make an order of +magnitude estimation for the mass transfer rate and the brightness of the system. In +§4 we explore alternative scenarios for the explanation of the observed VLPP, with +particular attention to the cyclic magnetic variation. In §5 we provide some final +comments on the new results and its observational imprint on FS Aurigae’s features. + +REVISITING FS AURIGAE +3 +TABLE 1 +SUMMARY OF PERIODICITIES DETECTED IN FS Aur. +Name/Acronym +Value +Source +Reference +Comments +Spin Period of WD (SP) +1.m68 −1.m75 +light curve +(Neustroev et al. 2005) +inconclusive +Orbital Period (OP) +85.m79736 +RVa +(Thorstensen et al. 1996) +firmly +±0.00004 +core of H lines +unpublished data +established +Long Spectr. Period (LSP) +147m +RVb +(Tovmassian et al. 2003) +beat between +wings of H lines +OP and LPP +Long Phot. Period (LPP) +205.m45013 +light curve +(Tovmassian et al. 2003) +stable +±0.0006 +over ∼ 3000d +Previous Very Long Phot. Period +875d ±50d +light curve +(Chavez et al. 2012) +based on +(VLPP) +∼ 5000d coverage +New Very Long Phot. Period +857d ±78d +light curve +this work +based on +(VLPP) +∼ 7500d coverage +ameasured in the core of emission lines +bmeasured in the extreme wings of emission lines +2. THE LONG AND PERMANENT PHOTOMETRIC BEHAVIOUR OF FS AUR. +Here, we use a data set 1.4 times larger than the one used earlier, covering more +than 7,500 days of observations, coming from the AAVSO public data base. From +our analysis, we conclude that the long period is still present in the light curve and +confirm the phenomenon reported in CH2012. The power spectrum of the data is +displayed in Figure1. The data set spans over 20 years and almost nine periods of +∼ 850 days, peaking in the periodogram at the 0.001167 day−1 frequency. The other +low–frequency peak of similar strength at f = 0.003919day−1 is an alias related to +the one year observational cycle. When taking into account a larger set of data, +the estimated period is 857 ± 78 days, and coincides well with the one previously +reported (875 ±50 days) within the estimated error. +The upper panel of Figure 2 corresponds to the long-term light curve for FS Aur +in the V band. The bottom panel of Figure 2 displays the folded light curve adjusted +with a VLPP period of 857 days. The amount of data for the folded light curve was +reduced averaging the magnitude per phase to appreciate in detail the sinusoidal be- +haviour. We calculated the best sinusoidal fit for the bottom panel of Figure 2, shown +in red in the figure, we found that the amplitude of the best fit is ≈ 0.4 magnitudes, +but it is also clear that the data points are disperse, then we also calculated the differ- +ence between the maximum and minimum magnitude of the observed data finding +1.1 magnitude. +3. REVISITING THE TRIPLE CATACLYSMIC VARIABLE SYSTEM +HYPOTHESIS +A CV is a binary system that is composed by a primary massive star, a white +dwarf, and a low mass main sequence K–L type star with a predominant population + +4 +CHAVEZ ET AL. +0 +0.002 +0.004 +0.006 +0.008 +0.01 +0.012 +Frequency +0 +0.2 +0.4 +0.6 +0.8 +1 +Power +Fourier Spectrum +Lomb-Scargle Spectrum +fVLPP +alias +f += 0.001167 day += 0.003919 day +-1 +-1 +Fig. 1. Normalized power spectrum of the quiescent light curve of FS Aur . Solid black curve +corresponds to our Fourier analysis and red dashed curve corresponds to the Lomb–Scargle +method. The strongest peak fVLPP = 0.001167 day−1 corresponds to the Very Long Photomet- +ric Period. The second–highest peak frequency in the power spectrum falias = 0.003919 day−1 +corresponds to an alias created by yearly observational cycle fY = 0.002739 day−1 and fVLPP. +of M (red dwarf) stars. They are so close to each other that the secondary star fills its +Roche lobe and its surface is close to the L1 Lagrangian point. +The material that the secondary loses cannot fall directly to the primary, but in- +stead it forms a disk of material around the primary and references therein (Ritter +2008). This disk is so bright that outshines the brightness of both stars. In fact, +its brightness is proportional to the mass transfer rate or to the mass accretion rate +(Warner 1995). Therefore, if there is a change in the mass transfer rate, there will be +also a change in the system’s brightness.Therefore, any change in the location of the +Lagrangian L1 point will change the mass transfer and therefore the brightness of the +system. +We recall that there is a huge disparity between the VLPP and all other periods. +This lead CH2012 to seek the cause of the variable mass transfer rate and therefore of +the disk brightness not related to the binary itself but to propose a third body orbiting +the binary. +The presence of a third body in the system would result in perturbing the orbit +of the stellar binary on different timescales. These timescales depend on the mass, +eccentricity and semi-major axis of the unseen companion. Therefore, knowing the +period of the long–term variability of the light curve of FS Aur can help us place +constraints on the mass and orbital configuration of the potential companion. +For that purpose, we can make use of some previously derived analytical results. + +REVISITING FS AURIGAE +5 +0 +2000 +4000 +6000 +8000 +HJD +2454000 +14 +15 +16 +17 +18 +Mag [V] +Data presented in Chávez et al. 2012 +New AAVSO observations +-2 +-1 +0 +1 +2 +Phase (P = 856 days) +15 +15.5 +16 +16.5 +17 +Mag [V] +Fig. 2. Upper panel, long-term light curve of FS Aur over the past 20 years, 1.4 times larger +than in CH2012 (black filled circles correspond to new observations). Bottom panel, folded +light curve in quiescence using the VLPP of 857 days. We also show in red the best sinusoidal +fit for this curve. +In a series of papers, Georgakarakos (2002, 2003, 2004, 2006, 2009, 2015, 2016) +studied the orbital evolution of hierarchical triple systems. Part of those studies were +on the secular evolution of such systems. The analytical results derived there can +give us an estimate about the frequency and the period of motion of the stellar bi- +nary. Therefore, we can estimate which mass values and orbital configurations of a +hypothetical third companion can yield the secular period observed in the light curve +of FS Aur. +For a coplanar system with a perturber on a low eccentricity orbit we make use +of the results of Georgakarakos (2009), while for coplanar systems with eccentric +perturbers those of Georgakarakos (2003). Finally, for systems with low eccentricity +orbits and low mutual inclinations (i < 39.23◦,that angle is the limit before Kozai +resonances becomes important as explained in Kozai (1962) ) we can use the relevant +material of Georgakarakos (2004). +3.1. Initial parameters +Here we discuss briefly the origin of all parameters used in this work. In CH2012 +we used the following parameters: total mass MT = M1 + M2 = 0.84 M⊙ with the + +6 +CHAVEZ ET AL. +TABLE 2 +INITIAL PARAMETERS OF FS Aur. +Parameter +Value +Reference +Orbital Period +1.42996 hours +Thorstensen et al. (1996) +Orbital semi–major axis of the Binary +0.6R⊙ +Knigge et al. (2011) +Secondary star mass +0.08 M⊙ +Knigge et al. (2011) +Secondary star radius +0.12 R⊙ +Knigge et al. (2011) +Primary star mass +0.75 M⊙ +Knigge et al. (2011) +Primary star radius +0.01 R⊙ +Knigge et al. (2011) +Log Secondary star mass loss rate +-10.25 +� +M⊙ +yr +� +Knigge et al. (2011) +Secondary star Temperature/Spectral Type +2600/M7.0 +Knigge et al. (2011) +Mass ratio +0.1 +– +primary mass M1 = 0.75 M⊙, and the secondary one M2 = 0.09 M⊙. +We decided to revisit these parameters, starting with the mass and radius of the +secondary. Here we use the values that appear in Knigge et al. (2011), in which +they use the eclipsing CVs and theoretical constrains to obtain a semi–empirical +donor sequence for CVs with orbital periods Porb ≤ 6h. They give all key physical +and photometric parameters of CVs secondaries, as well as their spectral types, as a +function of Porb. +We use the data that appear on the above authors’ Table 6 and Table 8 to obtain +the best physical parameters for FS Aur. We interpolate between values to find the +best possible ones for our dynamical study, these are shown in Table 2. We obtain the +following mass ratio between secondary and primary q = M2/M1 = 0.1 as shown in +Table 2. The primary mass was obtained from Knigge et al. (2011) and is based on +the value that they previously obtained in Knigge et al. (2006). That value was cal- +culated as the mean value of the WD mass among the eclipsing CV sample available +at the time ⟨M1⟩ = 0.75 ±0.05M⊙. They stated that when adding new data the mean +increases but not significantly, so they decided to retain the M1 = 0.75M⊙ value as a +representative WD mass. +We performed simulations of the CV with a hypothetical third body. In all nu- +merical integrations, except the ones that are stated otherwise, in the subsequent +subsections, we used the high–order Runge–Kutta–Nystr¨om RKN 12(10) 17M in- +tegrator of Brankin et al. (1989) for the equations of motion of the full three–body +problem in the barycentre inertial reference frame. In our integrations, the total en- +ergy is monitored and it is conserved up to 10−5, or better, for all experiments. At +each time step, the instantaneous eccentricity of the binary is computed. +As pointed out in CH2012, tidal deformation of the stars in the close binary three- +body problem can be an important effect. However, CH2012 have shown that these +tidal effects are not important for this system and the two objects can be considered +as point masses. + +REVISITING FS AURIGAE +7 +3.2. The third body on a close near-circular and co–planar orbit +Hierarchical triple systems consist of two stars in a close orbit and a third body +orbiting the barycentre of the close binary. +In Chavez et al. 2012 we ruled out that the VLPP could correspond directly to the +period of a third body, since the object would be too far for having an important effect +on the inner binary. There, we performed a series of numerical integrations in which +we proved that indeed the effect is very small and could not explain the VLPP of the +CV. Instead, we concluded that a third light-weight body can produce a disturbance +on the central binary and such perturbation may have a much longer period compared +to the orbital period of the perturber (e.g. Mazeh & Shaham 1979, Soderhjelm 1982, +Soderhjelm 1984, Georgakarakos 2002, Georgakarakos 2009). The third compan- +ion induces a long-term (secular) eccentricity modulation, as shown for example in +Soderhjelm (1984). +Here, just like in CH2012, we consider a binary formed by two point masses +initially in circular orbit. A third point mass (perturber) moves initially on its own +circular orbit, farther away and in the same orbital plane as the other two. Its mass +M3 and orbital period P3 are varied across an ensemble of numerical experiments. +The upper panel of Figure3 shows the log10 of the resulting periods of the long- +term modulation of the binary eccentricity (vertical axis) as a function of the mass +of the perturber (horizontal axis), for the entire ensemble of our numerical experi- +ments. Each curve corresponds to different P3/P2 ratios taken from a range of values +between 12 to 48; bottom and top curves, respectively. The thick horizontal line cor- +responds to the VLPP value. For example, the curve with P3/P2 = 12 does not cross +the line and therefore it is a value that cannot explain the VLPP observed. For per- +turbers whose orbital period is smaller than 12 binary periods no solution is possible, +since their respective curves do not reach the VLPP value. For perturbers with peri- +ods longer than that, but shorter than 19 binary periods, two solutions are possible: +one at low mass and another at an increasingly larger mass. Finally, perturbers with +longer periods than 19 produce only one solution at the large mass range. +The curve in the middle panel of Figure 3 shows the perturber’s orbit semi-major +axis but only for the solutions that could explain the observed VLPP value; i.e solu- +tions that cross the solid line on the upper panel. The lower panel shows the ampli- +tude of the eccentricity perturbation for the solutions presented in the middle panel. +The most efficient case would be the one in which the VLPP is the predominant effect +and the eccentricity pumped in the inner binary is the largest; that is, the minimum +in semi-major axis and the maximum in eccentricity. According to this study, the +maximum amplitude is achieved for a system that has a third body with M3 = 29MJ +and P3/P2 = 12.7. +All curves in the upper panel of Figure3 gets to its maximum value for smaller +values of the mass compared to Fig. 8 upper panel of CH2012 for the same initial +conditions. Therefore, in the middle panel of Figure 3, we also obtain smaller values +for the masses of the possible third body compared to the middle panel of Fig. 8 +of CH2012 for the same initial conditions. Then, the minimum of this curve in this +research is obtained when M3 = 29MJ and P3/P2 = 12.7, while the minimum in +CH2012 was obtained when M3 = 48MJ and P3/P2 = 13.4. + +8 +CHAVEZ ET AL. +Fig. 3. The upper panel shows the logarithm of the period of the long–term modulation in the +binary eccentricity as a function of the perturber mass (in Jupiter masses). Each curve corre- +sponds to different P3/P2 ratios taken from 12.5 to 40.8; the values are 12.5, 12.7, 12.9, 13.1, +13.4, 15.6, 19, 22, 30.6, 33.6, 37.2, 40.8, rom bottom to top. The thick horizontal line shows +the observed value of the VLPP (857 days). Only solutions that cross this line can explain +the VLPP. The middle panel shows the perturber mass and semi–major axis combinations that +result in a long–term modulation of the binary orbit equal to the VLPP, that is the solutions +that cross the black thick line. The lower panel shows the amplitude of the binary eccentricity +perturbation for those solutions. See text for discussion. +The relative eccentricity amplitudes of these three modulations (inner binary pe- +riod, third body period and secular VLPP) depend on the mass and size of the orbit of +the perturber. The VLPP modulation becomes the predominant effect in the range of +masses for a third body of 20MJ < M3 < 45MJ. The envelope of the calculated long- +term modulation of the binary eccentricity for our best case is remarkably similar to +the waveform of the VLPP. +3.3. The third body on an eccentric and inclined orbit +Now we investigate the effect of the eccentricity and inclination of the third body +on the outcome of the VLPP. +Figure 4 contains two plots for various dynamical scenarios. It is clear that there +is a variety of combinations of masses and semi-major axes of the hypothetical com- +panion that can produce the observed long term variation in the light curve of FS Aur. +The perturber’s eccentricity does not seem to affect very much when we compare the +two analytical solutions for e3 = 0.2 and e3 = 0.5. The low e3 solution seems to be a +bit different in the range M3/MJ = 30−50. Similarly, there is some difference among +the solutions as the mutual inclination increases. + +5.0 +4.5 +Log Pmod(day) +4.0 +3.5 +3.0 +2.5 +0.040 +0.035 +0.030 +(AU) +0.025 +0.020 +0.015 +0.005 +0.004 +0.003 +0.002 +0.001 +0.000 +0 +20 +40 +60 +80 +100 +120 +140 +M3/MJREVISITING FS AURIGAE +9 +The orbital solutions based on our analytical estimates yield a wide range of +masses for our hypothetical companion, from sub-Jupiter mass bodies to big brown +dwarfs. However, all solutions may not be dynamically stable. According to the +empirical criterion developed by Holman and Wiegert (1999), the smallest stable +semi-major axis for our unseen companion is 0.0055 AU. This value is valid for +small values of e3, as the criterion was based on simulations of massless particles +initially on circular orbits around the binary star. For initially eccentric orbits around +the stellar binary the value of the stable semi-major axis may be different. The same +holds when the companion has a mass comparable to the secondary; M2 = 0.079M⊙ +which is about 83MJ, and therefore the empirical criterion of Holman and Wiegert is +valid only for masses in the left part of our plots. In this case, we can get an idea about +the stability limit from Table A1 of Georgakarakos (2013) which provides values for +three dimensional systems, but only for initially circular orbits however. Considering +the outer mass to cover the range we have in our plots, we find that for coplanar and +low inclination systems (i = 20◦) the stability limit is around a3 = 0.01AU. +3.4. Effect of Post–Newtonian correction +Here we consider the possible dynamical effects that a first order post–Newtonian +correction to the binary’s orbit may produce the long–term signal we observe in the +light curve of the stellar binary. That is the first order general relativity correction in +the precessional rate of the longitude of the pericentre. +For the stellar binary under investigation, although its total mass is under one +solar mass, the small semi-major axis of its orbit makes it an interesting case to +consider a post-Newtonian correction. The consequence of including this effect +to our orbit results in the precession of the pericentre at the following rate (Geor- +gakarakos, & Eggl 2015, Naoz et al. 2015): +˙̟ = 3G +3 +2 (M1 + M2) +3 +2 +c2a +5 +2 +1 (1 −e2 +1) +, +(1) +where G is the gravitational constant and c is the speed of light in vacuum. +Based on the precession rate given by the above equation, the period of the peri- +centre circulation for our system is 6812 days (18.65 yrs). Since this number is +much larger than the 857 day signal we observe in the light curve of the system, we +conclude that general relativity (GR) by itself cannot explain it. +3.5. Estimation of the effect of the third body on the mass transfer rate and +brightness of the system +Now that we have established that a third body can explain the VLPP observed, +we estimate how the modulation of the inner binary due to the secular perturbation +of the third body affects the mass transfer and then the brightness of the system. +The results of our numerical integrations for the third body on a close near- +circular and co–planar orbit, the most efficient solution is used for all calculations + +10 +CHAVEZ ET AL. +Fig. 4. Perturber mass and semi–major axis combinations that result in a long–term modula- +tion of the binary orbit equal to the VLPP of 857 days. These results were obtained using the +analytical formulas described in the text. In the top plot we explore the effect of the eccentric- +ity of the third body, the inclination for all systems remains constant i = 0◦. The bottom plot +explores the effect of the orbital inclination, the initial eccentricities for all systems is e3 = 0 . +See text for discussion. + +0.03 +0.025 +0.02 +as(AU) +0.015 +e,=cte=0 +1i=0° +0.01 +i=150 +i=30° +0.005 +0 +10 +20 +30 +40 +50 +60 +70 +80 +Ms/MJ0.03 +0.025 +0.02 +a,(AU) +0.015 +i=cte=0° +e3=0 +0.01 +e3=0.2 +e3=0.5 +0.005 +0 +10 +20 +30 +40 +50 +60 +70 +80 +M3/MJREVISITING FS AURIGAE +11 +in this subsection; that is M3 = 29MJ, P3/P2 = 12.7, P3 = 18.16 h. In order to es- +timate the mass loss of the secondary we make use of the concept of RL(2). Since +calculating the volume of the Roche lobe is difficult, we can define an equivalent ra- +dius of the Roche Lobe as the radius, RL(2), of a sphere with the same volume as that +the Roche lobe. This radius RL(2) has been widely studied for different mass ratios +(q = M1/M2) between the primary and the secondary. Equation 2 by Eggleton (1983) +is widely used since is valid in a wide range of mass ratios (valid for 0 < q < ∞) and +accurate to better than 1%. That equation assumes that the orbit is circular and that +the semi–major axis is constant. +Sepinsky et al. 2007 studied the definition of RL(2) for eccentric binaries finding +the following generalisation: +RL(2) = r12(t) +0.49q2/3 +0.6q2/3 +ln(1 +q1/3), +(2) +where r12 is the distance between the two stars at a given time. Since we have +that distance from our integration of the most efficient case, we can plot RL(2) as a +function of time as in shown in Figure5. +We can calculate the maximum RL(2)max = 8.844×107m and RL(2)min = 8.796× +107m, from here in principle we can estimate the mass transfer rate ˙M(2) and from +here the luminosity of the Cataclysmic Variable. +We proceed as follows. First we assume that the secondary is a polytrope of +index 3/2 (we assume certain shape of the Roche Lobe). Also that the density around +L1 point is given by Eq. 2.11 of Warner (1995), ρL1 = ρ0e−(∆R/H′)2; where ρ0 is the +density of the isothermal atmosphere, and H′ is a scale height given by Lubow & +Shu (1975). +We can estimate the mass transfer rate using the Eq. 2.12 of Warner (1995), +˙M(2) = −C M(2) +P12 +� ∆R +R(2) +�3 +, +(3) +where C is a dimensional constant ≈ 10 − 20 and ∆R is the amount by which the +secondary overfills its Roche Lobe: ∆R = R(2) − RL(2). The R(2) distance needs to +be calculated carefully since the equation for ˙M(2) is very sensitive to the amount of +overfill. We decided to adjust the R(2) to obtain the ˙M(2) that we report here in Table +2; the logarithm of the secondary star mass loss rate of −10.25� M⊙ +yr +�. Since RL(2) is +a function of the time we use the mean value of RL(2)mean = 8.821 × 107 m for the +RL(2) value. Hence we obtain the value R(2) = 8.820 ×107 m. +Therefore, we can calculate the maximum and minimum of the mass transfer rate +by using the values of RL(2)max and RL(2)min. We obtained ˙M(2)max = 7.1×1018 kg/s +and ˙M(2)min = 5.8 ×1018 kg/s. +We make an estimation on the luminosity due to the accretion (Warner 1995). +First, calculate the luminosity due to the so called hot spot (the place where the +stream of stellar mass crosses the L1 point and collides with the disk): +L(S P) ≈ GM(1) ˙M(2) +rd +, +(4) + +12 +CHAVEZ ET AL. +Fig. 5. +Location of RL(2) as a function of the time, RL(2) is the radius of the sphere with +volume equal to that of the Roche lobe of the system. See text for discussion. +where L(S P) is the luminosity due to the hot spot, the radius of the disk is typ- +ically rd ≈ 0.40 × a12, where a12 is the semi–major axis of the inner binary, both +given in Table 2. Applying this equation to our extreme values on RL(2) we obtain: +L(S P)max ≈ 4.2×1030 Watts and L(S P)min ≈ 3.2×1030 Watts. The luminosity of the +accretion disk ,using Eq. 2.22a of Warner (1995), is: +L(d) ≈ 1 +2 +GM(1) ˙M(2) +R1 +, +(5) +Using this equation for L(d) we can obtain the extreme values of L(d)max ≈ 4.8× +1031 Watts and L(d)min ≈ 3.6 ×1031 Watts. The total luminosity for each extreme is +obtained by adding the estimated luminosity of the hot spot plus the luminosity of +the disk, obtaining: L(d)Tmax ≈ 5.2 ×1031Watts and L(d)Tmin ≈ 4.0 ×1031 Watts. +We can calculate the bolometric magnitude using Mbol = −2.5log� L +L0 +�, with L0 = +3.0128×1028 Watts. For the extreme values we obtained MBmax = −8.09 and MBmin = +−7.79, giving us a magnitude difference of ∆MB = 0.29. +The observed change on magnitude at quiescence is ≈ 0.4 magnitudes when using +a sinusoidal best fit, as shown in Figure 2, but the data points are quite disperse, so we +also calculated the difference between the maximum and minimum magnitude of the +observed data finding 1.1 magnitude. The most efficient parameters model give us +an expected change of magnitude of ≈ 0.29. We remind the reader that the later was +an order of magnitude estimate with simplifications, assumptions and estimations. +4. ALTERNATIVE SCENARIOS FOR THE VLPP +One possible explanation to the VLPP is the cyclic magnetic variation, analogue +to the Solar cycles, in the secondary star which may lead to mass transfer variations. +Long variations have been observed in CVs as mentioned in Richman et al. (1994), +where they concluded that this explanation is plausible. But they found that these + +REVISITING FS AURIGAE +13 +cycles did not show any strict periodicity and are decades long. In Table 3 in Mas- +care˜no et al. (2016), the magnetic cycle of medium to late M stars is calculated and +found to be 7.1 years for a sample of this type of stars. +As pointed out at the end of Section 3.1 in this research, the secondary star on +FS-Aur is expected to be a very late M star, their internal structure not being the +same as their normal main sequence star counterpart with the same mass. Stars with +M ≈ 0.4M⊙ become fully convective as the mass decreases, the density increases and +the internal temperature decreases, leading to the partial degeneracy of the core. Ap- +proaching the minimum hydrogen-burning mass of 0.08M⊙, the increased electron +degeneracy induces structural changes on the secondary. Making the star magnetic +but with very few spots. +Works of Bianchi (1992) and Hessman et al. (2000) found evidence of a possible +relation between mass accretion variations and solar cycle type phenomena. The +evidence showed variations on the timescales of decades on overall system brightness +and gave theoretical support for star-spots migrating to the L1 region (Howell 2004). +This migration would help to correlate the star-spot to the changes in the position of +the L1 point due to a possible third body. +Nevertheless, the magnetic cycles in very late M stars have not been studied in +detail for secondaries in CVs. and we recognise this mechanism as a strong alterna- +tive to the mechanism proposed here. +5. SUMMARY AND FINAL COMMENTS +We confirm the presence of VLPP with a refined period of 857 days based on +5 more years (20 years total) of observations for FS Aur. This result also helps in +confirming the authenticity of this signal. +We also revisited the triple CV hypothesis in which a massive planet, or a sub- +stellar object, pumps eccentricity into the inner binary orbit by secular perturbations. +New parameters of mass, radius and temperature for the binary members of the CV +FS Aur Knigge et al. 2011 were calculated, and we used these to recalculate the +most efficient parameters for the third body as defined earlier. The most efficient +combination that explains the 857 day period is a third body with M3 = 29MJ and +P3/P2 = 12.7 (P3 = 18.16 h). This new value is 1.7 times less massive than our +previous estimation and is well within the limits of planetary mass. For example, +the planet HD 169142b has a similar mass Fedele et al. 2017. All these numerical +calculations were made for a third body in an initial circular and planar orbit as in +CH2012. +We also explored more complications to the model to study the secular perturba- +tions of systems with eccentric and inclined orbits, using previous analytical results +(Georgakarakos 2002, 2003, 2004, 2006, 2009). We found that as the eccentricity +increases the most efficient candidate third body has a larger mass: M3 = 47MJ for +an eccentricity of 0.2, and M3 = 48MJ for an eccentricity of 0.5 of the third body. +When the mutual inclination is explored the most efficient candidate for the third +body has larger mass: if the inclination is 15◦ the expected most efficient mass is +about M3 = 58MJ, but when the inclination is 30◦ the expected most efficient mass +now is about M3 = 72MJ. + +14 +CHAVEZ ET AL. +We considered other dynamical effects that might produce this VLPP, such as the +first order post–Newtonian correction. We found that for FS Aur the period of the +pericentre circulation is 6812 day (18.65 yrs), that is much larger than the 857 day +period observed. +We calculated a first order estimation of the effect of the secular period due of +the third object on the mass transfer rate and then on the brightness of the system; a +change of magnitude of the order of only ∆Mbol = 0.29 was obtained. Even when this +change is not the 0.4–magnitude observed, is quite close for an order of magnitude +calculation. It also gave us insights on how sensitive is the system to even smallest +changes in the parameters to calculate ˙M(2), to show that we changed the distance +R(2) by less than 0.01% and we obtained the 0.4–magnitude observed. The R(2) +adjustment was based on the value of ˙M(2) that appears in Table 2 taken from Knigge +et al. 2011 and that value was calculated using statistics. The change in magnitude +of FS Aur are may be a mechanism to explain the VLPP observed. +We examined alternative scenarios for the VLPP. A possible explanation by a +solar type magnetic cycle of the secondary cannot be ruled out for the VLPP, since +the VLPP is only 2.346 years and most of the cyclic type magnetic periods in mid to +late M stars are of the order of decades.However there are no studies for the magnetic +cyles of very late M stars in CVs to asses further this hypothesis, then making this +alternative a plausible one. +In summary, we find (a) that the new extended data confirms that there is a VLPP, +but with a new value of 857 days, (b) These new data is consistent with a triple- +system for FS Aur, (c) that combining such data with new initial conditions yield a +reduction (from M3 = 50MJ to 29MJ) in the mass estimate for the third-body most +efficient candidate in FS Aur., (d) an order of magnitude estimation for the mass +transfer rate and the brightness of the system has been done, with the initial condi- +tions used here, lead to a change on magnitude of 0.3. This value was 25% times +smaller than the observed but we found that changes of less than 0.01% in the R(2) +parameter increases the change in magnitude to the observed one. +Acknowledgements +We would like to thank all the amateur observers who do a great hard job in +collecting professional grade data with persistence. We are particularly indebted to +Joe Patterson, who guides the amateur community engaged in CV monitoring and +who made possible the dense observational coverage of FS Aur. We acknowledge +with thanks the variable star observations from the AAVSO International Database +contributed by observers worldwide and used in this research. CC acknowledges +UANL PAICYT grant. We appreciate the comments, suggestions and corrections by +the anonymous referee, which helped us to greatly improve the quality and content +of this research. +REFERENCES +Bianchi, L., 1992, A&A, 253, 447–450. +Brankin, R.; Gladwell, I.; Dormand, J.; Prince, P.; Seward, W, 1989, ACM T. M. S., 15, 31. + +REVISITING FS AURIGAE +15 +Beuermann, K., Hessman, F. V., Dreizler, S., et al. 2010, A&A, 521, L60 +Beuermann, K., Buhlmann, J., Diese, J., et al. 2011, A&A, 526, A53 +Bruch, A. 2014, A&A, 566, A101 +Chavez, C., Tovmassian, G., Aguilar, L., Zharikov, S., Henden, A., 2012, A&A, 538, A122. +Eggleton, P. P., 1983, APJ, 268, 368. +Fedele, D.; Carney, M. R.; Hogerheijde, M. R.; Walsh, C.; Miotello, A.; Klaassen, P.; Bruderer, +S.; Henning, Th.; van Dishoeck, E. F., 2017, A&A, 600, A72. +Georgakarakos, N., 2002, MNRAS, 337, 559. +Georgakarakos, N., 2003, MNRAS, 345, 340. +Georgakarakos, N., 2004, CeMDA, 89, 63. +Georgakarakos, N., 2006, MNRAS, 366, 566. +Georgakarakos, N., 2009, MNRAS, 392, 1253. +Georgakarakos, N., 2013, NewA, 23, 41. +Georgakarakos, N. & Eggl, S., 2015, APJ, 802, article id. 94. +Georgakarakos, N.; Dobbs–Dixon, I.; Way, M. J., 2016, MNRAS, 461, 1512. +Getley, A. K.; Carter, B.; KIng, R.; OToole, S., 2017, MNRAS, 468, 2932. +Hessman, F. V.; Gansicke, B. T.; Mattei, J. A., 2000, A&A, 361, 952. +Holman, M.; Wiegert, P., 1999, APJ, 117, 621. +Howell, S. B., 2004, ASP Conference Proceedings, 315, 353. +Knigge, C. 2006, MNRAS, 373, 484 +Knigge, C.; Baraffe, I.; Patterson, J., 2011, APJ Supplement Series, 194, 48. +Kozai, Y. 1962, AJ, 67, 591 +Lee, J. W., Kim, S.-L., Kim, C.-H., et al. 2009, AJ, 137, 3181 +Li, K., Hu, S., Zhou, J., et al. 2017, PASJ, 69, 28 +Lubow, S. H.; Shu, F. H., 1975, APJ, 198, 383. +Mascareno, A.; Rebolo, R.; Gonzalez Hernandez, J. I., 2016, A&A, 595, A12. +Mazeh, T.; Shaham, J., 1979, A&A, 77, 145. +Naoz, S.; Kocsis, B.; Loeb, A.; Yunes, N., 2015, APJ, 773, article id. 187. +Neustroev, V., Zharikov, S., Tovmassian, G., Shearer, A., 2005, MNRAS, 362, 1472. +Qian, S. B.; Zhu, L. Y.; Dai, Z. B.; Fernandez–Lajus, E.; Xiang, F. Y.; and He, J. J., 2012a, +APJL, 745, article id. L23 +Qian S. B.; Liu, L.; Zhu, L. Y.; Dai, Z. B.; Fernandez–Lajus, E.; Baume, G., L., 2012b, MN- +RAS, 422, L24. +Richman, H. R., Applegate, J. H., Patterson, J., 1994, PASP, 106, 1075. +Ritter, H. 2008, Mem. Soc. Astron. Italiana, Proceedings of the School of Astrophysics, 14. +Sepinsky, J. F.; Willems, B.; Kalogera, V., 2007, APJ, 660, 1624–1635. +Soderhjelm, S., 1982, A&A, 107, 54. +Soderhjelm, S., 1984, A&A, 141, 232. +Thorstensen, John R., Patterson, Joseph O., Shambrook, Anouk, Thomas, Gino, 1996, PASP, +108, 73. +Tovmassian, G., Zharikov, S., Michel, R., Neustroev, V., Greiner, J., Skillman, D.R., Harvey, +D.A., Fried, R.E. & Patterson, J. 2003, PASP, 115, 725. +Tovmassian, G., Zharikov, S., & Neustroev, V., 2007, APJ, 655, 466. +Warner, B. 1995, Cataclysmic Variable Stars (Cambridge University Press). + +16 +CHAVEZ ET AL. +Chavez C.E and Aviles A: Universidad Auton´oma de Nuevo Le´on, Facultad de +Ingenier´ıa Mec´anica y El´ectrica, San Nicol´as de los Garza, NL, M´exico (Car- +los.ChavezPch@uanl.edu.mx). +Georgakarakos N: New York University Abu Dhabi, Saadiyat Island, P.O. Box +129188, Abu Dhabi, UAE. +Ramos C: Universidad Auton´oma de Nuevo Le´on, Facultad de Ciencias F´ısico– +Matem´aticas, San Nicol´as de los Garza, N.L. M´exico. +Ramos C: Centro de Investigaci´on y de Estudios Avanzados del Instituto Polit´ecnico +Nacional, San Pedro Zacatenco, Ciudad de M´exico, 07360, M´exico. +Aceves H, Tovmassian G, Zharikov S: Universidad Nacional Aut´onoma de M´exico, +Instituto de Astronom´ıa, Ensenada 22860, B.C., M´exico,. + diff --git a/R9E3T4oBgHgl3EQfDQnp/content/tmp_files/load_file.txt b/R9E3T4oBgHgl3EQfDQnp/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..82f88642cb23d62a071aa86b2e9dfa3775a5ed09 --- /dev/null +++ b/R9E3T4oBgHgl3EQfDQnp/content/tmp_files/load_file.txt @@ -0,0 +1,734 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf,len=733 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='04286v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='SR] 11 Jan 2023 Manuscript for Revista Mexicana de Astronom´ıa y Astrof´ısica (2007) REVISITING FS AURIGAE AND ITS TRIPLE CATACLYSMIC VARIABLE SYSTEM HYPOTHESIS Carlos E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Chavez,1 Andres Aviles,1 Nikolaos Georgakarakos,2 Cesar Ramos,3,5 Hector Aceves,4 Gagik Tovmassian,4 Sergey Zharikov,4 Draft version: January 12, 2023 RESUMEN Una variabilidad de muy larga duraci´on (VLPP), con un periodo de 875 d´ıas, fue observado en la curva de luz de FS Aur en 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' El periodo fue calculado con 6 ciclos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Reexaminamos el periodo con nuevas observaciones de los pasados 5 a˜nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Un total de 18 a˜nos de observaciones confirman la hip´otesis de un tercer cuerpo perturbando de manera secular la variable catacl´ısmica (VC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Mejoras al modelo como ´orbitas exc´entricas e inclinadas para el tercer cuerpo y una correcci´on post– Newtoniana para la binaria son consideradas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Confirmamos el VLPP de FS Aur y encontramos el nuevo periodo de 857 ± 78 d´ıas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Las perturbaciones seculares son m´as eficientes cuando la masa del tercer cuerpo es M3 ≈ 29MJ, menor a M3 ≈ 50MJ reportado en 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Estimamos el efecto del tercer cuerpo en la tasa de transferencia de masa y del brillo del sistema.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Consideramos otras explicaciones para el VLPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Estos nuevos datos y an´alisis apoyan la hip´otesis de una VC triple para FS Aur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' ABSTRACT A very long term variability (VLPP), with period of 875 days, was observed in the long-term light curve of FS Aurigae (FS Aur) in 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' This periodicity was cal- culated on 6 cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We re–examine the periodicity with new observations over of the past 5 yrs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' A total of 18 yrs of observations confirm the hypothesis of a third body perturbing in a secular way the cataclysmic variable (CV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Improvements to the model such as eccentric and inclined orbits for the third body and a binary post– Newtonian correction are considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We confirm the VLPP of FS Aur and find the new period of 857 ± 78 days.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The secular perturbations are most efficient when the mass of the third body is M3 ≈ 29 MJ, much less than the 50 MJ reported in 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We estimate the effect of the third body on the mass transfer rate and the brightness of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We consider alternative scenarios for the VLPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The new data and analysis supports the hypothesis that FS Aur is a CV in a triple system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Key Words: Stars: binaries (including multiple) — Stars: individual (FS Aur) — Stars: novae, cataclysmic variables 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' INTRODUCTION FS Aur is a Cataclysmic Variable (CV) that shows a wide range of light periodic signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' It has a short orbital period of just 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='7 min (Thorstensen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 1996), a long 1FIME-UANL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' M´exico.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2New York University Abu Dhabi, UAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 3FCFM-UANL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' M´exico 4IA-UNAM, Ensenada.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' M´exico 5CINVESTAV, Ciudad de M´exico.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' M´exico 1 2 CHAVEZ ET AL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' photometric period of 205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='5 min (Tovmassian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2003) and a long spectroscopic period of 147 min (Tovmassian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The latter two periods are attributed to the precession of a fast rotating magnetic white dwarf and its beat with the orbital period, respectively (see Table 1 for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' All these frequencies were discussed in more detail in Chavez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' (2012, hereafter CH2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In that paper we showed the presence of a very long photometric period (VLPP) modulation observed in the long-term FS Aur light curve, with a 2–mag amplitude and a period around 900 days.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We argued that the origin of such modulation could be a third substellar-body (25 to 65 times Jupiter’s mass) that perturbs the eccentricity of the inner binary star system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' This triple–system hypothesis provided an explanation for the VLPP, and it was also suggested that it might give a plausible answer for other observed peculiarities of FS Aur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' More importantly is perhaps the fact that it offers a new possibility for detecting planets in accretion disk environments, where other methods fail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' There are other binary systems claimed to have a third object in a close orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' LX Ser possess an extra component of 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='5 times the mass of Jupiter that explains a sinusoidal oscillation observed in the O – C diagram with a period of 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='8 years (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Another example is V893 Scorpi where observed variations of the eclipse period of 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='2 years are interpreted as a light travel time effect caused by the presence of a giant planet with 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='5 times the mass of Jupiter (Bruch 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Finally DP Leonis (Beuermann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2011), HW Vir (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2009), NN Ser (Beuermann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2010), NY Virginis (Qian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2012a), RR Caeli (Qian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2012b) and KIC 5095269 (Getley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2017) are part of this small group of post-CE binaries suspected to possess planets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The purpose of this paper is to make use of 5 more years of observations of FS Aurigae to see whether the VLPP signal reported in CH2012 is stronger or, on the contrary, is disappearing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We also want to model the hierarchical triple hypothesis in a more realistic manner by including eccentric and inclined orbits and also first order post–Newtonian correction, that is a first order general relativity correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Then studying the effect these complications have on the range of possible values on mass and semi–major axis that may explain the VLPP by secular perturbations on the Cataclysmic Variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' This paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In §2, we review observational data of FS Aur in search of the very long photometric period (VLPP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='1 we revisit the initial conditions used in our previous research and more recent and more accurate parameters for our system are indicated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='2 we examine the scenario where the perturber moves on a circular and coplanar orbit, whose period is much shorter than the long period, and yet produces a binary eccentricity variation with the latter period by secular perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='3 we extend this to eccentric and inclined orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The range and properties of the allowed solutions are shown.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='4 we check if the VLPP could be explained as a consequence of the precession effect of the orbit due to first order general relativity corrections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='5 we make an order of magnitude estimation for the mass transfer rate and the brightness of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In §4 we explore alternative scenarios for the explanation of the observed VLPP, with particular attention to the cyclic magnetic variation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In §5 we provide some final comments on the new results and its observational imprint on FS Aurigae’s features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' REVISITING FS AURIGAE 3 TABLE 1 SUMMARY OF PERIODICITIES DETECTED IN FS Aur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Name/Acronym Value Source Reference Comments Spin Period of WD (SP) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='m68 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='m75 light curve (Neustroev et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2005) inconclusive Orbital Period (OP) 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='m79736 RVa (Thorstensen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 1996) firmly ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='00004 core of H lines unpublished data established Long Spectr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Period (LSP) 147m RVb (Tovmassian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2003) beat between wings of H lines OP and LPP Long Phot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Period (LPP) 205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='m45013 light curve (Tovmassian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2003) stable ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='0006 over ∼ 3000d Previous Very Long Phot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Period 875d ±50d light curve (Chavez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2012) based on (VLPP) ∼ 5000d coverage New Very Long Phot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Period 857d ±78d light curve this work based on (VLPP) ∼ 7500d coverage ameasured in the core of emission lines bmeasured in the extreme wings of emission lines 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' THE LONG AND PERMANENT PHOTOMETRIC BEHAVIOUR OF FS AUR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Here, we use a data set 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='4 times larger than the one used earlier, covering more than 7,500 days of observations, coming from the AAVSO public data base.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' From our analysis, we conclude that the long period is still present in the light curve and confirm the phenomenon reported in CH2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The power spectrum of the data is displayed in Figure1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The data set spans over 20 years and almost nine periods of ∼ 850 days, peaking in the periodogram at the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='001167 day−1 frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The other low–frequency peak of similar strength at f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='003919day−1 is an alias related to the one year observational cycle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' When taking into account a larger set of data, the estimated period is 857 ± 78 days, and coincides well with the one previously reported (875 ±50 days) within the estimated error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The upper panel of Figure 2 corresponds to the long-term light curve for FS Aur in the V band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The bottom panel of Figure 2 displays the folded light curve adjusted with a VLPP period of 857 days.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The amount of data for the folded light curve was reduced averaging the magnitude per phase to appreciate in detail the sinusoidal be- haviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We calculated the best sinusoidal fit for the bottom panel of Figure 2, shown in red in the figure, we found that the amplitude of the best fit is ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='4 magnitudes, but it is also clear that the data points are disperse, then we also calculated the differ- ence between the maximum and minimum magnitude of the observed data finding 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='1 magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' REVISITING THE TRIPLE CATACLYSMIC VARIABLE SYSTEM HYPOTHESIS A CV is a binary system that is composed by a primary massive star, a white dwarf, and a low mass main sequence K–L type star with a predominant population 4 CHAVEZ ET AL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='004 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='006 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='008 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='012 Frequency 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='8 1 Power Fourier Spectrum Lomb-Scargle Spectrum fVLPP alias f = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='001167 day = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='003919 day 1 1 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Normalized power spectrum of the quiescent light curve of FS Aur .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Solid black curve corresponds to our Fourier analysis and red dashed curve corresponds to the Lomb–Scargle method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The strongest peak fVLPP = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='001167 day−1 corresponds to the Very Long Photomet- ric Period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The second–highest peak frequency in the power spectrum falias = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='003919 day−1 corresponds to an alias created by yearly observational cycle fY = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='002739 day−1 and fVLPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' of M (red dwarf) stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' They are so close to each other that the secondary star fills its Roche lobe and its surface is close to the L1 Lagrangian point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The material that the secondary loses cannot fall directly to the primary, but in- stead it forms a disk of material around the primary and references therein (Ritter 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' This disk is so bright that outshines the brightness of both stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In fact, its brightness is proportional to the mass transfer rate or to the mass accretion rate (Warner 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Therefore, if there is a change in the mass transfer rate, there will be also a change in the system’s brightness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='Therefore, any change in the location of the Lagrangian L1 point will change the mass transfer and therefore the brightness of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We recall that there is a huge disparity between the VLPP and all other periods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' This lead CH2012 to seek the cause of the variable mass transfer rate and therefore of the disk brightness not related to the binary itself but to propose a third body orbiting the binary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The presence of a third body in the system would result in perturbing the orbit of the stellar binary on different timescales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' These timescales depend on the mass, eccentricity and semi-major axis of the unseen companion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Therefore, knowing the period of the long–term variability of the light curve of FS Aur can help us place constraints on the mass and orbital configuration of the potential companion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' For that purpose, we can make use of some previously derived analytical results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' REVISITING FS AURIGAE 5 0 2000 4000 6000 8000 HJD +2454000 14 15 16 17 18 Mag [V] Data presented in Chávez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2012 New AAVSO observations 2 1 0 1 2 Phase (P = 856 days) 15 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='5 16 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='5 17 Mag [V] Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Upper panel, long-term light curve of FS Aur over the past 20 years, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='4 times larger than in CH2012 (black filled circles correspond to new observations).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Bottom panel, folded light curve in quiescence using the VLPP of 857 days.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We also show in red the best sinusoidal fit for this curve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In a series of papers, Georgakarakos (2002, 2003, 2004, 2006, 2009, 2015, 2016) studied the orbital evolution of hierarchical triple systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Part of those studies were on the secular evolution of such systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The analytical results derived there can give us an estimate about the frequency and the period of motion of the stellar bi- nary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Therefore, we can estimate which mass values and orbital configurations of a hypothetical third companion can yield the secular period observed in the light curve of FS Aur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' For a coplanar system with a perturber on a low eccentricity orbit we make use of the results of Georgakarakos (2009), while for coplanar systems with eccentric perturbers those of Georgakarakos (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Finally, for systems with low eccentricity orbits and low mutual inclinations (i < 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='23◦,that angle is the limit before Kozai resonances becomes important as explained in Kozai (1962) ) we can use the relevant material of Georgakarakos (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Initial parameters Here we discuss briefly the origin of all parameters used in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In CH2012 we used the following parameters: total mass MT = M1 + M2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='84 M⊙ with the 6 CHAVEZ ET AL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' TABLE 2 INITIAL PARAMETERS OF FS Aur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Parameter Value Reference Orbital Period 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='42996 hours Thorstensen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' (1996) Orbital semi–major axis of the Binary 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='6R⊙ Knigge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' (2011) Secondary star mass 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='08 M⊙ Knigge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' (2011) Secondary star radius 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='12 R⊙ Knigge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' (2011) Primary star mass 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='75 M⊙ Knigge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' (2011) Primary star radius 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='01 R⊙ Knigge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' (2011) Log Secondary star mass loss rate 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='25 � M⊙ yr � Knigge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' (2011) Secondary star Temperature/Spectral Type 2600/M7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='0 Knigge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' (2011) Mass ratio 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='1 – primary mass M1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='75 M⊙, and the secondary one M2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='09 M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We decided to revisit these parameters, starting with the mass and radius of the secondary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Here we use the values that appear in Knigge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' (2011), in which they use the eclipsing CVs and theoretical constrains to obtain a semi–empirical donor sequence for CVs with orbital periods Porb ≤ 6h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' They give all key physical and photometric parameters of CVs secondaries, as well as their spectral types, as a function of Porb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We use the data that appear on the above authors’ Table 6 and Table 8 to obtain the best physical parameters for FS Aur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We interpolate between values to find the best possible ones for our dynamical study, these are shown in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We obtain the following mass ratio between secondary and primary q = M2/M1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='1 as shown in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The primary mass was obtained from Knigge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' (2011) and is based on the value that they previously obtained in Knigge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' That value was cal- culated as the mean value of the WD mass among the eclipsing CV sample available at the time ⟨M1⟩ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='75 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='05M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' They stated that when adding new data the mean increases but not significantly, so they decided to retain the M1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='75M⊙ value as a representative WD mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We performed simulations of the CV with a hypothetical third body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In all nu- merical integrations, except the ones that are stated otherwise, in the subsequent subsections, we used the high–order Runge–Kutta–Nystr¨om RKN 12(10) 17M in- tegrator of Brankin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' (1989) for the equations of motion of the full three–body problem in the barycentre inertial reference frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In our integrations, the total en- ergy is monitored and it is conserved up to 10−5, or better, for all experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' At each time step, the instantaneous eccentricity of the binary is computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' As pointed out in CH2012, tidal deformation of the stars in the close binary three- body problem can be an important effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' However, CH2012 have shown that these tidal effects are not important for this system and the two objects can be considered as point masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' REVISITING FS AURIGAE 7 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The third body on a close near-circular and co–planar orbit Hierarchical triple systems consist of two stars in a close orbit and a third body orbiting the barycentre of the close binary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In Chavez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2012 we ruled out that the VLPP could correspond directly to the period of a third body, since the object would be too far for having an important effect on the inner binary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' There, we performed a series of numerical integrations in which we proved that indeed the effect is very small and could not explain the VLPP of the CV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Instead, we concluded that a third light-weight body can produce a disturbance on the central binary and such perturbation may have a much longer period compared to the orbital period of the perturber (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Mazeh & Shaham 1979, Soderhjelm 1982, Soderhjelm 1984, Georgakarakos 2002, Georgakarakos 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The third compan- ion induces a long-term (secular) eccentricity modulation, as shown for example in Soderhjelm (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Here, just like in CH2012, we consider a binary formed by two point masses initially in circular orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' A third point mass (perturber) moves initially on its own circular orbit, farther away and in the same orbital plane as the other two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Its mass M3 and orbital period P3 are varied across an ensemble of numerical experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The upper panel of Figure3 shows the log10 of the resulting periods of the long- term modulation of the binary eccentricity (vertical axis) as a function of the mass of the perturber (horizontal axis), for the entire ensemble of our numerical experi- ments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Each curve corresponds to different P3/P2 ratios taken from a range of values between 12 to 48;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' bottom and top curves, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The thick horizontal line cor- responds to the VLPP value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' For example, the curve with P3/P2 = 12 does not cross the line and therefore it is a value that cannot explain the VLPP observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' For per- turbers whose orbital period is smaller than 12 binary periods no solution is possible, since their respective curves do not reach the VLPP value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' For perturbers with peri- ods longer than that, but shorter than 19 binary periods, two solutions are possible: one at low mass and another at an increasingly larger mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Finally, perturbers with longer periods than 19 produce only one solution at the large mass range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The curve in the middle panel of Figure 3 shows the perturber’s orbit semi-major axis but only for the solutions that could explain the observed VLPP value;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='e solu- tions that cross the solid line on the upper panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The lower panel shows the ampli- tude of the eccentricity perturbation for the solutions presented in the middle panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The most efficient case would be the one in which the VLPP is the predominant effect and the eccentricity pumped in the inner binary is the largest;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' that is, the minimum in semi-major axis and the maximum in eccentricity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' According to this study, the maximum amplitude is achieved for a system that has a third body with M3 = 29MJ and P3/P2 = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' All curves in the upper panel of Figure3 gets to its maximum value for smaller values of the mass compared to Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 8 upper panel of CH2012 for the same initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Therefore, in the middle panel of Figure 3, we also obtain smaller values for the masses of the possible third body compared to the middle panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 8 of CH2012 for the same initial conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Then, the minimum of this curve in this research is obtained when M3 = 29MJ and P3/P2 = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='7, while the minimum in CH2012 was obtained when M3 = 48MJ and P3/P2 = 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 8 CHAVEZ ET AL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The upper panel shows the logarithm of the period of the long–term modulation in the binary eccentricity as a function of the perturber mass (in Jupiter masses).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Each curve corre- sponds to different P3/P2 ratios taken from 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='5 to 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='8;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' the values are 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='5, 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='7, 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='9, 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='1, 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='4, 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='6, 19, 22, 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='6, 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='6, 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='2, 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='8, rom bottom to top.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The thick horizontal line shows the observed value of the VLPP (857 days).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Only solutions that cross this line can explain the VLPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The middle panel shows the perturber mass and semi–major axis combinations that result in a long–term modulation of the binary orbit equal to the VLPP, that is the solutions that cross the black thick line.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The lower panel shows the amplitude of the binary eccentricity perturbation for those solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' See text for discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The relative eccentricity amplitudes of these three modulations (inner binary pe- riod, third body period and secular VLPP) depend on the mass and size of the orbit of the perturber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The VLPP modulation becomes the predominant effect in the range of masses for a third body of 20MJ < M3 < 45MJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The envelope of the calculated long- term modulation of the binary eccentricity for our best case is remarkably similar to the waveform of the VLPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The third body on an eccentric and inclined orbit Now we investigate the effect of the eccentricity and inclination of the third body on the outcome of the VLPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Figure 4 contains two plots for various dynamical scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' It is clear that there is a variety of combinations of masses and semi-major axes of the hypothetical com- panion that can produce the observed long term variation in the light curve of FS Aur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The perturber’s eccentricity does not seem to affect very much when we compare the two analytical solutions for e3 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='2 and e3 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The low e3 solution seems to be a bit different in the range M3/MJ = 30−50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Similarly, there is some difference among the solutions as the mutual inclination increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='5 Log Pmod(day) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='040 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='035 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='030 (AU) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='025 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='020 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='015 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='005 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='004 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='003 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='000 0 20 40 60 80 100 120 140 M3/MJREVISITING FS AURIGAE 9 The orbital solutions based on our analytical estimates yield a wide range of masses for our hypothetical companion, from sub-Jupiter mass bodies to big brown dwarfs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' However, all solutions may not be dynamically stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' According to the empirical criterion developed by Holman and Wiegert (1999), the smallest stable semi-major axis for our unseen companion is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='0055 AU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' This value is valid for small values of e3, as the criterion was based on simulations of massless particles initially on circular orbits around the binary star.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' For initially eccentric orbits around the stellar binary the value of the stable semi-major axis may be different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The same holds when the companion has a mass comparable to the secondary;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' M2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='079M⊙ which is about 83MJ, and therefore the empirical criterion of Holman and Wiegert is valid only for masses in the left part of our plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In this case, we can get an idea about the stability limit from Table A1 of Georgakarakos (2013) which provides values for three dimensional systems, but only for initially circular orbits however.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Considering the outer mass to cover the range we have in our plots, we find that for coplanar and low inclination systems (i = 20◦) the stability limit is around a3 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='01AU.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Effect of Post–Newtonian correction Here we consider the possible dynamical effects that a first order post–Newtonian correction to the binary’s orbit may produce the long–term signal we observe in the light curve of the stellar binary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' That is the first order general relativity correction in the precessional rate of the longitude of the pericentre.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' For the stellar binary under investigation, although its total mass is under one solar mass, the small semi-major axis of its orbit makes it an interesting case to consider a post-Newtonian correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The consequence of including this effect to our orbit results in the precession of the pericentre at the following rate (Geor- gakarakos, & Eggl 2015, Naoz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2015): ˙̟ = 3G 3 2 (M1 + M2) 3 2 c2a 5 2 1 (1 −e2 1) , (1) where G is the gravitational constant and c is the speed of light in vacuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Based on the precession rate given by the above equation, the period of the peri- centre circulation for our system is 6812 days (18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='65 yrs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Since this number is much larger than the 857 day signal we observe in the light curve of the system, we conclude that general relativity (GR) by itself cannot explain it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Estimation of the effect of the third body on the mass transfer rate and brightness of the system Now that we have established that a third body can explain the VLPP observed, we estimate how the modulation of the inner binary due to the secular perturbation of the third body affects the mass transfer and then the brightness of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The results of our numerical integrations for the third body on a close near- circular and co–planar orbit, the most efficient solution is used for all calculations 10 CHAVEZ ET AL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Perturber mass and semi–major axis combinations that result in a long–term modula- tion of the binary orbit equal to the VLPP of 857 days.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' These results were obtained using the analytical formulas described in the text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In the top plot we explore the effect of the eccentric- ity of the third body, the inclination for all systems remains constant i = 0◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The bottom plot explores the effect of the orbital inclination, the initial eccentricities for all systems is e3 = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' See text for discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='025 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='02 as(AU) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='015 e,=cte=0 1i=0° 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='01 i=150 i=30° 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='005 0 10 20 30 40 50 60 70 80 Ms/MJ0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='025 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='02 a,(AU) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='015 i=cte=0° e3=0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='01 e3=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='2 e3=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='005 0 10 20 30 40 50 60 70 80 M3/MJREVISITING FS AURIGAE 11 in this subsection;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' that is M3 = 29MJ, P3/P2 = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='7, P3 = 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='16 h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In order to es- timate the mass loss of the secondary we make use of the concept of RL(2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Since calculating the volume of the Roche lobe is difficult, we can define an equivalent ra- dius of the Roche Lobe as the radius, RL(2), of a sphere with the same volume as that the Roche lobe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' This radius RL(2) has been widely studied for different mass ratios (q = M1/M2) between the primary and the secondary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Equation 2 by Eggleton (1983) is widely used since is valid in a wide range of mass ratios (valid for 0 < q < ∞) and accurate to better than 1%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' That equation assumes that the orbit is circular and that the semi–major axis is constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Sepinsky et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2007 studied the definition of RL(2) for eccentric binaries finding the following generalisation: RL(2) = r12(t) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='49q2/3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='6q2/3 +ln(1 +q1/3), (2) where r12 is the distance between the two stars at a given time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Since we have that distance from our integration of the most efficient case, we can plot RL(2) as a function of time as in shown in Figure5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We can calculate the maximum RL(2)max = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='844×107m and RL(2)min = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='796× 107m, from here in principle we can estimate the mass transfer rate ˙M(2) and from here the luminosity of the Cataclysmic Variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We proceed as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' First we assume that the secondary is a polytrope of index 3/2 (we assume certain shape of the Roche Lobe).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Also that the density around L1 point is given by Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='11 of Warner (1995), ρL1 = ρ0e−(∆R/H′)2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' where ρ0 is the density of the isothermal atmosphere, and H′ is a scale height given by Lubow & Shu (1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We can estimate the mass transfer rate using the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='12 of Warner (1995), ˙M(2) = −C M(2) P12 � ∆R R(2) �3 , (3) where C is a dimensional constant ≈ 10 − 20 and ∆R is the amount by which the secondary overfills its Roche Lobe: ∆R = R(2) − RL(2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The R(2) distance needs to be calculated carefully since the equation for ˙M(2) is very sensitive to the amount of overfill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We decided to adjust the R(2) to obtain the ˙M(2) that we report here in Table 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' the logarithm of the secondary star mass loss rate of −10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='25� M⊙ yr �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Since RL(2) is a function of the time we use the mean value of RL(2)mean = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='821 × 107 m for the RL(2) value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Hence we obtain the value R(2) = 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='820 ×107 m.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Therefore, we can calculate the maximum and minimum of the mass transfer rate by using the values of RL(2)max and RL(2)min.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We obtained ˙M(2)max = 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='1×1018 kg/s and ˙M(2)min = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='8 ×1018 kg/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We make an estimation on the luminosity due to the accretion (Warner 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' First, calculate the luminosity due to the so called hot spot (the place where the stream of stellar mass crosses the L1 point and collides with the disk): L(S P) ≈ GM(1) ˙M(2) rd , (4) 12 CHAVEZ ET AL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Location of RL(2) as a function of the time, RL(2) is the radius of the sphere with volume equal to that of the Roche lobe of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' See text for discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' where L(S P) is the luminosity due to the hot spot, the radius of the disk is typ- ically rd ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='40 × a12, where a12 is the semi–major axis of the inner binary, both given in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Applying this equation to our extreme values on RL(2) we obtain: L(S P)max ≈ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='2×1030 Watts and L(S P)min ≈ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='2×1030 Watts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The luminosity of the accretion disk ,using Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='22a of Warner (1995), is: L(d) ≈ 1 2 GM(1) ˙M(2) R1 , (5) Using this equation for L(d) we can obtain the extreme values of L(d)max ≈ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='8× 1031 Watts and L(d)min ≈ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='6 ×1031 Watts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The total luminosity for each extreme is obtained by adding the estimated luminosity of the hot spot plus the luminosity of the disk, obtaining: L(d)Tmax ≈ 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='2 ×1031Watts and L(d)Tmin ≈ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='0 ×1031 Watts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We can calculate the bolometric magnitude using Mbol = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='5log� L L0 �, with L0 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='0128×1028 Watts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' For the extreme values we obtained MBmax = −8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='09 and MBmin = −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='79, giving us a magnitude difference of ∆MB = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The observed change on magnitude at quiescence is ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='4 magnitudes when using a sinusoidal best fit, as shown in Figure 2, but the data points are quite disperse, so we also calculated the difference between the maximum and minimum magnitude of the observed data finding 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='1 magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The most efficient parameters model give us an expected change of magnitude of ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We remind the reader that the later was an order of magnitude estimate with simplifications, assumptions and estimations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' ALTERNATIVE SCENARIOS FOR THE VLPP One possible explanation to the VLPP is the cyclic magnetic variation, analogue to the Solar cycles, in the secondary star which may lead to mass transfer variations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Long variations have been observed in CVs as mentioned in Richman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' (1994), where they concluded that this explanation is plausible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' But they found that these REVISITING FS AURIGAE 13 cycles did not show any strict periodicity and are decades long.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In Table 3 in Mas- care˜no et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' (2016), the magnetic cycle of medium to late M stars is calculated and found to be 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='1 years for a sample of this type of stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' As pointed out at the end of Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='1 in this research, the secondary star on FS-Aur is expected to be a very late M star, their internal structure not being the same as their normal main sequence star counterpart with the same mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Stars with M ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='4M⊙ become fully convective as the mass decreases, the density increases and the internal temperature decreases, leading to the partial degeneracy of the core.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Ap- proaching the minimum hydrogen-burning mass of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='08M⊙, the increased electron degeneracy induces structural changes on the secondary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Making the star magnetic but with very few spots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Works of Bianchi (1992) and Hessman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' (2000) found evidence of a possible relation between mass accretion variations and solar cycle type phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The evidence showed variations on the timescales of decades on overall system brightness and gave theoretical support for star-spots migrating to the L1 region (Howell 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' This migration would help to correlate the star-spot to the changes in the position of the L1 point due to a possible third body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Nevertheless, the magnetic cycles in very late M stars have not been studied in detail for secondaries in CVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' and we recognise this mechanism as a strong alterna- tive to the mechanism proposed here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' SUMMARY AND FINAL COMMENTS We confirm the presence of VLPP with a refined period of 857 days based on 5 more years (20 years total) of observations for FS Aur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' This result also helps in confirming the authenticity of this signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We also revisited the triple CV hypothesis in which a massive planet, or a sub- stellar object, pumps eccentricity into the inner binary orbit by secular perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' New parameters of mass, radius and temperature for the binary members of the CV FS Aur Knigge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2011 were calculated, and we used these to recalculate the most efficient parameters for the third body as defined earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The most efficient combination that explains the 857 day period is a third body with M3 = 29MJ and P3/P2 = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='7 (P3 = 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='16 h).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' This new value is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='7 times less massive than our previous estimation and is well within the limits of planetary mass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' For example, the planet HD 169142b has a similar mass Fedele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' All these numerical calculations were made for a third body in an initial circular and planar orbit as in CH2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We also explored more complications to the model to study the secular perturba- tions of systems with eccentric and inclined orbits, using previous analytical results (Georgakarakos 2002, 2003, 2004, 2006, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We found that as the eccentricity increases the most efficient candidate third body has a larger mass: M3 = 47MJ for an eccentricity of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='2, and M3 = 48MJ for an eccentricity of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='5 of the third body.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' When the mutual inclination is explored the most efficient candidate for the third body has larger mass: if the inclination is 15◦ the expected most efficient mass is about M3 = 58MJ, but when the inclination is 30◦ the expected most efficient mass now is about M3 = 72MJ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 14 CHAVEZ ET AL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We considered other dynamical effects that might produce this VLPP, such as the first order post–Newtonian correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We found that for FS Aur the period of the pericentre circulation is 6812 day (18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='65 yrs), that is much larger than the 857 day period observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We calculated a first order estimation of the effect of the secular period due of the third object on the mass transfer rate and then on the brightness of the system;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' a change of magnitude of the order of only ∆Mbol = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='29 was obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Even when this change is not the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='4–magnitude observed, is quite close for an order of magnitude calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' It also gave us insights on how sensitive is the system to even smallest changes in the parameters to calculate ˙M(2), to show that we changed the distance R(2) by less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='01% and we obtained the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='4–magnitude observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The R(2) adjustment was based on the value of ˙M(2) that appears in Table 2 taken from Knigge et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2011 and that value was calculated using statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' The change in magnitude of FS Aur are may be a mechanism to explain the VLPP observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We examined alternative scenarios for the VLPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' A possible explanation by a solar type magnetic cycle of the secondary cannot be ruled out for the VLPP, since the VLPP is only 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='346 years and most of the cyclic type magnetic periods in mid to late M stars are of the order of decades.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='However there are no studies for the magnetic cyles of very late M stars in CVs to asses further this hypothesis, then making this alternative a plausible one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' In summary, we find (a) that the new extended data confirms that there is a VLPP, but with a new value of 857 days, (b) These new data is consistent with a triple- system for FS Aur, (c) that combining such data with new initial conditions yield a reduction (from M3 = 50MJ to 29MJ) in the mass estimate for the third-body most efficient candidate in FS Aur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', (d) an order of magnitude estimation for the mass transfer rate and the brightness of the system has been done, with the initial condi- tions used here, lead to a change on magnitude of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' This value was 25% times smaller than the observed but we found that changes of less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='01% in the R(2) parameter increases the change in magnitude to the observed one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Acknowledgements We would like to thank all the amateur observers who do a great hard job in collecting professional grade data with persistence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We are particularly indebted to Joe Patterson, who guides the amateur community engaged in CV monitoring and who made possible the dense observational coverage of FS Aur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We acknowledge with thanks the variable star observations from the AAVSO International Database contributed by observers worldwide and used in this research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' CC acknowledges UANL PAICYT grant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' We appreciate the comments, suggestions and corrections by the anonymous referee, which helped us to greatly improve the quality and content of this research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' REFERENCES Bianchi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 1992, A&A, 253, 447–450.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Brankin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Gladwell, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Dormand, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Prince, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Seward, W, 1989, ACM T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 15, 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' REVISITING FS AURIGAE 15 Beuermann, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Hessman, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Dreizler, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2010, A&A, 521, L60 Beuermann, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Buhlmann, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Diese, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2011, A&A, 526, A53 Bruch, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2014, A&A, 566, A101 Chavez, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Tovmassian, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Aguilar, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Zharikov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Henden, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2012, A&A, 538, A122.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Eggleton, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 1983, APJ, 268, 368.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Fedele, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Carney, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Hogerheijde, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Walsh, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Miotello, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Klaassen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Bruderer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Henning, Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' van Dishoeck, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2017, A&A, 600, A72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Georgakarakos, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2002, MNRAS, 337, 559.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Georgakarakos, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2003, MNRAS, 345, 340.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Georgakarakos, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2004, CeMDA, 89, 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Georgakarakos, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2006, MNRAS, 366, 566.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Georgakarakos, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2009, MNRAS, 392, 1253.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Georgakarakos, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2013, NewA, 23, 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Georgakarakos, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' & Eggl, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2015, APJ, 802, article id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Georgakarakos, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Dobbs–Dixon, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Way, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2016, MNRAS, 461, 1512.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Getley, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Carter, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' KIng, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' OToole, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2017, MNRAS, 468, 2932.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Hessman, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Gansicke, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Mattei, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2000, A&A, 361, 952.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Holman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Wiegert, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 1999, APJ, 117, 621.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Howell, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2004, ASP Conference Proceedings, 315, 353.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Knigge, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2006, MNRAS, 373, 484 Knigge, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Baraffe, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Patterson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2011, APJ Supplement Series, 194, 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Kozai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 1962, AJ, 67, 591 Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Kim, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Kim, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2009, AJ, 137, 3181 Li, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Hu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2017, PASJ, 69, 28 Lubow, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Shu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 1975, APJ, 198, 383.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Mascareno, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Rebolo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Gonzalez Hernandez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2016, A&A, 595, A12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Mazeh, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Shaham, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 1979, A&A, 77, 145.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Naoz, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Kocsis, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Loeb, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Yunes, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2015, APJ, 773, article id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 187.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Neustroev, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Zharikov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Tovmassian, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Shearer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2005, MNRAS, 362, 1472.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Qian, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Zhu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Dai, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Fernandez–Lajus, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Xiang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' and He, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2012a, APJL, 745, article id.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' L23 Qian S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Liu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Zhu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Dai, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Fernandez–Lajus, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Baume, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2012b, MN- RAS, 422, L24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Richman, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Applegate, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Patterson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 1994, PASP, 106, 1075.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Ritter, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2008, Mem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Italiana, Proceedings of the School of Astrophysics, 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Sepinsky, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Willems, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Kalogera, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2007, APJ, 660, 1624–1635.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Soderhjelm, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 1982, A&A, 107, 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Soderhjelm, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 1984, A&A, 141, 232.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Thorstensen, John R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Patterson, Joseph O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Shambrook, Anouk, Thomas, Gino, 1996, PASP, 108, 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Tovmassian, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Zharikov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Michel, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Neustroev, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Greiner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Skillman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Harvey, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Fried, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' & Patterson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 2003, PASP, 115, 725.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Tovmassian, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', Zharikov, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', & Neustroev, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', 2007, APJ, 655, 466.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Warner, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 1995, Cataclysmic Variable Stars (Cambridge University Press).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' 16 CHAVEZ ET AL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Chavez C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='E and Aviles A: Universidad Auton´oma de Nuevo Le´on, Facultad de Ingenier´ıa Mec´anica y El´ectrica, San Nicol´as de los Garza, NL, M´exico (Car- los.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='ChavezPch@uanl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='mx).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Georgakarakos N: New York University Abu Dhabi, Saadiyat Island, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Box 129188, Abu Dhabi, UAE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Ramos C: Universidad Auton´oma de Nuevo Le´on, Facultad de Ciencias F´ısico– Matem´aticas, San Nicol´as de los Garza, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' M´exico.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Ramos C: Centro de Investigaci´on y de Estudios Avanzados del Instituto Polit´ecnico Nacional, San Pedro Zacatenco, Ciudad de M´exico, 07360, M´exico.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=' Aceves H, Tovmassian G, Zharikov S: Universidad Nacional Aut´onoma de M´exico, Instituto de Astronom´ıa, Ensenada 22860, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} +page_content=', M´exico,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/R9E3T4oBgHgl3EQfDQnp/content/2301.04286v1.pdf'} diff --git a/RdA0T4oBgHgl3EQfDv9U/vector_store/index.pkl b/RdA0T4oBgHgl3EQfDv9U/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..f6ea8649f0d5a679f6f4e4d2aa3340afc2182e5a --- /dev/null +++ b/RdA0T4oBgHgl3EQfDv9U/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b4959342e7c862b22871c5c54455597d50c55dadc3229b576be132eacaf4bbe0 +size 129893 diff --git a/RdAzT4oBgHgl3EQf0P6C/content/tmp_files/2301.01781v1.pdf.txt b/RdAzT4oBgHgl3EQf0P6C/content/tmp_files/2301.01781v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..726e9d9265e3a79b671aa80d2c576151d9233de8 --- /dev/null +++ b/RdAzT4oBgHgl3EQf0P6C/content/tmp_files/2301.01781v1.pdf.txt @@ -0,0 +1,1558 @@ +arXiv:2301.01781v1 [quant-ph] 4 Jan 2023 +Optimal one-shot entanglement sharing +Vikesh Siddhu and John Smolin +IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA +January 4, 2023 +Abstract +Sharing entanglement across quantum interconnects is fundamental for quantum information process- +ing. We discuss a practical setting where this interconnect, modeled by a quantum channel, is used once +with the aim of sharing high fidelity entanglement. For any channel, we provide methods to easily find both +this maximum fidelity and optimal inputs that achieve it. Unlike most metrics for sharing entanglement, +this maximum fidelity can be shown to be multiplicative. This ensures a complete understanding in the +sense that the maximum fidelity and optimal inputs found in our one-shot setting extend even when the +channel is used multiple times, possibly with other channels. Optimal inputs need not be fully entangled. +We find the minimum entanglement in these optimal inputs can even vary discontinuously with channel +noise. Generally, noise parameters are hard to identify and remain unknown for most channels. However, +for all qubit channels with qubit environments, we provide a rigorous noise parametrization which we ex- +plain in-terms of no-cloning. This noise parametrization and a channel representation we call the standard +Kraus decomposition have pleasing properties that make them both useful more generally. +Contents +1 +Introduction +2 +2 +Preliminaries +3 +2.1 +Operator-Ket duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +4 +3 +Quantum channels +5 +3.1 +A standard Kraus decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +6 +3.2 +Dual channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +7 +3.3 +Extreme qubit channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +7 +4 +High fidelity entanglement +9 +4.1 +Multiplicativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +11 +5 +Applications +12 +5.1 +Extremal qubit channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +12 +5.2 +Qubit Pauli channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +13 +5.3 +Some qutrit channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . +15 +6 +Discussion +16 +1 + +1 +Introduction +Quantum computation and communication requires faithful transmission of quantum information be- +tween various separated parties. These parties may be closely separated quantum computing nodes or +widely separated receivers and transmitters of quantum states. The former appear in models of a quantum +intranet [1] while the latter appear in discussions of a quantum internet [2, 3]. Noise in these, and other +such setups hinders their use. A dominant source of noise is the quantum interconnect carrying quan- +tum information between parties. This interconnect is modeled mathematically by a quantum channel, a +completely positive trace preserving map. Quantum information sent and processed across this channel is +equivalent to entanglement shared and processed using the channel [4]. Without investigating methods, +metrics, protocols and characteristics of sharing entanglement across quantum channels, our understanding +and ability to control and scale quantum computation and communication remains partial. +Related work. The most well studied setting for sharing entanglement allows asymptotically many +channel uses [5, 6]. Across all channels used together, local pre- and post-processing of entanglement is +allowed along with classical communication from channel input to output. Using these allowed operations, +the largest number of fully entangled states, per channel use, shared with asymptotically vanishing error +defines the quantum capacity of the channel. Studies of this metric reveal that while theoretically beauti- +ful [7–11] a channel’s quantum capacity is hard to compute and non-trivial to understand in general [12,13]. +Both these features come from super-additivity. Super-additivity of quantum capacity implies that the +quantum capacity of several channels used jointly is not completely specified by the quantum capacity of +each channel [14,15]. +Asymptotic channel capacities provide rich conceptual and practical difficulties. For these reasons, it +is desirable to study entanglement transmission with as little encoding and decoding as possible. The +simplest setting here is a single use of a channel (which can itself be joint uses of many channels) with no +post-processing. This setting need not allow sharing of noiseless entanglement. Thus, one may define a +metric for sharing entanglement with some acceptable level of noise. One such metric, called the one-shot +quantum capacity, is roughly the largest fully entangled state than can be shared across a channel with +at most a fixed, but arbitrary error [16]. This one-shot capacity, its connection to asymptotic capacities, +and method for understanding and achieving these have been recently explored [17–27]. However, we +don’t fully understand notions of additivity for this capacity; ways of computing and explicit protocols for +achieving the one-shot capacity are not completely known. +A key metric in the one-shot setting is the highest fidelity between the state shared across the channel and +a maximally entangled state [5,28]. This fidelity characterizes optimal performance of various teleportation +based tasks [29]. +The optimal fidelity between a pure entangled state shared across the channel and +a maximally entangled state is known [30, 31]. +Surprisingly, the optimal pure state input need not be +maximally entangled which is consistent with fidelity not being an entanglement monotone. +The one-shot setting is augmented by post-processing using one round of local operations and two-way +classical communication (2-LOCC) [31–34]. However, in this setting it is unknown if the optimal fidelity is +multiplicative (analog of additivity in this setting). There is no known method for computing or explicit +protocol for achieving this optimal fidelity in general. The only exception is qubit channels, where optimal +protocols use pure state inputs and don’t require 2-LOCC [32, 34]. Surprisingly, the behaviour of such +optimal protocols for the simplest of qubit channels is not fully known. +One way to understand a metric for sharing entanglement across a specific channel is to study variation +in the metric with the amount of noise in the channel. Surprisingly, even for the simplest qubit channels, +noise parameters are only partially understood. +A +N +B +R +R +ρRA +ρRB +Figure 1: Diagram representing one-shot entanglement passing. +2 + +Results. In this work, we introduce and solve the problem for sharing entanglement in a one-shot +setting where an arbitrary mixed state ρRA may be prepared across a reference system R and channel input +A. This input is sent via a fixed channel N : A �→ B (see Fig. 1) to achieve the maximum fidelity O(N) +between the channel output ρRB and a maximally entangled state across R and B. We reformulate O(N) +via a semi-definite program [35] in two useful ways (see Sec. 4 with Th. 1). First, using what we define (in +Sec. 3.1) as a channel’s standard Kraus decomposition, and second, in terms of the operator norm of a +channel’s Choi–Jamiołkowski operator. We show the maximum fidelity O is multiplicative (see Th. 2). Not +only can O(N) be achieved using pure states but also using a variety of mixed states. We give a recipe to +construct these pure and mixed states. For all extremal qubit channels, we compute optimal inputs and the +minimum amount of entanglement E required to create these inputs. We identify rigorous noise parameters +for extremal qubit channels (see Sec. 3.3). Somewhat surprisingly, the minimum entanglement E is found +to be discontinuous in these noise parameters. Typically, E is less than its maximal value of one, but O is +high enough for the channel to be useful for teleportation, even if the channel has no quantum capacity (see +Sec. 5.1). For very noisy qubit Pauli channels we find separable inputs that achieve the same fidelity as +maximally entangled ones found previously (see Sec. 5.2). We also find optimal inputs for qutrit channels +have a much richer structure than qubit channels (see Sec. 5.3). +Unlike other metrics in settings for entanglement sharing, O is multiplicative. Thus, even when a channel +N is used multiple times, possibly with other channels, its maximum fidelity O(N) fully characterizes its +ability for sharing high fidelity entanglement without post-processing. Our results also give rigorous lower +bounds on entanglement fidelities that can be achieved when allowing for multiple rounds of 2-LOCC. +These bounds are tight for one round of 2-LOCC using qubit channels. +Characterization of the noise +parameters for all extremal qubit channels presented here pave the way for a stronger understanding of +quantum channels and quantum protocols across channels. +2 +Preliminaries +Let x denote a vector in n-dimensional real space, Rn, xi denote the (i + 1)th coordinate of x, and |xi| +denote its absolute value. Coordinates of x rearranged in decreasing order give x↓, a vector satisfying +x↓ +0 ≥ x↓ +1 ≥ · · · ≥ x↓ +n−1. Euclidean norm of x, |x| := +�� +i x2 +i . Let |ψ⟩ denote a ket in a Hilbert space H of +finite dimension d and ||ψ⟩| := +� +⟨ψ|ψ⟩ denote its norm. A pure quantum state is represented by a ket with +unit norm. Let L(H) denote the space of linear operators on H. For any two quantum states |ψ⟩ and |φ⟩, the +dyad |ψ⟩⟨φ| ∈ L(H) and the projector onto |ψ⟩, |ψ⟩⟨ψ| ∈ L(H). The Frobenius inner product between two +operators N and O in L(H), +⟨N, O⟩ := Tr(N †O), +(1) +where N † represents the adjoint (conjugate transpose) of N. A Hermitian operator H ∈ L(H), satisfying +H = H†, represents an observable. This operator has an eigendecomposition, +H = +� +i +xi|ψi⟩⟨ψi|, +(2) +where xi ∈ R is an eigenvalue of H corresponding to eigenvector |ψi⟩ and the collection of eigenvectors +{|ψi⟩} form an orthonormal basis of H, ⟨ψi|ψj⟩ = δij, where δij is the Kronecker delta function. Support of +H is the subspace spanned by its eigenvectors with non-zero eigenvalues. In (2), if xi ≥ 0 for all i, then we +say H is positive semi-definite (PSD), H ⪰ 0. This PSD operator’s square root, +√ +H, is obtained by replacing +xi in (2) with √xi. For any operator O ∈ L(H), +||O|| := max +||ψ⟩|≤1|O|ψ⟩|, +||O||1 := Tr( +√ +OO†), +and +||O||2 := +� +Tr(OO†), +(3) +denote the spectral norm, the trace norm, and the Frobenius norm, respectively. For H in (2), +||H|| = |x↓ +1|, +||H||1 = +� +i +|xi|, +and +||H||2 = |x|. +(4) +3 + +A density operator ρ ∈ L(H) is a positive semi-definite operator with unit trace, Tr(ρ) = 1, it represents +a mixed quantum state. Its von-Neumann entropy, +S(ρ) = −Tr(ρ log ρ), +(5) +where log is base 2. The fidelity between two density operators ρ and σ, +F(ρ, σ) := ||√ρ√σ||1. +(6) +Let HA and HB be two Hilbert spaces of dimensions dA and dB, respectively, and HAB denote the tensor +product space HA ⊗ HB. Given a pure state |ψ⟩AB ∈ HAB, density operators +ψA = TrB(|ψ⟩⟨ψ|) +and +ψB = TrA(|ψ⟩⟨ψ|) +(7) +denote the partial trace of |ψ⟩⟨ψ| over HB and HA, respectively. The entanglement of formation of a pure +state |ψ⟩AB, +Ef(|ψ⟩AB) = S(ψA), +(8) +and for a mixed state ρAB, +Ef(ρAB) = min +� +i +piEf(|ψi⟩AB), +(9) +is the minimum average entanglement Ef over all pure state decompositions, ρAB = � +i pi|ψi⟩⟨ψi|, pi ≥ 0 +and � +i pi = 1. +Let A = {|ai⟩} and B = {|bj⟩} be orthonormal bases, of HA and HB, respectively, i.e., +⟨ai|aj⟩ = ⟨bi|bj⟩ = δij. +(10) +Using these bases A and B we can represent any linear operator L : HA �→ HB as a matrix, +L = +� +ij +[L]ij|bi⟩⟨aj|, +(11) +with elements [L]ij. We can define two basis dependent linear maps, +L∗ = +� +ij +[L]∗ +ij|bi⟩⟨aj|, +and +LT = +� +ij +[L]ij|aj⟩⟨bi|, +(12) +representing complex conjugate and transpose, respectively. In contrast to L∗ and LT, the adjoint L† = +(L∗)T = (LT )∗ is basis independent. If HA and HB have the same dimension d, then one can choose A and +B to be the same, say the standard basis {|i⟩}, and construct an identity map IA←B : HB �→ HA, +IA←B|i⟩B = |i⟩A. +(13) +This subscript notation A ← B is dropped shortly after defining how the identity map above is used to map +a ket |φ⟩B ∈ HB, an operator OB ∈ L(HB) and part of an operator LAB ∈ L(HAB) to +|φ⟩A = IA←B|ψ⟩B, +OA = IA←BOBIB←A, +and +LAA = (IA←B ⊗ IA)LBA(IB←A ⊗ IA), +(14) +respectively, here IA is identity on the HA space. Later, these mappings are done implicitly by simply +replacing the subscripts in an obvious way. +2.1 +Operator-Ket duality +Operator-ket duality is the concept of fixing an orthonormal basis A = {|ai⟩} of HA and using an un- +normalized maximally entangled state on HA ⊗ HA, +|γ⟩AA = +� +i +|ai⟩ ⊗ |ai⟩, +(15) +4 + +to associate with any linear operator K : HA �→ HB a ket, |ψ⟩AB = (IA ⊗ K)|γ⟩, obtained by acting K +on one-half of |γ⟩. Conversely, for fixed orthonormal basis A, one associates with any ket |ψ⟩AB, a linear +operator +K = +� +i +|χi⟩⟨ai|, +where +|χi⟩B = (⟨ai|A ⊗ IB)|ψ⟩AB. +(16) +In analogy to the discussion above, fixing an orthonormal basis B = {|bj⟩} of HB one associates with the +ket |ψ⟩AB an operator L : HB �→ HA. This operator L = KT where the transpose operation is taken using +basis A and B as described in (12). +In what follows, we use the notation |K⟩ ∈ HAB for a ket associated with the operator K : HA �→ HB +through the operator-ket duality above where basis A is fixed. This ket and operator pair satisfy +|K⟩AB = (I ⊗ K)|γ⟩AA. +(17) +For any two maps K and K′ from HA to HB and associated kets |K⟩AB and |K′⟩AB, respectively, one can +show that +⟨K, K′⟩ = ⟨K|K′⟩. +(18) +Using the orthonormal basis B of HB, one can associate with K† : HB �→ HA the ket |K†⟩BA. In this ket, +swapping the spaces HA and HB (see discussion below (13)) gives |K†⟩AB which then satisfies +|K†⟩AB = |K⟩∗ +AB +(19) +where complex conjugation of any ket |χ⟩AB = � +ij cij|ai⟩ ⊗ |bj⟩, is defined using basis A and B as +|χ⟩∗ +AB = � +ij c∗ +ij|ai⟩ ⊗ |bj⟩. +3 +Quantum channels +Let HA, HB, and HC be three Hilbert spaces and V : HA �→ HB ⊗ HC be an isometry, i.e., V †V = IA. +This isometry defines a pair of quantum channels N and N c, i.e., a pair of completely positive trace +preserving (CPTP) maps with superoperators +N(O) = TrC(V OV †) +and +N c(O) = TrB(V OV †), +(20) +taking O ∈ L(HA) to L(HB) and L(HC), respectively. The quantum channel N is called degradable and N c +anti-degradable if there exists a quantum channel D such that D ◦ N = N c [11]. +Let IA be the identity map from L(HA) to itself. Using an un-normalized maximally entangled state +|γ⟩AA (15) we define the Choi–Jamiołkowski [36,37] operator of the linear map N as +JN +AB = IA ⊗ N(|γ⟩⟨γ|) = +� +ij +|ai⟩⟨aj| ⊗ N(|ai⟩⟨aj|). +(21) +This operator contains all information about N. For instance, +N(|ai⟩⟨aj|) = (⟨ai| ⊗ IB)JN +AB(|aj⟩ ⊗ IB), +(22) +N is completely positive (CP) if and only if JN +AB is positive semi-definite, and +TrB(JN +AB) = IA +(23) +if and only if N is trace-preserving, Tr +� +N(O) +� += Tr(O) for all O. Equivalently, a linear map N : L(HA) �→ +L(HB) is CP if and only if it can be written in the form +N(O) = +� +i +KiOK† +i , +(24) +where Ki : HA �→ HB is a linear operator, and the collection {Ki} are called Kraus operators. The map +in (24) is trace preserving when these Kraus operators satisfy � +i K† +i Ki = IA. +When N is unital, i.e., +N(IA) = IB, the Kraus operators satisfy � +i KiK† +i = IB. If HA and HB have the same dimension, then +they are isomorphic to one another and can be denoted by H. If these Kraus operators on H are Hermitian +operators (or normal operators) then the channel is automatically unital. +5 + +3.1 +A standard Kraus decomposition +For a given channel N : L(HA) �→ L(HB), the set of Kraus operators is not unique. However, one can +construct what can be called a standard Kraus decomposition with some pleasing properties. +Consider the eigendecomposition of the Choi–Jamiołkowski operator in (21), +JN +AB = +� +i +e↓ +i |Li⟩⟨Li|, +(25) +where eigenvalues e↓ +0 ≥ e↓ +2 ≥ · · · ≥ e↓ +dAdB−1 ≥ 0 and eigenvectors {|Li⟩} form an orthonormal basis of HAB, +⟨Li|Lj⟩ = δij. +(26) +Applying operator-ket duality using orthonormal basis A = {|ai⟩} to kets {|Li⟩} results in a collection of +orthonormal operators {Li} that map HA to HB (see Sec. 2.1). Using these operators define Ki : HA �→ HB, +Ki := +� +e↓ +i Li. +(27) +Lemma 1. Operators {Ki} form a Kraus decomposition of N, +N(O) = +� +i +KiOK† +i . +(28) +Proof. In (25) use (17) to obtain +JN +AB = +� +i +e↓ +i (IA ⊗ Li)|γ⟩⟨γ|(IA ⊗ Li)† +(29) += +� +i +(IA ⊗ Ki)|γ⟩⟨γ|(IA ⊗ Ki)†, +(30) +where the second inequality uses (27). This second inequality, together with (22) gives, +N(|ak⟩⟨al|) = +� +i +Ki(|ak⟩⟨al|)K† +i +(31) +This equality, together with linearity of N proves this lemma. +■ +Using (25), (26), and (27) one can show that the Kraus operators {Ki} satisfy +⟨Ki, Kj⟩ = ⟨Ki, Ki⟩δij +and +⟨Ki, Ki⟩ ≥ ⟨Kj, Kj⟩, +(32) +where i ≤ j and we use ⟨Ki, Ki⟩ = e↓ +i . In addition to being orthogonal and ordered in the way captured +by the above equation, the Kraus operators {Ki} have several other useful properties. The total number +of non-zero operators {Ki} is the rank of the Choi-Jamiołkowsi operator J N +AB. This rank is the minimum +number of Kraus operators required to represent the channel N. When the eigenvalues of JN +AB are distinct, +the norm ⟨Ki, Ki⟩ of each Kraus operator is simply the (i+1)th largest eigenvalue of J N +AB. From these Kraus +operators, one can obtain the Choi-Jamiołkowsi operator (21), +J N +AB = +� +i +|Ki⟩⟨Ki|, +(33) +where we have applied operator-ket duality (see Sec. 2.1) to convert operators Ki : HA �→ HB to kets +|Ki⟩ ∈ HAB using basis A = {|ai⟩}. Notice |Ki⟩ is an un-normalized eigenvectors of J N +AB with eigenvalue +⟨Ki, Ki⟩. We call {Ki} in Lemma (1) to be a standard Kraus decomposition. +6 + +3.2 +Dual channel +Given a map N : L(HA) �→ L(HB), its dual N † : L(LB) �→ L(HA) is defined via ∗ +Tr +� +N †(O)ρ +� += Tr +� +ON(ρ) +� +, +(34) +where ρ ∈ L(HA) and O ∈ L(HB). A quantum channel N evolves a quantum state ρ and its dual channel +N † evolves an observable O. The right side of the above equality represents the expectation value of the +evolved quantum state N(ρ) with respect to a fixed observable O while the left side of the equality gives the +expectation value of a fixed state ρ with respect to the evolved observable N †(O). If N is CP and has Kraus +decomposition (24) then N † is also CP with Kraus operators {K† +i }, and if N is trace-preserving then N † is +unital (see Ch.6 in [38]). A CP map N with standard Kraus operators {Ki} has dual map N † with standard +Kraus operators {K† +i } since +⟨K† +i , K† +j ⟩ = (⟨Ki, Kj⟩)∗. +(35) +The Choi-Jamiołkowsi operator (21) of the dual channel, +JN † +BA = +� +i +|K† +i ⟩⟨K† +i |, +(36) +where {|K† +i ⟩} in HBA are defined via operator-ket duality using basis B = {|bj⟩}. Interchanging B and A +in (36) and using (19), (33) gives +JN +AB = (JN † +AB)∗. +(37) +The Choi-Jamiołkowsi operator of a channel and its dual can be taken to be complex conjugates of one +another. +3.3 +Extreme qubit channels +The set of quantum channels from L(HA) to L(HB) is convex, i.e., if N and M are quantum channels +then +K = λN + (1 − λ)M, +(38) +is a quantum channel for any 0 ≤ λ ≤ 1. Any quantum channel K is extremal, i.e., it is an extreme point +of the set of quantum channels, if equality of the type (38) holds only when λ = 0 or λ = 1, or the only +channels N and M satisfying the equality both equal K. +A quantum channel N : L(HA) �→ L(HB) is called a qubit channel when HA and HB are two- +dimensional. For these two dimensional spaces, we can use the standard basis {|i⟩}, where i ∈ {0, 1}, +to define Pauli operators, +X = |0⟩⟨1| + |1⟩⟨0|, +Y = −i|0⟩⟨1| + i|1⟩⟨0|, +and +Z = |0⟩⟨0| − |1⟩⟨1|. +(39) +Extreme points of qubit channels are studied in various works [40–44]. A qubit channel is extremal if it +has a single Kraus operator, given by a unitary operator, or it has two Kraus operators, each not proportional +to a unitary operator (see Cor. 15 in [44]). Up to local unitaries at the channel input and output, a qubit +channel N with two Kraus operators can be written as [42] +N(O) = K0OK† +0 + K1OK† +1, +(40) +where, +K0 = +�cos( v−u +2 ) +0 +0 +cos( v+u +2 ) +� +, +K1 = +� +0 +sin( v+u +2 ) +sin( v−u +2 ) +0 +� +, +(41) +are expressed in the standard basis {|i⟩} at HA and HB, u ∈ [0, 2π] and v ∈ [0, π). +∗This definition of dual map (34), common in quantum information (see Def.(6.2) in [38] or below eq.(1.44) in [39]), differs from +another, ⟨N †(O), ρ⟩ = ⟨O, N (ρ)⟩, found in mathematics literature. +The two definitions coincide for maps satisfying, N (ρ†) = +� +N (ρ)�†, but can differ when this property is not satisfied. For example if N (ρ) = cρ, and c complex then the two definitions give +different dual maps. +7 + +While u and v parametrize the channel (40), they don’t necessarily represent noise parameters that have +a monotonic relationship with the amount of noise introduced by the channel. In certain special cases, noise +parameters can be arrived at intuitively. For instance when u = 0, +N(O) = cos2(v +2)O + sin2(v +2)XOX, +(42) +is a qubit dephasing channel with dephasing probability sin2(v/2) †. By performing a unitary, X, at the +input channel input HA, this dephasing channel (42) can be converted to another dephasing channel with +dephasing probability 1 − sin2(v/2). Thus a dephasing probability of half gives maximum dephasing. This +dephasing probability is an intuitive noise parameter in the sense that as this probability is increased from +zero to a half, the channel becomes noisier. +Another special case is when u + v = 2π. Here, if kets |0⟩ and |1⟩ are interchanged at the channel +input and output, N becomes a qubit amplitude damping channel. The qubit amplitude damping channel +fixes |0⟩⟨0| but |1⟩⟨1| decays to |0⟩⟨0| with probability sin2 v. Intuitively, this damping probability is a noise +parameter in the sense that as the damping probability is increased from zero to one, the channel becomes +noisier. Except for these special cases of dephasing and amplitude damping, suitable noise parameters are +not necessarily easy to guess. +As discussed above, when N represents amplitude damping noise, the noise parameter is the damping +probability. In all other cases, this qubit channel N can be generated from an isometry (see discussion in +Sec. 3) of a special form. A isometry of this pcubed form [45], +V |αi⟩ = |βi⟩ ⊗ |γi⟩, +(43) +where i ∈ {0, 1}, takes some special input pure states {|αi⟩} that are not necessarily orthogonal but form a +basis of HA, to product of pure states {|βi⟩} at the HB output and {|γi⟩} at the HC output. The Gram matrices +GA, GB, and GC of {|αi⟩}, {|βj⟩} and {|γk⟩}, respectively, satisfy +[GA]ij = ⟨αi|αj⟩ = ⟨βi|βj⟩⟨γi|γj⟩ = [GB]ij[GC]ij +(44) +if and only if V is an isometry, i.e., V †V = IA [45]. These matrices take the form +GA = +�1 +a +a +1 +� +, +GB = +�1 +b +b +1 +� +, +and +GC = +�1 +c +c +1 +� +, +(45) +where −1 < a < 1, −1 ≤ b ≤ 1, −1 ≤ c ≤ 1, and a = bc. The parameters b and c completely specify the +isometry V in (43) and thus the channel N. One may parametrize |αi⟩ using the standard basis as +|αi⟩ = +� +1 + a +2 +|0⟩ + (−1)i +� +1 − a +2 +|1⟩. +(46) +In this parametrization replacing a with b gives |βi⟩ and replacing a with c gives |γi⟩. The parameters b and +c are related to u and v in (41) as follows, +sin2 v = +1 − c2 +1 − (bc)2 , +and +cos2 u = +1 − b2 +1 − (bc)2 , +(47) +where |bc| ̸= 1. The Kraus operators in (41) can be written as +K0 = + + +� +(1+b)(1+c) +2(1+bc) +0 +0 +� +(1−b)(1+c) +2(1−bc) + + +and +K1 = + + +0 +� +(1+b)(1−c) +2(1−bc) +� +(1−b)(1−c) +2(1+bc) +0 + + . +(48) +While these Kraus operators look more complicated than those in (41), several other channel properties +simplify when using the parameters b and c. +For instance, the channel N with parameters b and c is +degradable if |b/c| < 1, otherwise |b/c| ≥ 1 and the channel is anti-degradable [45]. +†Notice, the dephasing channel is not extremal since each of its Kraus operators are proportional to a unitary operator (see +discussion above (40)). +8 + +In general, −1 ≤ b ≤ 1 and −1 ≤ c ≤ 1, however one can simplify the parameter space. In the discussion +above, replacing b with −b while keeping c fixed results in a new channel ˜ +N which is equivalent to N up to +local unitaries at the channel input and output. To see this, notice this replacement defines a new isometry +˜V of the pcubed form, +˜V |˜αi⟩ = |˜βi⟩ ⊗ |γi⟩, +(49) +where |˜αi⟩ and |˜βi⟩ are kets obtained from |αi⟩ and |βi⟩ (see definition below eq. (46)) by replacing a and b +with −a and −b, respectively. This new isometry ˜V is related to V in (43), via local unitaries as follows, +(IC ⊗ XB) ˜V = V XA, +(50) +where X is defined in (39). In a similar vein, a channel with parameters b and c is equivalent up to local +unitaries to a channel with parameters b and −c. These equivalences allow us to restrict the parameter space +−1 ≤ b ≤ 1 and −1 ≤ c ≤ 1 to the positive quadrant 0 ≤ b ≤ 1 and 0 ≤ c ≤ 1. +We show that any channel N with parameters b and c can simulate another channel N ′ with parameters +b and c′ ≤ c, in the sense, +N ′ = N ◦ M, +(51) +where M is a quantum channel. Proof of the above equation is easy to see from a pcubed point of view. +Let N : L(HA) �→ L(HB) be generated by the isometry in (43), N ′ : L(HA) �→ L(HB) be generated by an +isometry V ′ : HA �→ HB ⊗ HC′ of the same form as V in (43), however +V ′|α′ +i⟩ = |βi⟩ ⊗ |γ′ +i⟩ +(52) +where c′ = ⟨γ′ +0|γ′ +1⟩ and a′ = ⟨α′ +0|α′ +1⟩ = bc′. The M : L(HA) �→ L(HA) channel in (51) is generated by an +isometry W : HA �→ HA ⊗ HD of the form (43) with +W|α′ +i⟩ = |αi⟩ ⊗ |δi⟩, +(53) +where d := ⟨δ0|δ1⟩ = c′/c takes values between 0 and 1 since 0 ≤ c′ ≤ c. The relationship in (51) ensures +that N ′ is noisier than N. As a result, for fixed b, if one decreases c then the channel N becomes noisier. +This parameter c captures lack of distinguishability between pure states being arriving at the environ- +ment. +If c is decreased, more information flows to the environment. +The no-cloning theorem [46–48] +indicates that such a flow to the environment must come at the cost of information flow to the output. Thus +N becomes noisier with decreasing c. We shall be interested in using c as the noise parameter with b fixed. +In the limiting b = 0 case, N becomes the qubit dephasing channel (42) with dephasing probability (1−c)/2. +Here, decreasing c from 1 to 0 increases the dephasing probability from 0 to half. +4 +High fidelity entanglement +Consider two parties Alice and Bob, connected by some quantum channel N : L(HA) �→ L(HB) where +HA and HB have the same dimension d. Suppose Alice has access to a second d-dimensional system with +Hilbert space HR. What bipartite state ρRA should Alice prepare such that sharing with Bob one half of this +state across the channel N results in a state ρRB with highest fidelity F(ρRB, φRB) to a maximally entangled +state, +|φ⟩RB = +1 +√ +d +|γ⟩RB, +(54) +between reference HR and output HB? The optimal state prepared by Alice, which we denote by ΛRA, and +the maximum fidelity, +O(N) := F(ΛRB, φRB), +(55) +have been characterized previously in terms of the channel’s Choi-Jamiołkowski operator [30,31,34] when +ρRA is pure. For possibly mixed ρRA, our reformulation of these results in terms of the standard Kraus +decomposition of a channel and the operator norm of the channel’s Choi-Jamiołkowski operator agree with +these previous characterizations. We extend these results by finding families of mixed input states ΛRB that +9 + +achieve O(N). This reformulation and extension is used later in our study. We begin our reformulation +using a semi-definite program +maximize F(ρRB, φRB) +subject to ρRB = IR ⊗ N(ρRA), +ρRA ⪰ 0, +Tr(ρRA) = 1. +(56) +The optimum value of the above program gives O(N) and the density operator which achieves this optimum +gives ΛRA. The following Theorem captures the solution to the above problem. +Theorem 1. Given a channel N with standard Kraus operators {Ki}, +O(N) = 1 +d⟨K0, K0⟩ = 1 +d||JN +RB|| = F(ΛRB, φRB), +(57) +where the input ΛRA has support in the span of {|K† +i ⟩RA} satisfying ⟨Ki, Ki⟩ = ⟨K0, K0⟩. +Proof. Using eq. (6) along with the fact that φRB is a pure state, one writes F(ρRB, φRB) as an inner product +⟨ρRB, φRB⟩. This inner product is re-written as ⟨IR⊗N(ρRA), φRB⟩ using the first equality constraint in (56). +This re-writing can be reduced to ⟨ρRA, (IR ⊗ N)†(φRB)⟩ using definition (34) of the dual channel. Using +discussion below (34), or otherwise, one can show that the dual of the tensor product of two channels is the +tensor product of the dual of individual channels. Thus ⟨ρRA, (IR ⊗ N)†(φRB)⟩ = ⟨ρRA, IR ⊗ N †(φRB)⟩, +where we used that fact that I† +R is IR. +Next, notice (IR ⊗ N †)φRB is just J N † +RA /d (21). +Using these +observations, re-write (56) as +maximize 1 +d⟨ρRA, J N † +RA ⟩ +subject to ρRA ⪰ 0, +Tr(ρRA) = 1. +(58) +Solution to this semi-definite program is (1/d) times the maximum eigenvalue of JN † +RA obtained by setting +ρRA = ΛRA where ΛRA is any density operator with support on the eigenspace of this maximum eigenvalue. +This largest eigenvalue can be written as ⟨K† +0, K† +0⟩ = ⟨K0, K0⟩ using (32) and (35). The largest eigenvalue +can also be written as the spectral norm, ||JN +RB||, by applying definition (4). The support of the largest +eigenvalue, ⟨K0, K0⟩, of JN † +RA is the span of the collection of eigenvectors corresponding to this value. +This collection contains eigenvectors |K† +i ⟩ of JN † +RA (see (36)) with eigenvalue ⟨K† +i , K† +i ⟩ equaling the largest +eigenvalue ⟨K† +0, K† +0⟩. The eigenvalues of JN † +RA can be shown to equal corresponding eigenvalues of JN +RA +using (37), i.e., one can show that ⟨K† +i , K† +i ⟩ = ⟨Ki, Ki⟩. +■ +The fidelity between a fixed state ρAB and a fully entangled state, maximized over all possible fully +entangled states is called the fully entangled fraction [5,29] +Fe(ρAB) = max +UA F +� +ρAB, (UA ⊗ IB)φAB(UA ⊗ IB)†� +, +(59) +where UA is a unitary operator on HA. +Lemma 2. The largest fully entangled fraction obtained by sending one half of a mixed state ρRA across the +channel N, maximized over all ρRA equals O(N) (55). +Proof. Notice that the largest fully entangled fraction can be found by modifying the optimization prob- +lem (56) as follows: replace φRB with χRB = (UR⊗IB)φRB(UR ⊗IB)† and optimize over both unitary matri- +ces UR and density operators ρRA. Notice, in this larger optimization problem, one can simplify the objective +function F(ρRB, χRB) = F(ρ′ +RB, φRB) where ρ′ +RB = (UR ⊗ IB)†ρRB(UR ⊗ IB). Since ρ′ +RB = I ⊗ N(ρ′ +RA), +where ρ′ +RA = (UR ⊗ IA)†ρRA(UR ⊗ IA), one can rephrase this optimization at hand purely in terms of a +single new variable ρ′ +RA, satisfying Tr(ρ′ +RA) ⪰ 0 and Tr(ρ′ +RA) = 1. In this rephrasing variable UR no longer +participates. However the new problem in terms of ρ′ +RA is identical to (55). +■ +10 + +The above result generalizes to mixed state what was implicitly found for pure states in the proof of +Lemma 2 in [31]. +Let ΛRA be the state in Th. 1. We are interested in the minimum amount of entanglement over all states +of this type. To capture this minimum, we use entanglement of formation (9). When ΛRA is a unique pure +state we write the input entanglement +E(N) = S(σA), +(60) +when ΛRA can be chosen to be mixed, we write +E(N) = min +ΛRA Ef(ΛRA), +(61) +where ΛRA are states in Th. 1. When ΛRA can be chosen to be a separable state, E(N) = 0. +4.1 +Multiplicativity +Suppose Alice and Bob are connected by two independent channels, that may be same or different. What +state should Alice prepare such that sending one half of it across the joint channel results in Alice and Bob +sharing a joint state with maximum fidelity to a fully entangled state? What is this maximum fidelity? Can +one hope to use correlations across the two channels connecting Alice and Bob to get more fidelity than +what can be achieved without using any correlation across the channels? Variants of these natural questions +have been asked about transmission of information across asymptotically many uses of quantum channels. +Those questions have been hard to answer. Here we mathematically formulate and answer the questions +we posed above. +Let the two channels connecting Alice and Bob be N1 : L(HA1) �→ L(HB1) and N2 : L(HA2) �→ L(HB2), +here dA1 = dB1 and dA2 = dB2. +For each channel input HA1 and HA2, define auxiliary spaces HR1 +and HR2. Let IR1 and IR2 be identity maps on these auxiliary spaces, L(HR1) and L(HR2), respectively, +HA := HA1 ⊗ HA2, HB := HB1 ⊗ HB2, HR = HR1 ⊗ HR2, N = N1 ⊗ N2, and IR = IR1 ⊗ IR2. If Alice +prepares a state which does not correlate inputs to the two channels IR1 ⊗ N1 and IR2 ⊗ N2 then the +maximum fidelity with a fully entangled state across auxiliary space HR and the channel output HB can be +found as follows: +maximize F(ρRB, φRB) +subject to ρRB = (IR ⊗ N)ρRA, +ρRA = ρR1A1 ⊗ ρR2A2 +ρRA ⪰ 0, +Tr(ρRA) = 1. +(62) +The optimum of the above problem is simply O(N1)O(N2). It is obtained at ΛRA = ΛR1A1 ⊗ ΛR2A2 where +ΛR1A1 and ΛR2A2 are optima to optimizations of the form (56) for N1 and N2, respectively. On the other +hand, if Alice prepares a state that may correlate the inputs to IR1 ⊗ N1 and IR2 ⊗ N2 then the maximum +fidelity O(N1 ⊗ N2) is found by solving (62) without the product constraint, ρRA = ρR1A1 ⊗ ρR2A2. This +fidelity maximum O(N1 ⊗ N2) can be higher +O(N1 ⊗ N2) ≥ O(N1)O(N2), +(63) +since the optimum O(N1)O(N2) of (62) bounds from below the optimum of (62) without the product +constraint, ρRA = ρR1A1 ⊗ ρR2A2. +Theorem 2. The maximum fidelity O(N1 ⊗ N2) is multiplicative, i.e., equality holds in (63) +O(N1 ⊗ N2) = O(N1)O(N2), +(64) +Proof. Let N1 and N2 have standard Kraus decomposition {Jq} and {Kr}, respectively. Using Th. 1, we +write +O(N1) = +1 +dA1 +⟨J0, J0⟩ +and +O(N2) = +1 +dA1 +⟨K0, K0⟩. +(65) +11 + +A standard Kraus decomposition {Lp} for N1 ⊗ N2 can be chosen such that each Lp is of the form Jq ⊗ Kr +for some q and r. When q = r = 0, then p can be chosen to be 0, +L0 = J0 ⊗ K0 +(66) +since +⟨L0, L0⟩ = ⟨J0, J0⟩⟨K0, K0⟩ ≥ ⟨Jq, Jq⟩⟨Kr, Kr⟩ = ⟨Lp, Lp⟩ +(67) +for all q, r and corresponding p. Using (66), and Th. 1 on N1 ⊗ N2 gives +O(N1 ⊗ N2) = +1 +dA1dA2 +⟨L0, L0⟩. +(68) +The above equality, together with (65) and (67) proves the result. +Alternatively, notice +JN +RB = +� +p +|Lp⟩⟨Lp| = +� +qr +|Jq⟩⟨Jq| ⊗ |Kr⟩⟨Kr| = JN1 +R1B1 ⊗ JN2 +R2B2. +(69) +where the first equality follows from (33). Using Th. 1, write +O(N1) = +1 +dA1 +||JN1 +R1B1||, +O(N2) = +1 +dA2 +||JN2 +R2B2||, +and +O(N1 ⊗ N2) = 1 +dA +||JN +RB||, +(70) +where dA = dA1dA2. The operator norm is sub-multiplicative (see Sec.1.1.3 in [49]), +||AB|| ≤ ||A|| · ||B||, +(71) +it implies +||A ⊗ B|| ≤ ||A|| · ||B||. +(72) +Using the above equation along with (63) and (70) also proves the result. +■ +5 +Applications +5.1 +Extremal qubit channels +A qubit channel N has dA = dB = 2. If the channel has one Kraus operator then the channel is simply +conjugation with a unitary matrix and O(N) = 1. The next simplest qubit channel has two Kraus operators, +given in (40). One special case of this channel is the qubit amplitude damping channel. Kraus operators for +this amplitude channel can be written as, +K0 = +�1 +0 +0 +√1 − p +� +, +and +K1 = +�0 +√p +0 +0 +� +, +(73) +where 0 ≤ p ≤ 1 is the probability that the state |1⟩⟨1| damps to |0⟩⟨0|. A simple calculation shows that +these Kraus operators constitute a standard Kraus decomposition of N. Using this decomposition in Th. 1, +we find +O(N) = 1 − p/2 +and +ΛRA = |K0⟩⟨K0| +⟨K0, K0⟩ , +(74) +a result that agree with [33]. In general, the amount of entanglement generated at the input (see def. in (60)), +E(N) = h( +1 +2 − p), +(75) +where h(x) := −x log x − (1 − x) log(1 − x) is the binary entropy function with log base 2. This value is +nonzero, unless p = 1 where E(N) = 0 and ΛRA in (74) is a product state. +When the qubit channel N with two Kraus operators is not an amplitude damping channel, the channel +Kraus operators take the form (48). +These Kraus operators {K0, K1} have two parameters 0 ≤ b ≤ 1 +12 + +and 0 ≤ c ≤ 1. If b is fixed and c is decreased from 1 the channel becomes more noisy (see discussion +containing (51)). Operators {K0, K1} form a standard Kraus decomposition. Using them in Th. 1, gives +O(N) = (1 + c)(1 − b2c) +2(1 − b2c2) +and +ΛRA = + + + +|K† +0⟩⟨K† +0| +⟨K† +0,K† +0⟩ +if +b ̸= 1 and c ̸= 0 +� +ij fij|K† +i ⟩⟨K† +j | +if +b = 1 or c = 0 +. +(76) +where complex numbers fij are free except that they result in a valid density operator ΛRA. At b = 1 or +c = 0, ΛRA is supported on a two-dimensional space spanned by {|K† +0⟩RA, |K† +1⟩RA}. This two-dimensional +space is a subspace of a two qubit space HRA. Quite generally, such a subspace has at least one product +state (see Lemma in [50]), but typically there are two [42,45]. In the c = 0 case, these product states take the +simple form +|+⟩R ⊗ |ψ+⟩A +and +|−⟩R ⊗ |ψ−⟩A, +(77) +where |ψ+⟩A = +1 +√ +2( +√ +1 + b|0⟩ + +√ +1 − b|1⟩), |ψ−⟩A = +1 +√ +2( +√ +1 + b|0⟩ − +√ +1 − b|1⟩), |+⟩A = +1 +√ +2(|0⟩ + |1⟩), and +|−⟩A = +1 +√ +2(|0⟩ − |1⟩). +At b = 1 or c = 0 one can choose ΛRA to be a projector onto a product state. As a result, at b = 1 or c = 0, +the input entanglement, defined in (8), is zero. In general, +E(N) = +� +0 +if +b = 1 or c = 0 +h( (1+b)(1−bc) +2(1−b2c) ) +otherwise +(78) +where expressions for E(N) at b ̸= 1 and c ̸= 0 comes from using the form of ΛRA in (76). In Fig. 2 we fix +b and plot E(N) as a function of c; increasing c makes N less noisy (see discussion containing eq. (51)). In +these plots, as c is increased from zero, the value of E(N) dis-continuously increases from 0, at c = 0, and +continues to monotonically increase until c = 1, where N becomes a perfect channel. Across various plots +with fixed b, we notice increasing b decrease E(N), which ultimately goes to zero as b �→ 1 for all bc ̸= 1. +All these features mentioned above are intriguing. In the parameter range 0 < c < 1, one finds an +expected result [34] that the minimum amount of entanglement at the input to have maximum fidelity +with a fully entangled output is strictly less than one. In particular, if one generates more than E(N) < 1 +entanglement at the input, the fidelity with a maximally entangled output is strictly less. The key addition +here is the quantification of the amount of entanglement and a parametrization of the channel in such a way +that the amount of entanglement is monotone in the noise parameters of the channel. +Next, at c = 0, there is a discontinuous change in E(N) which starts at zero and then takes a large finite +value ≃ h +� +(1 + b)/2 +� +. From a mathematical standpoint, the discontinuity arises because the solution to +the optimization (56) becomes degenerate and this degeneracy allows more freedom in choosing optimum +inputs. Due to the structure of qubit channels, this input can be chosen to be separable, as mentioned in the +discussion containing (77). +5.2 +Qubit Pauli channels +A qubit Pauli channel N : HA �→ HB can be written as +N(ρ) = +� +i +piσiρσ† +i , +(79) +where pi ≥ 0, � +i pi = 1, and the Kraus operators {√piσi}, σi : HA �→ HB, are proportional to Pauli +matrices. These matrices can be written in the standard {|0⟩, |1⟩} basis of HA and HB as +σ0 = I = +� +1 +0 +0 +1 +� +, +σ1 = X = +� +0 +1 +1 +0 +� +, +σ2 = Y = +� +0 +−i +i +0 +� +, +and +σ3 = Z = +� +1 +0 +0 +−1 +� +. +(80) +Without loss of generality we can assume p0 ≥ pi for all i ∈ {1, 2, 3}. This assumption comes from the +following argument. Assume pi ≥ pj for some i ̸= 0 and all j ∈ {0, 1, 2, 3}, then conjugating the input ρ +with σi will still result in a Pauli channel (79). However, this resulting channel will have p0 ≥ pi for all +i ∈ {1, 2, 3}. +13 + +0 +0.2 +0.4 +0.6 +0.8 +1 +0.5 +0.6 +0.7 +0.8 +0.9 +1 +c +E(N) +b = 0 +b = 1/4 +b = 1/2 +b = 3/4 +Figure 2: Plot of E(M) as a function of c for various b values. The open circle indicates that the value is zero. +0 +0.2 +0.4 +0.6 +0.8 +1 +0.5 +0.6 +0.7 +0.8 +0.9 +1 +c +O(N) +b = 0 +b = 1/4 +b = 1/2 +b = 3/4 +Figure 3: Plot of O(M) as a function of c for various b values. +For qubit Pauli channels, the value of O(N) and the fact that it can be achieved using a maximally +entangled input state ΛRA was found in [34], however we note later that one can also achieve O(N) using +a separable pure state when N is very noisy. Since the Pauli matrices are orthogonal to each other, in a +standard Kraus decomposition, {Ki}, of N we can always chose each Ki to be √pjσj for some j. As p0 ≥ pi, +K0 = √p0σ0 and from Th. 1 we get +O(N) = p0. +(81) +When p0 > pj for all j, ΛRA = |σ† +0⟩⟨σ† +0|/2, i.e., ΛRA is a projector onto a maximally entangled state and thus +E(N) = 1. However, if for some i, p0 = pi then ΛRA is any density operator with support in a space spanned +by {|σ† +0⟩RA, |σ† +i ⟩RA}. This space is a two-dimensional subspace of a two qubit space HRA. Following the +discussion containing (77), this subspace contains at least one product state. As a result, for any i if p0 = pi +we can choose ΛRA to be a product state and thus E(N) = 0. Consequently, +E(N) = +� +1 +if +p0 > pi ∀i, +0 +if +p0 = pi for some i. . +(82) +When p0 = pi, the best fidelity with a maximally entangled state at the output is achieved by sending a +14 + +separable input ΛRA. Consequently, the output ΛRB is also separable. This separable output is expected to +have a small fidelity with a fully entangled state. This expectation is met, the condition p0 = pi together +with � +i pi = 1 forces p0 ≤ 1/2, and thus O(N) ≤ 1/2. Such a value of half for fidelity with a maximally +entangled state |φ⟩AB is considered small since this value of half can be achieved by a simple separable state +ρRB = 1 +2(|00⟩⟨00| + |11⟩⟨11|). +One may wonder which qubit Pauli channels satisfy p0 = pi ≥ pj. Any qubit Pauli channel of this type +is anti-degradable. In general, N in (79) with p0 ≥ pi is anti-degradable [50–52] if and only if +p1 + p2 + p3 + √p1p2 + √p1p3 + √p2p3 ≥ 1/2. +(83) +We are interested in the case where p0 = pi for some i. The above condition remains unaffected when +permuting pi and pj, thus we let p0 = p1 = p, denote p2 by q then p3 = 1 − 2p − q. Using these substitutions +on the left side of (83), together with 1 ≥ p ≥ q ≥ 0 and p ≥ 1 − 2p − q we find that the above inequality (83) +is always satisfied. Thus p0 = pi ≥ pj implies that the qubit Pauli channel N is anti-degradable. +Pauli channels (79) have a key property, up to local unitaries at the channel input and output, any unital +qubit channel can always be written as a Pauli channel [42]. An interesting observation about qubit channels +is that ΛRA in Th. 1 can be chosen to be a maximally entangled state if and only if N is unital [34]. It is +interesting for that reason to ask if such a result holds in higher dimension. In this next section, we find that +it doesn’t. +In the case of qubit Pauli channels, but also for extremal qubit channels, we found that it is possible to +find separable input states ΛRA that achieve the most fidelity with a fully entangled state at the channel +output. +This separable state appeared when a qubit channel N’s standard Kraus decomposition {Ki} +satisfied the condition ⟨K0, K0⟩ = ⟨Kj, Kj⟩, for at least one j ̸= 0. Using eq. (33), this condition reduces to +the channel’s Choi-Jamiołkowsi operator JN +RB having its largest eigenvalue be degenerate. In general, we +have the following lemma. +Lemma 3. If N is a qubit channel and the largest eigenvalue of JN +RB is degenerate, then ΛRA in Th. 1 can be +chosen to be separable. +Proof. Let {Ki} be a standard Kraus decomposition of N. Since JN +RB is degenerate, ⟨K0, K0⟩ = ⟨K1, K1⟩ and +ΛRA has support in the span of {|K† +0⟩, |K† +1⟩}. This support is a two-dimensional subspace of a two-qubit +space, and thus contains a product state. Hence ΛRA can be chosen to be a projector onto this product +state. +■ +While it may be tempting to conjecture that the above result holds in higher dimensional channels, we +show in the next section that it doesn’t. +5.3 +Some qutrit channels +We construct two qutrit channels. The first channel, M, is not unital but its optimal input state ΛRA, +defined in Th. 1, is unique and maximally entangled. The second channel, P, is unital, however its optimal +input state ΛRA is neither maximally entangled nor separable. Using the second channel, we demonstrate +that when the largest eigenvalue of JN +RB is degenerate, ΛRA can still be entangled. The demonstration +contrasts with Lemma 3. +Let HA and HB be three-dimensional Hilbert spaces. Let M : L(HA) �→ L(HB) be a channel with Kraus +operators +K0 = +√ +λI, +K1 = +√ +1 − λ(|0⟩⟨1| + |1⟩⟨0|), +and +K2 = +√ +1 − λ|1⟩⟨2|, +(84) +where 0 ≤ λ ≤ 1. This channel M is not unital, except when λ = 1. When 2/5 < λ < 1, {Ki} is a standard +Kraus decomposition of M with ⟨K0, K0⟩ > ⟨Ki, Ki⟩ for all i ̸= 0. From Th. 1 we find +O(M) = λ, +ΛRA = 1 +3|I⟩⟨I|, +and +E(M) = log2 3. +(85) +Thus when 2/5 < λ < 1, the input ΛRA is unique, and it is maximally entangled, however the channel M is +not unital. +15 + +Let P : L(HA) �→ L(HB) be a qutrit channel with Kraus operators +L0 = +� +z + 2 +4 +� +|0⟩⟨1| + |1⟩⟨0| +� +, +L1 = +� +1 − z +2 +� +|1⟩⟨2| + |2⟩⟨1| +� +, +L2 = +� +1 − z +2 +� +|0⟩⟨2| + |2⟩⟨0| +� +, +and +L3 = +�z +4 +� +|0⟩⟨0| + |1⟩⟨1| − 2|2⟩⟨2| +� +, +(86) +where 0 ≤ z ≤ 1. Since each Kraus operator Li is Hermitian, P is unital (see discussion below (24)). Kraus +operators {Li} are standard and thus Th. 1 immediately gives O(M) = (z + 2)/6. When z ̸= 0, +ΛAR = |L† +0⟩⟨L† +0| +(87) +where |L† +0⟩RA = +1 +√ +2(|01⟩ + |10⟩) is not a maximally entangled state of two qutrits. When z = 0, L3 = 0, +⟨L0|L0⟩ = ⟨L1|L1⟩ = ⟨L2|L2⟩ and thus largest eigenvalue of JM +RB has a degenerate spectrum. In this case, +ΛRA has support in a subspace S spanned by {|L† +0⟩RA, |L† +1⟩RA, |L† +2⟩RA}. This subspace only contains non- +product vectors, i.e., it is completely entangled in the sense of Parthasarathy(see Def. 1.2 in [53]). Consequently, +any density operator ΛRA supported on this subspace is entangled. +6 +Discussion +In this work we considered a one-shot setting where one half of any bipartite mixed state may be sent +across a single use of a fixed channel N. The goal in this setting is to share a state with maximum fidelity +O(N) to a fully entangled state. Interestingly, maximum fidelity O defined in the one-shot setting fully +characterizes the ability of any channel to share high fidelity entanglement over multiple channel uses, +possibly used in parallel with other channels. +This extension follows from multiplicative nature of O, +proved in Sec. 4.1. +Using a semi-definite program, we reformulate the maximum fidelity, found previously for pure state +inputs [30,31,34]. The first reformulation in Theorem 1 lays greater emphasis on a channel’s Kraus operators +rather than its Choi-Jamiołkowski operator, as done previously. These two channel representations are +formally equivalent (see Sec. 3 for brief discussion), however the Kraus decomposition can sometimes be +easier to work with and can provide different insights when discussing maximum fidelity O(N), but perhaps +in other cases as well. In the present case, the standard Kraus operators (see Sec. 3.1 for definition) simplifies +the search for and broadens the types of channel inputs ΛRA which achieve O. +One way in which we have broadened the search for optimal inputs ΛRA is to identify channels N for +which ΛRA can be chosen to be separable. This choice appears in two notable cases. First, when N is an +extremal qubit channel. Here, separability of ΛRA leads to a discontinuous jump in the minimal amount of +entanglement E(N) generated to achieve maximum fidelity with a fully entangled state (see discussion with +Fig 2). A second notable case where ΛRA can be chosen to be separable is for noisy unital qubit channels +where the input may be ordinarily chosen to be fully entangled (see discussion containing eq. (82)). These +findings motivate a characterization of channels N for which ΛRA is possibly separable, i.e., E(N) = 0. One +typically expects such channels to not be useful for sharing entanglement in the type of one-shot setting +discussed in Sec. 4. One example of such channels is in Lemma 3. The lemma extends to channels with +Choi-Jamiołkowsi operator JN +AB having a greater than (d − 1)2 fold degeneracy in their largest eigenvalue. +The support of this largest eigenvalue subspace always has a product state (proof for this can be constructed +using Prop 1.4 in [53]) and thus, ΛRA can be chosen to be a product state and E(N) = 0. On the other hand, +we also find a channel whose Choi-Jamiołkowsi operator has a degeneracy in its largest eigenvalue but the +optimal input for the channel must be entangled. +Another way in which we have broadened the search for optimal inputs ΛRA is to consider extension of +results found previously. For qubit channels, a fully entangled input was known to achieve O if and only +if the channel was unital. In higher dimensions, we find this result no longer holds. We construct a unital +qutrit channel for which the optimal input must be less than fully entangled. We also construct a qutrit +channel which is not unital, but for which a fully entangled input is necessary to obtain the largest overlap. +Our second reformulation of O(N) in Theorem 1 notes that it equals the operator norm of the channel’s +Choi-Jamiołkowski operator, upto normalization. This observation can not only simplify discussions about +16 + +O(N) (for instance see proof of Th. 2), it also gives the operator norm of the Choi-Jamiołkowski operator a +simple interpretation. +The single channel use setting discussed here can be extended by allowing the reference system and the +channel output system to be processed using local operations and one-way or two-way classical communi- +cation, labeled 1-LOCC and 2-LOCC respectively. Building on ideas in [32,54], it has been shown for qubit +channels that maximum fully entangled fraction allowing a single round of 2-LOCC, O′, equals O [34]. +Understanding O′ in higher dimensional channels while exploring optimal protocols and multiplicativity +of O′ may form an interesting direction of future work. Another direction can come from extending results +in Sec. 5.2 where we show that that a set of qubit Pauli channels with E(N) = 0 also have no quantum +capacity Q. It could be interesting to study the relation of O and E to Q. +Along the way to analyzing the maximum fidelity, we found it useful to study extremal qubit channels. +These simple channels can be considered the most basic qubit channels. +However, to our knowledge, +noise parameters for these channels have not been adequately discussed. In Sec. 3.3, we show the pcubed +point of view allows one to identify noise parameters for this channel in such a way that channel becomes +demonstrably noisier as a parameter is varied monotonically. Hope is that such identification makes this +channel class a better understood and non-trivial test-bed for ideas in quantum information science. We +also flesh out two useful properties of general channels. First, in Sec. 3.1 the existence of a standard Kraus +decomposition where the Kraus operators are orthogonal and their norm is ordered. Second, in Sec. 3.2, +we show how the Choi–Jamiołkowski operator of a channel and its dual can always be taken to be complex +conjugates of each other. +References +[1] Jerry M. Chow. +Quantum intranet. +IET Quantum Communication, +2(1):26–27, +Mar 2021. +doi:10.1049/qtc2.12002. +[2] H. J. Kimble. The quantum internet. Nature, 453(7198):1023–1030, Jun 2008. doi:10.1038/nature07127. +[3] Stephanie Wehner, David Elkouss, and Ronald Hanson. Quantum internet: A vision for the road +ahead. Science, 362(6412), 2018. doi:10.1126/science.aam9288. +[4] Charles H. Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K. +Wootters. +Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen +channels. Phys. Rev. Lett., 70:1895–1899, Mar 1993. doi:10.1103/PhysRevLett.70.1895. +[5] Charles H. Bennett, David P. DiVincenzo, John A. Smolin, and William K. Wootters. +Mixed- +state entanglement and quantum error correction. +Phys. Rev. A, 54:3824–3851, Nov 1996. +doi:10.1103/PhysRevA.54.3824. +[6] Mark M. Wilde. +From Classical to Quantum Shannon Theory. +arXiv:1106.1445 [quant-ph], 2017. +doi:10.1017/9781316809976.001. arXiv: 1106.1445. +[7] Seth Lloyd. +Capacity of the noisy quantum channel. +Phys. Rev. A, 55:1613–1622, Mar 1997. +doi:10.1103/PhysRevA.55.1613. +[8] PeterW.Shor. Quantumerrorcorrection, Nov2002. http://www.msri.org/workshops/203/schedules/1181. +[9] N. Cai, A. Winter, and R. W. Yeung. Quantum privacy and quantum wiretap channels. Problems of +Information Transmission, 40(4):318–336, Oct 2004. doi:10.1007/s11122-005-0002-x. +[10] I. Devetak. The private classical capacity and quantum capacity of a quantum channel. IEEE Transactions +on Information Theory, 51(1):44–55, Jan 2005. doi:10.1109/TIT.2004.839515. +[11] I. Devetak and P. W. Shor. +The capacity of a quantum channel for simultaneous transmission of +classical and quantum information. +Communications in Mathematical Physics, 256(2):287–303, 2005. +doi:10.1007/s00220-005-1317-6. +17 + +[12] Graeme Smith and Jon Yard. +Quantum communication with zero-capacity channels. +Science, +321(5897):1812–1815, 2008. doi:10.1126/science.1162242. +[13] Toby Cubitt, David Elkouss, William Matthews, Maris Ozols, David Pérez-García, and Sergii Strelchuk. +Unbounded number of channel uses may be required to detect quantum capacity. Nature Communica- +tions, 6:6739, Mar 2015. doi:10.1038/ncomms7739. +[14] Vikesh Siddhu. Entropic singularities give rise to quantum transmission. Nature Communications, +12(1):5750, Oct 2021, arXiv: 2003.10367. doi:10.1038/s41467-021-25954-0. +[15] Felix Leditzky, Debbie Leung, Vikesh Siddhu, Graeme Smith, and John A. Smolin. Generic nonaddi- +tivity of quantum capacity in simple channels. arXiv preprint, 2022, arXiv: 2202.08377. +[16] Francesco Buscemi and Nilanjana Datta. +The Quantum Capacity of Channels With Arbitrar- +ily Correlated Noise. +IEEE Transactions on Information Theory, 56(3):1447–1460, March 2010. +doi:10.1109/TIT.2009.2039166. +[17] Nilanjana Datta and Min-Hsiu Hsieh. +The apex of the family tree of protocols: +opti- +mal rates and resource inequalities. +New Journal of Physics, 13(9):093042, September 2011. +doi:10.1088/1367-2630/13/9/093042. +[18] Nilanjana Datta and Min-Hsiu Hsieh. +One-shot entanglement-assisted quantum and clas- +sical communication. +IEEE Transactions on Information Theory, 59(3):1929–1939, March 2013. +doi:10.1109/TIT.2012.2228737. arXiv:1105.3321 [quant-ph]. +[19] William Matthews and Stephanie Wehner. +Finite Blocklength Converse Bounds for Quan- +tum Channels. +IEEE Transactions on Information Theory, +60(11):7317–7329, November 2014. +doi:10.1109/TIT.2014.2353614. +[20] Salman Beigi, Nilanjana Datta, and Felix Leditzky. Decoding quantum information via the Petz recovery +map. Journal of Mathematical Physics, 57(8):082203, August 2016. doi:10.1063/1.4961515. +[21] Marco Tomamichel, Mario Berta, and Joseph M. Renes. Quantum coding with finite resources. Nature +Communications, 7(1):11419, September 2016. doi:10.1038/ncomms11419. +[22] Corsin Pfister, M. Adriaan Rol, Atul Mantri, Marco Tomamichel, and Stephanie Wehner. Capacity esti- +mation and verification of quantum channels with arbitrarily correlated errors. Nature Communications, +9(1):27, January 2018. doi:10.1038/s41467-017-00961-2. +[23] Anurag Anshu, Rahul Jain, and Naqueeb Ahmad Warsi. Building Blocks for Communication Over +Noisy Quantum Networks. IEEE Transactions on Information Theory, 65(2):1287–1306, February 2019. +doi:10.1109/TIT.2018.2851297. +[24] Xin Wang, Kun Fang, and Runyao Duan. Semidefinite programming converse bounds for quantum +communication. IEEE Transactions on Information Theory, 65(4):2583–2592, 2018, arXiv: 1709.00200. +[25] Farzin Salek, Anurag Anshu, Min-Hsiu Hsieh, Rahul Jain, and Javier Rodriguez Fonollosa. One-Shot +Capacity Bounds on the Simultaneous Transmission of Classical and Quantum Information. IEEE +Transactions on Information Theory, 66(4):2141–2164, April 2020. doi:10.1109/TIT.2019.2945800. +[26] Yoshifumi Nakata, Eyuri Wakakuwa, and Hayata Yamasaki. +One-shot quantum error cor- +rection of classical and quantum information. +Physical Review A, 104(1):012408, July 2021. +doi:10.1103/PhysRevA.104.012408. +[27] Sumeet Khatri and Mark M. Wilde. Principles of quantum communication theory: A modern approach, +2020. arXiv: 2011.04672. +[28] Charles H. Bennett, Gilles Brassard, Sandu Popescu, Benjamin Schumacher, John A. Smolin, and +William K. Wootters. Purification of Noisy Entanglement and Faithful Teleportation via Noisy Chan- +nels. Physical Review Letters, 76(5):722–725,January 1996. doi:10.1103/PhysRevLett.76.722. arXiv:quant- +ph/9511027. +18 + +[29] Michał Horodecki, +Paweł Horodecki, +and Ryszard Horodecki. +General teleportation chan- +nel, singlet fraction, and quasidistillation. +Physical Review A, 60(3):1888–1898, September 1999. +doi:10.1103/PhysRevA.60.1888. +[30] Frank +Verstraete +and +Henri +Verschelde. +On +quantum +channels, +January +2003. +http://arxiv.org/abs/quant-ph/0202124. arXiv:quant-ph/0202124. +[31] Rajarshi Pal and Somshubhro Bandyopadhyay. Entanglement sharing via qudit channels Nonmaxi- +mally entangled states may be necessary for one-shot optimal singlet fraction and negativity. Physical +Review A, 97(3):032322, March 2018. doi:10.1103/PhysRevA.97.032322. +[32] Frank Verstraete and Henri Verschelde. Optimal Teleportation with a Mixed State of Two Qubits. +Physical Review Letters, 90(9):097901, March 2003. doi:10.1103/PhysRevLett.90.097901. +[33] Somshubhro Bandyopadhyay and Anindita Ghosh. +Optimal fidelity for a quantum channel may +be attained by nonmaximally entangled states. +Physical Review A, 86(2):020304, August 2012. +doi:10.1103/PhysRevA.86.020304. +[34] Rajarshi Pal, Somshubhro Bandyopadhyay, and Sibasish Ghosh. Entanglement sharing through noisy +qubit channels: One-shot optimal singlet fraction. Physical Review A, 90(5):052304, November 2014. +doi:10.1103/PhysRevA.90.052304. +[35] Lieven Vandenberghe and Stephen Boyd. Semidefinite programming. SIAM Review, 38(1):49–95, 1996. +doi:10.1137/1038003. +[36] A. Jamiołkowski. Linear transformations which preserve trace and positive semidefiniteness of opera- +tors. Reports on Mathematical Physics, 3(4):275–278, 1972. doi:10.1016/0034-4877(72)90011-0. +[37] Man-Duen Choi. Completely positive linear maps on complex matrices. Linear Algebra and its Applica- +tions, 10(3):285 – 290, 1975. doi:10.1016/0024-3795(75)90075-0. +[38] A. +S. +Holevo. +Quantum +Systems, +Channels, +Information. +De +Gruyter, +2012. +doi:doi:10.1515/9783110273403.346. +[39] Michael M. Wolf. +Quantum Channels and Operations - Guided Tour. +Lecture notes, +2012, +arXiv: http://www-m5.ma.tum.de/foswiki/pub/M5/Allgemeines/MichaelWolf/QChannelLecture.pdf. +[40] A. Fujiwara and P. Algoet. Affine parameterization of quantum channels. In Proceedings. 1998 IEEE +International Symposium on Information Theory (Cat. No.98CH36252), page 87, Cambridge, MA, USA, +1998. IEEE. doi:10.1109/ISIT.1998.708673. +[41] Chi-Sheng Niu and Robert B. Griffiths. Two-qubit copying machine for economical quantum eaves- +dropping. Phys. Rev. A, 60:2764–2776, Oct 1999. doi:10.1103/PhysRevA.60.2764. +[42] Mary Beth Ruskai, Stanislaw Szarek, and Elisabeth Werner. +An analysis of completely-positive +trace-preserving maps on m2. +Linear Algebra and its Applications, 347(1–3):159 – 187, 2002. +doi:10.1016/S0024-3795(01)00547-X. +[43] Michael M. Wolf and David Pérez-García. Quantum capacities of channels with small environment. +Phys. Rev. A, 75:012303, Jan 2007. doi:10.1103/PhysRevA.75.012303. +[44] Shmuel Friedland and Raphael Loewy. On the extreme points of quantum channels, October 2014. +http://arxiv.org/abs/1309.5898. arXiv:1309.5898 [math-ph, physics:quant-ph]. +[45] Vikesh Siddhu and Robert B. Griffiths. Degradable quantum channels using pure-state to product-of- +pure-state isometries. Phys. Rev. A, 94:052331, Nov 2016. doi:10.1103/PhysRevA.94.052331. +[46] J. L. Park. The concept of transition in quantum mechanics. Foundations of Physics, 1:23–33, Mar 1970. +doi:10.1007/BF00708652. +19 + +[47] D. +Dieks. +Communication +by +epr +devices. +Physics +Letters +A, +92:271–272, +Nov +1982. +doi:10.1016/0375-9601(82)90084-6. +[48] W. K. Wootters and W. H. Zurek. A single quantum cannot be cloned. Nature, 299:802, Oct 1982. +doi:10.1038/299802a0. +[49] John Watrous. The Theory of Quantum Information. Cambridge University Press, 1 edition, Apr 2018. +doi:10.1017/9781316848142. +[50] Chi-Sheng Niu and Robert B. Griffiths. Optimal copying of one quantum bit. Phys. Rev. A, 58:4377–4393, +Dec 1998. doi:10.1103/PhysRevA.58.4377. +[51] Nicolas J. Cerf. +Pauli cloning of a quantum bit. +Phys. Rev. Lett., 84:4497–4500, May 2000. +doi:10.1103/PhysRevLett.84.4497. +[52] Toby S. Cubitt, Mary Beth Ruskai, and Graeme Smith. The structure of degradable quantum channels. +Journal of Mathematical Physics, 49(10):–, 2008. doi:10.1063/1.2953685. +[53] K. R. Parthasarathy. On the maximal dimension of a completely entangled subspace for finite level quan- +tum systems. Proceedings Mathematical Sciences, 114(4):365–374, Nov 2004. doi:10.1007/BF02829441. +[54] Frank Verstraete and Henri Verschelde. Fidelity of mixed states of two qubits. Physical Review A, +66(2):022307, August 2002. doi:10.1103/PhysRevA.66.022307. +20 + diff --git a/RdAzT4oBgHgl3EQf0P6C/content/tmp_files/load_file.txt b/RdAzT4oBgHgl3EQf0P6C/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..46585f3a000d5818b9d990f180faea4893d0db7b --- /dev/null +++ b/RdAzT4oBgHgl3EQf0P6C/content/tmp_files/load_file.txt @@ -0,0 +1,1263 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf,len=1262 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='01781v1 [quant-ph] 4 Jan 2023 Optimal one-shot entanglement sharing Vikesh Siddhu and John Smolin IBM Quantum, IBM T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Watson Research Center, Yorktown Heights, NY 10598, USA January 4, 2023 Abstract Sharing entanglement across quantum interconnects is fundamental for quantum information process- ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We discuss a practical setting where this interconnect, modeled by a quantum channel, is used once with the aim of sharing high fidelity entanglement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' For any channel, we provide methods to easily find both this maximum fidelity and optimal inputs that achieve it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Unlike most metrics for sharing entanglement, this maximum fidelity can be shown to be multiplicative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This ensures a complete understanding in the sense that the maximum fidelity and optimal inputs found in our one-shot setting extend even when the channel is used multiple times, possibly with other channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Optimal inputs need not be fully entangled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We find the minimum entanglement in these optimal inputs can even vary discontinuously with channel noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Generally, noise parameters are hard to identify and remain unknown for most channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' However, for all qubit channels with qubit environments, we provide a rigorous noise parametrization which we ex- plain in-terms of no-cloning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This noise parametrization and a channel representation we call the standard Kraus decomposition have pleasing properties that make them both useful more generally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Contents 1 Introduction 2 2 Preliminaries 3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1 Operator-Ket duality .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 4 3 Quantum channels 5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1 A standard Kraus decomposition .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 6 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2 Dual channel .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 7 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='3 Extreme qubit channels .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 7 4 High fidelity entanglement 9 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1 Multiplicativity .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 11 5 Applications 12 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1 Extremal qubit channels .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 12 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2 Qubit Pauli channels .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 13 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='3 Some qutrit channels .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 15 6 Discussion 16 1 1 Introduction Quantum computation and communication requires faithful transmission of quantum information be- tween various separated parties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' These parties may be closely separated quantum computing nodes or widely separated receivers and transmitters of quantum states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The former appear in models of a quantum intranet [1] while the latter appear in discussions of a quantum internet [2, 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Noise in these, and other such setups hinders their use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A dominant source of noise is the quantum interconnect carrying quan- tum information between parties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This interconnect is modeled mathematically by a quantum channel, a completely positive trace preserving map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Quantum information sent and processed across this channel is equivalent to entanglement shared and processed using the channel [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Without investigating methods, metrics, protocols and characteristics of sharing entanglement across quantum channels, our understanding and ability to control and scale quantum computation and communication remains partial.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Related work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The most well studied setting for sharing entanglement allows asymptotically many channel uses [5, 6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Across all channels used together, local pre- and post-processing of entanglement is allowed along with classical communication from channel input to output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Using these allowed operations, the largest number of fully entangled states, per channel use, shared with asymptotically vanishing error defines the quantum capacity of the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Studies of this metric reveal that while theoretically beauti- ful [7–11] a channel’s quantum capacity is hard to compute and non-trivial to understand in general [12,13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Both these features come from super-additivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Super-additivity of quantum capacity implies that the quantum capacity of several channels used jointly is not completely specified by the quantum capacity of each channel [14,15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Asymptotic channel capacities provide rich conceptual and practical difficulties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' For these reasons, it is desirable to study entanglement transmission with as little encoding and decoding as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The simplest setting here is a single use of a channel (which can itself be joint uses of many channels) with no post-processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This setting need not allow sharing of noiseless entanglement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Thus, one may define a metric for sharing entanglement with some acceptable level of noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' One such metric, called the one-shot quantum capacity, is roughly the largest fully entangled state than can be shared across a channel with at most a fixed, but arbitrary error [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This one-shot capacity, its connection to asymptotic capacities, and method for understanding and achieving these have been recently explored [17–27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' However, we don’t fully understand notions of additivity for this capacity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' ways of computing and explicit protocols for achieving the one-shot capacity are not completely known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A key metric in the one-shot setting is the highest fidelity between the state shared across the channel and a maximally entangled state [5,28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This fidelity characterizes optimal performance of various teleportation based tasks [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The optimal fidelity between a pure entangled state shared across the channel and a maximally entangled state is known [30, 31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Surprisingly, the optimal pure state input need not be maximally entangled which is consistent with fidelity not being an entanglement monotone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The one-shot setting is augmented by post-processing using one round of local operations and two-way classical communication (2-LOCC) [31–34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' However, in this setting it is unknown if the optimal fidelity is multiplicative (analog of additivity in this setting).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' There is no known method for computing or explicit protocol for achieving this optimal fidelity in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The only exception is qubit channels, where optimal protocols use pure state inputs and don’t require 2-LOCC [32, 34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Surprisingly, the behaviour of such optimal protocols for the simplest of qubit channels is not fully known.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' One way to understand a metric for sharing entanglement across a specific channel is to study variation in the metric with the amount of noise in the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Surprisingly, even for the simplest qubit channels, noise parameters are only partially understood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A N B R R ρRA ρRB Figure 1: Diagram representing one-shot entanglement passing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 2 Results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In this work, we introduce and solve the problem for sharing entanglement in a one-shot setting where an arbitrary mixed state ρRA may be prepared across a reference system R and channel input A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This input is sent via a fixed channel N : A �→ B (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1) to achieve the maximum fidelity O(N) between the channel output ρRB and a maximally entangled state across R and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We reformulate O(N) via a semi-definite program [35] in two useful ways (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 4 with Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' First, using what we define (in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1) as a channel’s standard Kraus decomposition, and second, in terms of the operator norm of a channel’s Choi–Jamiołkowski operator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We show the maximum fidelity O is multiplicative (see Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Not only can O(N) be achieved using pure states but also using a variety of mixed states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We give a recipe to construct these pure and mixed states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' For all extremal qubit channels, we compute optimal inputs and the minimum amount of entanglement E required to create these inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We identify rigorous noise parameters for extremal qubit channels (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Somewhat surprisingly, the minimum entanglement E is found to be discontinuous in these noise parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Typically, E is less than its maximal value of one, but O is high enough for the channel to be useful for teleportation, even if the channel has no quantum capacity (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' For very noisy qubit Pauli channels we find separable inputs that achieve the same fidelity as maximally entangled ones found previously (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We also find optimal inputs for qutrit channels have a much richer structure than qubit channels (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Unlike other metrics in settings for entanglement sharing, O is multiplicative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Thus, even when a channel N is used multiple times, possibly with other channels, its maximum fidelity O(N) fully characterizes its ability for sharing high fidelity entanglement without post-processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Our results also give rigorous lower bounds on entanglement fidelities that can be achieved when allowing for multiple rounds of 2-LOCC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' These bounds are tight for one round of 2-LOCC using qubit channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Characterization of the noise parameters for all extremal qubit channels presented here pave the way for a stronger understanding of quantum channels and quantum protocols across channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 2 Preliminaries Let x denote a vector in n-dimensional real space, Rn, xi denote the (i + 1)th coordinate of x, and |xi| denote its absolute value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Coordinates of x rearranged in decreasing order give x↓, a vector satisfying x↓ 0 ≥ x↓ 1 ≥ · · · ≥ x↓ n−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Euclidean norm of x, |x| := �� i x2 i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Let |ψ⟩ denote a ket in a Hilbert space H of finite dimension d and ||ψ⟩| := � ⟨ψ|ψ⟩ denote its norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A pure quantum state is represented by a ket with unit norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Let L(H) denote the space of linear operators on H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' For any two quantum states |ψ⟩ and |φ⟩, the dyad |ψ⟩⟨φ| ∈ L(H) and the projector onto |ψ⟩, |ψ⟩⟨ψ| ∈ L(H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The Frobenius inner product between two operators N and O in L(H), ⟨N, O⟩ := Tr(N †O), (1) where N † represents the adjoint (conjugate transpose) of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A Hermitian operator H ∈ L(H), satisfying H = H†, represents an observable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This operator has an eigendecomposition, H = � i xi|ψi⟩⟨ψi|, (2) where xi ∈ R is an eigenvalue of H corresponding to eigenvector |ψi⟩ and the collection of eigenvectors {|ψi⟩} form an orthonormal basis of H, ⟨ψi|ψj⟩ = δij, where δij is the Kronecker delta function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Support of H is the subspace spanned by its eigenvectors with non-zero eigenvalues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In (2), if xi ≥ 0 for all i, then we say H is positive semi-definite (PSD), H ⪰ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This PSD operator’s square root, √ H, is obtained by replacing xi in (2) with √xi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' For any operator O ∈ L(H), ||O|| := max ||ψ⟩|≤1|O|ψ⟩|, ||O||1 := Tr( √ OO†), and ||O||2 := � Tr(OO†), (3) denote the spectral norm, the trace norm, and the Frobenius norm, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' For H in (2), ||H|| = |x↓ 1|, ||H||1 = � i |xi|, and ||H||2 = |x|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (4) 3 A density operator ρ ∈ L(H) is a positive semi-definite operator with unit trace, Tr(ρ) = 1, it represents a mixed quantum state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Its von-Neumann entropy, S(ρ) = −Tr(ρ log ρ), (5) where log is base 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The fidelity between two density operators ρ and σ, F(ρ, σ) := ||√ρ√σ||1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (6) Let HA and HB be two Hilbert spaces of dimensions dA and dB, respectively, and HAB denote the tensor product space HA ⊗ HB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Given a pure state |ψ⟩AB ∈ HAB, density operators ψA = TrB(|ψ⟩⟨ψ|) and ψB = TrA(|ψ⟩⟨ψ|) (7) denote the partial trace of |ψ⟩⟨ψ| over HB and HA, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The entanglement of formation of a pure state |ψ⟩AB, Ef(|ψ⟩AB) = S(ψA), (8) and for a mixed state ρAB, Ef(ρAB) = min � i piEf(|ψi⟩AB), (9) is the minimum average entanglement Ef over all pure state decompositions, ρAB = � i pi|ψi⟩⟨ψi|, pi ≥ 0 and � i pi = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Let A = {|ai⟩} and B = {|bj⟩} be orthonormal bases, of HA and HB, respectively, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=', ⟨ai|aj⟩ = ⟨bi|bj⟩ = δij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (10) Using these bases A and B we can represent any linear operator L : HA �→ HB as a matrix, L = � ij [L]ij|bi⟩⟨aj|, (11) with elements [L]ij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We can define two basis dependent linear maps, L∗ = � ij [L]∗ ij|bi⟩⟨aj|, and LT = � ij [L]ij|aj⟩⟨bi|, (12) representing complex conjugate and transpose, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In contrast to L∗ and LT, the adjoint L† = (L∗)T = (LT )∗ is basis independent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' If HA and HB have the same dimension d, then one can choose A and B to be the same, say the standard basis {|i⟩}, and construct an identity map IA←B : HB �→ HA, IA←B|i⟩B = |i⟩A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (13) This subscript notation A ← B is dropped shortly after defining how the identity map above is used to map a ket |φ⟩B ∈ HB, an operator OB ∈ L(HB) and part of an operator LAB ∈ L(HAB) to |φ⟩A = IA←B|ψ⟩B, OA = IA←BOBIB←A, and LAA = (IA←B ⊗ IA)LBA(IB←A ⊗ IA), (14) respectively, here IA is identity on the HA space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Later, these mappings are done implicitly by simply replacing the subscripts in an obvious way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1 Operator-Ket duality Operator-ket duality is the concept of fixing an orthonormal basis A = {|ai⟩} of HA and using an un- normalized maximally entangled state on HA ⊗ HA, |γ⟩AA = � i |ai⟩ ⊗ |ai⟩, (15) 4 to associate with any linear operator K : HA �→ HB a ket, |ψ⟩AB = (IA ⊗ K)|γ⟩, obtained by acting K on one-half of |γ⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Conversely, for fixed orthonormal basis A, one associates with any ket |ψ⟩AB, a linear operator K = � i |χi⟩⟨ai|, where |χi⟩B = (⟨ai|A ⊗ IB)|ψ⟩AB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (16) In analogy to the discussion above, fixing an orthonormal basis B = {|bj⟩} of HB one associates with the ket |ψ⟩AB an operator L : HB �→ HA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This operator L = KT where the transpose operation is taken using basis A and B as described in (12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In what follows, we use the notation |K⟩ ∈ HAB for a ket associated with the operator K : HA �→ HB through the operator-ket duality above where basis A is fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This ket and operator pair satisfy |K⟩AB = (I ⊗ K)|γ⟩AA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (17) For any two maps K and K′ from HA to HB and associated kets |K⟩AB and |K′⟩AB, respectively, one can show that ⟨K, K′⟩ = ⟨K|K′⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (18) Using the orthonormal basis B of HB, one can associate with K† : HB �→ HA the ket |K†⟩BA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In this ket, swapping the spaces HA and HB (see discussion below (13)) gives |K†⟩AB which then satisfies |K†⟩AB = |K⟩∗ AB (19) where complex conjugation of any ket |χ⟩AB = � ij cij|ai⟩ ⊗ |bj⟩, is defined using basis A and B as |χ⟩∗ AB = � ij c∗ ij|ai⟩ ⊗ |bj⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 3 Quantum channels Let HA, HB, and HC be three Hilbert spaces and V : HA �→ HB ⊗ HC be an isometry, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=', V †V = IA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This isometry defines a pair of quantum channels N and N c, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=', a pair of completely positive trace preserving (CPTP) maps with superoperators N(O) = TrC(V OV †) and N c(O) = TrB(V OV †), (20) taking O ∈ L(HA) to L(HB) and L(HC), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The quantum channel N is called degradable and N c anti-degradable if there exists a quantum channel D such that D ◦ N = N c [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Let IA be the identity map from L(HA) to itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Using an un-normalized maximally entangled state |γ⟩AA (15) we define the Choi–Jamiołkowski [36,37] operator of the linear map N as JN AB = IA ⊗ N(|γ⟩⟨γ|) = � ij |ai⟩⟨aj| ⊗ N(|ai⟩⟨aj|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (21) This operator contains all information about N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' For instance, N(|ai⟩⟨aj|) = (⟨ai| ⊗ IB)JN AB(|aj⟩ ⊗ IB), (22) N is completely positive (CP) if and only if JN AB is positive semi-definite, and TrB(JN AB) = IA (23) if and only if N is trace-preserving, Tr � N(O) � = Tr(O) for all O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Equivalently, a linear map N : L(HA) �→ L(HB) is CP if and only if it can be written in the form N(O) = � i KiOK† i , (24) where Ki : HA �→ HB is a linear operator, and the collection {Ki} are called Kraus operators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The map in (24) is trace preserving when these Kraus operators satisfy � i K† i Ki = IA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' When N is unital, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=', N(IA) = IB, the Kraus operators satisfy � i KiK† i = IB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' If HA and HB have the same dimension, then they are isomorphic to one another and can be denoted by H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' If these Kraus operators on H are Hermitian operators (or normal operators) then the channel is automatically unital.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1 A standard Kraus decomposition For a given channel N : L(HA) �→ L(HB), the set of Kraus operators is not unique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' However, one can construct what can be called a standard Kraus decomposition with some pleasing properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Consider the eigendecomposition of the Choi–Jamiołkowski operator in (21), JN AB = � i e↓ i |Li⟩⟨Li|, (25) where eigenvalues e↓ 0 ≥ e↓ 2 ≥ · · · ≥ e↓ dAdB−1 ≥ 0 and eigenvectors {|Li⟩} form an orthonormal basis of HAB, ⟨Li|Lj⟩ = δij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (26) Applying operator-ket duality using orthonormal basis A = {|ai⟩} to kets {|Li⟩} results in a collection of orthonormal operators {Li} that map HA to HB (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Using these operators define Ki : HA �→ HB, Ki := � e↓ i Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (27) Lemma 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Operators {Ki} form a Kraus decomposition of N, N(O) = � i KiOK† i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (28) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In (25) use (17) to obtain JN AB = � i e↓ i (IA ⊗ Li)|γ⟩⟨γ|(IA ⊗ Li)† (29) = � i (IA ⊗ Ki)|γ⟩⟨γ|(IA ⊗ Ki)†, (30) where the second inequality uses (27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This second inequality, together with (22) gives, N(|ak⟩⟨al|) = � i Ki(|ak⟩⟨al|)K† i (31) This equality, together with linearity of N proves this lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' ■ Using (25), (26), and (27) one can show that the Kraus operators {Ki} satisfy ⟨Ki, Kj⟩ = ⟨Ki, Ki⟩δij and ⟨Ki, Ki⟩ ≥ ⟨Kj, Kj⟩, (32) where i ≤ j and we use ⟨Ki, Ki⟩ = e↓ i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In addition to being orthogonal and ordered in the way captured by the above equation, the Kraus operators {Ki} have several other useful properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The total number of non-zero operators {Ki} is the rank of the Choi-Jamiołkowsi operator J N AB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This rank is the minimum number of Kraus operators required to represent the channel N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' When the eigenvalues of JN AB are distinct, the norm ⟨Ki, Ki⟩ of each Kraus operator is simply the (i+1)th largest eigenvalue of J N AB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' From these Kraus operators, one can obtain the Choi-Jamiołkowsi operator (21), J N AB = � i |Ki⟩⟨Ki|, (33) where we have applied operator-ket duality (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1) to convert operators Ki : HA �→ HB to kets |Ki⟩ ∈ HAB using basis A = {|ai⟩}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Notice |Ki⟩ is an un-normalized eigenvectors of J N AB with eigenvalue ⟨Ki, Ki⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We call {Ki} in Lemma (1) to be a standard Kraus decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 6 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2 Dual channel Given a map N : L(HA) �→ L(HB), its dual N † : L(LB) �→ L(HA) is defined via ∗ Tr � N †(O)ρ � = Tr � ON(ρ) � , (34) where ρ ∈ L(HA) and O ∈ L(HB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A quantum channel N evolves a quantum state ρ and its dual channel N † evolves an observable O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The right side of the above equality represents the expectation value of the evolved quantum state N(ρ) with respect to a fixed observable O while the left side of the equality gives the expectation value of a fixed state ρ with respect to the evolved observable N †(O).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' If N is CP and has Kraus decomposition (24) then N † is also CP with Kraus operators {K† i }, and if N is trace-preserving then N † is unital (see Ch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='6 in [38]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A CP map N with standard Kraus operators {Ki} has dual map N † with standard Kraus operators {K† i } since ⟨K† i , K† j ⟩ = (⟨Ki, Kj⟩)∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (35) The Choi-Jamiołkowsi operator (21) of the dual channel, JN † BA = � i |K† i ⟩⟨K† i |, (36) where {|K† i ⟩} in HBA are defined via operator-ket duality using basis B = {|bj⟩}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Interchanging B and A in (36) and using (19), (33) gives JN AB = (JN † AB)∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (37) The Choi-Jamiołkowsi operator of a channel and its dual can be taken to be complex conjugates of one another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='3 Extreme qubit channels The set of quantum channels from L(HA) to L(HB) is convex, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=', if N and M are quantum channels then K = λN + (1 − λ)M, (38) is a quantum channel for any 0 ≤ λ ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Any quantum channel K is extremal, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=', it is an extreme point of the set of quantum channels, if equality of the type (38) holds only when λ = 0 or λ = 1, or the only channels N and M satisfying the equality both equal K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A quantum channel N : L(HA) �→ L(HB) is called a qubit channel when HA and HB are two- dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' For these two dimensional spaces, we can use the standard basis {|i⟩}, where i ∈ {0, 1}, to define Pauli operators, X = |0⟩⟨1| + |1⟩⟨0|, Y = −i|0⟩⟨1| + i|1⟩⟨0|, and Z = |0⟩⟨0| − |1⟩⟨1|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (39) Extreme points of qubit channels are studied in various works [40–44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A qubit channel is extremal if it has a single Kraus operator, given by a unitary operator, or it has two Kraus operators, each not proportional to a unitary operator (see Cor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 15 in [44]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Up to local unitaries at the channel input and output, a qubit channel N with two Kraus operators can be written as [42] N(O) = K0OK† 0 + K1OK† 1, (40) where, K0 = �cos( v−u 2 ) 0 0 cos( v+u 2 ) � , K1 = � 0 sin( v+u 2 ) sin( v−u 2 ) 0 � , (41) are expressed in the standard basis {|i⟩} at HA and HB, u ∈ [0, 2π] and v ∈ [0, π).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' ∗This definition of dual map (34), common in quantum information (see Def.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2) in [38] or below eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='44) in [39]), differs from another, ⟨N †(O), ρ⟩ = ⟨O, N (ρ)⟩, found in mathematics literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The two definitions coincide for maps satisfying, N (ρ†) = � N (ρ)�†, but can differ when this property is not satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' For example if N (ρ) = cρ, and c complex then the two definitions give different dual maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 7 While u and v parametrize the channel (40), they don’t necessarily represent noise parameters that have a monotonic relationship with the amount of noise introduced by the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In certain special cases, noise parameters can be arrived at intuitively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' For instance when u = 0, N(O) = cos2(v 2)O + sin2(v 2)XOX, (42) is a qubit dephasing channel with dephasing probability sin2(v/2) †.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' By performing a unitary, X, at the input channel input HA, this dephasing channel (42) can be converted to another dephasing channel with dephasing probability 1 − sin2(v/2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Thus a dephasing probability of half gives maximum dephasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This dephasing probability is an intuitive noise parameter in the sense that as this probability is increased from zero to a half, the channel becomes noisier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Another special case is when u + v = 2π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Here, if kets |0⟩ and |1⟩ are interchanged at the channel input and output, N becomes a qubit amplitude damping channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The qubit amplitude damping channel fixes |0⟩⟨0| but |1⟩⟨1| decays to |0⟩⟨0| with probability sin2 v.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Intuitively, this damping probability is a noise parameter in the sense that as the damping probability is increased from zero to one, the channel becomes noisier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Except for these special cases of dephasing and amplitude damping, suitable noise parameters are not necessarily easy to guess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' As discussed above, when N represents amplitude damping noise, the noise parameter is the damping probability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In all other cases, this qubit channel N can be generated from an isometry (see discussion in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 3) of a special form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A isometry of this pcubed form [45], V |αi⟩ = |βi⟩ ⊗ |γi⟩, (43) where i ∈ {0, 1}, takes some special input pure states {|αi⟩} that are not necessarily orthogonal but form a basis of HA, to product of pure states {|βi⟩} at the HB output and {|γi⟩} at the HC output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The Gram matrices GA, GB, and GC of {|αi⟩}, {|βj⟩} and {|γk⟩}, respectively, satisfy [GA]ij = ⟨αi|αj⟩ = ⟨βi|βj⟩⟨γi|γj⟩ = [GB]ij[GC]ij (44) if and only if V is an isometry, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=', V †V = IA [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' These matrices take the form GA = �1 a a 1 � , GB = �1 b b 1 � , and GC = �1 c c 1 � , (45) where −1 < a < 1, −1 ≤ b ≤ 1, −1 ≤ c ≤ 1, and a = bc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The parameters b and c completely specify the isometry V in (43) and thus the channel N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' One may parametrize |αi⟩ using the standard basis as |αi⟩ = � 1 + a 2 |0⟩ + (−1)i � 1 − a 2 |1⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (46) In this parametrization replacing a with b gives |βi⟩ and replacing a with c gives |γi⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The parameters b and c are related to u and v in (41) as follows, sin2 v = 1 − c2 1 − (bc)2 , and cos2 u = 1 − b2 1 − (bc)2 , (47) where |bc| ̸= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The Kraus operators in (41) can be written as K0 = \uf8eb \uf8ed � (1+b)(1+c) 2(1+bc) 0 0 � (1−b)(1+c) 2(1−bc) \uf8f6 \uf8f8 and K1 = \uf8eb \uf8ed 0 � (1+b)(1−c) 2(1−bc) � (1−b)(1−c) 2(1+bc) 0 \uf8f6 \uf8f8 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (48) While these Kraus operators look more complicated than those in (41), several other channel properties simplify when using the parameters b and c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' For instance, the channel N with parameters b and c is degradable if |b/c| < 1, otherwise |b/c| ≥ 1 and the channel is anti-degradable [45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' †Notice, the dephasing channel is not extremal since each of its Kraus operators are proportional to a unitary operator (see discussion above (40)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 8 In general, −1 ≤ b ≤ 1 and −1 ≤ c ≤ 1, however one can simplify the parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In the discussion above, replacing b with −b while keeping c fixed results in a new channel ˜ N which is equivalent to N up to local unitaries at the channel input and output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' To see this, notice this replacement defines a new isometry ˜V of the pcubed form, ˜V |˜αi⟩ = |˜βi⟩ ⊗ |γi⟩, (49) where |˜αi⟩ and |˜βi⟩ are kets obtained from |αi⟩ and |βi⟩ (see definition below eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (46)) by replacing a and b with −a and −b, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This new isometry ˜V is related to V in (43), via local unitaries as follows, (IC ⊗ XB) ˜V = V XA, (50) where X is defined in (39).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In a similar vein, a channel with parameters b and c is equivalent up to local unitaries to a channel with parameters b and −c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' These equivalences allow us to restrict the parameter space −1 ≤ b ≤ 1 and −1 ≤ c ≤ 1 to the positive quadrant 0 ≤ b ≤ 1 and 0 ≤ c ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We show that any channel N with parameters b and c can simulate another channel N ′ with parameters b and c′ ≤ c, in the sense, N ′ = N ◦ M, (51) where M is a quantum channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Proof of the above equation is easy to see from a pcubed point of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Let N : L(HA) �→ L(HB) be generated by the isometry in (43), N ′ : L(HA) �→ L(HB) be generated by an isometry V ′ : HA �→ HB ⊗ HC′ of the same form as V in (43), however V ′|α′ i⟩ = |βi⟩ ⊗ |γ′ i⟩ (52) where c′ = ⟨γ′ 0|γ′ 1⟩ and a′ = ⟨α′ 0|α′ 1⟩ = bc′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The M : L(HA) �→ L(HA) channel in (51) is generated by an isometry W : HA �→ HA ⊗ HD of the form (43) with W|α′ i⟩ = |αi⟩ ⊗ |δi⟩, (53) where d := ⟨δ0|δ1⟩ = c′/c takes values between 0 and 1 since 0 ≤ c′ ≤ c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The relationship in (51) ensures that N ′ is noisier than N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' As a result, for fixed b, if one decreases c then the channel N becomes noisier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This parameter c captures lack of distinguishability between pure states being arriving at the environ- ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' If c is decreased, more information flows to the environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The no-cloning theorem [46–48] indicates that such a flow to the environment must come at the cost of information flow to the output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Thus N becomes noisier with decreasing c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We shall be interested in using c as the noise parameter with b fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In the limiting b = 0 case, N becomes the qubit dephasing channel (42) with dephasing probability (1−c)/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Here, decreasing c from 1 to 0 increases the dephasing probability from 0 to half.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 4 High fidelity entanglement Consider two parties Alice and Bob, connected by some quantum channel N : L(HA) �→ L(HB) where HA and HB have the same dimension d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Suppose Alice has access to a second d-dimensional system with Hilbert space HR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' What bipartite state ρRA should Alice prepare such that sharing with Bob one half of this state across the channel N results in a state ρRB with highest fidelity F(ρRB, φRB) to a maximally entangled state, |φ⟩RB = 1 √ d |γ⟩RB, (54) between reference HR and output HB?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The optimal state prepared by Alice, which we denote by ΛRA, and the maximum fidelity, O(N) := F(ΛRB, φRB), (55) have been characterized previously in terms of the channel’s Choi-Jamiołkowski operator [30,31,34] when ρRA is pure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' For possibly mixed ρRA, our reformulation of these results in terms of the standard Kraus decomposition of a channel and the operator norm of the channel’s Choi-Jamiołkowski operator agree with these previous characterizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We extend these results by finding families of mixed input states ΛRB that 9 achieve O(N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This reformulation and extension is used later in our study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We begin our reformulation using a semi-definite program maximize F(ρRB, φRB) subject to ρRB = IR ⊗ N(ρRA), ρRA ⪰ 0, Tr(ρRA) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (56) The optimum value of the above program gives O(N) and the density operator which achieves this optimum gives ΛRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The following Theorem captures the solution to the above problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Given a channel N with standard Kraus operators {Ki}, O(N) = 1 d⟨K0, K0⟩ = 1 d||JN RB|| = F(ΛRB, φRB), (57) where the input ΛRA has support in the span of {|K† i ⟩RA} satisfying ⟨Ki, Ki⟩ = ⟨K0, K0⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Using eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (6) along with the fact that φRB is a pure state, one writes F(ρRB, φRB) as an inner product ⟨ρRB, φRB⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This inner product is re-written as ⟨IR⊗N(ρRA), φRB⟩ using the first equality constraint in (56).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This re-writing can be reduced to ⟨ρRA, (IR ⊗ N)†(φRB)⟩ using definition (34) of the dual channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Using discussion below (34), or otherwise, one can show that the dual of the tensor product of two channels is the tensor product of the dual of individual channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Thus ⟨ρRA, (IR ⊗ N)†(φRB)⟩ = ⟨ρRA, IR ⊗ N †(φRB)⟩, where we used that fact that I† R is IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Next, notice (IR ⊗ N †)φRB is just J N † RA /d (21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Using these observations, re-write (56) as maximize 1 d⟨ρRA, J N † RA ⟩ subject to ρRA ⪰ 0, Tr(ρRA) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (58) Solution to this semi-definite program is (1/d) times the maximum eigenvalue of JN † RA obtained by setting ρRA = ΛRA where ΛRA is any density operator with support on the eigenspace of this maximum eigenvalue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This largest eigenvalue can be written as ⟨K† 0, K† 0⟩ = ⟨K0, K0⟩ using (32) and (35).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The largest eigenvalue can also be written as the spectral norm, ||JN RB||, by applying definition (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The support of the largest eigenvalue, ⟨K0, K0⟩, of JN † RA is the span of the collection of eigenvectors corresponding to this value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This collection contains eigenvectors |K† i ⟩ of JN † RA (see (36)) with eigenvalue ⟨K† i , K† i ⟩ equaling the largest eigenvalue ⟨K† 0, K† 0⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The eigenvalues of JN † RA can be shown to equal corresponding eigenvalues of JN RA using (37), i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=', one can show that ⟨K† i , K† i ⟩ = ⟨Ki, Ki⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' ■ The fidelity between a fixed state ρAB and a fully entangled state, maximized over all possible fully entangled states is called the fully entangled fraction [5,29] Fe(ρAB) = max UA F � ρAB, (UA ⊗ IB)φAB(UA ⊗ IB)†� , (59) where UA is a unitary operator on HA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The largest fully entangled fraction obtained by sending one half of a mixed state ρRA across the channel N, maximized over all ρRA equals O(N) (55).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Notice that the largest fully entangled fraction can be found by modifying the optimization prob- lem (56) as follows: replace φRB with χRB = (UR⊗IB)φRB(UR ⊗IB)† and optimize over both unitary matri- ces UR and density operators ρRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Notice, in this larger optimization problem, one can simplify the objective function F(ρRB, χRB) = F(ρ′ RB, φRB) where ρ′ RB = (UR ⊗ IB)†ρRB(UR ⊗ IB).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Since ρ′ RB = I ⊗ N(ρ′ RA), where ρ′ RA = (UR ⊗ IA)†ρRA(UR ⊗ IA), one can rephrase this optimization at hand purely in terms of a single new variable ρ′ RA, satisfying Tr(ρ′ RA) ⪰ 0 and Tr(ρ′ RA) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In this rephrasing variable UR no longer participates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' However the new problem in terms of ρ′ RA is identical to (55).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' ■ 10 The above result generalizes to mixed state what was implicitly found for pure states in the proof of Lemma 2 in [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Let ΛRA be the state in Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We are interested in the minimum amount of entanglement over all states of this type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' To capture this minimum, we use entanglement of formation (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' When ΛRA is a unique pure state we write the input entanglement E(N) = S(σA), (60) when ΛRA can be chosen to be mixed, we write E(N) = min ΛRA Ef(ΛRA), (61) where ΛRA are states in Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' When ΛRA can be chosen to be a separable state, E(N) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1 Multiplicativity Suppose Alice and Bob are connected by two independent channels, that may be same or different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' What state should Alice prepare such that sending one half of it across the joint channel results in Alice and Bob sharing a joint state with maximum fidelity to a fully entangled state?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' What is this maximum fidelity?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Can one hope to use correlations across the two channels connecting Alice and Bob to get more fidelity than what can be achieved without using any correlation across the channels?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Variants of these natural questions have been asked about transmission of information across asymptotically many uses of quantum channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Those questions have been hard to answer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Here we mathematically formulate and answer the questions we posed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Let the two channels connecting Alice and Bob be N1 : L(HA1) �→ L(HB1) and N2 : L(HA2) �→ L(HB2), here dA1 = dB1 and dA2 = dB2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' For each channel input HA1 and HA2, define auxiliary spaces HR1 and HR2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Let IR1 and IR2 be identity maps on these auxiliary spaces, L(HR1) and L(HR2), respectively, HA := HA1 ⊗ HA2, HB := HB1 ⊗ HB2, HR = HR1 ⊗ HR2, N = N1 ⊗ N2, and IR = IR1 ⊗ IR2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' If Alice prepares a state which does not correlate inputs to the two channels IR1 ⊗ N1 and IR2 ⊗ N2 then the maximum fidelity with a fully entangled state across auxiliary space HR and the channel output HB can be found as follows: maximize F(ρRB, φRB) subject to ρRB = (IR ⊗ N)ρRA, ρRA = ρR1A1 ⊗ ρR2A2 ρRA ⪰ 0, Tr(ρRA) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (62) The optimum of the above problem is simply O(N1)O(N2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' It is obtained at ΛRA = ΛR1A1 ⊗ ΛR2A2 where ΛR1A1 and ΛR2A2 are optima to optimizations of the form (56) for N1 and N2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' On the other hand, if Alice prepares a state that may correlate the inputs to IR1 ⊗ N1 and IR2 ⊗ N2 then the maximum fidelity O(N1 ⊗ N2) is found by solving (62) without the product constraint, ρRA = ρR1A1 ⊗ ρR2A2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This fidelity maximum O(N1 ⊗ N2) can be higher O(N1 ⊗ N2) ≥ O(N1)O(N2), (63) since the optimum O(N1)O(N2) of (62) bounds from below the optimum of (62) without the product constraint, ρRA = ρR1A1 ⊗ ρR2A2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The maximum fidelity O(N1 ⊗ N2) is multiplicative, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=', equality holds in (63) O(N1 ⊗ N2) = O(N1)O(N2), (64) Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Let N1 and N2 have standard Kraus decomposition {Jq} and {Kr}, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Using Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1, we write O(N1) = 1 dA1 ⟨J0, J0⟩ and O(N2) = 1 dA1 ⟨K0, K0⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (65) 11 A standard Kraus decomposition {Lp} for N1 ⊗ N2 can be chosen such that each Lp is of the form Jq ⊗ Kr for some q and r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' When q = r = 0, then p can be chosen to be 0, L0 = J0 ⊗ K0 (66) since ⟨L0, L0⟩ = ⟨J0, J0⟩⟨K0, K0⟩ ≥ ⟨Jq, Jq⟩⟨Kr, Kr⟩ = ⟨Lp, Lp⟩ (67) for all q, r and corresponding p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Using (66), and Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1 on N1 ⊗ N2 gives O(N1 ⊗ N2) = 1 dA1dA2 ⟨L0, L0⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (68) The above equality, together with (65) and (67) proves the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Alternatively, notice JN RB = � p |Lp⟩⟨Lp| = � qr |Jq⟩⟨Jq| ⊗ |Kr⟩⟨Kr| = JN1 R1B1 ⊗ JN2 R2B2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (69) where the first equality follows from (33).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Using Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1, write O(N1) = 1 dA1 ||JN1 R1B1||, O(N2) = 1 dA2 ||JN2 R2B2||, and O(N1 ⊗ N2) = 1 dA ||JN RB||, (70) where dA = dA1dA2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The operator norm is sub-multiplicative (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='3 in [49]), ||AB|| ≤ ||A|| · ||B||, (71) it implies ||A ⊗ B|| ≤ ||A|| · ||B||.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (72) Using the above equation along with (63) and (70) also proves the result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' ■ 5 Applications 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1 Extremal qubit channels A qubit channel N has dA = dB = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' If the channel has one Kraus operator then the channel is simply conjugation with a unitary matrix and O(N) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The next simplest qubit channel has two Kraus operators, given in (40).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' One special case of this channel is the qubit amplitude damping channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Kraus operators for this amplitude channel can be written as, K0 = �1 0 0 √1 − p � , and K1 = �0 √p 0 0 � , (73) where 0 ≤ p ≤ 1 is the probability that the state |1⟩⟨1| damps to |0⟩⟨0|.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A simple calculation shows that these Kraus operators constitute a standard Kraus decomposition of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Using this decomposition in Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1, we find O(N) = 1 − p/2 and ΛRA = |K0⟩⟨K0| ⟨K0, K0⟩ , (74) a result that agree with [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In general, the amount of entanglement generated at the input (see def.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' in (60)), E(N) = h( 1 2 − p), (75) where h(x) := −x log x − (1 − x) log(1 − x) is the binary entropy function with log base 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This value is nonzero, unless p = 1 where E(N) = 0 and ΛRA in (74) is a product state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' When the qubit channel N with two Kraus operators is not an amplitude damping channel, the channel Kraus operators take the form (48).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' These Kraus operators {K0, K1} have two parameters 0 ≤ b ≤ 1 12 and 0 ≤ c ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' If b is fixed and c is decreased from 1 the channel becomes more noisy (see discussion containing (51)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Operators {K0, K1} form a standard Kraus decomposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Using them in Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1, gives O(N) = (1 + c)(1 − b2c) 2(1 − b2c2) and ΛRA = \uf8f1 \uf8f2 \uf8f3 |K† 0⟩⟨K† 0| ⟨K† 0,K† 0⟩ if b ̸= 1 and c ̸= 0 � ij fij|K† i ⟩⟨K† j | if b = 1 or c = 0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (76) where complex numbers fij are free except that they result in a valid density operator ΛRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' At b = 1 or c = 0, ΛRA is supported on a two-dimensional space spanned by {|K† 0⟩RA, |K† 1⟩RA}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This two-dimensional space is a subspace of a two qubit space HRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Quite generally, such a subspace has at least one product state (see Lemma in [50]), but typically there are two [42,45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In the c = 0 case, these product states take the simple form |+⟩R ⊗ |ψ+⟩A and |−⟩R ⊗ |ψ−⟩A, (77) where |ψ+⟩A = 1 √ 2( √ 1 + b|0⟩ + √ 1 − b|1⟩), |ψ−⟩A = 1 √ 2( √ 1 + b|0⟩ − √ 1 − b|1⟩), |+⟩A = 1 √ 2(|0⟩ + |1⟩), and |−⟩A = 1 √ 2(|0⟩ − |1⟩).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' At b = 1 or c = 0 one can choose ΛRA to be a projector onto a product state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' As a result, at b = 1 or c = 0, the input entanglement, defined in (8), is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In general, E(N) = � 0 if b = 1 or c = 0 h( (1+b)(1−bc) 2(1−b2c) ) otherwise (78) where expressions for E(N) at b ̸= 1 and c ̸= 0 comes from using the form of ΛRA in (76).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 2 we fix b and plot E(N) as a function of c;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' increasing c makes N less noisy (see discussion containing eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (51)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In these plots, as c is increased from zero, the value of E(N) dis-continuously increases from 0, at c = 0, and continues to monotonically increase until c = 1, where N becomes a perfect channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Across various plots with fixed b, we notice increasing b decrease E(N), which ultimately goes to zero as b �→ 1 for all bc ̸= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' All these features mentioned above are intriguing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In the parameter range 0 < c < 1, one finds an expected result [34] that the minimum amount of entanglement at the input to have maximum fidelity with a fully entangled output is strictly less than one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In particular, if one generates more than E(N) < 1 entanglement at the input, the fidelity with a maximally entangled output is strictly less.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The key addition here is the quantification of the amount of entanglement and a parametrization of the channel in such a way that the amount of entanglement is monotone in the noise parameters of the channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Next, at c = 0, there is a discontinuous change in E(N) which starts at zero and then takes a large finite value ≃ h � (1 + b)/2 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' From a mathematical standpoint, the discontinuity arises because the solution to the optimization (56) becomes degenerate and this degeneracy allows more freedom in choosing optimum inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Due to the structure of qubit channels, this input can be chosen to be separable, as mentioned in the discussion containing (77).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2 Qubit Pauli channels A qubit Pauli channel N : HA �→ HB can be written as N(ρ) = � i piσiρσ† i , (79) where pi ≥ 0, � i pi = 1, and the Kraus operators {√piσi}, σi : HA �→ HB, are proportional to Pauli matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' These matrices can be written in the standard {|0⟩, |1⟩} basis of HA and HB as σ0 = I = � 1 0 0 1 � , σ1 = X = � 0 1 1 0 � , σ2 = Y = � 0 −i i 0 � , and σ3 = Z = � 1 0 0 −1 � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (80) Without loss of generality we can assume p0 ≥ pi for all i ∈ {1, 2, 3}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This assumption comes from the following argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Assume pi ≥ pj for some i ̸= 0 and all j ∈ {0, 1, 2, 3}, then conjugating the input ρ with σi will still result in a Pauli channel (79).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' However, this resulting channel will have p0 ≥ pi for all i ∈ {1, 2, 3}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 13 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='8 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='9 1 c E(N) b = 0 b = 1/4 b = 1/2 b = 3/4 Figure 2: Plot of E(M) as a function of c for various b values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The open circle indicates that the value is zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='8 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='9 1 c O(N) b = 0 b = 1/4 b = 1/2 b = 3/4 Figure 3: Plot of O(M) as a function of c for various b values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' For qubit Pauli channels, the value of O(N) and the fact that it can be achieved using a maximally entangled input state ΛRA was found in [34], however we note later that one can also achieve O(N) using a separable pure state when N is very noisy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Since the Pauli matrices are orthogonal to each other, in a standard Kraus decomposition, {Ki}, of N we can always chose each Ki to be √pjσj for some j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' As p0 ≥ pi, K0 = √p0σ0 and from Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1 we get O(N) = p0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (81) When p0 > pj for all j, ΛRA = |σ† 0⟩⟨σ† 0|/2, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=', ΛRA is a projector onto a maximally entangled state and thus E(N) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' However, if for some i, p0 = pi then ΛRA is any density operator with support in a space spanned by {|σ† 0⟩RA, |σ† i ⟩RA}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This space is a two-dimensional subspace of a two qubit space HRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Following the discussion containing (77), this subspace contains at least one product state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' As a result, for any i if p0 = pi we can choose ΛRA to be a product state and thus E(N) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Consequently, E(N) = � 1 if p0 > pi ∀i, 0 if p0 = pi for some i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (82) When p0 = pi, the best fidelity with a maximally entangled state at the output is achieved by sending a 14 separable input ΛRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Consequently, the output ΛRB is also separable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This separable output is expected to have a small fidelity with a fully entangled state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This expectation is met, the condition p0 = pi together with � i pi = 1 forces p0 ≤ 1/2, and thus O(N) ≤ 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Such a value of half for fidelity with a maximally entangled state |φ⟩AB is considered small since this value of half can be achieved by a simple separable state ρRB = 1 2(|00⟩⟨00| + |11⟩⟨11|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' One may wonder which qubit Pauli channels satisfy p0 = pi ≥ pj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Any qubit Pauli channel of this type is anti-degradable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In general, N in (79) with p0 ≥ pi is anti-degradable [50–52] if and only if p1 + p2 + p3 + √p1p2 + √p1p3 + √p2p3 ≥ 1/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (83) We are interested in the case where p0 = pi for some i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The above condition remains unaffected when permuting pi and pj, thus we let p0 = p1 = p, denote p2 by q then p3 = 1 − 2p − q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Using these substitutions on the left side of (83), together with 1 ≥ p ≥ q ≥ 0 and p ≥ 1 − 2p − q we find that the above inequality (83) is always satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Thus p0 = pi ≥ pj implies that the qubit Pauli channel N is anti-degradable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Pauli channels (79) have a key property, up to local unitaries at the channel input and output, any unital qubit channel can always be written as a Pauli channel [42].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' An interesting observation about qubit channels is that ΛRA in Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1 can be chosen to be a maximally entangled state if and only if N is unital [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' It is interesting for that reason to ask if such a result holds in higher dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In this next section, we find that it doesn’t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In the case of qubit Pauli channels, but also for extremal qubit channels, we found that it is possible to find separable input states ΛRA that achieve the most fidelity with a fully entangled state at the channel output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This separable state appeared when a qubit channel N’s standard Kraus decomposition {Ki} satisfied the condition ⟨K0, K0⟩ = ⟨Kj, Kj⟩, for at least one j ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Using eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (33), this condition reduces to the channel’s Choi-Jamiołkowsi operator JN RB having its largest eigenvalue be degenerate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In general, we have the following lemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' If N is a qubit channel and the largest eigenvalue of JN RB is degenerate, then ΛRA in Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1 can be chosen to be separable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Let {Ki} be a standard Kraus decomposition of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Since JN RB is degenerate, ⟨K0, K0⟩ = ⟨K1, K1⟩ and ΛRA has support in the span of {|K† 0⟩, |K† 1⟩}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This support is a two-dimensional subspace of a two-qubit space, and thus contains a product state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Hence ΛRA can be chosen to be a projector onto this product state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' ■ While it may be tempting to conjecture that the above result holds in higher dimensional channels, we show in the next section that it doesn’t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='3 Some qutrit channels We construct two qutrit channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The first channel, M, is not unital but its optimal input state ΛRA, defined in Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1, is unique and maximally entangled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The second channel, P, is unital, however its optimal input state ΛRA is neither maximally entangled nor separable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Using the second channel, we demonstrate that when the largest eigenvalue of JN RB is degenerate, ΛRA can still be entangled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The demonstration contrasts with Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Let HA and HB be three-dimensional Hilbert spaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Let M : L(HA) �→ L(HB) be a channel with Kraus operators K0 = √ λI, K1 = √ 1 − λ(|0⟩⟨1| + |1⟩⟨0|), and K2 = √ 1 − λ|1⟩⟨2|, (84) where 0 ≤ λ ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This channel M is not unital, except when λ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' When 2/5 < λ < 1, {Ki} is a standard Kraus decomposition of M with ⟨K0, K0⟩ > ⟨Ki, Ki⟩ for all i ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' From Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1 we find O(M) = λ, ΛRA = 1 3|I⟩⟨I|, and E(M) = log2 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (85) Thus when 2/5 < λ < 1, the input ΛRA is unique, and it is maximally entangled, however the channel M is not unital.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 15 Let P : L(HA) �→ L(HB) be a qutrit channel with Kraus operators L0 = � z + 2 4 � |0⟩⟨1| + |1⟩⟨0| � , L1 = � 1 − z 2 � |1⟩⟨2| + |2⟩⟨1| � , L2 = � 1 − z 2 � |0⟩⟨2| + |2⟩⟨0| � , and L3 = �z 4 � |0⟩⟨0| + |1⟩⟨1| − 2|2⟩⟨2| � , (86) where 0 ≤ z ≤ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Since each Kraus operator Li is Hermitian, P is unital (see discussion below (24)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Kraus operators {Li} are standard and thus Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1 immediately gives O(M) = (z + 2)/6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' When z ̸= 0, ΛAR = |L† 0⟩⟨L† 0| (87) where |L† 0⟩RA = 1 √ 2(|01⟩ + |10⟩) is not a maximally entangled state of two qutrits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' When z = 0, L3 = 0, ⟨L0|L0⟩ = ⟨L1|L1⟩ = ⟨L2|L2⟩ and thus largest eigenvalue of JM RB has a degenerate spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In this case, ΛRA has support in a subspace S spanned by {|L† 0⟩RA, |L† 1⟩RA, |L† 2⟩RA}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This subspace only contains non- product vectors, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=', it is completely entangled in the sense of Parthasarathy(see Def.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2 in [53]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Consequently, any density operator ΛRA supported on this subspace is entangled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 6 Discussion In this work we considered a one-shot setting where one half of any bipartite mixed state may be sent across a single use of a fixed channel N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The goal in this setting is to share a state with maximum fidelity O(N) to a fully entangled state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Interestingly, maximum fidelity O defined in the one-shot setting fully characterizes the ability of any channel to share high fidelity entanglement over multiple channel uses, possibly used in parallel with other channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This extension follows from multiplicative nature of O, proved in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Using a semi-definite program, we reformulate the maximum fidelity, found previously for pure state inputs [30,31,34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The first reformulation in Theorem 1 lays greater emphasis on a channel’s Kraus operators rather than its Choi-Jamiołkowski operator, as done previously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' These two channel representations are formally equivalent (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 3 for brief discussion), however the Kraus decomposition can sometimes be easier to work with and can provide different insights when discussing maximum fidelity O(N), but perhaps in other cases as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In the present case, the standard Kraus operators (see Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1 for definition) simplifies the search for and broadens the types of channel inputs ΛRA which achieve O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' One way in which we have broadened the search for optimal inputs ΛRA is to identify channels N for which ΛRA can be chosen to be separable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This choice appears in two notable cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' First, when N is an extremal qubit channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Here, separability of ΛRA leads to a discontinuous jump in the minimal amount of entanglement E(N) generated to achieve maximum fidelity with a fully entangled state (see discussion with Fig 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A second notable case where ΛRA can be chosen to be separable is for noisy unital qubit channels where the input may be ordinarily chosen to be fully entangled (see discussion containing eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' (82)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' These findings motivate a characterization of channels N for which ΛRA is possibly separable, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=', E(N) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' One typically expects such channels to not be useful for sharing entanglement in the type of one-shot setting discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' One example of such channels is in Lemma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The lemma extends to channels with Choi-Jamiołkowsi operator JN AB having a greater than (d − 1)2 fold degeneracy in their largest eigenvalue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The support of this largest eigenvalue subspace always has a product state (proof for this can be constructed using Prop 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='4 in [53]) and thus, ΛRA can be chosen to be a product state and E(N) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' On the other hand, we also find a channel whose Choi-Jamiołkowsi operator has a degeneracy in its largest eigenvalue but the optimal input for the channel must be entangled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Another way in which we have broadened the search for optimal inputs ΛRA is to consider extension of results found previously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' For qubit channels, a fully entangled input was known to achieve O if and only if the channel was unital.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In higher dimensions, we find this result no longer holds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We construct a unital qutrit channel for which the optimal input must be less than fully entangled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We also construct a qutrit channel which is not unital, but for which a fully entangled input is necessary to obtain the largest overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Our second reformulation of O(N) in Theorem 1 notes that it equals the operator norm of the channel’s Choi-Jamiołkowski operator, upto normalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' This observation can not only simplify discussions about 16 O(N) (for instance see proof of Th.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 2), it also gives the operator norm of the Choi-Jamiołkowski operator a simple interpretation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The single channel use setting discussed here can be extended by allowing the reference system and the channel output system to be processed using local operations and one-way or two-way classical communi- cation, labeled 1-LOCC and 2-LOCC respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Building on ideas in [32,54], it has been shown for qubit channels that maximum fully entangled fraction allowing a single round of 2-LOCC, O′, equals O [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Understanding O′ in higher dimensional channels while exploring optimal protocols and multiplicativity of O′ may form an interesting direction of future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Another direction can come from extending results in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2 where we show that that a set of qubit Pauli channels with E(N) = 0 also have no quantum capacity Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' It could be interesting to study the relation of O and E to Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Along the way to analyzing the maximum fidelity, we found it useful to study extremal qubit channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' These simple channels can be considered the most basic qubit channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' However, to our knowledge, noise parameters for these channels have not been adequately discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='3, we show the pcubed point of view allows one to identify noise parameters for this channel in such a way that channel becomes demonstrably noisier as a parameter is varied monotonically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Hope is that such identification makes this channel class a better understood and non-trivial test-bed for ideas in quantum information science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' We also flesh out two useful properties of general channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' First, in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1 the existence of a standard Kraus decomposition where the Kraus operators are orthogonal and their norm is ordered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Second, in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2, we show how the Choi–Jamiołkowski operator of a channel and its dual can always be taken to be complex conjugates of each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' References [1] Jerry M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Chow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Quantum intranet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' IET Quantum Communication, 2(1):26–27, Mar 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1049/qtc2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='12002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [2] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Kimble.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The quantum internet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Nature, 453(7198):1023–1030, Jun 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1038/nature07127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [3] Stephanie Wehner, David Elkouss, and Ronald Hanson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Quantum internet: A vision for the road ahead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Science, 362(6412), 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='aam9288.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [4] Charles H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Bennett, Gilles Brassard, Claude Crépeau, Richard Jozsa, Asher Peres, and William K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Wootters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=', 70:1895–1899, Mar 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1895.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [5] Charles H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Bennett, David P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' DiVincenzo, John A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Smolin, and William K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Wootters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Mixed- state entanglement and quantum error correction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A, 54:3824–3851, Nov 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='3824.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [6] Mark M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Wilde.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' From Classical to Quantum Shannon Theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' arXiv:1106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1445 [quant-ph], 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1017/9781316809976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' arXiv: 1106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1445.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [7] Seth Lloyd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Capacity of the noisy quantum channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A, 55:1613–1622, Mar 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1613.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [8] PeterW.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='Shor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Quantumerrorcorrection, Nov2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='msri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='org/workshops/203/schedules/1181.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [9] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Cai, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Winter, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Yeung.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Quantum privacy and quantum wiretap channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Problems of Information Transmission, 40(4):318–336, Oct 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1007/s11122-005-0002-x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [10] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Devetak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The private classical capacity and quantum capacity of a quantum channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' IEEE Transactions on Information Theory, 51(1):44–55, Jan 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1109/TIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='839515.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [11] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Devetak and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Shor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The capacity of a quantum channel for simultaneous transmission of classical and quantum information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Communications in Mathematical Physics, 256(2):287–303, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1007/s00220-005-1317-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 17 [12] Graeme Smith and Jon Yard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Quantum communication with zero-capacity channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Science, 321(5897):1812–1815, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1162242.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [13] Toby Cubitt, David Elkouss, William Matthews, Maris Ozols, David Pérez-García, and Sergii Strelchuk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Unbounded number of channel uses may be required to detect quantum capacity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Nature Communica- tions, 6:6739, Mar 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1038/ncomms7739.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [14] Vikesh Siddhu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Entropic singularities give rise to quantum transmission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Nature Communications, 12(1):5750, Oct 2021, arXiv: 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='10367.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1038/s41467-021-25954-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [15] Felix Leditzky, Debbie Leung, Vikesh Siddhu, Graeme Smith, and John A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Smolin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Generic nonaddi- tivity of quantum capacity in simple channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' arXiv preprint, 2022, arXiv: 2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='08377.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [16] Francesco Buscemi and Nilanjana Datta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The Quantum Capacity of Channels With Arbitrar- ily Correlated Noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' IEEE Transactions on Information Theory, 56(3):1447–1460, March 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1109/TIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2039166.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [17] Nilanjana Datta and Min-Hsiu Hsieh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The apex of the family tree of protocols: opti- mal rates and resource inequalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' New Journal of Physics, 13(9):093042, September 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1088/1367-2630/13/9/093042.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [18] Nilanjana Datta and Min-Hsiu Hsieh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' One-shot entanglement-assisted quantum and clas- sical communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' IEEE Transactions on Information Theory, 59(3):1929–1939, March 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1109/TIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2228737.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' arXiv:1105.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='3321 [quant-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [19] William Matthews and Stephanie Wehner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Finite Blocklength Converse Bounds for Quan- tum Channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' IEEE Transactions on Information Theory, 60(11):7317–7329, November 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1109/TIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2353614.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [20] Salman Beigi, Nilanjana Datta, and Felix Leditzky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Decoding quantum information via the Petz recovery map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Journal of Mathematical Physics, 57(8):082203, August 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='4961515.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [21] Marco Tomamichel, Mario Berta, and Joseph M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Renes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Quantum coding with finite resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Nature Communications, 7(1):11419, September 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1038/ncomms11419.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [22] Corsin Pfister, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Adriaan Rol, Atul Mantri, Marco Tomamichel, and Stephanie Wehner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Capacity esti- mation and verification of quantum channels with arbitrarily correlated errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Nature Communications, 9(1):27, January 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1038/s41467-017-00961-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [23] Anurag Anshu, Rahul Jain, and Naqueeb Ahmad Warsi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Building Blocks for Communication Over Noisy Quantum Networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' IEEE Transactions on Information Theory, 65(2):1287–1306, February 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1109/TIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2851297.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [24] Xin Wang, Kun Fang, and Runyao Duan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Semidefinite programming converse bounds for quantum communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' IEEE Transactions on Information Theory, 65(4):2583–2592, 2018, arXiv: 1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='00200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [25] Farzin Salek, Anurag Anshu, Min-Hsiu Hsieh, Rahul Jain, and Javier Rodriguez Fonollosa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' One-Shot Capacity Bounds on the Simultaneous Transmission of Classical and Quantum Information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' IEEE Transactions on Information Theory, 66(4):2141–2164, April 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1109/TIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2945800.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [26] Yoshifumi Nakata, Eyuri Wakakuwa, and Hayata Yamasaki.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' One-shot quantum error cor- rection of classical and quantum information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Physical Review A, 104(1):012408, July 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='012408.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [27] Sumeet Khatri and Mark M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Wilde.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Principles of quantum communication theory: A modern approach, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' arXiv: 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='04672.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [28] Charles H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Bennett, Gilles Brassard, Sandu Popescu, Benjamin Schumacher, John A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Smolin, and William K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Wootters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Purification of Noisy Entanglement and Faithful Teleportation via Noisy Chan- nels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Physical Review Letters, 76(5):722–725,January 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='722.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' arXiv:quant- ph/9511027.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 18 [29] Michał Horodecki, Paweł Horodecki, and Ryszard Horodecki.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' General teleportation chan- nel, singlet fraction, and quasidistillation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Physical Review A, 60(3):1888–1898, September 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1888.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [30] Frank Verstraete and Henri Verschelde.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' On quantum channels, January 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='org/abs/quant-ph/0202124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' arXiv:quant-ph/0202124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [31] Rajarshi Pal and Somshubhro Bandyopadhyay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Entanglement sharing via qudit channels Nonmaxi- mally entangled states may be necessary for one-shot optimal singlet fraction and negativity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Physical Review A, 97(3):032322, March 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='032322.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [32] Frank Verstraete and Henri Verschelde.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Optimal Teleportation with a Mixed State of Two Qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Physical Review Letters, 90(9):097901, March 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='097901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [33] Somshubhro Bandyopadhyay and Anindita Ghosh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Optimal fidelity for a quantum channel may be attained by nonmaximally entangled states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Physical Review A, 86(2):020304, August 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='020304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [34] Rajarshi Pal, Somshubhro Bandyopadhyay, and Sibasish Ghosh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Entanglement sharing through noisy qubit channels: One-shot optimal singlet fraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Physical Review A, 90(5):052304, November 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='052304.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [35] Lieven Vandenberghe and Stephen Boyd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Semidefinite programming.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' SIAM Review, 38(1):49–95, 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1137/1038003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [36] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Jamiołkowski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Linear transformations which preserve trace and positive semidefiniteness of opera- tors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Reports on Mathematical Physics, 3(4):275–278, 1972.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1016/0034-4877(72)90011-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [37] Man-Duen Choi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Completely positive linear maps on complex matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Linear Algebra and its Applica- tions, 10(3):285 – 290, 1975.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1016/0024-3795(75)90075-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [38] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Holevo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Quantum Systems, Channels, Information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' De Gruyter, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1515/9783110273403.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='346.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [39] Michael M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Wolf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Quantum Channels and Operations - Guided Tour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Lecture notes, 2012, arXiv: http://www-m5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='ma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='tum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='de/foswiki/pub/M5/Allgemeines/MichaelWolf/QChannelLecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [40] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Fujiwara and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Algoet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Affine parameterization of quantum channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' In Proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 1998 IEEE International Symposium on Information Theory (Cat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='98CH36252), page 87, Cambridge, MA, USA, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' IEEE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1109/ISIT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='708673.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [41] Chi-Sheng Niu and Robert B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Griffiths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Two-qubit copying machine for economical quantum eaves- dropping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A, 60:2764–2776, Oct 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2764.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [42] Mary Beth Ruskai, Stanislaw Szarek, and Elisabeth Werner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' An analysis of completely-positive trace-preserving maps on m2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Linear Algebra and its Applications, 347(1–3):159 – 187, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1016/S0024-3795(01)00547-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [43] Michael M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Wolf and David Pérez-García.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Quantum capacities of channels with small environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A, 75:012303, Jan 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='012303.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [44] Shmuel Friedland and Raphael Loewy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' On the extreme points of quantum channels, October 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' http://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='org/abs/1309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='5898.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' arXiv:1309.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='5898 [math-ph, physics:quant-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [45] Vikesh Siddhu and Robert B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Griffiths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Degradable quantum channels using pure-state to product-of- pure-state isometries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A, 94:052331, Nov 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='052331.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [46] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Park.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The concept of transition in quantum mechanics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Foundations of Physics, 1:23–33, Mar 1970.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1007/BF00708652.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 19 [47] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Dieks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Communication by epr devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Physics Letters A, 92:271–272, Nov 1982.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1016/0375-9601(82)90084-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [48] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Wootters and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Zurek.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A single quantum cannot be cloned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Nature, 299:802, Oct 1982.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1038/299802a0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [49] John Watrous.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The Theory of Quantum Information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Cambridge University Press, 1 edition, Apr 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1017/9781316848142.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [50] Chi-Sheng Niu and Robert B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Griffiths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Optimal copying of one quantum bit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' A, 58:4377–4393, Dec 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='4377.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [51] Nicolas J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Cerf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Pauli cloning of a quantum bit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=', 84:4497–4500, May 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1103/PhysRevLett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='4497.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [52] Toby S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Cubitt, Mary Beth Ruskai, and Graeme Smith.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' The structure of degradable quantum channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Journal of Mathematical Physics, 49(10):–, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1063/1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='2953685.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [53] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Parthasarathy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' On the maximal dimension of a completely entangled subspace for finite level quan- tum systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Proceedings Mathematical Sciences, 114(4):365–374, Nov 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1007/BF02829441.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' [54] Frank Verstraete and Henri Verschelde.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Fidelity of mixed states of two qubits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' Physical Review A, 66(2):022307, August 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='1103/PhysRevA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content='022307.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} +page_content=' 20' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/RdAzT4oBgHgl3EQf0P6C/content/2301.01781v1.pdf'} diff --git a/RdE3T4oBgHgl3EQfygvM/vector_store/index.pkl b/RdE3T4oBgHgl3EQfygvM/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..ff36bcae7fa32d961361e57744a49968b4efd168 --- /dev/null +++ b/RdE3T4oBgHgl3EQfygvM/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a0d3aa1d7e975956b584270d53db0588d1eaaed157cc51b89f1b768c9999b7fd +size 349518 diff --git a/S9E2T4oBgHgl3EQfswjv/content/2301.04064v1.pdf b/S9E2T4oBgHgl3EQfswjv/content/2301.04064v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..52eb18cf1836b8eb3152aff4d2059dd4888278aa --- /dev/null +++ b/S9E2T4oBgHgl3EQfswjv/content/2301.04064v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:09fb9523d60ea55ba0f2e3bc59a81425fdd28c074c2fa1fc28c69fc140303844 +size 290361 diff --git a/S9E2T4oBgHgl3EQfswjv/vector_store/index.faiss b/S9E2T4oBgHgl3EQfswjv/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..94ba0cc9cdd9ffd45da1d84b440547d8ee03bdf2 --- /dev/null +++ b/S9E2T4oBgHgl3EQfswjv/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:60fe198b2deb8d6f8dfabe6129180723d2bb452c5948d73c29f134d7972735d2 +size 2883629 diff --git a/S9E2T4oBgHgl3EQfswjv/vector_store/index.pkl b/S9E2T4oBgHgl3EQfswjv/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..d06110985d1db8d4a36f131e40945121d5d8bcf0 --- /dev/null +++ b/S9E2T4oBgHgl3EQfswjv/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8875e1eca79186f2ff18d7312b366c696683824975c1ebf83a063a02df14cb48 +size 109918 diff --git a/SdAyT4oBgHgl3EQfVPfZ/content/tmp_files/2301.00142v1.pdf.txt b/SdAyT4oBgHgl3EQfVPfZ/content/tmp_files/2301.00142v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..9a367f8a2c793bdc049a1618fe8a09301e5ca083 --- /dev/null +++ b/SdAyT4oBgHgl3EQfVPfZ/content/tmp_files/2301.00142v1.pdf.txt @@ -0,0 +1,1216 @@ +Computational Charisma – +A Brick by Brick Blueprint for Building +Charismatic Artificial Intelligence +Bj¨orn W. Schuller 1,2, Shahin Amiriparian 1, Anton Batliner 1, +Alexander Gebhard 1, Maurice Gerzcuk 1, Vincent Karas 1, Alexander Kathan 1, +Lennart Seizer 3, Johanna L¨ochner 3 +1EIHW – Chair of Embedded Intelligence for Health Care and Wellbeing, University +of Augsburg, Augsburg, Germany +2GLAM – Group on Language, Audio, & Music, Imperial College London, London, +United Kingdom +3Department of Child and Adolescent Psychiatry, Eberhard-Karls University, +T¨ubingen, Germany +Correspondence*: +Bj¨orn W. Schuller, Johanna L¨ochner +schuller@ieee.org, Johanna.Loechner@med.uni-tuebingen.de +ABSTRACT +Charisma is considered as one’s ability to attract and potentially also influence others. Clearly, +there can be considerable interest from an artificial intelligence’s (AI) perspective to provide it with +such skill. Beyond, a plethora of use cases opens up for computational measurement of human +charisma, such as for tutoring humans in the acquisition of charisma, mediating human-to-human +conversation, or identifying charismatic individuals in big social data. While charisma is a subject +of research in its own right, a number of models exist that base it on various ‘pillars’, that is, +dimensions, often following the idea that charisma is given if someone could and would help +others. Examples of such pillars, therefore, include influence (could help) and affability (would +help) in scientific studies or power (could help), presence, and warmth (both would help) as +a popular concept. Modelling high levels in these dimensions, i. e., high influence and high +affability or high power, presence, and warmth for charismatic AI of the future, e. g., for humanoid +robots or virtual agents, seems accomplishable. Beyond, also automatic measurement appears +quite feasible with the recent advances in the related fields of Affective Computing and Social +Signal Processing. Here, we, thereforem present a blueprint for building machines that can +appear charismatic, but also analyse the charisma of others. To this end, we first provide the +psychological perspective including different models of charisma and behavioural cues of it. We +then switch to conversational charisma in spoken language as an exemplary modality that is +essential for human-human and human-computer conversations. The computational perspective +then deals with the recognition and generation of charismatic behaviour by AI. This includes +an overview of the state of play in the field and the aforementioned blueprint. We then name +exemplary use cases of computational charismatic skills before switching to ethical aspects and +concluding this overview and perspective on building charisma-enabled AI – will tomorrow’s +influencers be artificial? +Keywords: Charisma, AI, Empathy, Mimicry, Affective Computing, Social Signal Processing +1 +arXiv:2301.00142v1 [cs.HC] 31 Dec 2022 + +Schuller et al. +Computational Charisma +A +B +Power +Warmth +Presence +Empathy +Authenticity +Emotional +intelligence +Mindfulness +Skills +Intelligence +Attention +Competence +Humour +Exhibition of ease and +comfort +Persuasion +Enthusiasm +Motivation +Confidence +Affective communication +Rapport +Leader +Presence +Influence +Smile +Comfort +Get Along +Influence +Affability +Figure 1. Comparison of the models of Tskhay (A) Tskhay et al. (2018) and Fox Cabane (B) Fox Cabane +(2013) +1 +INTRODUCTION +Charisma. An irresistible force that, apart from beauty or rhetoric, captivates people. A miracle cure +for professional success and an almost effortless rise to the top of power. A plethora of popular science +literature, podcasts, and discussions rotate around this fascination, providing training to adopt a charismatic +style – going along with the great promise of being successful and attractive to others. Besides this great +uptake, the topic of charismatic behaviour also has a research tradition in sociology and psychology and is +now increasingly trending in computation. This is promising, since computational charisma may be applied +to numerous fields such as leadership training, mental health care, and education and enhance outcomes in +several ways: more efficient leadership, increased comfort in recipients, better teamwork, and reduction of +reluctance and irritation. However, charismatic behaviour is not bound to particular values and initially +exists independently of an ideology. This also makes the appropriation of charisma a potential danger if +it is misused for unethical purposes. In this article – section by section –, we initially discuss the myth +about charisma from a scientific, but also popular science perspective (functional aspects of charisma), +to follow up with several layers of markers for charisma (formal aspects of charisma), computational +aspects of charisma to finish with the motivation based on applications and rendering these more attractive +and effective and ethics of computational charisma. Thereby, we focus on spoken language and audio as +indelible key features of charismatic behaviour, that play undoubtedly a key role in times of remote and +digital – hence restricted visual – communication. +2 +FUNCTIONAL ASPECTS OF CHARISMA: PSYCHOLOGICAL MODELS +Although charisma is a ubiquitous and frequently discussed phenomenon, and people seem to agree on +which person inherits this trait, a certain mysteriousness surrounds the exact definition. And yet, although +some popular figures in history are frequently characterised as being charismatic. In this first section, we +discuss charisma from a sociological, psychological and also popular science perspective and aim to untidy +the concrete characterisations of charisma. In contrast to other research fields, the subjective perception of +charisma and popular science uptake of this phenomenon is particularly interesting, since it is part of its +definition and hence, immanent. +This is a provisional file, not the final typeset article +2 + +Schuller et al. +Computational Charisma +2.1 +Origin and Definition +The word charisma originally comes from the Greek (χ´αρισµα) and means ‘gift of grace’. Even the +ancient Greeks assumed that charisma is a gift from God that some have, and others do not. Today, the word +is typically used as a descriptor for people who are attractive to others and manage to gather a following +around them (for the good or bad) such as Princess Diana, Oprah Winfrey, Martin Luther King, or Adolf +Hitler. Although everybody has an intuitive understanding of the concept of charisma and there is a high +agreement in the population about which persons are charismatic, a scientifically sound and commonly +used definition is still discussed (Antonakis, 2012). This may partly be explained by the fact that the study +of charisma is relatively young and still mostly restricted to economic psychology in terms of leadership +research. Naturally, children are even less likely to have a defined concept of what charisma actually +means; however, they are well capable of voting the ‘captain’. Hence, Antonakis and Dalgas asked 5-13 +years-olds to rate the ‘captain’ among a selection of pairwise displayed photographs of French candidates +for the presidency, resulting in an 85 % hit rate (Antonakis and Dalgas, 2009). Although these results +rely on visual data only, it was shown that attractiveness is not the key feature of charisma. For example, +in a study predicting success in relationships and academic careers, charisma was more predictive than +attractiveness and visuals (Orzeatja, 2011). The sociologist Max Weber defined charisma at the beginning +of the 20th century as an ‘extraordinary quality of a personality’, as a ‘supernatural or superhuman power’ +(Weber, 1922). Based on this work, House (House, 1976) provided the first operationalisation. Thereby, +charisma was defined as the ability to inspire others toward a common goal and identity by appealing +to their emotions and collective identity in order to impart an idealised vision to their followers – thus, +the central role of charisma in leadership research. In the following decades, more specific traits and +behaviours have been associated with charisma (Antonakis, 2012). A key quality lies in the ability to +connect with other people and exhibit ease, trust, and comfort in the audience paving the ground to +become a leader. In addition, a charismatic person is highly persuasive (Mhatre and Riggio, 2014). Several +definitions of such phenomena are discussed in the literature including properties such as authenticity, +emotional competence (e. g., understanding emotions in oneself and others, or managing own emotions), +empathy, persuasiveness, spending attention to others, passion, enthusiasm, and obtaining strong opinions +to name a few. However, such qualities may not only be used for charity aspects. Welsh and colleagues +investigated the associations of psychopathy, charisma and success. They found that psychopathy was +positively associated with leadership charisma and the influence component of general charisma (Welsh and +Lenzenweger, 2021); in addition, charisma moderated the association of psychopathic traits and perceived +success in form of the evading detection and punishment. +Charisma models or concepts were proposed as either inherent personality traits (Burke and Brinkerhoff, +1981), observer perception and outcomes (Awamleh and Gardner, 1999), or both (Conger et al., 2009). +Aiming to provide a more comprehensive model of charisma based on empirical data, Tskhay et al. (2018) +created an empirical model of charisma: They investigated characteristics of charisma by rigorous and +repeated questioning of people how they use to describe charismatic people, and subsequently applied +factor analyses to identify the most important components. Their analyses resulted in a two-factor model +with one factor – influence – consisting of items that describe leadership ability and influence in a group +setting, and another factor – affability – that consists of items describing a pleasant and inviting disposition +toward others. The factors with more detailed descriptions and an exemplary list of behaviours that are +associated with each are given in this section, with no claim to completeness. While influence and affability +are separate qualities, somehow, in the combination of traits and behaviours associated with these two, +charisma emerges as a novel trait. Charisma is thereby defined as a multi-dimensional construct of traits +and behaviours in contrast to ‘just’ being a likeable person. Similarly, Keating (2011) argued that dominant +Frontiers +3 + +Schuller et al. +Computational Charisma +behaviour triggers avoidance reactions in others, whereas emotionally warm behaviour triggers approach +reactions. She further claims that the perception of charisma emerges specifically through the simultaneous +elicitation of avoidance and approach reactions by the combination of influence(dominance, power) and +affability (emotionality, approachability) in a charismatic person. +Model +GCI Item +Associated constructs +Influence +Influence +Presence +Leader +Has the ability to influence people +Has a presence in a room +Knows how to lead a group +Convergent: +Emotional +Intelligence, +Positive Affect, +Extraversion, +Openness, +Conscientiousness, Political Skill, +Competence +Discriminant: Negative Affect, Neuroticism +Affability +Get along +Comfort +Smile +Can get along with everyone +Makes people feel comfortable +Smiles at people often +Convergent: Emotional Intelligence, Positive +Affect, Confidence, Extraversion, Openness, +Conscientiousness, Agreeableness, Political +Skill, Competence, Warmth +Discriminant: Negative Affect, Neuroticism +Table 1. Detailed overview of the Tskhay et al. model +There are several psychological constructs that may be convergent or discriminant to charisma. In a +validation study of the influence-affability model, the uniqueness or relatedness of charisma to other +individual difference measures was tested in multiple samples ((Tskhay et al., 2018); see Table 1). Thereby, +influence and affability were both found to be significantly related to emotional intelligence, i. e., the +appraisal, expression, regulation, and utilisation of emotions in a variety of contexts (Schutte et al., 1998). +In terms of emotionality experienced by oneself, positive affect was positively related to the two charisma +factors, while negative affect was negatively related to both. Political skill, defined by the four dimensions +of social astuteness, interpersonal influence, networking ability, and apparent sincerity (Ferris et al., 2005), +is often used as a metric of charismatic leadership and accordingly was found to be positively related to +influence and affability. Intelligence is a trait that is often ascribed to charismatic individuals in lay theories; +however, intelligence, as determined by Raven’s Matrices (Raven and Court, 1998), was not associated with +influence or affability, indicating that charisma may rely more on interpersonal skills in social interactions +rather than intelligence. Further, the general confidence of an individual as the degree to which one feels +certain about both the world and idiosyncratic surroundings and their ability to deal with stress (Keller +et al., 2011) was positively related to affability, but not associated with influence. In terms of personality +traits as the Big Five (McCrae et al., 1999), openness, consciousness, and extraversion were positively +related to both influence and affability, while agreeableness was only related to affability. Neuroticism on +the other hand was negatively associated with influence and affability. Of the dimensions competence and +warmth – two essential elements of both social behaviour and personal characteristics (Fiske et al., 2007) – +influence was only related to competence, while affability was related to both warmth and competence. +Another model of charisma was proposed by Fox Cabane (2013), in which she refers to charisma as +deriving from three pillars: presence, power, and warmth. Presence is displayed by dwelling in the current +moment, active listening, and responding adequately. The focus of attention lies on the person one is +talking to and taking an honest interest in the conversation partner. Power is not defined as actual power +like being in a position as president or high-rank manager. It is rather understood as high competence due to +certain skills, abilities, or intelligence a person obtains. Warmth requires a high level of empathy, openness, +This is a provisional file, not the final typeset article +4 + +Schuller et al. +Computational Charisma +and positivity. The pillar warmth has frequently been studied as part of the two-dimensional warmth and +competence (W&C) model (Wang and Chanel, 2021; Fraser et al., 2021, 2022), where warmth indicates +the nature of the sender’s intent towards the receiver, and competence the ability of the sender to enact +this intent. The combination of these dimensions evokes emotional responses ranging from admiration +to disgust (Fraser et al., 2022). Thus, warmth is closely related to the perceptions of attractiveness and +empathy. Therefore, charismatic individuals usually radiate acceptance and friendliness that one otherwise +experiences only from family members or friends. It is discussed whether one or two of the three qualities +may be sufficient to appear charismatic, as Steve Jobs, for instance, scored with presence and power, but +lacked warmth . In contrast, Martin Luther King showed all three qualities. Hence, the pillars warmth and +power may relate to affability and to the influence of the two-factor model by Tskhay et al. (Tskhay et al., +2018), while the pillar presence was discussed as a non-latent, i. e., secondary, variable in their empirically +found model by a factor analysis following questioning participants (see Figure 1A). +Very similarly, the concept of rapport is defined and may well serve as part of charismatic behaviour. +Tickle-Degnen and Rosenthal (1990) conceptualised the nature of rapport in terms of a dynamic structure +of three interrelating components: mutual attentiveness, positivity, and coordination; these are differently +weighted and present over time in a relationship. Hence, rapport is characterised by agreement, mutual +understanding, or empathy that makes communication possible or easy, establishing ease and comfort in +communication partners. In consequence, a charismatic individual is capable of establishing rapport. +Conclusively, charisma is a person-specific descriptor that emerges specifically in social situations through +the attribution of a certain set of traits to an individual. Despite heterogeneous conceptualisation and the +inherent complexity, there is a consensus that charismatic individuals exert influence over others, have +extraordinary social skills, comfort and connect to others, inspire followership, and are prone to leadership +roles (Tskhay et al., 2018)(Antonakis, 2012). Breaking charisma down to such concrete properties reveals a +combination of personality traits and skills that are partly inherited, socially acquired, and trained. In social +psychology, the processes that leads us to form impressions about other people are referred to as person +perception (Moskowitz and Gill, 2013). Some methods of perceiving another person involve inferring +details about them based on observations of their activities. Other types of personal perception happen +more immediately and only need one to view another person. In building a machine that people perceive +as charismatic, a bias in human inference processes can be exploited, namely the fundamental attribution +error: People tend to ascribe observed behaviours to internal factors like personality or character rather than +to external factors such as situational constraints (Colman, 2016). Thus, by mimicking certain appearance +cues, characteristics, and behaviours programmatically to elicit the perception of charisma-associated traits, +it should be possible to build a “charismatic artificial intelligence”. +2.2 +Acquisition of Charismatic Behaviour +In consequence, charismatic behaviour can be acquired and there is a plethora of trainings offered +especially in the field of leadership coaching. Overall, the two key qualities, i. e., factors, introduced by +Tskhay et al. (2018) may be achieved especially through confidence and skills (influence ), emotional +intelligence, and empathy (affability ). As is conclusive from the above (see also Figure 1), they may also +be complemented by a third pillar or factor suggested by Fox Cabane (2013) – mindfulness (presence). +Following Fox Cabane (2013) and Tskhay et al. (2018), such characteristics will elicit an increased +impression of attractiveness, energy, persuasiveness, power, and empathy, and establish rapport between +communication partners. +Focusing on leadership trainings, and translating charismatic behaviour into more concrete tactics, +Antonakis et al. (2012) investigated twelve techniques to increase charisma – the so-called “charismatic +Frontiers +5 + +Schuller et al. +Computational Charisma +leadership tactics” (CLTs). Similar to athletes who follow a training schedule, leaders who aim to become +influential, trustworthy and “leaderlike” are recommended to practice certain tactics regularly. For this +purpose, they examined the nomination speeches of all candidates for president in the U. S. between 1916 +and 2008. The analysis revealed that the use of figurative language, anecdotes, proverbs, and the proper use +of body language had a significant impact on the outcome of the election. Despite humour, repetition, and +talking about sacrifices, such verbal and non-verbal techniques were shown to have the greatest impact +in any context. The nine verbal techniques are metaphors, similes, and analogies; stories and anecdotes; +contrasts; rhetorical questions; expressions of moral conviction; reflections of the group’s sentiments; +three-part lists; the setting of high goals; and conveying confidence that they can be achieved. For example, +the metaphor of being on a boat in a storm may serve as a metaphor for a critical period. Even without +being a born raconteur one can tell the compelling story of taking a deep breath as “anchor” and visualise +the north star for guidance. Another example to motivate followers through a challenging period would be +an anecdote of a personal story, as climbing a mountain when a thunderstorm arises and how the team must +have kept going. In addition, there are three non-verbal techniques: animated voice, facial expressions, and +gestures. Keeping with voice-associated techniques to improve oneself’s charisma, or rather the perception +of charisma in others, it is suggested to speak clearly, fluently, forcefully, and in an engaging manner +that invokes images, energy, and action; moreover, the delivery’s pace and intonation should be varied, +with a general upbeat tempo and an occasionally slowing down to create tension (Tubbs, 2019). Similarly, +Fox Cabane (2013) recommends lowering the tone of one’s voice at the end of each statement and make +frequent pauses while speaking. Despite these strategies to develop or improve charisma, the debate on +whether charisma can be learnt or simply is a trait with set between-subject variation is still ongoing +(Tubbs, 2019). It is of note that, even in human generation of charisma, an attribution error can apply: when +speakers learn to speak with a ‘charismatic voice’, people perceive them as charismatic, even when their +personality does not change. +Hence, very concrete acquired behaviour was shown to lead to a more charismatic behaviour of individuals +and hence, can be installed on who- or whatever to some extent: A person might not be charismatic in +themselves but may appear this way, due to, e. g., speaking in a charismatic way. Note that it was shown +that appearance is not the key factor in ‘charismatic appearance’. Antonakis et al. (2012) observed that +in eight out of ten U. S. presidential races, candidates who deployed such verbal CLTs won more often. +Since communication nowadays is primarily technology-mediated, Ernst et al. (2022) investigated CLT in +a recent prospective meta-analysis on virtual charismatic leadership. The meta-analytic effect of CLTs on +performance (Cohen’s d = 0.52 in-person, k = 4; Cohen’s d = 0.21 overall, k = 10) and engagement in an +extra-role task (Cohen’s d = 0.19 overall; k = 6) indicated large to moderate effects. Yet, for performance +in a virtual context, Cohen’s d ranged from −0.25 to 0.17 (Cohen’s d = 0.01 overall; k = 6). In summary, +disentangling especially phonetic and linguistic markers for charisma may be particularly beneficial in +times of virtual communication in all kind of fields. +In the following section, this article focuses on the specific phonetic, linguistic, and other markers that +are associated with charisma. +3 +FORMAL ASPECTS OF CHARISMA: PHONETIC, LINGUISTIC, AND OTHER +MARKERS +The marking of charisma is definitely multi-modal, and trading relations exist both between and within +modalities – i. e., a more pronounced but not exaggerated marking in one parameter can compensate for +weak signalling in another parameter, see Niebuhr et al. (2020b). Ranking the importance of modalities is +This is a provisional file, not the final typeset article +6 + +Schuller et al. +Computational Charisma +futile and either based on intuition or on one or only a few studies with their specific databases, designs, +and methods; see the ‘7 %-myth’ (Mehrabian and Wiener, 1967) and (Schuller and Batliner, 2014, p. 14). +In the following, we concentrate on speech and language, i. e., on vocal and verbal parameters. This +appears reasonable, given the focus on today’s AI often communicating with users by this modality; in +addition, also when analysing human interaction, spoken language plays a key role. Yet, we will as well +present a sketchy overview of charisma conveyed within the other modalities. We will start with phonetic +markers of charismatic speech in Section 3.1; then follow linguistic markers in Section 3.2, and other +modalities Section 3.3. +The intuitive understanding of charisma is mirrored in equally intuitive characterisations such as attractive, +inspiring, animated, enthusiastic, warm, likeable, or pleasant. In this section, we now report the state of the +art in mapping these terms onto markers that can be measured and counted. +3.1 +Phonetic Markers +Arguably, Rosenberg and Hirschberg described the first sets of studies on charismatic speech (Rosenberg +and Hirschberg, 2009). So far, most of them addressed charisma in politics (candidate speeches) and +Marketing (Zoghaib, 2019) and concentrate on prosody. Related are states and traits such as leadership +(Weninger et al., 2012), competence/trustworthiness (Yang et al., 2020; Davidson, 2021), likability (Weiss +and Burkhardt, 2010; Schuller et al., 2015), and (sexual) attractivity (Trouvain et al., 2020). Charisma can be +tied to performing something, e. g., a candidate speech, and can be switched on and off; see Rosenberg and +Hirschberg (2009): “Speakers were rated as more charismatic when they were delivering a stump speech +(mean rating of 3.28) than when they are being interviewed (2.90).” So, at least the ‘acoustics of charisma’ +are not in an ‘always one-to-one relationship to personality. Of course, this makes it possible for it to be +taught and acquired. An infamous example is Adolf Hitler where the only recording of non-public speech +(https://www.youtube.com/watch?v=WE6mnPmztoQ) reveals a relaxed, almost likeable style +of speaking, much different from his public speeches. We can distinguish ‘dark charisma’ (Fragouli, 2018), +where, e. g., anger can be strongly marked with prosodic means, when this is in accordance with the +audience, from ‘bright charisma’ which can be rather marked prosodically (Barack Obama) or linguistically +and by the context (Mahatma Gandhi); see D’Errico et al. (2013). Even psychopaths can display traits +of bright charisma in discordance to their personality (Weatherby et al., 2016). Intervening factors can +be gender, age, and culture (D’Errico et al., 2013). Laryngealised, ‘creaky’ voice – that is at the same +time indicating very low but also irregular pitch – can make men more cool and attractive (Davidson, +2021), whereas a breathy voice is preferred for women (Greer et al., 2015); this, however, mostly holds for +younger women (Anderson et al., 2014), whereas in business and academia, a creaky voice can be a sign +of competence for both females and men. Klofstad et al. (2016) summarise the experiment on leadership: +“... males with lower-pitched voices tend to be perceived as more attractive, physically stronger, and more +‘dominant’ ... For females, the standard is dichotomous: Women with higher-pitched voices tend to be +considered more attractive, whereas those with lower-pitched voices are perceived as more dominant.”; +see as well Anderson and Klofstad (2012); Klofstad et al. (2015); Zoghaib (2019). Niebuhr et al. (2020a) +compared customer and investor keynotes of Steve Jobs and Mark Zuckerberg. Jobs, commonly perceived +as the more charismatic speaker, produced a higher pitch level (even approaching that of female speakers), +and almost twice the pitch range of Zuckerberg. Jobs used shorter phrases, had fewer disfluencies, and +scored higher in the voice quality metrics. However, he did not exceed Zuckerberg in terms of intensity +variability. Both showed significant differences when addressing customers and investors, showing again +that charisma is situation-dependent. +Frontiers +7 + +Schuller et al. +Computational Charisma +ETHICS +FORMAL MEANS +prosody: +pitch: (not too) high, variation +duration: rather long, variation (rhythm, pauses) +loudness: variation +spectral energy: at low frequencies +voice quality: 'normal‘ (modal); not tense +vowel space: not centralised +linguistics: +vocabulary: elaborated +syntax: elaborated but not too complex +disfluencies: none +pronouns: second person, not first person +adjectives: related to social/moral for affability, +able/agentic for influence +FUNCTIONS +(i) motivation/intention: +leadership, education, health care, persuasion, +personalisation, attractiveness +(ii) models: +three pillars: +warmth, presence, power +two factors: +influence, affability +(iii) perception/impressions: +attractive: averaging, reduced irregularities +energetic: variability +power, warmth, presence: greater vocal space, +voice quality, centre of gravity +rapport (interactive): convergence +APPLICATIONS +humanoids, virtual agents +reaction/interaction/training +monitoring, tutoring, games +… +Figure 2. Overview of concepts and components: three stage FUNCTIONS of charisma; (i) higher +level motivation/intentions employ (ii) models (three pillars and two factors) to create (iii) specific +perception/impressions conveyed via speech by using prosody and linguistics (FORMAL MEANS); this +charisma is then used in APPLICATIONS in human-machine-interactions that ETHICS has to take care +of. +Low-level descriptors of the voice have been shown to convey perceptions of speaker personality traits +(Schuller et al., 2015). The likeability of a person can be predicted using pitch frequency F0, articulation +rate, and spectral parameters such as MFCC (Weiss and Burkhardt, 2010). D’Errico et al. (2013) conducted +a cross-cultural study showing the effects of pitch and the duration of speech pauses on the perception of two +dimensions aggregated from 67 traits and conforming to proactivity-attractiveness and calm-benevolence. +As far as prosody is concerned, we can sum up with Yang et al. (2020): “... voices that are louder, higher, +faster, and with greater fluctuation in pitch were rated as more charismatic.” Now, we ‘only’ have to define +the acceptable range of these prosodic varieties; too great an intensification will certainly yield undesirable +consequences such as the impression of distortion or a lower discriminability, see (Hamilton and Stewart, +1993), (Holz et al., 2021). Moreover, higher pitch range and overall, more variability characterising +charismatic speech, differ from less variability and lower pitch, characterising competence; see again +(Rosenberg and Hirschberg, 2009). Other prosodic parameters as well, and other acoustic parameters +such as spectral distributions, favourable for conveying charisma, can be described as ‘well-balanced’ +and ‘well-shaped’: neither too integrating nor too isolating prosodic phrasing – i. e., not too many but not +too few pauses; more spectral energy at low frequencies (‘full voice’); and more precise articulation (no +centralisation of vowels). A charismatic voice is definitely not characterised by dysphonia, i. e., disordered +voice (hypophonia, i. e., soft voice, or the opposite, hyperphonia, i. e., tense, harsh voice). Based on all +these findings, Niebuhr et al. (2020b) describe a system for charisma profiling. +Figure 2 summarises the formal acoustic aspects dealt with in this subsection and the linguistic aspects +described in Section 3.2; at the same time, it relates these formal aspects to the functional aspects: the +motivation behind creating charismatic agents; the models employed by us; and the perception and +impression that such charismatic agents have on the human interaction partners. These components are +employed to create applications where charisma is harnessed to achieve their specific goals. Ethics has to +assess and possibly restrict the use of charisma in these applications, see Section 6. +This is a provisional file, not the final typeset article +8 + +Schuller et al. +Computational Charisma +3.2 +Linguistic Markers +As far as linguistic markers are concerned, the use of informal language, high occurrence of pronouns, +and avoidance of synonyms can be used to elicit greater warmth, while the opposite holds for formal, +complex language. For pronouns, those that involve the audience, e. g., we and you, are useful for creating +a better first impression (Biancardi et al., 2019). In addition, Rosenberg and Hirschberg (2009) found that +using first-person pronouns positively correlated with the charisma ratings of political candidates in spoken +but not in written form. +Adjectives can serve as markers for the charismatic content of language. They can be clustered via +concepts such as sociability and morality for warmth or ability and agency for competence (Fraser et al., +2021). The usage of adjectives, as opposed to nouns in describing persons, affects the generated impressions, +with nouns conveying a greater sense of defining, immutable traits (Fraser et al., 2022). When referring to +groups of people, the choice of descriptor can evoke various impressions of warmth and competence via +associated stereotypes; consider, e. g., the differences between the elderly, old people, old folks and senior +citizens (Fraser et al., 2022). +The clarity of the intended message also affects the perception of charisma. A lower amount of disfluencies +may make a speaker appear more confident and focused. The negative effect of disfluency is more +pronounced for linguistics than for prosody according to a comparison between speech and transcripts by +Rosenberg and Hirschberg (2009), possibly because the audience may expect it in spoken but not in written +form. Regarding the content of a message, conveying more information is not necessarily beneficial from a +charisma perspective; for speakers with a lower ratio of function to content, words can be rated as more +charismatic, possibly due to higher rhetorical complexity (Rosenberg and Hirschberg, 2009). +Charisma is closely related to being able to influence others, thus, here we also examine linguistic +markers of persuasion. Guerini et al. (2003) propose a taxonomy resting on four pillars: cognitive state, +social relations, emotional state, and interaction context. Here, cognitive elements refer to goals and +beliefs of agents and concepts related to them, social elements deal with power dynamics between relevant +persons, emotional elements can be used to enhance or diminish a message, and contextual elements can +add useful information. Persuasion strategies are then grouped by their objective: inducing a change in +beliefs, and inducing a change in actions. The former can be achieved by appealing, e. g., to the opinions of +experts, to public opinion, or to empirical evidence. The latter may follow a social strategy by appealing to +someone from whom the target derives standards or morals, or to the target’s social image at large. Another +option would be to present imaginary consequences, either positive via promises or negative via threats. A +charismatic agent may select and modify these strategies to improve the success rate. +3.3 +Vision, Touch, and More: Markers in Other Modalities +Charisma without spoken or written language may hardly exist, but obviously, other channels contribute, +e. g., in the visual modality gestures, body pose, facial expressions, and gaze behaviour. While today’s +interaction and communication with AI is largely focused on spoken and written language, future AI is +expected to be doing so multimodally, detecting the user state and responding in real-time to generate a +favourable, human-like impression Biancardi (2017). +Cuddy et al. (2008) investigated how warmth and competence are perceived based on behaviour at +interpersonal and intergroup levels. Smiling, as well as engaging gestures, touch, and mirroring were +found to increase the impression of presence and warmth, while disengagement and creating physical +distance by leaning back or turning away decrease it. Expansive and open body poses, suggesting power +and dominance, resulted in higher impressions of competence. For hand gestures, the use of object adaptors +Frontiers +9 + +Schuller et al. +Computational Charisma +and ideationals (relating to spoken words) improved the speaker competence, while self-adaptors decrease +it (Biancardi et al., 2017). +In general, a speaker’s delivery can have a great influence on their credibility, i. e., a strong delivery is +more likely to lead to high credibility than is a weak one (Holladay and Coombs, 1993). Factors contributing +to a good delivery include eye contact, gestures, and facial expressions (Holladay and Coombs, 1993). This +is not surprising as gestures and facial expressions can innately radiate charisma (Towler, 2003). Since +these characteristics are settled in the visual domain, they have to be considered apart from audio. +Regarding conversational interaction, when a person’s gaze is focused on the conversation partner, this +is a sign of attention and shows both interest in the conversation and commitment to the conversation +partner (Knight and Simmons, 2013; Freeth and Bugembe, 2019). That is, if the gaze is wandering through +the surroundings it may evoke the impression that a person is not fully listening and wants to distract +themselves with seemingly more interesting things. Thus, to recognise the attentiveness and presence in a +conversation, one of the easiest approaches might be to track eye contact and face gaze in general. +Another tool of nonverbal behaviour and conveying (intimate) emotions is the sense of touch. Touch +is crucial for social development and necessary for children in order to grow up healthy (Van Erp and +Toet, 2015; Weiss et al., 2000). Out of all nonverbal modalities, affective touch is our primary channel for +expressing intimate emotions and can effortlessly establish social presence (Van Erp and Toet, 2015). In +addition to distinct emotions like love, anger, and fear, touch can also convey more complex emotional +patterns such as trust, receptivity, and affection (Van Erp and Toet, 2015; Hertenstein et al., 2006, 2009; +Burgoon, 1991). As previously mentioned, charismatic persons radiate characteristics like trustability, +presence, and warmth, which makes affective touch an essential modality next to audio – if appropriate in +the specific situation. +4 +COMPUTATIONAL ASPECTS OF CHARISMA: MODELLING +After analysing the markers of charisma in Section 3, we now deal in this section with the modelling of +charisma from a computational perspective. Automatic recognition of charisma describes the detection of +the sociological and psychological markers for charismatic behaviour using machine learning approaches. +Similarly, the automatic generation of charisma outlines methods for generating auditory or visual +charismatic traits. +4.1 +Automatic Recognition of Charisma +Charisma can be registered via a wide range of modalities, ranging from facial movements and gestures to +speech and physiological attributes like heart rate and skin conductance. Since charisma is an interpersonal +effect, computational analysis can focus either on the sender projecting charisma, on a receiver forming +an impression, or on dyadic interactions between the two (Wang and Chanel, 2021). Here, we take up +the stated sociological, psychological, and popular science perspective and translate it into computational +aspects of phonetics, linguistics, and other modalities in automatic recognition of charisma. +4.1.1 +Audio +The quality of speech transmission has an impact on the perception of charisma. Gallardo (2018) +investigated the effect of bandwidth on perception of male and female speakers selected for extreme +values of warmth-attractiveness (WAAT). Shifts in traits such as maturity, sympathy, and confidence for +males and competence for females can be explained with alterations of F0 resulting from the narrow-band +transmission. Another study (Gallardo and Sanchez-Iborra, 2019) assessed the impact of various encoding +and transmission properties on the binary classification of warmth and attractiveness via Random Forest +This is a provisional file, not the final typeset article +10 + +Schuller et al. +Computational Charisma +and Support Vector Machines. Narrowband codecs were found to degrade performance to near chance +level. Packet loss also confused the classifiers, while jitter had minor effects. +In the early years of prosody research in automatic speech processing (Batliner and M¨obius, 2020), +the focus was on detecting and classifying linguistic phenomena such as phrase accents, boundaries, +disfluencies, sentence modality, and dialogue acts; such explicit modelling was then superseded by implicit +modelling in AI approaches. Yet, it might gain momentum in our context, when we want to model markers +for charisma. Asking questions during a conversation indicates that a person is listening and interested +in what the conversation partner says; thus, it can indicate the presence in a conversation. In this context, +acoustic and phonetic features are deployed, at which lexical features can also be crucial for the correct +identification of declarative questions (Ando et al., 2018). Furthermore, recurrent neural networks (RNNs) +are applied in order to obtain the high-level contextual information over time (Tang et al., 2016). +Before asking a question, it can also be beneficial to make a short pause, in order to show that one thinks +about what the conversation partner has said, before giving an answer. This can convince the other person +that one is listening carefully and is present in the conversation. Trouvain and Werner (2022) define these +types of pauses as “gaps at turn changes in conversations” and do not regard them as typical speech pauses +that are defined as “pauses in connected speech section”. Regarding speech production and the temporal +structure of speech, pauses also play a crucial role (Trouvain and Werner, 2022). We have to distinguish +between silent pauses and filled pauses such as “uh” or “uhm” (Batliner et al., 1995; Bilac et al., 2017; +Trouvain and Werner, 2022). Bilac et al. (2017) extract Mel-frequency cepstral coefficients (MFCC) audio +features and apply support vector machines (SVMs) and random forest (RF) as classification methods. +Silent speech pauses and silence in audio can long since also be automatically detected, though (Xu et al., +2020; Iqbal et al., 2018). +Power, described by Fox Cabane (2013) as high competence due to skills, abilities, or intelligence, +can mainly be detected from audio by analysis of features related to fluency, such as speech rate and +pauses. Luzardo et al. (2014) perform an automated evaluation of student presentation skills and found a +formant-based detection of filled pauses useful for classifying the overall quality of presentations. Further, +they observed that speech rate is positively correlated with a speaker’s self-confidence. A similar approach +based on detecting filled pauses is taken by Ochoa et al. (2018) in the audio modality of their automatic +feedback system for presentation skills. +The mimicry of a conversation partner can help establish a connection in dyadic interactions. This may +happen either subconsciously, or deliberately to project greater warmth and presence. Amiriparian et al. +(2019) investigate ‘synchronisation’ (i. e., the mutual adaptation of conversation partners) in such dyadic +conversations, using acoustic and linguistic features on a dataset with 394 speakers of six different cultures. +For the acoustic analysis, both handcrafted EGEMAPS and deep DEEPSPECTRUM features are extracted. +Autoencoders are then used to measure the degree of synchronicity by training on one person and then +reconstructing on their conversation partner. As the conversation continues, the reconstruction error tends +to decrease across the six cultures, indicating that speakers are mutually adapting to each other. +4.1.2 +Language +A textual analysis lacks the information of prosody from a speech signal and must instead focus on +linguistic cues. For purely text-based empathy and warmth recognition, we highlight two applications here: +mental health support and stereotyping in social media. For presence, we also examine synchronicity in +conversations. +Frontiers +11 + +Schuller et al. +Computational Charisma +Sharma et al. (2020) investigated empathy in the context of seeker-response interactions on text-based +support platforms. Their framework, adapted for asynchronous communication, includes three mechanisms: +emotional reactions to the seeker, interpretations conveying understanding, and explorations to improve +understanding. A dataset of interactions collected from TalkLife and mental health subreddits was annotated +in terms of empathy and rationales (text snippets motivating the empathy annotation). Then, a multi-task +model based on two pre-trained ROBERTA encoders acting on seeker and response posts and a single +attention layer combining their embeddings was proposed. The inclusion of seeker post and attention was +found beneficial while fine-tuning the encoders and adding the rationale task gave minor improvements. +Stereotypes are frequently encountered in social media posts, and may positively or negatively shape +opinions on groups. Fraser et al. (2022) apply the warmth and competence model to stereotype identification +by constructing a synthetic training set and building a model that can identify stereotypes in crowd-sourced +data. First, using a seed lexicon, polar directions for warmth and competence are defined in a word +embedding subspace. Then, sentences are created via templates filled with words of known polarity +from the lexicon. For the word embeddings, ROBERTA is used, with GLOVE vectors serving as the +baseline. A combination of ROBERTA embeddings with intermediate dimensionality reduction via +partial Least-Squares performed best. Also, the generation of sentences combining both warmth and +competence-associated words improved accuracy by increasing the orthogonality of training pairs. +Amiriparian et al. (2019) use WORD2VEC to extract embeddings. The conversations are split into two +parts, and the cosine similarity between their embeddings is computed. In addition, the co-occurrence of +words between subjects in each part is counted and normalised with the total number of words. The word +embeddings showed little synchronisation (i. e., mutual adaptation of conversation partners) compared to +the audio features, possibly indicating that the effect was happening too gradually on the linguistic level +to measure during the short conversations. Word usage showed a clearer correlation but strongly differed +across cultures, being most pronounced in British subjects. +4.1.3 +Other Modalities +In order to recognise a charismatic person, it is obvious to also consider other modalities, such as videos, +images, and tactile sensors, as we mentioned earlier. In this context, videos and images might be especially +beneficial for recognising how present and involved a person is in conversations by considering eye contact +and facial expressions. +Some studies already try to use eye tracking in order to analyse attention and gaze patterns during social +interactions (Rogers et al., 2018; Vehlen et al., 2021). Rogers et al. (2018) also point out that some people +show a preference towards mouth gaze, some for eye gaze, and others tend to vary the extent of their +gaze between eyes and mouth. The authors apply a standard remote infrared eye tracker, consisting of +an infrared sensor and a corresponding camera. Vehlen et al. (2021), on the other hand, employ special +eye-tracking glasses enabling the opportunity for real-world experiments. In order to avoid expensive +high-end processing devices, Zdarsky et al. (2021) introduce a convolutional neural network (CNN) relying +on video frames from low-cost web cameras. Another study also aims at making eye tracking available for +everyone owning a mobile device with a camera (Krafka et al., 2016). +Besides our eyes, facial expressions are a very important tool to express excitement and emotions. Erez +et al. (2008) state that charismatic leaders exhibit more aroused behaviours than non-charismatic leaders. +For instance, smiles are arguably among the most visible and frequent markers and can convey a feeling +of warmth and intimacy but also of fear or compliance (Awamleh et al., 2003). There are already several +approaches for automatic facial expression recognition (FER), most of them utilising deep learning (DL) +and some sort of CNN in particular (Li and Deng, 2020; Revina and Emmanuel, 2021; Minaee et al., 2021; +This is a provisional file, not the final typeset article +12 + +Schuller et al. +Computational Charisma +Wang et al., 2020). The rough pipeline is to feed an input face image to a trained network and obtain a +probability for a certain emotion category, such as happy or sad. In addition to using CNNs as the basic +architecture blocks, there are extensions to improve performance, e. g., adding an attention mechanism to +the network (Li et al., 2018). +4.2 +Automatic Generation of Charisma +We can approach the task of automatically generating charisma in two different ways. On the one hand, +we can use an approach to try to imitate the charismatic characteristics of people previously defined in the +literature. Charismatic persons are – as outlined above – characterised by a certain way of speaking (e. g., +pitch, duration, or rhythm during the conversation). The characteristics assigned to charismatic individuals +can be obtained from previous works, such as Davidson (2021) or Klofstad et al. (2016) and the many +listed above, and thus represent an expert-based definition. Using this information in combination with +generative machine learning methods, precisely these properties can be enforced when generating speech, +resulting in a more charismatic perception. On the other hand, methods such as reinforcement learning can +also be used to generate charisma. The advantage of using this method is that new, previously unknown +charismatic factors can be learnt. +4.2.1 +Expert-based Generation of Charisma +To simulate charismatic behaviour, the previously identified building blocks must be taken into account +when generating spoken language (or other modalities). In recent years, progress has been made in two +main areas: First, generative methods (Borsos et al., 2022) for creating completely new audio outputs, +and second, constrained audio generation, as well as style transfer, approaches, e. g., (Zhang et al., 2019; +Huzaifah bin Md Shahrin and Wyse, 2020; Manzelli et al., 2018), where an existing audio file is stylistically +adapted to pre-defined properties. +The latest results of generative methods for speech such as AudioLM are almost indistinguishable from +real speech by humans (Borsos et al., 2022). The high audio quality of the generated samples paves the +path for further charismatic audio generation. Based on this, style control and style transfer approaches can +be used to change certain features of the voice (Zhang et al., 2019; Huzaifah bin Md Shahrin and Wyse, +2020). For example, Baird et al. (2019) analysed if deep generative audio can be emotional. In doing so, +they changed pitch as an important speech characteristic. In a similar way, other features can be adapted, +leading to a more charismatic voice. +In addition to the audio modality, this approach can be extended to other modalities, such as video or +text. Based on findings from previous work investigating which features are perceived as particularly +charismatic in the respective modality, these constraints can be considered in generative methods. For +example, Ghorbani et al. (2022) explore gesture generation from speech. Based on this work, charismatic +gesture features can be taken into account, resulting in an overall charismatic perception of an AI such as +by a virtual agent. +4.2.2 +Learning-based Generation of Charisma +Automatically generating charisma can also be formulated as a weakly supervised machine learning task. +For example, reinforcement learning methods have become increasingly popular in recent years in audio +processing (and beyond) and are based on rewarding desired and punishing undesired behaviours (Latif +et al., 2022). +Applied to charisma generation, various characteristics of the speech are exploratively tried during +generation. In doing so, the reward function includes usually indirect feedback from users on how +charismatic the generated output is perceived. For example, pitch shifting, ranging from a low up to a +Frontiers +13 + +Schuller et al. +Computational Charisma +very high pitch, can be explored. Taking user feedback into account, the optimal pitch that is perceived as +most charismatic (or seems to be so, as it best solves a task that is best solved with high charisma) can +be determined. In addition to direct user feedback, automatic charisma recognition approaches can be +applied as a reward function to evaluate whether the generated behaviour is charismatic. In the context of +generating emotional speech, Liu et al. (2021) present such a paradigm. In a reinforcement learning setting, +they train an automatic text-to-speech model to generate speech with emotions that can be discriminated by +an automatic speech emotion recognition model. Another advantage of reinforcement learning is that new, +so far unknown charismatic traits can be discovered using this method. This could range from obvious +charismatic traits to entirely new charismatic behaviours that are as yet undiscovered in the literature and +no one has thought of before, e. g., as in Baker et al. (2019) in a different context. +Obviosuly, in addition to the audio modality, reinforcement learning for charisma generation can be +similarly applied to video and text and beyond. For instance, it might be beneficial for robots or virtual +humans/agents to imitate charismatic gestures and appearance in general. In another use case, Won et al. +(2021) have already physically simulated humanoids performing competitive two-player sports, boxing +and fencing, in a high degree-of-freedom environment. The applied control policies generated responsive +and natural-looking behaviours (Won et al., 2021). +5 +MOTIVATION AND APPLICATIONS OF COMPUTATIONAL CHARISMA +A general motivation of charisma as a feature has been addressed in the introduction – we now, however, +turn to more specific examples of application use cases. +As outlined above, charisma is often associated with charm and ‘magnetism’, empowering to influence +and inspire. Even if AI is not ‘experiencing’ or showing charisma as humans could, it can be trained or +programmed to appear charismatic. This leads to a plethora of use cases which motivate its realisation, but +also often come with a number of risks and dangers. Below, we list examples broadly grouped. +Let us first consider different aspects of communication: AI empowered with charisma may lead +conversations with humans in potentially more convincing ways, engaging them, and potentially influence +them towards decisions in favour of the AI’s goals. Similarly, it can simulate empathy and in general +be perceived as more intelligent due to socioemotional intelligence skills. Charimsatic techniques may +improve everyday conversations by creating an emotional connection within communication partners or +followers, make someone appear more powerful, competent, and worthy of respect Antonakis et al. (2012). +This holds in conversations, but also in public speeches via means of AI in the future – potentially to +large audiences via the internet or in real-life settings. In automatic translation, AI could help translate +charismatically or preserve charismatic traits in the target language. If AI is used for communication +analysis, such as in mediation between human conversational partners, it can sense who is being more +charismatic, more influencing, or more affected by the other party in a somewhat quantitative and subjective +neutral manner. +Let us now turn to aspects of leadership: The great majority of use cases in research but also real-world +applications is the training of charisma for enhanced leadership. More specifically, leaders in a variety of +fields as politics, religion, or business highly benefit from being persuasive and likeable to achieve specific +team goals and overcome potential resistance within employees or party members. Leaders may benefit +greatly to win the trust of followers, manage delicate operations, punish and reward, and achieve their goals +(Antonakis et al., 2012). Levay (2010) even argues that charismatic leaders are invariably proponents of +change. Charisma may help AI inspire and motivate teams – including encouraging and guidance through +difficult challenges. Beyond, charisma can help AI to build and bind teams and communities in the first +This is a provisional file, not the final typeset article +14 + +Schuller et al. +Computational Charisma +place. Especially in times of remote work and digital delivered social interaction as video calls and emails, +such qualities of team coherence and trust and commitment are highly challenged. More specifically, +team leaders may be fed back easily in their communication style with an AI that recognises charismatic +language and enhances team outcomes, putting the team members at ease and comfort by simultaneously +persuading them of a new idea. However, obtaining charisma – including by humans that are trained on +charisma skills by AI – should not be abused for unethical goals (see section ethics of computational +charisma below). Furthermore, a charismatic AI could also recruit new staff potentially more successfully +than a non-charismatic one. However, it can also help it in negotiations within teams or with other parties +in persuasive ways. If AI assists in decision making, charisma may help it to get the decisions across to the +humans it presents it to. +Healthcare next appears suited field for charismatic AI: Be it for mental health or general health care +– charismatic AI could provide a compassionate, empathetic, and reassurance and support providing +communication and assistance during diagnosis or interventions and therapy. Recognising charisma can +also provide benefits for improving mental health. Mental health issues are widespread, affecting nearly one +in five people worldwide (Holmes et al., 2018) and incurring enormous human suffering and economic costs. +The majority of patients prefer therapy to medication (Holmes et al., 2018), requiring the development +of new solutions to improve the effectiveness of treatment. Depending on the application, those systems +may either work in real-time for live session support or in an offline fashion for reviewing progress. A +system that can process interactions and estimate the charismatic content may be a valuable tool for +training professional practitioners. An effective therapist or counsellor can provide a sense of engagement +and empathy to the patient, which in terms of charismatic dimensions involves both warmth (to show +sympathy) and competence (to comprehend and engage with a patient’s problems). In particular, this holds +in case patients are reluctant or not sufficiently committed to overcome adverse feelings that sometime go +along with behaviour change as for instance, confronting oneself with an anxiety-eliciting situation or the +acquisition of new behaviours that feel initially uncomfortable. Both, therapists and clients could benefit +from the rapport, empathy, believe of the ability to help, or persuasiveness of the therapist that go along +with charisma. An AI solution that can help review and train these skills will likely also be beneficial for +the increasingly popular digital support platforms, to improve the qualification of responders (Sharma et al., +2020). Although therapists are usually trained in providing ease, comfort, and being empathetic and receive +supervision in doing so, the deployed speech in regard of influence and affability may remain neglected, +although there is a great potential. Providing AI-generated automated feedback on the interaction and +conversation style between therapist and client may improve the communication style and hence, therapy +outcomes to a great extent. Considering the human-to-human conversation mediation alluded to above, this +could include couple or other counseling endowed with active listening, and empathetic moderation. +Beside such fields, numerous other applications may benefit from charisma as an omnipotent quality: In +education, a charismatic AI may be more engaging and captivating for students taught by it. Furthermore, as +a coach and mentor, charismatic AI could be more motivating. However, an AI that can sense and measure +charisma can also help in tutoring about charisma, i. e., teach humans to be charismatic by monitoring +their progress. Further, in customer service, marketing and sales, charismatic AI could provide friendly +and likable service, but also persuade customers. In social media, charisma-empowered AI could interact +with the social media users and generate a large group of followers, e. g., to influence opinions or provide +positive brand connotation. This would include charismatic interaction with followers, responses to public +reactions, or creation of new content in engaging ways. AI that has an understanding of charisma can also +analyse charismatic behaviour and skills of users – be it, e. g., for scientific analyses or identifying potential +influencers early on. As to gaming, non-player-characters (NPCs) driven by AI could be charismatic +Frontiers +15 + +Schuller et al. +Computational Charisma +in oncoming games leading to an increasingly immersive gaming sensation. When it comes to event +management and hospitality, charisma-empowered AI could provide engaging interaction with attendees of +future virtual events. These may encompass a wide variety of events reaching from online conferences +and workshops to virtual fair trades, virtual tours of galleries, museums, real-estate properties, or virtual +concerts, festivals, parties, and other entertainment events. In particular, this could even include fundraising +at suited events, where a charismatic AI could interact with donors persuasively. Beyond, hospitality +at virtual or real-world occasions including checking guests at hotels in and out, question answering, +recommendation giving, and furthermore, could be realised more charismatic by accordingly enabling +future AIs. +More generally, any form of embodied or virtual AI – e. g., assistive or companion agents – could +largely benefit from charismatic skills in the interaction with their users. This could help them in their +communication and motivation as well as companionship including with lonely individuals. Across use +cases, charismatic AI may be better positioned to personalise services to users by gaining access to their +individual preferences, context, and history. +6 +ETHICS OF COMPUTATIONAL CHARISMA +Of course, we do not aim at dark charisma for appealing to the baser human instinct; moreover, we do not +want to harness ‘deceiving charisma’, i. e., bright charisma for achieving goals that are per se unethical. As +for spoken language as modality, a cover term might be ‘emotional speech’ in the sense of adding more +credibility and user attachment to human-computer interaction. Charisma is thus not a goal in itself, but +a means to better achieve its goal. Bright charismatic speech in itself cannot be unethical or ethical – it +always depends on the application we are envisioning. Thus, out of all the (ethical) cornerstones relevant +for applications defined in (Batliner et al., 2022b), most might be ‘secondary’ for charisma, i. e., depend +on the (type of) applications that use charismatic speech to pursue its goals. Yet, by providing charisma +as a tool, we have to account for the possibility that this tool can be used for ‘dark goals’ or, simply, that +the outcome is not favourable. Thus, ethical requirements can be higher. In the same way, dealing with +vulnerable groups of course puts higher requirements on ethics, as for instance, privacy and avoiding harm +are concerned (Batliner et al., 2022a). +A self-learning system can adapt to templates and users the same way as the chatbot Tay learnt racist +language from its users (Wolf et al., 2017). This is a problem for every empathic virtual agent (Pamungkas, +2019). Both dark charisma and bright charisma employed for dark goals can be created unwillingly or on +purpose. In the first case, not only do algorithmic measures have to be taken, and in both cases, society has +to define red lines against them. Guerini and Stock (2005) reason about different capabilities of persuasive +agents in case of ethical dilemmas (conflicting goals): (i) detect them and pass them on to a human; (ii) +compute a possible conduct and pass this on to a human for final decision; (iii) make own decisions. So +far, we cannot envision artificial agents capable of doing this kind of reasoning in a reliable way. Thus, +two principles should be followed: first, ethical dilemmas should be avoided by design, and if they are +encountered, the decision has to be passed on to a human. +The most prominent specific ethical requirement might be disclosure of automation (Mohammad, 2022), +belonging to the ethical cornerstones transparency and accountability: An according charismatic AI +application has to make clear that the user is not interacting with some human being but with a computer. +This must not be done in the small print but in a way that is really visible to the user. Transparency and +accountability seem to be the primary cornerstones that impact autonomy, i. e., provide the possibility for +the user to be aware of the artificial charisma the application / the agent is equipped with. Then comes +This is a provisional file, not the final typeset article +16 + +Schuller et al. +Computational Charisma +intrusive: ethical requirements are higher, the more intrusive the application is. Carlos Montemayor et al. +(2022) claim that genuine empathy in healthcare is not possible for AI because it cannot be really emotional. +Yet, a charismatic agent might at least act as-if but we have to make it clear towards the patients that +the AI (robots, avatars) is artificial and does not have emotions or empathy itself, in order to prevent this +erroneous and dangerous attribution that even can lead the user to fall in love with such a charismatic +artificial agent. The illusion of humanness can create the ‘uncanny valley’ effect (Mori et al., 2012) when +emotional/charismatic agents are close to human but still not close enough, by that irritating the human +interaction partner. Both this uncanny valley and a too perfect humanness might be avoided by explicitly +mentioning the artificial character of the agent, or by creating it in such a way that its non-human character +is evident. Note that some authors argue, under certain premises, in favour of anthropomorphous robots +(Darling, 2017) or deception-capable robots (Isaac and Bridewell, 2017). Although possible benefits might +be evident, it is not clear at all how any dishonest use of such robots – or, in our case, charismatic agents - +could be prevented if not banned from the beginning. +7 +CONCLUSION AND OUTLOOK +We discussed a ‘blueprint’ for a charisma-savvy Artificial Intelligence – able to analyse human charisma +and generate charismatic behaviour itself. To this end, we introduced the origin and concept of charisma. We +then discussed functional aspects of charsima by psychological models, mainly introducing two concepts +based on the factors influence and affability as well as the theoretical concept of power, presence, and +warmth as pillars of charisma. We argued that charismatic behaviour can be acquired and presented a brief +summary of the literature on its acquisition. We then moved to formal aspects giving specific details on +charisma as portrayed in spoken language. The choice to first focus on this modality was made, as today’s +AI largely interacts via spoken language with humans, and other modalities such as facial expression or +body posture are yet to gain relevance. We further outlined computational aspects of modelling charisma. +Here, we summarised the small body of literature on the automatic recognition and generation of charisma +for audio, language, but also other modalities. As to the generation of charisma, we highlighted two +avenues: First, based on the findings in the literature summarised up to that point in this article, one could +design a charisma-empowered AI based on expert knowledge. Alternatively, weakly supervised machine +learning could be exploited by either active learning methods questioning users about charisma skills +of an AI or even by learning reinforced. In the latter, an AI would gain charismatic skills – potentially +even such unknown to date to humans – that would help better accomplish its goal by interacting with +users in real-world tasks – ideally at scale. We then moved towards the plethora of potential use-cases of +charisma-enabled AI, before introducing major ethical concepts to be considered at all times. +Given the state-of-knowledge on charisma and the state-of-play in today’s AI, it seems perfectly possible +to endow AI with charisma skills. Currently, the literature on using machine learning for the recognition +or generation of charisma or traits thereof largely focuses on the individual in isolation related to fields +such as Affective Computing. However, disciplines such as Social Signal Processing moved also the +consideration of the interplay between communicating parties into the foreground, which can be crucial for +modelling charisma, e. g., when it comes to mimicry. Further, audio, text, and video have so far been mostly +considered, but touch, and more general haptics, have been touched upon as well. In the future, other +modalities including smell, and further biological signals could be included. Further, the loop between +recognition and generation of charismatic behaviour might be fully closed learning charismatic input/output +of an AI ‘end-to-end’. +Overall, we envision a plethora of use-cases with great value of charsima-savvy AI. However, weakly- +supervised AI learning from large data may easily lead to new charismatic behaviours found by AI +Frontiers +17 + +Schuller et al. +Computational Charisma +potentially reflecting back on human-to-human charismatic behaviour. Charismatic AI may also empower +‘dark’ purposes or lead to negative effects such as AI influencing voters, e-shoppers, getting users addicted +to or fall in love with the AI, and many more. As a community, we have to always contribute best to +assure positive usage and the protection of users – including in particular also from a technical end. A +blueprint therefore might be considerably more challenging. Let us be best prepared for the rapid advent of +charismatic AI. +CONFLICT OF INTEREST STATEMENT +The authors declare that the research was conducted in the absence of any commercial or financial +relationships that could be construed as a potential conflict of interest. +AUTHOR CONTRIBUTIONS +All authors contributed equally to writing, revising, and editing the manuscript and approved the final +version of the manuscript. +FUNDING +This work is supported by the DFG’s Reinhart Koselleck project No. 442218748 (AUDI0NOMOUS). +REFERENCES +Amiriparian, S., Han, J., Schmitt, M., Baird, A., Mallol-Ragolta, A., Milling, M., et al. (2019). +Synchronization in interpersonal speech. Frontiers in Robotics and AI 6 +Anderson, R. C. and Klofstad, C. A. (2012). Preference for Leaders with Masculine Voices Holds in the +Case of Feminine Leadership Roles. Plos one 7, e51216 +Anderson, R. C., Klofstad, C. A., Mayew, W. J., and Venkatachalam, M. (2014). Vocal Fry May Undermine +the Success of Young Women in the Labor Market. Plos one 9, e97506 +Ando, A., Asakawa, R., Masumura, R., Kamiyama, H., Kobashikawa, S., and Aono, Y. (2018). +Automatic question detection from acoustic and phonetic features using feature-wise pre-training. +In INTERSPEECH. 1731–1735 +Antonakis, J. (2012). Transformational and charismatic leadership. The nature of leadership , 256–288 +Antonakis, J. and Dalgas, O. (2009). Predicting elections: Child’s play! Science 323, 1183. doi:10.1126/ +science.1167748 +Antonakis, J., Fenley, M., and Liechti, S. (2012). Learning Charisma Transform yourself into the person +others want to follow. Tech. rep., Academy of Management Learning and Education +Awamleh, R. and Gardner, W. L. (1999). Perceptions of leader charisma and effectiveness: The effects of +vision content, delivery, and organizational performance. Leadership Quarterly 10, 345–373 +Awamleh, R. et al. (2003). +Towards a model of charismatic non-verbal impression management. +International Business & Economics Research Journal (IBER) 2 +Baird, A., Amiriparian, S., and Schuller, B. (2019). Can deep generative audio be emotional? towards an +approach for personalised emotional audio generation. In 2019 IEEE 21st International Workshop on +Multimedia Signal Processing (MMSP) (IEEE), 1–5 +Baker, B., Kanitscheider, I., Markov, T., Wu, Y., Powell, G., McGrew, B., et al. (2019). Emergent tool use +from multi-agent autocurricula. arXiv preprint arXiv:1909.07528 +Batliner, A., Hantke, S., and Schuller, B. (2022a). Ethics and good practice in computational paralinguistics. +IEEE Transactions on Affective Computing 13, 1236–1253. doi:10.1109/taffc.2020.3021015 +This is a provisional file, not the final typeset article +18 + +Schuller et al. +Computational Charisma +Batliner, A., Kießling, A., Burger, S., and N¨oth, E. (1995). Filled Pauses in Spontaneous Speech. In Proc. +of ICPhS. vol. 3, 472–475 +Batliner, A. and M¨obius, B. (2020). Prosody in Automatic Speech Processing. In The Oxford Handbook of +Language Prosody, eds. C. Gussenhoven and A. Chen (Oxford, UK: Oxford University Press). 633–645 +Batliner, A., Neumann, M., Burkhardt, F., Baird, A., Meyer, S., Vu, N. T., et al. (2022b). Ethical awareness +in paralinguistics: A taxonomy of applications. International Journal of Human–Computer Interaction +0, 1–18. doi:10.1080/10447318.2022.2140385 +Biancardi, B. (2017). Towards a computational model for first impressions generation. In Proceedings of +the 19th ACM International Conference on Multimodal Interaction (New York, NY, USA: Association +for Computing Machinery), ICMI ’17, 628–632. doi:10.1145/3136755.3137031 +Biancardi, B., Cafaro, A., and Pelachaud, C. (2017). +Analyzing first impressions of warmth and +competence from observable nonverbal cues in expert-novice interactions. +In Proceedings of the +19th ACM International Conference on Multimodal Interaction (New York, NY, USA: Association for +Computing Machinery), ICMI ’17, 341–349. doi:10.1145/3136755.3136779 +Biancardi, B., Wang, C., Mancini, M., Cafaro, A., Chanel, G., and Pelachaud, C. (2019). A computational +model for managing impressions of an embodied conversational agent in real-time. +In 2019 8th +International Conference on Affective Computing and Intelligent Interaction (ACII). 1–7. doi:10.1109/ +ACII.2019.8925495 +Bilac, M., Chamoux, M., and Lim, A. (2017). Gaze and filled pause detection for smooth human-robot +conversations. In 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids) +(IEEE), 297–304 +Borsos, Z., Marinier, R., Vincent, D., Kharitonov, E., Pietquin, O., Sharifi, M., et al. (2022). Audiolm: a +language modeling approach to audio generation. arXiv preprint arXiv:2209.03143 +Burgoon, J. K. (1991). Relational message interpretations of touch, conversational distance, and posture. +Journal of Nonverbal behavior 15, 233–259 +Burke, K. and Brinkerhoff, M. B. (1981). Capturing charisma: Notes on an elusive concept. Journal for +the Scientific Study of Religion 20, 274 +Carlos Montemayor, Jodi Halpern, and Abrol Fairweather (2022). In principle obstacles for empathic AI: +why we can’t replace human empathy in healthcare. AI & SOCIETY 37, 1353–1359 +Colman, A. M. (2016). Game theory and experimental games: The study of strategic interaction (Elsevier) +Conger, J. A., Kanungo, R. N., Menon, S. T., and Mathur, P. (2009). Measuring charisma: Dimensionality +and validity of the conger-kanungo scale of charismatic leadership. Canadian Journal of Administrative +Sciences-revue Canadienne Des Sciences De L Administration 14, 290–301 +Cuddy, A. J. C., Fiske, S. T., and Glick, P. (2008). Warmth and competence as universal dimensions of +social perception: The stereotype content model and the bias map. Advances in experimental social +psychology 40, 61–149 +Darling, K. (2017). “Who’s Johnny?” Anthropomorphic Framing in Human-Robot Interaction, Integration, +and Policy. In Robot Ethics 2.0: From Autonomous Cars to Artificial Intelligence, eds. P. Lin, K. Abney, +and R. Jenkins (Oxford, UK: Oxford University Press). 1–22 +Davidson, L. (2021). The versatility of creaky phonation: Segmental, prosodic, and sociolinguistic uses in +the world’s languages. WIREs Cogn Sci. 12, e1547 +D’Errico, F., Signorello, R., Demolin, D., and Poggi, I. (2013). The perception of charisma from voice: A +cross-cultural study. In 2013 Humaine Association Conference on Affective Computing and Intelligent +Interaction. 552–557. doi:10.1109/ACII.2013.97 +Frontiers +19 + +Schuller et al. +Computational Charisma +Erez, A., Misangyi, V. F., Johnson, D. E., LePine, M. A., and Halverson, K. C. (2008). Stirring the hearts +of followers: Charismatic leadership as the transferal of affect. Journal of applied psychology 93, 602 +Ernst, B. A., Banks, G. C., Loignon, A. C., Frear, K. A., Williams, C. E., Arciniega, L. M., et al. (2022). +Virtual charismatic leadership and signaling theory: A prospective meta-analysis in five countries. The +Leadership Quarterly 33, 101541. doi:10.1016/j.leaqua.2021.101541 +Ferris, G. R., Treadway, D. C., Kolodinsky, R. W., Hochwarter, W. A., Kacmar, C. J., Douglas, C., et al. +(2005). Development and validation of the political skill inventory. Journal of management 31, 126–152 +Fiske, S. T., Cuddy, A. J., and Glick, P. (2007). Universal dimensions of social cognition: Warmth and +competence. Trends in cognitive sciences 11, 77–83 +Fox Cabane, O. (2013). The Charisma Myth: How Anyone Can Master the Art and Science of Personal +Magnetism, vol. 1 (Portfolio Trade) +Fragouli, E. (2018). The dark-side of charisma and charismatic leadership. business management review 9, +298–307 +Fraser, K. C., Kiritchenko, S., and Nejadgholi, I. (2022). Computational modeling of stereotype content in +text. Frontiers in Artificial Intelligence 5. doi:10.3389/frai.2022.826207 +[Dataset] Fraser, K. C., Nejadgholi, I., and Kiritchenko, S. (2021). +Understanding and countering +stereotypes: A computational approach to the stereotype content model. doi:10.48550/ARXIV.2106. +02596 +Freeth, M. and Bugembe, P. (2019). Social partner gaze direction and conversational phase; factors +affecting social attention during face-to-face conversations in autistic adults? Autism 23, 503–513 +Gallardo, L. F. (2018). Effects of transmitted speech bandwidth on subjective assessments of speaker +characteristics. In 2018 Tenth International Conference on Quality of Multimedia Experience (QoMEX). +1–5. doi:10.1109/QoMEX.2018.8463395 +Gallardo, L. F. and Sanchez-Iborra, R. (2019). On the impact of voice encoding and transmission on the +predictions of speaker warmth and attractiveness. ACM Trans. Knowl. Discov. Data 13. doi:10.1145/ +3332146 +Ghorbani, S., Ferstl, Y., Holden, D., Troje, N. F., and Carbonneau, M.-A. (2022). Zeroeggs: Zero-shot +example-based gesture generation from speech. arXiv preprint arXiv:2209.07556 +Greer, S., , and Winters, S. (2015). The perception of coolness: Differences in evaluating voice quality +in male and female speakers. In Proceedings of the 18th international congress of phonetic sciences +(Glasgow, Scotland), 1–102 +Guerini, M. and Stock, O. (2005). Toward ethical persuasive agents. In Proceedings of the International +Joint Conference of Artificial Itelligence Workshop on Computational Models of Natural Argument +(Edinburgh,Scottland), 1–5 +Guerini, M., Stock, O., and Zancanaro, M. (2003). Persuasion models for intelligent interfaces. In +Proceedings of the IJCAI Workshop on Computational Models of Natural Argument (Acapulco, Mexico), +1–6 +Hamilton, M. A. and Stewart, B. L. (1993). Extending an information processing model of language +intensity effects. Communication Quarterly 41, 231–246 +Hertenstein, M. J., Holmes, R., McCullough, M., and Keltner, D. (2009). The communication of emotion +via touch. Emotion 9, 566 +Hertenstein, M. J., Keltner, D., App, B., Bulleit, B. A., and Jaskolka, A. R. (2006). Touch communicates +distinct emotions. Emotion 6, 528 +Holladay, S. J. and Coombs, W. T. (1993). Communicating visions: An exploration of the role of delivery +in the creation of leader charisma. Management Communication Quarterly 6, 405–427 +This is a provisional file, not the final typeset article +20 + +Schuller et al. +Computational Charisma +Holmes, E. A., Ghaderi, A., Harmer, C. J., Ramchandani, P. G., Cuijpers, P., Morrison, A. P., et al. (2018). +The lancet psychiatry commission on psychological treatments research in tomorrow’s science. The +Lancet Psychiatry 5, 237–286 +Holz, N., Larrouy-Maestri, P., and Poeppel, D. (2021). The paradoxical role of emotional intensity in the +perception of vocal affect. Nature, Scientific Reports 11, 9663 +House, R. J. (1976). A 1976 Theory of Charismatic Leadership. Working Paper Series 76-06. Tech. rep., +ERIC +Huzaifah bin Md Shahrin, M. and Wyse, L. (2020). Applying visual domain style transfer and texture +synthesis techniques to audio: Insights and challenges. Neural Comput. Appl. 32, 1051–1065. doi:10. +1007/s00521-019-04053-8 +Iqbal, T., Kong, Q., Plumbley, M. D., and Wang, W. (2018). +General-purpose audio tagging from +noisy labels using convolutional neural networks. In Proceedings of the Detection and Classification +of Acoustic Scenes and Events 2018 Workshop (DCASE2018 (Tampere University of Technology), +212–216 +Isaac, A. M. and Bridewell, W. (2017). White Lies on Silver Tongues: Why Robots Need to deceive (and +how). In Robot Ethics 2.0: From Autonomous Cars to Artificial Intelligence, eds. P. Lin, K. Abney, and +R. Jenkins (Oxford, UK: Oxford University Press). 157–172 +Keating, C. F. (2011). Channelling charisma through face and body status cues. Social psychological +dynamics , 93–111 +Keller, C., Siegrist, M., Earle, T. C., and Gutscher, H. (2011). The general confidence scale: coping with +environmental uncertainty and threat. Journal of Applied Social Psychology 41, 2200–2229 +Klofstad, C. A., Anderson, R. C., and Nowicki, S. (2015). Perceptions of Competence, Strength, and Age +Influence Voters to Select Leaders with Lower-Pitched Voices. Plos one 10, e0133779 +Klofstad, C. A., Nowicki, S., and Anderson, R. C. (2016). How Voice Pitch Influences Our Choice of +Leaders. American Scientist 104, 282 +Knight, H. and Simmons, R. (2013). Estimating human interest and attention via gaze analysis. In 2013 +IEEE International Conference on Robotics and Automation (IEEE), 4350–4355 +Krafka, K., Khosla, A., Kellnhofer, P., Kannan, H., Bhandarkar, S., Matusik, W., et al. (2016). Eye tracking +for everyone. In Proceedings of the IEEE conference on computer vision and pattern recognition. +2176–2184 +Latif, S., Cuay´ahuitl, H., Pervez, F., Shamshad, F., Ali, H. S., and Cambria, E. (2022). A survey on deep +reinforcement learning for audio-based applications. Artificial Intelligence Review , 1–48 +Levay, C. (2010). Charismatic leadership in resistance to change. The Leadership Quarterly 21, 127–143. +doi:10.1016/j.leaqua.2009.10.010 +Li, S. and Deng, W. (2020). Deep facial expression recognition: A survey. IEEE transactions on affective +computing +Li, Y., Zeng, J., Shan, S., and Chen, X. (2018). Occlusion aware facial expression recognition using cnn +with attention mechanism. IEEE Transactions on Image Processing 28, 2439–2450 +Liu, R., Sisman, B., and Li, H. (2021). Reinforcement Learning for Emotional Text-to-Speech Synthesis +with Improved Emotion Discriminability. In Interspeech 2021 (ISCA), 4648–4652. doi:10.21437/ +Interspeech.2021-1236 +Luzardo, G., Guam´an, B., Chiluiza, K., Castells, J., and Ochoa, X. (2014). Estimation of Presentations +Skills Based on Slides and Audio Features. In Proceedings of the 2014 ACM Workshop on Multimodal +Learning Analytics Workshop and Grand Challenge (Istanbul Turkey: ACM), 37–44. doi:10.1145/ +2666633.2666639 +Frontiers +21 + +Schuller et al. +Computational Charisma +Manzelli, R., Thakkar, V., Siahkamari, A., and Kulis, B. (2018). Conditioning Deep Generative Raw Audio +Models for Structured Automatic Music. In Proceedings of the 19th International Society for Music +Information Retrieval Conference (Paris, France), 1–8 +McCrae, R. R., Costa, P. T., John, O. P., Robins, R. W., and Pervin, L. A. (1999). Handbook of personality: +Theory and research. New York, NY: Guilford +Mehrabian, A. and Wiener, M. (1967). Decoding of inconsistent communications. Journal of Personality +and Social Psychology 6, 109–114 +Mhatre, K. H. and Riggio, R. E. (2014). Charismatic and Transformational Leadership (Oxford University +Press). doi:10.1093/oxfordhb/9780199755615.013.012 +Minaee, S., Minaei, M., and Abdolrashidi, A. (2021). Deep-emotion: Facial expression recognition using +attentional convolutional network. Sensors 21, 3046 +Mohammad, S. M. (2022). Ethics Sheet for Automatic Emotion ecognition and Sentiment Analysis. +Computational Linguistics 48, 239–278 +Mori, M., MacDorman, K. F., and Kageki, N. (2012). The uncanny valley. IEEE Robotics & Automation +Magazine 19, 98–100. doi:10.1109/MRA.2012.2192811. Japanese original 1970 +Moskowitz, G. B. and Gill, M. J. (2013). Person perception. In The Oxford handbook of cognitive +psychology, ed. D. Reisberg (Oxford University Press). 918–942 +Niebuhr, O., Brem, A., Michalsky, J., and Neitsch, J. (2020a). What makes business speakers sound +charismatic? A contrastive acoustic-melodic analysis of Steve Jobs and Mark Zuckerberg. Cadernos de +Linguistica e Teoria da Literatura 1 +Niebuhr, O., Neitsch, J., and Michalsky, J. (2020b). Akustisches Charisma Profiling – Auf dem Weg zur +digitalen Rhetorik. Akustik Journal 02, 7–22 +Ochoa, X., Dom´ınguez, F., Guam´an, B., Maya, R., Falcones, G., and Castells, J. (2018). The RAP system: +Automatic feedback of oral presentation skills using multimodal analysis and low-cost sensors. In +Proceedings of the 8th International Conference on Learning Analytics and Knowledge (Sydney New +South Wales Australia: ACM), 360–364. doi:10.1145/3170358.3170406 +Orzeatja, M. (2011). Leaders and their charisma management and socio-humanities. Review of the Air +Force Academy 9, 92–96 +Pamungkas, E. W. (2019). Emotionally-aware chatbots: A survey. CoRR abs/1906.09774 +Raven, J. C. and Court, J. H. (1998). Raven’s progressive matrices and vocabulary scales, vol. 759 (Oxford +pyschologists Press Oxford) +Revina, I. M. and Emmanuel, W. S. (2021). A survey on human face expression recognition techniques. +Journal of King Saud University-Computer and Information Sciences 33, 619–628 +Rogers, S. L., Speelman, C. P., Guidetti, O., and Longmuir, M. (2018). Using dual eye tracking to uncover +personal gaze patterns during social interaction. Scientific reports 8, 1–9 +Rosenberg, A. and Hirschberg, J. (2009). +Charisma perception from text and speech. +Speech +Communication 51, 640–655 +Schuller, B. and Batliner, A. (2014). Computational Paralinguistics – Emotion, Affect, and Personality in +Speech and Language Processing (Chichester, UK: Wiley) +Schuller, B., Steidl, S., Batliner, A., N¨oth, E., Vinciarelli, A., Burkhardt, F., et al. (2015). A Survey on +Perceived Speaker Traits: Personality, Likability, Pathology, and the First Challenge. Computer Speech +and Language, Special Issue on Next Generation Computational Paralinguistics 29, 100–131 +Schutte, N. S., Malouff, J. M., Hall, L. E., Haggerty, D. J., Cooper, J. T., Golden, C. J., et al. (1998). +Development and validation of a measure of emotional intelligence. +Personality and individual +differences 25, 167–177 +This is a provisional file, not the final typeset article +22 + +Schuller et al. +Computational Charisma +[Dataset] Sharma, A., Miner, A. S., Atkins, D. C., and Althoff, T. (2020). A computational approach to +understanding empathy expressed in text-based mental health support. doi:10.48550/ARXIV.2009.08441 +Tang, Y., Huang, Y., Wu, Z., Meng, H., Xu, M., and Cai, L. (2016). Question detection from acoustic +features using recurrent neural network with gated recurrent unit. In 2016 IEEE International Conference +on Acoustics, Speech and Signal Processing (ICASSP) (IEEE), 6125–6129 +Tickle-Degnen, L. and Rosenthal, R. (1990). +The nature of rapport and its nonverbal correlates. +Psychological Inquiry 1, 285–293. doi:10.1207/s15327965pli0104 1 +Towler, A. J. (2003). Effects of charismatic influence training on attitudes, behavior, and performance. +Personnel psychology 56, 363–381 +Trouvain, J., Weiss, B., and Barkat-Defradas, M. (2020). Voice Attractiveness: Concepts, Methods, and +Data. In Voice Attractiveness – Studies on Sexy, Likable, and Charismatic Speakers, eds. B. Weiss, +J. Trouvain, M. Barkat-Defradas, and J. J. Ohala (Singapore: Springer). 3–16 +Trouvain, J. and Werner, R. (2022). A phonetic view on annotating speech pauses and pause-internal +phonetic particles. Transkription und Annotation gesprochener Sprache und multimodaler Interaktion: +Konzepte, Probleme, L¨osungen , 55 +Tskhay, K. O., Zhu, R., Zou, C., and Rule, N. O. (2018). Charisma in everyday life: Conceptualization and +validation of the general charisma inventory. Journal of Personality and Social Psychology 114, 131 +Tubbs, R. S. (2019). Learning charisma. A Guide to the Scientific Career: Virtues, Communication, +Research and Academic Writing , 103–107 +Van Erp, J. B. and Toet, A. (2015). Social touch in human–computer interaction. Frontiers in digital +humanities 2, 2 +Vehlen, A., Spenthof, I., T¨onsing, D., Heinrichs, M., and Domes, G. (2021). Evaluation of an eye tracking +setup for studying visual attention in face-to-face conversations. Scientific reports 11, 1–16 +Wang, C. and Chanel, G. (2021). An open dataset for impression recognition from multimodal bodily +responses. In 2021 9th International Conference on Affective Computing and Intelligent Interaction +(ACII). 1–8. doi:10.1109/ACII52823.2021.9597421 +Wang, K., Peng, X., Yang, J., Lu, S., and Qiao, Y. (2020). Suppressing uncertainties for large-scale facial +expression recognition. In Proceedings of the IEEE/CVF conference on computer vision and pattern +recognition. 6897–6906 +Weatherby, G., Ochoa, N., and Nielsen, L. (2016). The Making of a Charismatic Killer. International +Journal of Forensic Sciences 1, 1–21 +Weber, M. (1922). Grundriß der Sozial¨okonomie. III. Abteilung. Wirschaft und Gesellschaft. Bearbeitet +von Max Weber (T¨ubingen: J.C.B. Mohr) +Weiss, B. and Burkhardt, F. (2010). Voice attributes affecting likability perception. In Proc. of Interspeech +(Makuhari, Japan), 1485–1488 +Weiss, S. J., Wilson, P., Hertenstein, M. J., and Campos, R. (2000). The tactile context of a mother’s +caregiving: implications for attachment of low birth weight infants. Infant Behavior and Development +23, 91–111 +Welsh, E. C. O. and Lenzenweger, M. F. (2021). Psychopathy, charisma, and success: A moderation +modeling approach to successful psychopathy. Journal of Research in Personality 95. doi:10.1016/j.jrp. +2021.104146 +Weninger, F., Krajewski, J., Batliner, A., and Schuller, B. (2012). The Voice of Leadership: Models and +Performances of Automatic Analysis in On-Line Speeches. IEEE Transactions on Affective Computing +3, 496–508 +Frontiers +23 + +Schuller et al. +Computational Charisma +Wolf, M. J., Miller, K., and Grodzinsky, F. S. (2017). Why we should have seen that coming: comments on +microsoft’s tay ‘experiment,’ and wider implications. ACM SIGCAS Computers and Society 47, 54–64 +Won, J., Gopinath, D., and Hodgins, J. (2021). Control strategies for physically simulated characters +performing two-player competitive sports. ACM Transactions on Graphics (TOG) 40, 1–11 +Xu, R., Wu, R., Ishiwaka, Y., Vondrick, C., and Zheng, C. (2020). Listening to sounds of silence for speech +denoising. Advances in Neural Information Processing Systems 33, 9633–9648 +Yang, Z., Huynh, J., Tabata, R., Cestero, N., Aharoni, T., and Hirschberg, J. (2020). What Makes a Speaker +Charismatic? Producing and Perceiving Charismatic Speech. In Proc. Speech Prosody 2020. 685–689. +doi:10.21437/SpeechProsody.2020-140 +Zdarsky, N., Treue, S., and Esghaei, M. (2021). A deep learning-based approach to video-based eye +tracking for human psychophysics. Frontiers in human neuroscience 15 +Zhang, Y.-J., Pan, S., He, L., and Ling, Z.-H. (2019). Learning latent representations for style control +and transfer in end-to-end speech synthesis. In ICASSP 2019-2019 IEEE International Conference on +Acoustics, Speech and Signal Processing (ICASSP) (IEEE), 6945–6949 +Zoghaib, A. (2019). Persuasion of voices: The effects of a speaker’s voice characteristics and gender on +consumers’ responses. Recherche et Applications en Marketing 34, 83–110 +This is a provisional file, not the final typeset article +24 + diff --git a/SdAyT4oBgHgl3EQfVPfZ/content/tmp_files/load_file.txt b/SdAyT4oBgHgl3EQfVPfZ/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..4bae9ec6b4769e95e4f0e1952e12c693aa587455 --- /dev/null +++ b/SdAyT4oBgHgl3EQfVPfZ/content/tmp_files/load_file.txt @@ -0,0 +1,1574 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf,len=1573 +page_content='Computational Charisma – A Brick by Brick Blueprint for Building Charismatic Artificial Intelligence Bj¨orn W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Schuller 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Shahin Amiriparian 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Anton Batliner 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Alexander Gebhard 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Maurice Gerzcuk 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Vincent Karas 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Alexander Kathan 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Lennart Seizer 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Johanna L¨ochner 3 1EIHW – Chair of Embedded Intelligence for Health Care and Wellbeing,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' University of Augsburg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Augsburg,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Germany 2GLAM – Group on Language,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Audio,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' & Music,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Imperial College London,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' London,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' United Kingdom 3Department of Child and Adolescent Psychiatry,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Eberhard-Karls University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' T¨ubingen,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Germany Correspondence*: Bj¨orn W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Schuller, Johanna L¨ochner schuller@ieee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='org, Johanna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='Loechner@med.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='uni-tuebingen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='de ABSTRACT Charisma is considered as one’s ability to attract and potentially also influence others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Clearly, there can be considerable interest from an artificial intelligence’s (AI) perspective to provide it with such skill.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Beyond, a plethora of use cases opens up for computational measurement of human charisma, such as for tutoring humans in the acquisition of charisma, mediating human-to-human conversation, or identifying charismatic individuals in big social data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' While charisma is a subject of research in its own right, a number of models exist that base it on various ‘pillars’, that is, dimensions, often following the idea that charisma is given if someone could and would help others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Examples of such pillars, therefore, include influence (could help) and affability (would help) in scientific studies or power (could help), presence, and warmth (both would help) as a popular concept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Modelling high levels in these dimensions, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', high influence and high affability or high power, presence, and warmth for charismatic AI of the future, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', for humanoid robots or virtual agents, seems accomplishable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Beyond, also automatic measurement appears quite feasible with the recent advances in the related fields of Affective Computing and Social Signal Processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Here, we, thereforem present a blueprint for building machines that can appear charismatic, but also analyse the charisma of others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' To this end, we first provide the psychological perspective including different models of charisma and behavioural cues of it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' We then switch to conversational charisma in spoken language as an exemplary modality that is essential for human-human and human-computer conversations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The computational perspective then deals with the recognition and generation of charismatic behaviour by AI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This includes an overview of the state of play in the field and the aforementioned blueprint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' We then name exemplary use cases of computational charismatic skills before switching to ethical aspects and concluding this overview and perspective on building charisma-enabled AI – will tomorrow’s influencers be artificial?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Keywords: Charisma, AI, Empathy, Mimicry, Affective Computing, Social Signal Processing 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='00142v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='HC] 31 Dec 2022 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma A B Power Warmth Presence Empathy Authenticity Emotional intelligence Mindfulness Skills Intelligence Attention Competence Humour Exhibition of ease and comfort Persuasion Enthusiasm Motivation Confidence Affective communication Rapport Leader Presence Influence Smile Comfort Get Along Influence Affability Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Comparison of the models of Tskhay (A) Tskhay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2018) and Fox Cabane (B) Fox Cabane (2013) 1 INTRODUCTION Charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' An irresistible force that, apart from beauty or rhetoric, captivates people.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A miracle cure for professional success and an almost effortless rise to the top of power.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A plethora of popular science literature, podcasts, and discussions rotate around this fascination, providing training to adopt a charismatic style – going along with the great promise of being successful and attractive to others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Besides this great uptake, the topic of charismatic behaviour also has a research tradition in sociology and psychology and is now increasingly trending in computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This is promising, since computational charisma may be applied to numerous fields such as leadership training, mental health care, and education and enhance outcomes in several ways: more efficient leadership, increased comfort in recipients, better teamwork, and reduction of reluctance and irritation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' However, charismatic behaviour is not bound to particular values and initially exists independently of an ideology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This also makes the appropriation of charisma a potential danger if it is misused for unethical purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In this article – section by section –, we initially discuss the myth about charisma from a scientific, but also popular science perspective (functional aspects of charisma), to follow up with several layers of markers for charisma (formal aspects of charisma), computational aspects of charisma to finish with the motivation based on applications and rendering these more attractive and effective and ethics of computational charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Thereby, we focus on spoken language and audio as indelible key features of charismatic behaviour, that play undoubtedly a key role in times of remote and digital – hence restricted visual – communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 2 FUNCTIONAL ASPECTS OF CHARISMA: PSYCHOLOGICAL MODELS Although charisma is a ubiquitous and frequently discussed phenomenon, and people seem to agree on which person inherits this trait, a certain mysteriousness surrounds the exact definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' And yet, although some popular figures in history are frequently characterised as being charismatic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In this first section, we discuss charisma from a sociological, psychological and also popular science perspective and aim to untidy the concrete characterisations of charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In contrast to other research fields, the subjective perception of charisma and popular science uptake of this phenomenon is particularly interesting, since it is part of its definition and hence, immanent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This is a provisional file, not the final typeset article 2 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1 Origin and Definition The word charisma originally comes from the Greek (χ´αρισµα) and means ‘gift of grace’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Even the ancient Greeks assumed that charisma is a gift from God that some have, and others do not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Today, the word is typically used as a descriptor for people who are attractive to others and manage to gather a following around them (for the good or bad) such as Princess Diana, Oprah Winfrey, Martin Luther King, or Adolf Hitler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Although everybody has an intuitive understanding of the concept of charisma and there is a high agreement in the population about which persons are charismatic, a scientifically sound and commonly used definition is still discussed (Antonakis, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This may partly be explained by the fact that the study of charisma is relatively young and still mostly restricted to economic psychology in terms of leadership research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Naturally, children are even less likely to have a defined concept of what charisma actually means;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' however, they are well capable of voting the ‘captain’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Hence, Antonakis and Dalgas asked 5-13 years-olds to rate the ‘captain’ among a selection of pairwise displayed photographs of French candidates for the presidency, resulting in an 85 % hit rate (Antonakis and Dalgas, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Although these results rely on visual data only, it was shown that attractiveness is not the key feature of charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' For example, in a study predicting success in relationships and academic careers, charisma was more predictive than attractiveness and visuals (Orzeatja, 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The sociologist Max Weber defined charisma at the beginning of the 20th century as an ‘extraordinary quality of a personality’, as a ‘supernatural or superhuman power’ (Weber, 1922).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Based on this work, House (House, 1976) provided the first operationalisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Thereby, charisma was defined as the ability to inspire others toward a common goal and identity by appealing to their emotions and collective identity in order to impart an idealised vision to their followers – thus, the central role of charisma in leadership research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In the following decades, more specific traits and behaviours have been associated with charisma (Antonakis, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A key quality lies in the ability to connect with other people and exhibit ease, trust, and comfort in the audience paving the ground to become a leader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In addition, a charismatic person is highly persuasive (Mhatre and Riggio, 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Several definitions of such phenomena are discussed in the literature including properties such as authenticity, emotional competence (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', understanding emotions in oneself and others, or managing own emotions), empathy, persuasiveness, spending attention to others, passion, enthusiasm, and obtaining strong opinions to name a few.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' However, such qualities may not only be used for charity aspects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Welsh and colleagues investigated the associations of psychopathy, charisma and success.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' They found that psychopathy was positively associated with leadership charisma and the influence component of general charisma (Welsh and Lenzenweger, 2021);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' in addition, charisma moderated the association of psychopathic traits and perceived success in form of the evading detection and punishment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Charisma models or concepts were proposed as either inherent personality traits (Burke and Brinkerhoff, 1981), observer perception and outcomes (Awamleh and Gardner, 1999), or both (Conger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Aiming to provide a more comprehensive model of charisma based on empirical data, Tskhay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2018) created an empirical model of charisma: They investigated characteristics of charisma by rigorous and repeated questioning of people how they use to describe charismatic people, and subsequently applied factor analyses to identify the most important components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Their analyses resulted in a two-factor model with one factor – influence – consisting of items that describe leadership ability and influence in a group setting, and another factor – affability – that consists of items describing a pleasant and inviting disposition toward others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The factors with more detailed descriptions and an exemplary list of behaviours that are associated with each are given in this section, with no claim to completeness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' While influence and affability are separate qualities, somehow, in the combination of traits and behaviours associated with these two, charisma emerges as a novel trait.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Charisma is thereby defined as a multi-dimensional construct of traits and behaviours in contrast to ‘just’ being a likeable person.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Similarly, Keating (2011) argued that dominant Frontiers 3 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma behaviour triggers avoidance reactions in others, whereas emotionally warm behaviour triggers approach reactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' She further claims that the perception of charisma emerges specifically through the simultaneous elicitation of avoidance and approach reactions by the combination of influence(dominance, power) and affability (emotionality, approachability) in a charismatic person.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Model GCI Item Associated constructs Influence Influence Presence Leader Has the ability to influence people Has a presence in a room Knows how to lead a group Convergent: Emotional Intelligence,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Positive Affect,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Extraversion,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Openness,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Conscientiousness,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Political Skill,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Competence Discriminant: Negative Affect,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Neuroticism Affability Get along Comfort Smile Can get along with everyone Makes people feel comfortable Smiles at people often Convergent: Emotional Intelligence,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Positive Affect,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Confidence,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Extraversion,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Openness,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Conscientiousness,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Agreeableness,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Political Skill,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Competence,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Warmth Discriminant: Negative Affect,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Neuroticism Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Detailed overview of the Tskhay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' model There are several psychological constructs that may be convergent or discriminant to charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In a validation study of the influence-affability model, the uniqueness or relatedness of charisma to other individual difference measures was tested in multiple samples ((Tskhay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2018);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' see Table 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Thereby, influence and affability were both found to be significantly related to emotional intelligence, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', the appraisal, expression, regulation, and utilisation of emotions in a variety of contexts (Schutte et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In terms of emotionality experienced by oneself, positive affect was positively related to the two charisma factors, while negative affect was negatively related to both.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Political skill, defined by the four dimensions of social astuteness, interpersonal influence, networking ability, and apparent sincerity (Ferris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2005), is often used as a metric of charismatic leadership and accordingly was found to be positively related to influence and affability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Intelligence is a trait that is often ascribed to charismatic individuals in lay theories;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' however, intelligence, as determined by Raven’s Matrices (Raven and Court, 1998), was not associated with influence or affability, indicating that charisma may rely more on interpersonal skills in social interactions rather than intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Further, the general confidence of an individual as the degree to which one feels certain about both the world and idiosyncratic surroundings and their ability to deal with stress (Keller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2011) was positively related to affability, but not associated with influence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In terms of personality traits as the Big Five (McCrae et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 1999), openness, consciousness, and extraversion were positively related to both influence and affability, while agreeableness was only related to affability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Neuroticism on the other hand was negatively associated with influence and affability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Of the dimensions competence and warmth – two essential elements of both social behaviour and personal characteristics (Fiske et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2007) – influence was only related to competence, while affability was related to both warmth and competence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Another model of charisma was proposed by Fox Cabane (2013), in which she refers to charisma as deriving from three pillars: presence, power, and warmth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Presence is displayed by dwelling in the current moment, active listening, and responding adequately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The focus of attention lies on the person one is talking to and taking an honest interest in the conversation partner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Power is not defined as actual power like being in a position as president or high-rank manager.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' It is rather understood as high competence due to certain skills, abilities, or intelligence a person obtains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Warmth requires a high level of empathy, openness, This is a provisional file, not the final typeset article 4 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma and positivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The pillar warmth has frequently been studied as part of the two-dimensional warmth and competence (W&C) model (Wang and Chanel, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Fraser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2021, 2022), where warmth indicates the nature of the sender’s intent towards the receiver, and competence the ability of the sender to enact this intent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The combination of these dimensions evokes emotional responses ranging from admiration to disgust (Fraser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Thus, warmth is closely related to the perceptions of attractiveness and empathy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Therefore, charismatic individuals usually radiate acceptance and friendliness that one otherwise experiences only from family members or friends.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' It is discussed whether one or two of the three qualities may be sufficient to appear charismatic, as Steve Jobs, for instance, scored with presence and power, but lacked warmth .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In contrast, Martin Luther King showed all three qualities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Hence, the pillars warmth and power may relate to affability and to the influence of the two-factor model by Tskhay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (Tskhay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2018), while the pillar presence was discussed as a non-latent, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', secondary, variable in their empirically found model by a factor analysis following questioning participants (see Figure 1A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Very similarly, the concept of rapport is defined and may well serve as part of charismatic behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Tickle-Degnen and Rosenthal (1990) conceptualised the nature of rapport in terms of a dynamic structure of three interrelating components: mutual attentiveness, positivity, and coordination;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' these are differently weighted and present over time in a relationship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Hence, rapport is characterised by agreement, mutual understanding, or empathy that makes communication possible or easy, establishing ease and comfort in communication partners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In consequence, a charismatic individual is capable of establishing rapport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Conclusively, charisma is a person-specific descriptor that emerges specifically in social situations through the attribution of a certain set of traits to an individual.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Despite heterogeneous conceptualisation and the inherent complexity, there is a consensus that charismatic individuals exert influence over others, have extraordinary social skills, comfort and connect to others, inspire followership, and are prone to leadership roles (Tskhay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2018)(Antonakis, 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Breaking charisma down to such concrete properties reveals a combination of personality traits and skills that are partly inherited, socially acquired, and trained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In social psychology, the processes that leads us to form impressions about other people are referred to as person perception (Moskowitz and Gill, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Some methods of perceiving another person involve inferring details about them based on observations of their activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Other types of personal perception happen more immediately and only need one to view another person.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In building a machine that people perceive as charismatic, a bias in human inference processes can be exploited, namely the fundamental attribution error: People tend to ascribe observed behaviours to internal factors like personality or character rather than to external factors such as situational constraints (Colman, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Thus, by mimicking certain appearance cues, characteristics, and behaviours programmatically to elicit the perception of charisma-associated traits, it should be possible to build a “charismatic artificial intelligence”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2 Acquisition of Charismatic Behaviour In consequence, charismatic behaviour can be acquired and there is a plethora of trainings offered especially in the field of leadership coaching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Overall, the two key qualities, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', factors, introduced by Tskhay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2018) may be achieved especially through confidence and skills (influence ), emotional intelligence, and empathy (affability ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' As is conclusive from the above (see also Figure 1), they may also be complemented by a third pillar or factor suggested by Fox Cabane (2013) – mindfulness (presence).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Following Fox Cabane (2013) and Tskhay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2018), such characteristics will elicit an increased impression of attractiveness, energy, persuasiveness, power, and empathy, and establish rapport between communication partners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Focusing on leadership trainings, and translating charismatic behaviour into more concrete tactics, Antonakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2012) investigated twelve techniques to increase charisma – the so-called “charismatic Frontiers 5 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma leadership tactics” (CLTs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Similar to athletes who follow a training schedule, leaders who aim to become influential, trustworthy and “leaderlike” are recommended to practice certain tactics regularly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' For this purpose, they examined the nomination speeches of all candidates for president in the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' between 1916 and 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The analysis revealed that the use of figurative language, anecdotes, proverbs, and the proper use of body language had a significant impact on the outcome of the election.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Despite humour, repetition, and talking about sacrifices, such verbal and non-verbal techniques were shown to have the greatest impact in any context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The nine verbal techniques are metaphors, similes, and analogies;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' stories and anecdotes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' contrasts;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' rhetorical questions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' expressions of moral conviction;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' reflections of the group’s sentiments;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' three-part lists;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' the setting of high goals;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and conveying confidence that they can be achieved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' For example, the metaphor of being on a boat in a storm may serve as a metaphor for a critical period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Even without being a born raconteur one can tell the compelling story of taking a deep breath as “anchor” and visualise the north star for guidance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Another example to motivate followers through a challenging period would be an anecdote of a personal story, as climbing a mountain when a thunderstorm arises and how the team must have kept going.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In addition, there are three non-verbal techniques: animated voice, facial expressions, and gestures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Keeping with voice-associated techniques to improve oneself’s charisma, or rather the perception of charisma in others, it is suggested to speak clearly, fluently, forcefully, and in an engaging manner that invokes images, energy, and action;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' moreover, the delivery’s pace and intonation should be varied, with a general upbeat tempo and an occasionally slowing down to create tension (Tubbs, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Similarly, Fox Cabane (2013) recommends lowering the tone of one’s voice at the end of each statement and make frequent pauses while speaking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Despite these strategies to develop or improve charisma, the debate on whether charisma can be learnt or simply is a trait with set between-subject variation is still ongoing (Tubbs, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' It is of note that, even in human generation of charisma, an attribution error can apply: when speakers learn to speak with a ‘charismatic voice’, people perceive them as charismatic, even when their personality does not change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Hence, very concrete acquired behaviour was shown to lead to a more charismatic behaviour of individuals and hence, can be installed on who- or whatever to some extent: A person might not be charismatic in themselves but may appear this way, due to, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', speaking in a charismatic way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Note that it was shown that appearance is not the key factor in ‘charismatic appearance’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Antonakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2012) observed that in eight out of ten U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' presidential races, candidates who deployed such verbal CLTs won more often.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Since communication nowadays is primarily technology-mediated, Ernst et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2022) investigated CLT in a recent prospective meta-analysis on virtual charismatic leadership.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The meta-analytic effect of CLTs on performance (Cohen’s d = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='52 in-person, k = 4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Cohen’s d = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='21 overall, k = 10) and engagement in an extra-role task (Cohen’s d = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='19 overall;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' k = 6) indicated large to moderate effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Yet, for performance in a virtual context, Cohen’s d ranged from −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='25 to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='17 (Cohen’s d = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='01 overall;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' k = 6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In summary, disentangling especially phonetic and linguistic markers for charisma may be particularly beneficial in times of virtual communication in all kind of fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In the following section, this article focuses on the specific phonetic, linguistic, and other markers that are associated with charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 3 FORMAL ASPECTS OF CHARISMA: PHONETIC, LINGUISTIC, AND OTHER MARKERS The marking of charisma is definitely multi-modal, and trading relations exist both between and within modalities – i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', a more pronounced but not exaggerated marking in one parameter can compensate for weak signalling in another parameter, see Niebuhr et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2020b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Ranking the importance of modalities is This is a provisional file, not the final typeset article 6 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma futile and either based on intuition or on one or only a few studies with their specific databases, designs, and methods;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' see the ‘7 %-myth’ (Mehrabian and Wiener, 1967) and (Schuller and Batliner, 2014, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In the following, we concentrate on speech and language, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', on vocal and verbal parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This appears reasonable, given the focus on today’s AI often communicating with users by this modality;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' in addition, also when analysing human interaction, spoken language plays a key role.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Yet, we will as well present a sketchy overview of charisma conveyed within the other modalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' We will start with phonetic markers of charismatic speech in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' then follow linguistic markers in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2, and other modalities Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The intuitive understanding of charisma is mirrored in equally intuitive characterisations such as attractive, inspiring, animated, enthusiastic, warm, likeable, or pleasant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In this section, we now report the state of the art in mapping these terms onto markers that can be measured and counted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1 Phonetic Markers Arguably, Rosenberg and Hirschberg described the first sets of studies on charismatic speech (Rosenberg and Hirschberg, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' So far, most of them addressed charisma in politics (candidate speeches) and Marketing (Zoghaib, 2019) and concentrate on prosody.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Related are states and traits such as leadership (Weninger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2012), competence/trustworthiness (Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Davidson, 2021), likability (Weiss and Burkhardt, 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2015), and (sexual) attractivity (Trouvain et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Charisma can be tied to performing something, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', a candidate speech, and can be switched on and off;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' see Rosenberg and Hirschberg (2009): “Speakers were rated as more charismatic when they were delivering a stump speech (mean rating of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='28) than when they are being interviewed (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='90).” So, at least the ‘acoustics of charisma’ are not in an ‘always one-to-one relationship to personality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Of course, this makes it possible for it to be taught and acquired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' An infamous example is Adolf Hitler where the only recording of non-public speech (https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='youtube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='com/watch?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='v=WE6mnPmztoQ) reveals a relaxed, almost likeable style of speaking, much different from his public speeches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' We can distinguish ‘dark charisma’ (Fragouli, 2018), where, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', anger can be strongly marked with prosodic means, when this is in accordance with the audience, from ‘bright charisma’ which can be rather marked prosodically (Barack Obama) or linguistically and by the context (Mahatma Gandhi);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' see D’Errico et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Even psychopaths can display traits of bright charisma in discordance to their personality (Weatherby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Intervening factors can be gender, age, and culture (D’Errico et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Laryngealised, ‘creaky’ voice – that is at the same time indicating very low but also irregular pitch – can make men more cool and attractive (Davidson, 2021), whereas a breathy voice is preferred for women (Greer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2015);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' this, however, mostly holds for younger women (Anderson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2014), whereas in business and academia, a creaky voice can be a sign of competence for both females and men.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Klofstad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2016) summarise the experiment on leadership: “.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' males with lower-pitched voices tend to be perceived as more attractive, physically stronger, and more ‘dominant’ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' For females, the standard is dichotomous: Women with higher-pitched voices tend to be considered more attractive, whereas those with lower-pitched voices are perceived as more dominant.”;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' see as well Anderson and Klofstad (2012);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Klofstad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2015);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Zoghaib (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Niebuhr et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2020a) compared customer and investor keynotes of Steve Jobs and Mark Zuckerberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Jobs, commonly perceived as the more charismatic speaker, produced a higher pitch level (even approaching that of female speakers), and almost twice the pitch range of Zuckerberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Jobs used shorter phrases, had fewer disfluencies, and scored higher in the voice quality metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' However, he did not exceed Zuckerberg in terms of intensity variability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Both showed significant differences when addressing customers and investors, showing again that charisma is situation-dependent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Frontiers 7 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=" Computational Charisma ETHICS FORMAL MEANS prosody: pitch: (not too) high, variation duration: rather long, variation (rhythm, pauses) loudness: variation spectral energy: at low frequencies voice quality: 'normal‘ (modal);" metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' not tense vowel space: not centralised linguistics: vocabulary: elaborated syntax: elaborated but not too complex disfluencies: none pronouns: second person,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' not first person adjectives: related to social/moral for affability,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' able/agentic for influence FUNCTIONS (i) motivation/intention: leadership,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' education,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' health care,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' persuasion,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' personalisation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' attractiveness (ii) models: three pillars: warmth,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' presence,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' power two factors: influence,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' affability (iii) perception/impressions: attractive: averaging,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' reduced irregularities energetic: variability power,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' warmth,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' presence: greater vocal space,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' voice quality,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' centre of gravity rapport (interactive): convergence APPLICATIONS humanoids,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' virtual agents reaction/interaction/training monitoring,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' tutoring,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' games … Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Overview of concepts and components: three stage FUNCTIONS of charisma;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (i) higher level motivation/intentions employ (ii) models (three pillars and two factors) to create (iii) specific perception/impressions conveyed via speech by using prosody and linguistics (FORMAL MEANS);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' this charisma is then used in APPLICATIONS in human-machine-interactions that ETHICS has to take care of.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Low-level descriptors of the voice have been shown to convey perceptions of speaker personality traits (Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The likeability of a person can be predicted using pitch frequency F0, articulation rate, and spectral parameters such as MFCC (Weiss and Burkhardt, 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' D’Errico et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2013) conducted a cross-cultural study showing the effects of pitch and the duration of speech pauses on the perception of two dimensions aggregated from 67 traits and conforming to proactivity-attractiveness and calm-benevolence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' As far as prosody is concerned, we can sum up with Yang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2020): “.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' voices that are louder, higher, faster, and with greater fluctuation in pitch were rated as more charismatic.” Now, we ‘only’ have to define the acceptable range of these prosodic varieties;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' too great an intensification will certainly yield undesirable consequences such as the impression of distortion or a lower discriminability, see (Hamilton and Stewart, 1993), (Holz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Moreover, higher pitch range and overall, more variability characterising charismatic speech, differ from less variability and lower pitch, characterising competence;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' see again (Rosenberg and Hirschberg, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Other prosodic parameters as well, and other acoustic parameters such as spectral distributions, favourable for conveying charisma, can be described as ‘well-balanced’ and ‘well-shaped’: neither too integrating nor too isolating prosodic phrasing – i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', not too many but not too few pauses;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' more spectral energy at low frequencies (‘full voice’);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and more precise articulation (no centralisation of vowels).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A charismatic voice is definitely not characterised by dysphonia, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', disordered voice (hypophonia, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', soft voice, or the opposite, hyperphonia, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', tense, harsh voice).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Based on all these findings, Niebuhr et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2020b) describe a system for charisma profiling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Figure 2 summarises the formal acoustic aspects dealt with in this subsection and the linguistic aspects described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' at the same time, it relates these formal aspects to the functional aspects: the motivation behind creating charismatic agents;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' the models employed by us;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and the perception and impression that such charismatic agents have on the human interaction partners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' These components are employed to create applications where charisma is harnessed to achieve their specific goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Ethics has to assess and possibly restrict the use of charisma in these applications, see Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This is a provisional file, not the final typeset article 8 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2 Linguistic Markers As far as linguistic markers are concerned, the use of informal language, high occurrence of pronouns, and avoidance of synonyms can be used to elicit greater warmth, while the opposite holds for formal, complex language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' For pronouns, those that involve the audience, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', we and you, are useful for creating a better first impression (Biancardi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In addition, Rosenberg and Hirschberg (2009) found that using first-person pronouns positively correlated with the charisma ratings of political candidates in spoken but not in written form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Adjectives can serve as markers for the charismatic content of language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' They can be clustered via concepts such as sociability and morality for warmth or ability and agency for competence (Fraser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The usage of adjectives, as opposed to nouns in describing persons, affects the generated impressions, with nouns conveying a greater sense of defining, immutable traits (Fraser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' When referring to groups of people, the choice of descriptor can evoke various impressions of warmth and competence via associated stereotypes;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' consider, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', the differences between the elderly, old people, old folks and senior citizens (Fraser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The clarity of the intended message also affects the perception of charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A lower amount of disfluencies may make a speaker appear more confident and focused.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The negative effect of disfluency is more pronounced for linguistics than for prosody according to a comparison between speech and transcripts by Rosenberg and Hirschberg (2009), possibly because the audience may expect it in spoken but not in written form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Regarding the content of a message, conveying more information is not necessarily beneficial from a charisma perspective;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' for speakers with a lower ratio of function to content, words can be rated as more charismatic, possibly due to higher rhetorical complexity (Rosenberg and Hirschberg, 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Charisma is closely related to being able to influence others, thus, here we also examine linguistic markers of persuasion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Guerini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2003) propose a taxonomy resting on four pillars: cognitive state, social relations, emotional state, and interaction context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Here, cognitive elements refer to goals and beliefs of agents and concepts related to them, social elements deal with power dynamics between relevant persons, emotional elements can be used to enhance or diminish a message, and contextual elements can add useful information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Persuasion strategies are then grouped by their objective: inducing a change in beliefs, and inducing a change in actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The former can be achieved by appealing, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', to the opinions of experts, to public opinion, or to empirical evidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The latter may follow a social strategy by appealing to someone from whom the target derives standards or morals, or to the target’s social image at large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Another option would be to present imaginary consequences, either positive via promises or negative via threats.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A charismatic agent may select and modify these strategies to improve the success rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='3 Vision, Touch, and More: Markers in Other Modalities Charisma without spoken or written language may hardly exist, but obviously, other channels contribute, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', in the visual modality gestures, body pose, facial expressions, and gaze behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' While today’s interaction and communication with AI is largely focused on spoken and written language, future AI is expected to be doing so multimodally, detecting the user state and responding in real-time to generate a favourable, human-like impression Biancardi (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Cuddy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2008) investigated how warmth and competence are perceived based on behaviour at interpersonal and intergroup levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Smiling, as well as engaging gestures, touch, and mirroring were found to increase the impression of presence and warmth, while disengagement and creating physical distance by leaning back or turning away decrease it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Expansive and open body poses, suggesting power and dominance, resulted in higher impressions of competence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' For hand gestures, the use of object adaptors Frontiers 9 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma and ideationals (relating to spoken words) improved the speaker competence, while self-adaptors decrease it (Biancardi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In general, a speaker’s delivery can have a great influence on their credibility, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', a strong delivery is more likely to lead to high credibility than is a weak one (Holladay and Coombs, 1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Factors contributing to a good delivery include eye contact, gestures, and facial expressions (Holladay and Coombs, 1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This is not surprising as gestures and facial expressions can innately radiate charisma (Towler, 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Since these characteristics are settled in the visual domain, they have to be considered apart from audio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Regarding conversational interaction, when a person’s gaze is focused on the conversation partner, this is a sign of attention and shows both interest in the conversation and commitment to the conversation partner (Knight and Simmons, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Freeth and Bugembe, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' That is, if the gaze is wandering through the surroundings it may evoke the impression that a person is not fully listening and wants to distract themselves with seemingly more interesting things.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Thus, to recognise the attentiveness and presence in a conversation, one of the easiest approaches might be to track eye contact and face gaze in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Another tool of nonverbal behaviour and conveying (intimate) emotions is the sense of touch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Touch is crucial for social development and necessary for children in order to grow up healthy (Van Erp and Toet, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Weiss et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Out of all nonverbal modalities, affective touch is our primary channel for expressing intimate emotions and can effortlessly establish social presence (Van Erp and Toet, 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In addition to distinct emotions like love, anger, and fear, touch can also convey more complex emotional patterns such as trust, receptivity, and affection (Van Erp and Toet, 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Hertenstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2006, 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Burgoon, 1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' As previously mentioned, charismatic persons radiate characteristics like trustability, presence, and warmth, which makes affective touch an essential modality next to audio – if appropriate in the specific situation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 4 COMPUTATIONAL ASPECTS OF CHARISMA: MODELLING After analysing the markers of charisma in Section 3, we now deal in this section with the modelling of charisma from a computational perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Automatic recognition of charisma describes the detection of the sociological and psychological markers for charismatic behaviour using machine learning approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Similarly, the automatic generation of charisma outlines methods for generating auditory or visual charismatic traits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1 Automatic Recognition of Charisma Charisma can be registered via a wide range of modalities, ranging from facial movements and gestures to speech and physiological attributes like heart rate and skin conductance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Since charisma is an interpersonal effect, computational analysis can focus either on the sender projecting charisma, on a receiver forming an impression, or on dyadic interactions between the two (Wang and Chanel, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Here, we take up the stated sociological, psychological, and popular science perspective and translate it into computational aspects of phonetics, linguistics, and other modalities in automatic recognition of charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1 Audio The quality of speech transmission has an impact on the perception of charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Gallardo (2018) investigated the effect of bandwidth on perception of male and female speakers selected for extreme values of warmth-attractiveness (WAAT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Shifts in traits such as maturity, sympathy, and confidence for males and competence for females can be explained with alterations of F0 resulting from the narrow-band transmission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Another study (Gallardo and Sanchez-Iborra, 2019) assessed the impact of various encoding and transmission properties on the binary classification of warmth and attractiveness via Random Forest This is a provisional file, not the final typeset article 10 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma and Support Vector Machines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Narrowband codecs were found to degrade performance to near chance level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Packet loss also confused the classifiers, while jitter had minor effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In the early years of prosody research in automatic speech processing (Batliner and M¨obius, 2020), the focus was on detecting and classifying linguistic phenomena such as phrase accents, boundaries, disfluencies, sentence modality, and dialogue acts;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' such explicit modelling was then superseded by implicit modelling in AI approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Yet, it might gain momentum in our context, when we want to model markers for charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Asking questions during a conversation indicates that a person is listening and interested in what the conversation partner says;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' thus, it can indicate the presence in a conversation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In this context, acoustic and phonetic features are deployed, at which lexical features can also be crucial for the correct identification of declarative questions (Ando et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Furthermore, recurrent neural networks (RNNs) are applied in order to obtain the high-level contextual information over time (Tang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Before asking a question, it can also be beneficial to make a short pause, in order to show that one thinks about what the conversation partner has said, before giving an answer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This can convince the other person that one is listening carefully and is present in the conversation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Trouvain and Werner (2022) define these types of pauses as “gaps at turn changes in conversations” and do not regard them as typical speech pauses that are defined as “pauses in connected speech section”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Regarding speech production and the temporal structure of speech, pauses also play a crucial role (Trouvain and Werner, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' We have to distinguish between silent pauses and filled pauses such as “uh” or “uhm” (Batliner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 1995;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Bilac et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Trouvain and Werner, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Bilac et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2017) extract Mel-frequency cepstral coefficients (MFCC) audio features and apply support vector machines (SVMs) and random forest (RF) as classification methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Silent speech pauses and silence in audio can long since also be automatically detected, though (Xu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Iqbal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Power, described by Fox Cabane (2013) as high competence due to skills, abilities, or intelligence, can mainly be detected from audio by analysis of features related to fluency, such as speech rate and pauses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Luzardo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2014) perform an automated evaluation of student presentation skills and found a formant-based detection of filled pauses useful for classifying the overall quality of presentations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Further, they observed that speech rate is positively correlated with a speaker’s self-confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A similar approach based on detecting filled pauses is taken by Ochoa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2018) in the audio modality of their automatic feedback system for presentation skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The mimicry of a conversation partner can help establish a connection in dyadic interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This may happen either subconsciously, or deliberately to project greater warmth and presence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Amiriparian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2019) investigate ‘synchronisation’ (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', the mutual adaptation of conversation partners) in such dyadic conversations, using acoustic and linguistic features on a dataset with 394 speakers of six different cultures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' For the acoustic analysis, both handcrafted EGEMAPS and deep DEEPSPECTRUM features are extracted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Autoencoders are then used to measure the degree of synchronicity by training on one person and then reconstructing on their conversation partner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' As the conversation continues, the reconstruction error tends to decrease across the six cultures, indicating that speakers are mutually adapting to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2 Language A textual analysis lacks the information of prosody from a speech signal and must instead focus on linguistic cues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' For purely text-based empathy and warmth recognition, we highlight two applications here: mental health support and stereotyping in social media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' For presence, we also examine synchronicity in conversations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Frontiers 11 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma Sharma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2020) investigated empathy in the context of seeker-response interactions on text-based support platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Their framework, adapted for asynchronous communication, includes three mechanisms: emotional reactions to the seeker, interpretations conveying understanding, and explorations to improve understanding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A dataset of interactions collected from TalkLife and mental health subreddits was annotated in terms of empathy and rationales (text snippets motivating the empathy annotation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Then, a multi-task model based on two pre-trained ROBERTA encoders acting on seeker and response posts and a single attention layer combining their embeddings was proposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The inclusion of seeker post and attention was found beneficial while fine-tuning the encoders and adding the rationale task gave minor improvements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Stereotypes are frequently encountered in social media posts, and may positively or negatively shape opinions on groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Fraser et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2022) apply the warmth and competence model to stereotype identification by constructing a synthetic training set and building a model that can identify stereotypes in crowd-sourced data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' First, using a seed lexicon, polar directions for warmth and competence are defined in a word embedding subspace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Then, sentences are created via templates filled with words of known polarity from the lexicon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' For the word embeddings, ROBERTA is used, with GLOVE vectors serving as the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A combination of ROBERTA embeddings with intermediate dimensionality reduction via partial Least-Squares performed best.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Also, the generation of sentences combining both warmth and competence-associated words improved accuracy by increasing the orthogonality of training pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Amiriparian et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2019) use WORD2VEC to extract embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The conversations are split into two parts, and the cosine similarity between their embeddings is computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In addition, the co-occurrence of words between subjects in each part is counted and normalised with the total number of words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The word embeddings showed little synchronisation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', mutual adaptation of conversation partners) compared to the audio features, possibly indicating that the effect was happening too gradually on the linguistic level to measure during the short conversations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Word usage showed a clearer correlation but strongly differed across cultures, being most pronounced in British subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='3 Other Modalities In order to recognise a charismatic person, it is obvious to also consider other modalities, such as videos, images, and tactile sensors, as we mentioned earlier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In this context, videos and images might be especially beneficial for recognising how present and involved a person is in conversations by considering eye contact and facial expressions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Some studies already try to use eye tracking in order to analyse attention and gaze patterns during social interactions (Rogers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Vehlen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Rogers et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2018) also point out that some people show a preference towards mouth gaze, some for eye gaze, and others tend to vary the extent of their gaze between eyes and mouth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The authors apply a standard remote infrared eye tracker, consisting of an infrared sensor and a corresponding camera.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Vehlen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2021), on the other hand, employ special eye-tracking glasses enabling the opportunity for real-world experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In order to avoid expensive high-end processing devices, Zdarsky et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2021) introduce a convolutional neural network (CNN) relying on video frames from low-cost web cameras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Another study also aims at making eye tracking available for everyone owning a mobile device with a camera (Krafka et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Besides our eyes, facial expressions are a very important tool to express excitement and emotions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Erez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2008) state that charismatic leaders exhibit more aroused behaviours than non-charismatic leaders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' For instance, smiles are arguably among the most visible and frequent markers and can convey a feeling of warmth and intimacy but also of fear or compliance (Awamleh et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' There are already several approaches for automatic facial expression recognition (FER), most of them utilising deep learning (DL) and some sort of CNN in particular (Li and Deng, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Revina and Emmanuel, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Minaee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This is a provisional file, not the final typeset article 12 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The rough pipeline is to feed an input face image to a trained network and obtain a probability for a certain emotion category, such as happy or sad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In addition to using CNNs as the basic architecture blocks, there are extensions to improve performance, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', adding an attention mechanism to the network (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2 Automatic Generation of Charisma We can approach the task of automatically generating charisma in two different ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' On the one hand, we can use an approach to try to imitate the charismatic characteristics of people previously defined in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Charismatic persons are – as outlined above – characterised by a certain way of speaking (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', pitch, duration, or rhythm during the conversation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The characteristics assigned to charismatic individuals can be obtained from previous works, such as Davidson (2021) or Klofstad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2016) and the many listed above, and thus represent an expert-based definition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Using this information in combination with generative machine learning methods, precisely these properties can be enforced when generating speech, resulting in a more charismatic perception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' On the other hand, methods such as reinforcement learning can also be used to generate charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The advantage of using this method is that new, previously unknown charismatic factors can be learnt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1 Expert-based Generation of Charisma To simulate charismatic behaviour, the previously identified building blocks must be taken into account when generating spoken language (or other modalities).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In recent years, progress has been made in two main areas: First, generative methods (Borsos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2022) for creating completely new audio outputs, and second, constrained audio generation, as well as style transfer, approaches, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Huzaifah bin Md Shahrin and Wyse, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Manzelli et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2018), where an existing audio file is stylistically adapted to pre-defined properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The latest results of generative methods for speech such as AudioLM are almost indistinguishable from real speech by humans (Borsos et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The high audio quality of the generated samples paves the path for further charismatic audio generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Based on this, style control and style transfer approaches can be used to change certain features of the voice (Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Huzaifah bin Md Shahrin and Wyse, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' For example, Baird et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2019) analysed if deep generative audio can be emotional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In doing so, they changed pitch as an important speech characteristic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In a similar way, other features can be adapted, leading to a more charismatic voice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In addition to the audio modality, this approach can be extended to other modalities, such as video or text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Based on findings from previous work investigating which features are perceived as particularly charismatic in the respective modality, these constraints can be considered in generative methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' For example, Ghorbani et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2022) explore gesture generation from speech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Based on this work, charismatic gesture features can be taken into account, resulting in an overall charismatic perception of an AI such as by a virtual agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2 Learning-based Generation of Charisma Automatically generating charisma can also be formulated as a weakly supervised machine learning task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' For example, reinforcement learning methods have become increasingly popular in recent years in audio processing (and beyond) and are based on rewarding desired and punishing undesired behaviours (Latif et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Applied to charisma generation, various characteristics of the speech are exploratively tried during generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In doing so, the reward function includes usually indirect feedback from users on how charismatic the generated output is perceived.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' For example, pitch shifting, ranging from a low up to a Frontiers 13 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma very high pitch, can be explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Taking user feedback into account, the optimal pitch that is perceived as most charismatic (or seems to be so, as it best solves a task that is best solved with high charisma) can be determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In addition to direct user feedback, automatic charisma recognition approaches can be applied as a reward function to evaluate whether the generated behaviour is charismatic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In the context of generating emotional speech, Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2021) present such a paradigm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In a reinforcement learning setting, they train an automatic text-to-speech model to generate speech with emotions that can be discriminated by an automatic speech emotion recognition model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Another advantage of reinforcement learning is that new, so far unknown charismatic traits can be discovered using this method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This could range from obvious charismatic traits to entirely new charismatic behaviours that are as yet undiscovered in the literature and no one has thought of before, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', as in Baker et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2019) in a different context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Obviosuly, in addition to the audio modality, reinforcement learning for charisma generation can be similarly applied to video and text and beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' For instance, it might be beneficial for robots or virtual humans/agents to imitate charismatic gestures and appearance in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In another use case, Won et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2021) have already physically simulated humanoids performing competitive two-player sports, boxing and fencing, in a high degree-of-freedom environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The applied control policies generated responsive and natural-looking behaviours (Won et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 5 MOTIVATION AND APPLICATIONS OF COMPUTATIONAL CHARISMA A general motivation of charisma as a feature has been addressed in the introduction – we now, however, turn to more specific examples of application use cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' As outlined above, charisma is often associated with charm and ‘magnetism’, empowering to influence and inspire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Even if AI is not ‘experiencing’ or showing charisma as humans could, it can be trained or programmed to appear charismatic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This leads to a plethora of use cases which motivate its realisation, but also often come with a number of risks and dangers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Below, we list examples broadly grouped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Let us first consider different aspects of communication: AI empowered with charisma may lead conversations with humans in potentially more convincing ways, engaging them, and potentially influence them towards decisions in favour of the AI’s goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Similarly, it can simulate empathy and in general be perceived as more intelligent due to socioemotional intelligence skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Charimsatic techniques may improve everyday conversations by creating an emotional connection within communication partners or followers, make someone appear more powerful, competent, and worthy of respect Antonakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This holds in conversations, but also in public speeches via means of AI in the future – potentially to large audiences via the internet or in real-life settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In automatic translation, AI could help translate charismatically or preserve charismatic traits in the target language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' If AI is used for communication analysis, such as in mediation between human conversational partners, it can sense who is being more charismatic, more influencing, or more affected by the other party in a somewhat quantitative and subjective neutral manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Let us now turn to aspects of leadership: The great majority of use cases in research but also real-world applications is the training of charisma for enhanced leadership.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' More specifically, leaders in a variety of fields as politics, religion, or business highly benefit from being persuasive and likeable to achieve specific team goals and overcome potential resistance within employees or party members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Leaders may benefit greatly to win the trust of followers, manage delicate operations, punish and reward, and achieve their goals (Antonakis et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Levay (2010) even argues that charismatic leaders are invariably proponents of change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Charisma may help AI inspire and motivate teams – including encouraging and guidance through difficult challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Beyond, charisma can help AI to build and bind teams and communities in the first This is a provisional file, not the final typeset article 14 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Especially in times of remote work and digital delivered social interaction as video calls and emails, such qualities of team coherence and trust and commitment are highly challenged.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' More specifically, team leaders may be fed back easily in their communication style with an AI that recognises charismatic language and enhances team outcomes, putting the team members at ease and comfort by simultaneously persuading them of a new idea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' However, obtaining charisma – including by humans that are trained on charisma skills by AI – should not be abused for unethical goals (see section ethics of computational charisma below).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Furthermore, a charismatic AI could also recruit new staff potentially more successfully than a non-charismatic one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' However, it can also help it in negotiations within teams or with other parties in persuasive ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' If AI assists in decision making, charisma may help it to get the decisions across to the humans it presents it to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Healthcare next appears suited field for charismatic AI: Be it for mental health or general health care – charismatic AI could provide a compassionate, empathetic, and reassurance and support providing communication and assistance during diagnosis or interventions and therapy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Recognising charisma can also provide benefits for improving mental health.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Mental health issues are widespread, affecting nearly one in five people worldwide (Holmes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2018) and incurring enormous human suffering and economic costs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The majority of patients prefer therapy to medication (Holmes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2018), requiring the development of new solutions to improve the effectiveness of treatment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Depending on the application, those systems may either work in real-time for live session support or in an offline fashion for reviewing progress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A system that can process interactions and estimate the charismatic content may be a valuable tool for training professional practitioners.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' An effective therapist or counsellor can provide a sense of engagement and empathy to the patient, which in terms of charismatic dimensions involves both warmth (to show sympathy) and competence (to comprehend and engage with a patient’s problems).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In particular, this holds in case patients are reluctant or not sufficiently committed to overcome adverse feelings that sometime go along with behaviour change as for instance, confronting oneself with an anxiety-eliciting situation or the acquisition of new behaviours that feel initially uncomfortable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Both, therapists and clients could benefit from the rapport, empathy, believe of the ability to help, or persuasiveness of the therapist that go along with charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' An AI solution that can help review and train these skills will likely also be beneficial for the increasingly popular digital support platforms, to improve the qualification of responders (Sharma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Although therapists are usually trained in providing ease, comfort, and being empathetic and receive supervision in doing so, the deployed speech in regard of influence and affability may remain neglected, although there is a great potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Providing AI-generated automated feedback on the interaction and conversation style between therapist and client may improve the communication style and hence, therapy outcomes to a great extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Considering the human-to-human conversation mediation alluded to above, this could include couple or other counseling endowed with active listening, and empathetic moderation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Beside such fields, numerous other applications may benefit from charisma as an omnipotent quality: In education, a charismatic AI may be more engaging and captivating for students taught by it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Furthermore, as a coach and mentor, charismatic AI could be more motivating.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' However, an AI that can sense and measure charisma can also help in tutoring about charisma, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', teach humans to be charismatic by monitoring their progress.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Further, in customer service, marketing and sales, charismatic AI could provide friendly and likable service, but also persuade customers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In social media, charisma-empowered AI could interact with the social media users and generate a large group of followers, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', to influence opinions or provide positive brand connotation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This would include charismatic interaction with followers, responses to public reactions, or creation of new content in engaging ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' AI that has an understanding of charisma can also analyse charismatic behaviour and skills of users – be it, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', for scientific analyses or identifying potential influencers early on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' As to gaming, non-player-characters (NPCs) driven by AI could be charismatic Frontiers 15 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma in oncoming games leading to an increasingly immersive gaming sensation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' When it comes to event management and hospitality, charisma-empowered AI could provide engaging interaction with attendees of future virtual events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' These may encompass a wide variety of events reaching from online conferences and workshops to virtual fair trades, virtual tours of galleries, museums, real-estate properties, or virtual concerts, festivals, parties, and other entertainment events.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In particular, this could even include fundraising at suited events, where a charismatic AI could interact with donors persuasively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Beyond, hospitality at virtual or real-world occasions including checking guests at hotels in and out, question answering, recommendation giving, and furthermore, could be realised more charismatic by accordingly enabling future AIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' More generally, any form of embodied or virtual AI – e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', assistive or companion agents – could largely benefit from charismatic skills in the interaction with their users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This could help them in their communication and motivation as well as companionship including with lonely individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Across use cases, charismatic AI may be better positioned to personalise services to users by gaining access to their individual preferences, context, and history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 6 ETHICS OF COMPUTATIONAL CHARISMA Of course, we do not aim at dark charisma for appealing to the baser human instinct;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' moreover, we do not want to harness ‘deceiving charisma’, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', bright charisma for achieving goals that are per se unethical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' As for spoken language as modality, a cover term might be ‘emotional speech’ in the sense of adding more credibility and user attachment to human-computer interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Charisma is thus not a goal in itself, but a means to better achieve its goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Bright charismatic speech in itself cannot be unethical or ethical – it always depends on the application we are envisioning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Thus, out of all the (ethical) cornerstones relevant for applications defined in (Batliner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2022b), most might be ‘secondary’ for charisma, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', depend on the (type of) applications that use charismatic speech to pursue its goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Yet, by providing charisma as a tool, we have to account for the possibility that this tool can be used for ‘dark goals’ or, simply, that the outcome is not favourable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Thus, ethical requirements can be higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In the same way, dealing with vulnerable groups of course puts higher requirements on ethics, as for instance, privacy and avoiding harm are concerned (Batliner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A self-learning system can adapt to templates and users the same way as the chatbot Tay learnt racist language from its users (Wolf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This is a problem for every empathic virtual agent (Pamungkas, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Both dark charisma and bright charisma employed for dark goals can be created unwillingly or on purpose.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In the first case, not only do algorithmic measures have to be taken, and in both cases, society has to define red lines against them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Guerini and Stock (2005) reason about different capabilities of persuasive agents in case of ethical dilemmas (conflicting goals): (i) detect them and pass them on to a human;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (ii) compute a possible conduct and pass this on to a human for final decision;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (iii) make own decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' So far, we cannot envision artificial agents capable of doing this kind of reasoning in a reliable way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Thus, two principles should be followed: first, ethical dilemmas should be avoided by design, and if they are encountered, the decision has to be passed on to a human.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The most prominent specific ethical requirement might be disclosure of automation (Mohammad, 2022), belonging to the ethical cornerstones transparency and accountability: An according charismatic AI application has to make clear that the user is not interacting with some human being but with a computer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' This must not be done in the small print but in a way that is really visible to the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Transparency and accountability seem to be the primary cornerstones that impact autonomy, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', provide the possibility for the user to be aware of the artificial charisma the application / the agent is equipped with.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Then comes This is a provisional file, not the final typeset article 16 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma intrusive: ethical requirements are higher, the more intrusive the application is.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Carlos Montemayor et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2022) claim that genuine empathy in healthcare is not possible for AI because it cannot be really emotional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Yet, a charismatic agent might at least act as-if but we have to make it clear towards the patients that the AI (robots, avatars) is artificial and does not have emotions or empathy itself, in order to prevent this erroneous and dangerous attribution that even can lead the user to fall in love with such a charismatic artificial agent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The illusion of humanness can create the ‘uncanny valley’ effect (Mori et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', 2012) when emotional/charismatic agents are close to human but still not close enough, by that irritating the human interaction partner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Both this uncanny valley and a too perfect humanness might be avoided by explicitly mentioning the artificial character of the agent, or by creating it in such a way that its non-human character is evident.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Note that some authors argue, under certain premises, in favour of anthropomorphous robots (Darling, 2017) or deception-capable robots (Isaac and Bridewell, 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Although possible benefits might be evident, it is not clear at all how any dishonest use of such robots – or, in our case, charismatic agents - could be prevented if not banned from the beginning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 7 CONCLUSION AND OUTLOOK We discussed a ‘blueprint’ for a charisma-savvy Artificial Intelligence – able to analyse human charisma and generate charismatic behaviour itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' To this end, we introduced the origin and concept of charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' We then discussed functional aspects of charsima by psychological models, mainly introducing two concepts based on the factors influence and affability as well as the theoretical concept of power, presence, and warmth as pillars of charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' We argued that charismatic behaviour can be acquired and presented a brief summary of the literature on its acquisition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' We then moved to formal aspects giving specific details on charisma as portrayed in spoken language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The choice to first focus on this modality was made, as today’s AI largely interacts via spoken language with humans, and other modalities such as facial expression or body posture are yet to gain relevance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' We further outlined computational aspects of modelling charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Here, we summarised the small body of literature on the automatic recognition and generation of charisma for audio, language, but also other modalities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' As to the generation of charisma, we highlighted two avenues: First, based on the findings in the literature summarised up to that point in this article, one could design a charisma-empowered AI based on expert knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Alternatively, weakly supervised machine learning could be exploited by either active learning methods questioning users about charisma skills of an AI or even by learning reinforced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In the latter, an AI would gain charismatic skills – potentially even such unknown to date to humans – that would help better accomplish its goal by interacting with users in real-world tasks – ideally at scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' We then moved towards the plethora of potential use-cases of charisma-enabled AI, before introducing major ethical concepts to be considered at all times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Given the state-of-knowledge on charisma and the state-of-play in today’s AI, it seems perfectly possible to endow AI with charisma skills.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Currently, the literature on using machine learning for the recognition or generation of charisma or traits thereof largely focuses on the individual in isolation related to fields such as Affective Computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' However, disciplines such as Social Signal Processing moved also the consideration of the interplay between communicating parties into the foreground, which can be crucial for modelling charisma, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', when it comes to mimicry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Further, audio, text, and video have so far been mostly considered, but touch, and more general haptics, have been touched upon as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In the future, other modalities including smell, and further biological signals could be included.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Further, the loop between recognition and generation of charismatic behaviour might be fully closed learning charismatic input/output of an AI ‘end-to-end’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Overall, we envision a plethora of use-cases with great value of charsima-savvy AI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' However, weakly- supervised AI learning from large data may easily lead to new charismatic behaviours found by AI Frontiers 17 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma potentially reflecting back on human-to-human charismatic behaviour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Charismatic AI may also empower ‘dark’ purposes or lead to negative effects such as AI influencing voters, e-shoppers, getting users addicted to or fall in love with the AI, and many more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' As a community, we have to always contribute best to assure positive usage and the protection of users – including in particular also from a technical end.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A blueprint therefore might be considerably more challenging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Let us be best prepared for the rapid advent of charismatic AI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' CONFLICT OF INTEREST STATEMENT The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' AUTHOR CONTRIBUTIONS All authors contributed equally to writing, revising, and editing the manuscript and approved the final version of the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' FUNDING This work is supported by the DFG’s Reinhart Koselleck project No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 442218748 (AUDI0NOMOUS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' REFERENCES Amiriparian, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Han, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Schmitt, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Baird, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Mallol-Ragolta, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Milling, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Synchronization in interpersonal speech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Frontiers in Robotics and AI 6 Anderson, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Klofstad, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Preference for Leaders with Masculine Voices Holds in the Case of Feminine Leadership Roles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Plos one 7, e51216 Anderson, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Klofstad, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Mayew, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Venkatachalam, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Vocal Fry May Undermine the Success of Young Women in the Labor Market.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Plos one 9, e97506 Ando, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Asakawa, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Masumura, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Kamiyama, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Kobashikawa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Aono, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Automatic question detection from acoustic and phonetic features using feature-wise pre-training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In INTERSPEECH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 1731–1735 Antonakis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Transformational and charismatic leadership.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The nature of leadership , 256–288 Antonakis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Dalgas, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Predicting elections: Child’s play!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Science 323, 1183.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1126/ science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1167748 Antonakis, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Fenley, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Liechti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Learning Charisma Transform yourself into the person others want to follow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Academy of Management Learning and Education Awamleh, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Gardner, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Perceptions of leader charisma and effectiveness: The effects of vision content, delivery, and organizational performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Leadership Quarterly 10, 345–373 Awamleh, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Towards a model of charismatic non-verbal impression management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' International Business & Economics Research Journal (IBER) 2 Baird, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Amiriparian, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Schuller, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Can deep generative audio be emotional?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' towards an approach for personalised emotional audio generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In 2019 IEEE 21st International Workshop on Multimedia Signal Processing (MMSP) (IEEE), 1–5 Baker, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Kanitscheider, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Markov, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Powell, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', McGrew, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Emergent tool use from multi-agent autocurricula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' arXiv preprint arXiv:1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='07528 Batliner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Hantke, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Schuller, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Ethics and good practice in computational paralinguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' IEEE Transactions on Affective Computing 13, 1236–1253.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1109/taffc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='3021015 This is a provisional file, not the final typeset article 18 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma Batliner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Kießling, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Burger, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and N¨oth, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Filled Pauses in Spontaneous Speech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' of ICPhS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 3, 472–475 Batliner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and M¨obius, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Prosody in Automatic Speech Processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In The Oxford Handbook of Language Prosody, eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Gussenhoven and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Chen (Oxford, UK: Oxford University Press).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 633–645 Batliner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Neumann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Burkhardt, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Baird, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Meyer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Vu, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2022b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Ethical awareness in paralinguistics: A taxonomy of applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' International Journal of Human–Computer Interaction 0, 1–18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1080/10447318.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2140385 Biancardi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Towards a computational model for first impressions generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Proceedings of the 19th ACM International Conference on Multimodal Interaction (New York, NY, USA: Association for Computing Machinery), ICMI ’17, 628–632.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1145/3136755.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='3137031 Biancardi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Cafaro, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Pelachaud, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Analyzing first impressions of warmth and competence from observable nonverbal cues in expert-novice interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Proceedings of the 19th ACM International Conference on Multimodal Interaction (New York, NY, USA: Association for Computing Machinery), ICMI ’17, 341–349.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1145/3136755.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='3136779 Biancardi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Mancini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Cafaro, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Chanel, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Pelachaud, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A computational model for managing impressions of an embodied conversational agent in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In 2019 8th International Conference on Affective Computing and Intelligent Interaction (ACII).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 1–7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1109/ ACII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='8925495 Bilac, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Chamoux, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Lim, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Gaze and filled pause detection for smooth human-robot conversations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In 2017 IEEE-RAS 17th International Conference on Humanoid Robotics (Humanoids) (IEEE), 297–304 Borsos, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Marinier, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Vincent, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Kharitonov, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Pietquin, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Sharifi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Audiolm: a language modeling approach to audio generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' arXiv preprint arXiv:2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='03143 Burgoon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Relational message interpretations of touch, conversational distance, and posture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Journal of Nonverbal behavior 15, 233–259 Burke, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Brinkerhoff, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Capturing charisma: Notes on an elusive concept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Journal for the Scientific Study of Religion 20, 274 Carlos Montemayor, Jodi Halpern, and Abrol Fairweather (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In principle obstacles for empathic AI: why we can’t replace human empathy in healthcare.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' AI & SOCIETY 37, 1353–1359 Colman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Game theory and experimental games: The study of strategic interaction (Elsevier) Conger, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Kanungo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Menon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Mathur, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Measuring charisma: Dimensionality and validity of the conger-kanungo scale of charismatic leadership.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Canadian Journal of Administrative Sciences-revue Canadienne Des Sciences De L Administration 14, 290–301 Cuddy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Fiske, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Glick, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Warmth and competence as universal dimensions of social perception: The stereotype content model and the bias map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Advances in experimental social psychology 40, 61–149 Darling, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' “Who’s Johnny?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Anthropomorphic Framing in Human-Robot Interaction, Integration, and Policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Robot Ethics 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='0: From Autonomous Cars to Artificial Intelligence, eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Lin, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Abney, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Jenkins (Oxford, UK: Oxford University Press).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 1–22 Davidson, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The versatility of creaky phonation: Segmental, prosodic, and sociolinguistic uses in the world’s languages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' WIREs Cogn Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 12, e1547 D’Errico, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Signorello, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Demolin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Poggi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The perception of charisma from voice: A cross-cultural study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In 2013 Humaine Association Conference on Affective Computing and Intelligent Interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 552–557.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1109/ACII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='97 Frontiers 19 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma Erez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Misangyi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Johnson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', LePine, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Halverson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Stirring the hearts of followers: Charismatic leadership as the transferal of affect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Journal of applied psychology 93, 602 Ernst, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Banks, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Loignon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Frear, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Williams, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Arciniega, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Virtual charismatic leadership and signaling theory: A prospective meta-analysis in five countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The Leadership Quarterly 33, 101541.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='leaqua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='101541 Ferris, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Treadway, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Kolodinsky, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Hochwarter, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Kacmar, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Douglas, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Development and validation of the political skill inventory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Journal of management 31, 126–152 Fiske, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Cuddy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Glick, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Universal dimensions of social cognition: Warmth and competence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Trends in cognitive sciences 11, 77–83 Fox Cabane, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The Charisma Myth: How Anyone Can Master the Art and Science of Personal Magnetism, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 1 (Portfolio Trade) Fragouli, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The dark-side of charisma and charismatic leadership.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' business management review 9, 298–307 Fraser, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Kiritchenko, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Nejadgholi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational modeling of stereotype content in text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Frontiers in Artificial Intelligence 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='3389/frai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='826207 [Dataset] Fraser, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Nejadgholi, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Kiritchenko, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Understanding and countering stereotypes: A computational approach to the stereotype content model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 02596 Freeth, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Bugembe, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Social partner gaze direction and conversational phase;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' factors affecting social attention during face-to-face conversations in autistic adults?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Autism 23, 503–513 Gallardo, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Effects of transmitted speech bandwidth on subjective assessments of speaker characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In 2018 Tenth International Conference on Quality of Multimedia Experience (QoMEX).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 1–5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1109/QoMEX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='8463395 Gallardo, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Sanchez-Iborra, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' On the impact of voice encoding and transmission on the predictions of speaker warmth and attractiveness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Knowl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Discov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Data 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1145/ 3332146 Ghorbani, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Ferstl, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Holden, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Troje, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Carbonneau, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='-A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Zeroeggs: Zero-shot example-based gesture generation from speech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' arXiv preprint arXiv:2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='07556 Greer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', , and Winters, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The perception of coolness: Differences in evaluating voice quality in male and female speakers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Proceedings of the 18th international congress of phonetic sciences (Glasgow, Scotland), 1–102 Guerini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Stock, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Toward ethical persuasive agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Proceedings of the International Joint Conference of Artificial Itelligence Workshop on Computational Models of Natural Argument (Edinburgh,Scottland), 1–5 Guerini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Stock, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Zancanaro, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Persuasion models for intelligent interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Proceedings of the IJCAI Workshop on Computational Models of Natural Argument (Acapulco, Mexico), 1–6 Hamilton, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Stewart, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Extending an information processing model of language intensity effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Communication Quarterly 41, 231–246 Hertenstein, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Holmes, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', McCullough, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Keltner, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The communication of emotion via touch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Emotion 9, 566 Hertenstein, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Keltner, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', App, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Bulleit, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Jaskolka, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Touch communicates distinct emotions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Emotion 6, 528 Holladay, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Coombs, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Communicating visions: An exploration of the role of delivery in the creation of leader charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Management Communication Quarterly 6, 405–427 This is a provisional file, not the final typeset article 20 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma Holmes, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Ghaderi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Harmer, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Ramchandani, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Cuijpers, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Morrison, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The lancet psychiatry commission on psychological treatments research in tomorrow’s science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The Lancet Psychiatry 5, 237–286 Holz, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Larrouy-Maestri, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Poeppel, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The paradoxical role of emotional intensity in the perception of vocal affect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Nature, Scientific Reports 11, 9663 House, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A 1976 Theory of Charismatic Leadership.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Working Paper Series 76-06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', ERIC Huzaifah bin Md Shahrin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Wyse, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Applying visual domain style transfer and texture synthesis techniques to audio: Insights and challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Neural Comput.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 32, 1051–1065.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 1007/s00521-019-04053-8 Iqbal, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Kong, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Plumbley, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Wang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' General-purpose audio tagging from noisy labels using convolutional neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Proceedings of the Detection and Classification of Acoustic Scenes and Events 2018 Workshop (DCASE2018 (Tampere University of Technology), 212–216 Isaac, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Bridewell, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' White Lies on Silver Tongues: Why Robots Need to deceive (and how).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Robot Ethics 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='0: From Autonomous Cars to Artificial Intelligence, eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Lin, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Abney, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Jenkins (Oxford, UK: Oxford University Press).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 157–172 Keating, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Channelling charisma through face and body status cues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Social psychological dynamics , 93–111 Keller, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Siegrist, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Earle, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Gutscher, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The general confidence scale: coping with environmental uncertainty and threat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Journal of Applied Social Psychology 41, 2200–2229 Klofstad, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Anderson, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Nowicki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Perceptions of Competence, Strength, and Age Influence Voters to Select Leaders with Lower-Pitched Voices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Plos one 10, e0133779 Klofstad, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Nowicki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Anderson, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' How Voice Pitch Influences Our Choice of Leaders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' American Scientist 104, 282 Knight, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Simmons, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Estimating human interest and attention via gaze analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In 2013 IEEE International Conference on Robotics and Automation (IEEE), 4350–4355 Krafka, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Khosla, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Kellnhofer, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Kannan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Bhandarkar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Matusik, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Eye tracking for everyone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Proceedings of the IEEE conference on computer vision and pattern recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 2176–2184 Latif, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Cuay´ahuitl, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Pervez, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Shamshad, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Ali, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Cambria, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A survey on deep reinforcement learning for audio-based applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Artificial Intelligence Review , 1–48 Levay, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Charismatic leadership in resistance to change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The Leadership Quarterly 21, 127–143.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='leaqua.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='010 Li, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Deng, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Deep facial expression recognition: A survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' IEEE transactions on affective computing Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Zeng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Shan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Occlusion aware facial expression recognition using cnn with attention mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' IEEE Transactions on Image Processing 28, 2439–2450 Liu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Sisman, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Reinforcement Learning for Emotional Text-to-Speech Synthesis with Improved Emotion Discriminability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Interspeech 2021 (ISCA), 4648–4652.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='21437/ Interspeech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2021-1236 Luzardo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Guam´an, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Chiluiza, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Castells, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Ochoa, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Estimation of Presentations Skills Based on Slides and Audio Features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Proceedings of the 2014 ACM Workshop on Multimodal Learning Analytics Workshop and Grand Challenge (Istanbul Turkey: ACM), 37–44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1145/ 2666633.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2666639 Frontiers 21 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma Manzelli, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Thakkar, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Siahkamari, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Kulis, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Conditioning Deep Generative Raw Audio Models for Structured Automatic Music.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Proceedings of the 19th International Society for Music Information Retrieval Conference (Paris, France), 1–8 McCrae, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Costa, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', John, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Robins, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Pervin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Handbook of personality: Theory and research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' New York, NY: Guilford Mehrabian, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Wiener, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (1967).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Decoding of inconsistent communications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Journal of Personality and Social Psychology 6, 109–114 Mhatre, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Riggio, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Charismatic and Transformational Leadership (Oxford University Press).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1093/oxfordhb/9780199755615.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='012 Minaee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Minaei, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Abdolrashidi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Deep-emotion: Facial expression recognition using attentional convolutional network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Sensors 21, 3046 Mohammad, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Ethics Sheet for Automatic Emotion ecognition and Sentiment Analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Linguistics 48, 239–278 Mori, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', MacDorman, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Kageki, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The uncanny valley.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' IEEE Robotics & Automation Magazine 19, 98–100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1109/MRA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2192811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Japanese original 1970 Moskowitz, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Gill, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Person perception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In The Oxford handbook of cognitive psychology, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Reisberg (Oxford University Press).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 918–942 Niebuhr, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Brem, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Michalsky, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Neitsch, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2020a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' What makes business speakers sound charismatic?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A contrastive acoustic-melodic analysis of Steve Jobs and Mark Zuckerberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Cadernos de Linguistica e Teoria da Literatura 1 Niebuhr, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Neitsch, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Michalsky, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2020b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Akustisches Charisma Profiling – Auf dem Weg zur digitalen Rhetorik.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Akustik Journal 02, 7–22 Ochoa, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Dom´ınguez, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Guam´an, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Maya, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Falcones, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Castells, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The RAP system: Automatic feedback of oral presentation skills using multimodal analysis and low-cost sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Proceedings of the 8th International Conference on Learning Analytics and Knowledge (Sydney New South Wales Australia: ACM), 360–364.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1145/3170358.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='3170406 Orzeatja, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Leaders and their charisma management and socio-humanities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Review of the Air Force Academy 9, 92–96 Pamungkas, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Emotionally-aware chatbots: A survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' CoRR abs/1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='09774 Raven, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Court, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Raven’s progressive matrices and vocabulary scales, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 759 (Oxford pyschologists Press Oxford) Revina, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Emmanuel, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A survey on human face expression recognition techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Journal of King Saud University-Computer and Information Sciences 33, 619–628 Rogers, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Speelman, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Guidetti, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Longmuir, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Using dual eye tracking to uncover personal gaze patterns during social interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Scientific reports 8, 1–9 Rosenberg, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Hirschberg, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Charisma perception from text and speech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Speech Communication 51, 640–655 Schuller, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Batliner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Paralinguistics – Emotion, Affect, and Personality in Speech and Language Processing (Chichester, UK: Wiley) Schuller, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Steidl, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Batliner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', N¨oth, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Vinciarelli, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Burkhardt, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A Survey on Perceived Speaker Traits: Personality, Likability, Pathology, and the First Challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computer Speech and Language, Special Issue on Next Generation Computational Paralinguistics 29, 100–131 Schutte, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Malouff, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Hall, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Haggerty, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Cooper, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Golden, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Development and validation of a measure of emotional intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Personality and individual differences 25, 167–177 This is a provisional file, not the final typeset article 22 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma [Dataset] Sharma, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Miner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Atkins, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Althoff, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A computational approach to understanding empathy expressed in text-based mental health support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='48550/ARXIV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='08441 Tang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Huang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Wu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Meng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Xu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Cai, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Question detection from acoustic features using recurrent neural network with gated recurrent unit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (IEEE), 6125–6129 Tickle-Degnen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Rosenthal, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (1990).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The nature of rapport and its nonverbal correlates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Psychological Inquiry 1, 285–293.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1207/s15327965pli0104 1 Towler, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Effects of charismatic influence training on attitudes, behavior, and performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Personnel psychology 56, 363–381 Trouvain, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Weiss, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Barkat-Defradas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Voice Attractiveness: Concepts, Methods, and Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Voice Attractiveness – Studies on Sexy, Likable, and Charismatic Speakers, eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Weiss, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Trouvain, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Barkat-Defradas, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Ohala (Singapore: Springer).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 3–16 Trouvain, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Werner, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A phonetic view on annotating speech pauses and pause-internal phonetic particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Transkription und Annotation gesprochener Sprache und multimodaler Interaktion: Konzepte, Probleme, L¨osungen , 55 Tskhay, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Zhu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Zou, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Rule, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Charisma in everyday life: Conceptualization and validation of the general charisma inventory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Journal of Personality and Social Psychology 114, 131 Tubbs, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Learning charisma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A Guide to the Scientific Career: Virtues, Communication, Research and Academic Writing , 103–107 Van Erp, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Toet, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Social touch in human–computer interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Frontiers in digital humanities 2, 2 Vehlen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Spenthof, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', T¨onsing, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Heinrichs, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Domes, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Evaluation of an eye tracking setup for studying visual attention in face-to-face conversations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Scientific reports 11, 1–16 Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Chanel, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' An open dataset for impression recognition from multimodal bodily responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In 2021 9th International Conference on Affective Computing and Intelligent Interaction (ACII).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 1–8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1109/ACII52823.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='9597421 Wang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Peng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Yang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Lu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Qiao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Suppressing uncertainties for large-scale facial expression recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 6897–6906 Weatherby, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Ochoa, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Nielsen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The Making of a Charismatic Killer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' International Journal of Forensic Sciences 1, 1–21 Weber, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (1922).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Grundriß der Sozial¨okonomie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Abteilung.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Wirschaft und Gesellschaft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Bearbeitet von Max Weber (T¨ubingen: J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Mohr) Weiss, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Burkhardt, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Voice attributes affecting likability perception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' of Interspeech (Makuhari, Japan), 1485–1488 Weiss, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Wilson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Hertenstein, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Campos, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The tactile context of a mother’s caregiving: implications for attachment of low birth weight infants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Infant Behavior and Development 23, 91–111 Welsh, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' and Lenzenweger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Psychopathy, charisma, and success: A moderation modeling approach to successful psychopathy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Journal of Research in Personality 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='jrp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='104146 Weninger, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Krajewski, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Batliner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Schuller, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' The Voice of Leadership: Models and Performances of Automatic Analysis in On-Line Speeches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' IEEE Transactions on Affective Computing 3, 496–508 Frontiers 23 Schuller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Computational Charisma Wolf, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Miller, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Grodzinsky, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Why we should have seen that coming: comments on microsoft’s tay ‘experiment,’ and wider implications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' ACM SIGCAS Computers and Society 47, 54–64 Won, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Gopinath, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Hodgins, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Control strategies for physically simulated characters performing two-player competitive sports.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' ACM Transactions on Graphics (TOG) 40, 1–11 Xu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Wu, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Ishiwaka, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Vondrick, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Zheng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Listening to sounds of silence for speech denoising.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Advances in Neural Information Processing Systems 33, 9633–9648 Yang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Huynh, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Tabata, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Cestero, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Aharoni, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Hirschberg, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' What Makes a Speaker Charismatic?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Producing and Perceiving Charismatic Speech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Speech Prosody 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' 685–689.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='21437/SpeechProsody.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='2020-140 Zdarsky, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Treue, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Esghaei, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' A deep learning-based approach to video-based eye tracking for human psychophysics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Frontiers in human neuroscience 15 Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', Pan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', He, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=', and Ling, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Learning latent representations for style control and transfer in end-to-end speech synthesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' In ICASSP 2019-2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (IEEE), 6945–6949 Zoghaib, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Persuasion of voices: The effects of a speaker’s voice characteristics and gender on consumers’ responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} +page_content=' Recherche et Applications en Marketing 34, 83–110 This is a provisional file, not the final typeset article 24' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/SdAyT4oBgHgl3EQfVPfZ/content/2301.00142v1.pdf'} diff --git a/SdE2T4oBgHgl3EQfCAaW/content/2301.03609v1.pdf b/SdE2T4oBgHgl3EQfCAaW/content/2301.03609v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f35644a1f2b856be5e992c623d9c6e0a7655e69f --- /dev/null +++ b/SdE2T4oBgHgl3EQfCAaW/content/2301.03609v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:989f7a32176cdad4be8ca196e970ee93a2497246d3988e36a2ca6b156ab481b7 +size 4297887 diff --git a/T9E4T4oBgHgl3EQfmg0h/vector_store/index.pkl b/T9E4T4oBgHgl3EQfmg0h/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..ae42dbd4188e46aa8430dd166a413d572b83c0a5 --- /dev/null +++ b/T9E4T4oBgHgl3EQfmg0h/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d83655ff7e418e4ef0922c4cfc5563f5b7acdade13f46edbe5cdf239f440e707 +size 172533 diff --git a/TNAzT4oBgHgl3EQfJftl/content/tmp_files/2301.01080v1.pdf.txt b/TNAzT4oBgHgl3EQfJftl/content/tmp_files/2301.01080v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..d730a2d238fffb067c0f6b58b11b6002dd69bed7 --- /dev/null +++ b/TNAzT4oBgHgl3EQfJftl/content/tmp_files/2301.01080v1.pdf.txt @@ -0,0 +1,1474 @@ +arXiv:2301.01080v1 [eess.SP] 3 Jan 2023 +1 +A Laplacian Gaussian Mixture Model for Surface +EMG Signals of Human Arm Activity +Durgesh Kusuru, Student Member, IEEE, Anish C. Turlapaty Member, IEEE and +Mainak Thakur Member, IEEE +Abstract—The probability density function (pdf) of surface +Electromyography (sEMG) signals follows any one of the stan- +dalone standard distributions: the Gaussian or the Laplacian. +Further, the choice of the model is dependent on muscle contrac- +tion force (MCF) levels. Hence, a unified model is proposed which +explains the statistical nature of sEMG signals at different MCF +levels. In this paper, we propose the Laplacian Gaussian Mixture +(LGM) model for the signals recorded from upper limbs. This +model is able to explain the sEMG signals from different activities +corresponding to different MCF levels. The model is tested on +different bench-mark sEMG data sets and is validated using both +the qualitative and quantitative perspectives. It is determined +that for low and medium contraction force levels the proposed +mixture model is more accurate than both the Laplacian and the +Gaussian models. Whereas for high contraction force level, the +LGM model behaves as a Gaussian model. The mixing weights +of the LGM model are analysed and it is observed that for +low and medium MCF levels both the mixing weights of LGM +model do contribute. Whereas for high contraction force levels +the Laplacian weight becomes weaker. The proposed LGM model +for sEMG signals from upper limbs explains sEMG signals at +different MCF levels. The proposed model helps in improved +understanding of statistical nature of sEMG signals and better +feature representation in the classification problems. +Index Terms—Surface electromyography (sEMG), Statistical +models, Probability density function(pdf), Mixture models, Mus- +cle contraction force, Parameter estimation, EM algorithm. +I. INTRODUCTION +A. Background +Modeling of surface Electromyography (sEMG) signals +has several applications such as 1) developing insights into +sEMG signal generation from the constituent motor unit action +potentials (MUAPs) that forms a basis for the sEMG signal +synthesis [1] and simulation studies [2], 2) improving inter- +pretation of the sEMG signals in clinical settings for example, +in the diagnosis of neuromuscular disorders [3], 3) analyzing +inter-relations between the sEMG signals and the source +muscle groups, for instance, in the sport sciences research +[4], [5], [6], and 4) building visualization tools to support +movement sciences [7], muscle physiology examinations and +the sport science education. +The sEMG signal models can +be classified based on 1) bio-electrical, 2) statistical, and 3) +machine learning principles. The earliest models were based +on the physiological characteristics and the electrical activity +This research is funded by SERB, Govt. of India under Project Grant No. +CRG/2019/003801. +The authors are with the Bio-signal Analysis Group, Indian Institute of +Information Technology Sri City, Chittoor, Andhra Pradesh, 517646, India. (e- +mails: durgesh.k@iiits.in, anish.turlapaty@iiits.in and mainak.thakur@iiits.in +in muscle fibers and motor units. For example, in [8] and +[9], the sEMG signal is represented as a linear combination +of MUAPs, where the action potential is modeled as a cur- +rent tripole propagating from the neuromuscular junction to +the fiber-tendon ending. In [10], a multi-scale physiological +muscle model was used to estimate the muscle force from the +sEMG signals corresponding to voluntary movements. +In the statistical approach, the sEMG signal is considered +as a random signal and the typical characteristics modeled +are the signal strength (samples), the temporal evolution of a +signal, the autocorrelation of a single channel, and the spatial +cross-correlations among multiple channels. The probabilistic +models of the sEMG signal strength have evolved considerably +during the last few decades as reviewed in the next section. +In the temporal models, sEMG signals are usually represented +by a linear autoregressive process [11] [12]. To estimate the +MUAPs, the sEMG signals obtained from isometric contrac- +tions are modeled as an output of a LTI system with non- +Gaussian white noise as an input [13]. In the variance based +model, a sEMG signal is treated as a compound random +process. For example, in a scale mixture model [14], the signal +strength is modeled as a Gaussian process conditioned on the +variance which is modeled as an inverse gamma variable. +The pattern classification of the sEMG signals plays a key +role in applications such as the orthotic exoskeleton control +[15], the human movement analysis [16], and the neuromus- +cular disease diagnosis. For example, they can provide suitable +inputs such as motor control parameters to drive a limb ex- +oskeleton. In the machine learning methods, suitable features +can be extracted based on the probability density function (pdf) +of the sEMG signal [17]. In the human movement analysis, +sEMG signals can be used for discrimination among different +actions, for example, hand gestures vs. grasping of objects +[18]. In the neuormuscular disease diagnosis they can be used +to study conditions such as myopathy which is related to the +skeletal muscles causing them to become weaker and leading +to muscle pain, weakness, fatigue and other symptoms [19]. +Decoding information contained in the sEMG signals is critical +and requires a reliable and precise solution. In human-machine +interaction applications, deep learning methods play a crucial +role and are used to achieve improved performance in tasks +such as the movement classification, the joint angle prediction, +and the force/torque estimation [20]–[22]. The focus of this +paper is statistical modeling of the sEMG signal strength. +B. Existing Models for pdf of sEMG strength +Typical applications of a statistical signal model for sEMG + +2 +signals are 1) a better understanding of statistical nature of +sEMG signals, 2) an improved feature representation in the +classification problems, and 3) a qualitative analysis of signals. +Depending on the muscle contraction level and the type of +muscle, the existing models of sEMG signal strength are based +on any of the standalone standard distributions such as the +Gaussian or the Laplacian pdf. Following is a summary, based +on studies since 1970s, of the existing models of the sEMG +signals acquired from different muscle groups of human upper +limbs. +In 1974, sEMG measurements were performed by Roesler +[23] and it was proposed that under constant force measure- +ment conditions, the sEMG signals follow a Gaussian distri- +bution. Miler-Brown et al. [24] observed that the distribution +of the sEMG signals recorded from the first dorsal interosseus +(FDI) muscle (back of a hand) at a lower force level has a +sharper peak around zero than the Gaussian distribution and +as the force level increases the sharpness near zero reduces. In +[25], the sEMG signals collected from biceps muscles were +observed to follow a Gaussian distribution for the low and +medium levels of MCF. Hunter et al. [26] analyzed the density +of the sEMG signals from the biceps under constant MCF +against a Gaussian density and reported that it has a narrow +peak around zero. Later, Bilodeau et al. [27] observed that for +lower MCF levels, the sEMG signals from the biceps have a +non-Gaussian nature with a peak near zero and at a higher +MCF level their distribution was observed to tend toward a +Gaussian model. Clancy and Hogan [28] experimentally found +that the density of sEMG signals at a constant MCF lies in +between a Gaussian and a Laplacian pdf. In [29], it was noticed +that the pdf of sEMG signal, 1) has a sharper peak near zero +and a longer tail than a usual Gaussian distribution at the low +and high levels of MCF, and 2) follows a Gaussian model +at a medium MCF level. In [30], at high MCF level, the +distribution of the sEMG signals was found to be a Gaussian. +Based on the recent studies, the sEMG signals at higher MCF +levels from the flexor digitorum superficialis [31], [32] and the +biceps [33], follow a Gaussian model. Based on this review, +there is no unique statistical model that explains the activity at +various contraction force levels. In many cases, it may not be +possible to describe the data using the standard single density +models. In such cases, often, modeling the data as a mixture +of densities is an appropriate approach. Contributions +• A unifying mixture model is proposed for the sEMG +signals that explains the statistical nature of the signal +for different levels of muscle contraction force. +• The proposed model is tested on multiple benchmark +sEMG datasets and the suitability of the model is com- +pared against the existing models using both qualitative +and quantitative methods. +• The weights of the mixture components are analyzed for +different activities and intensities and a possible inter- +relation is illustrated. +II. STATISTICAL MODEL AND PROBLEM DESCRIPTION +A. Laplacian Gaussian Mixture Model +In [34], a Laplacian Gaussian Mixture (LGM) model was +introduced and verified on a single sEMG dataset. In this +work, the LGM model is further analyzed and its suitability +is evaluated for various benchmark datasets corresponding +to distinct upper limb activities at different MCF levels. A +description of the proposed model follows. +Let the strength of the discrete time sEMG signal be +represented by a random variable Y . The LGM model is +written as +fY (y; Θ) = λ1f1(y; θ1) + λ2f2(y; θ2) +(1) +y denotes a realization of Y and Θ = [λ1, λ2, θ1, θ2] is the set +of unknown parameters. λ1 and λ2 are the mixing weights that +add to unity. θ1 and θ2 are parameters of component densities. +f1(y; θ1) is a Laplacian density defined as +f1(y; θ1) = +1 +2σ1 +exp +� +− |y − µ1| +σ1 +� +− ∞ < y < ∞ +(2) +and f2(y; θ2) a Gaussian density given by +f2(y; θ2) = +1 +� +2πσ2 +2 +exp +� +− (y − µ2)2 +2σ2 +2 +� +−∞ < y < ∞ (3) +note that θ1 = [µ1, σ1] +and +θ2 = [µ2, σ2 +2] are parameters +of the respective densities. As illustrated in (1), the mixing +weights λ1 and λ2 are the hidden parameters. The unknown +parameters of the LGM model are estimated from the sEMG +data using the expectation-maximization (EM) Algorithm [35]. +Note that the EM algorithm is commonly used for estimation +of parameters of the Gaussian mixture model based on which +a similar EM methodology is derived for the proposed model. +B. +Parameter Estimation Problem +Consider an array y = {yn}N−1 +n=0 where yn represents a +discrete sample of a sEMG signal. Based on the latent variable +used in Gaussian mixture models [35], a discrete random +vector w is defined as +w = {wn}N−1 +n=0 +(4) +here wn = [wn,1, wn,2] and has two distinct states with +corresponding likelihoods (mixing weights) +p(wn,1 = 1, wn,2 = 0) += +λ1 +(5) +p(wn,1 = 0, wn,2 = 1) += +λ2 +and the marginal likelihood of these hidden states is given by +p(wn) = λwn,1 +1 +λwn,2 +2 +(6) +The conditional pdf of yn given wn and Θ is +f(yn|wn; Θ) = +2 +� +j=1 +(fj(yn; θj))wn,j +(7) +Here, yn are i.i.d. The joint density of the data, the hidden +states and the unknown parameters is +f(y, w; Θ) = +N−1 +� +n=0 +2 +� +j=1 +(λjfj(yn; θj))wn,j +(8) +The estimation problem can be stated as follows: given the +data y which follows the LGM model (1), the objective is +to estimate the parameters Θ and the related statistics in the +model (1). The next section describes the parameter estimation +for the LGM model using the EM algorithm. + +3 +C. +EM-Algorithm +The complete data log-likelihood is +L(y, w; Θ) = +N−1 +� +n=0 +2 +� +j=1 +wn,j ln(λjfj(yn; θj)) +(9) +1) E-step: Given the data y and the recent estimate of Θ +represented by Θ(i), Λ(y, Θ, Θ(i)) is the expectation of the full +data log-likelihood evaluated with respect to the conditional +likelihood of hidden variables. +Λ(y, Θ, Θ(i)) = Ew|y,Θ(i) +� +L(y, w; Θ) +� +(10) +The posterior probability of wn is evaluated using Bayes +theorem as +P(wn,j = 1|yn; Θ(i)) = +f(yn|wn,j = 1; θ(i) +j )P(wn,j = 1) +�2 +l=1 f(yn|wn,l = 1; θ(i) +j )P(wn,l = 1) +(11) +note that the Bayesian estimate of wn is +E(wn|yn, Θ(i)) = P(wn,j = 1|yn, θ(i) +j ) +(12) +based on (7), for wn,j = 1 the conditional pdf f(yn|wn; Θ) +reduces to a component density. Then the estimate (12), +denoted by γ(i) +n,j, can be written as +γ(i) +n,j = +λjfj(yn; θ(i) +j ) +�2 +i=1 λifi(yn; θ(i) +i ) +(13) +Thus, the expectation on the complete data log likelihood +becomes +Λ(y, Θ, γ(i)) = +n +� +i=1 +2 +� +j=1 +γ(i) +n,j ln(λjfj(yn; θj)) +(14) +where +γ(i) = {γ(i) +0,1, γ(i) +2,1, ..., γ(i) +N−1,1, γ(i) +0,2, γ(i) +1,2, ..., γ(i) +N−1,2} +(15) +2) M-step: Substituting both the Laplacian pdf (3) and the +Gaussian pdf (2) in (14) leads to +Λ(y, Θ, γ(i)) += +N−1 +� +n=0 +γ(i) +n,j +� +ln λ1 − ln σ1 − |yn − µ1| +σ1 +ln λ2 − 1 +2 ln σ2 +2 − (yn − µ2)2 +2σ2 +2 +� +(16) +Based on the optimization problem given below, the parame- +ters are estimated iteratively. +Θ(i+1) = max +Θ +Λ(y, Θ, γ(i)) +(17) +By equating the partial derivatives of Λ(y, Θ, γ(i)) in (16) to +zero and solving the corresponding equations, the estimates of +the parameters are obtained as follows. +λ(i+1) +1 += +N1 +N +λ(i+1) +2 += +N2 +N +µ(i+1) +1 += +Median +��γ(i) +n,1 +N1 +, yn +�N−1 +n=0 +� +(σ1)(i+1) += +1 +N1 +N−1 +� +n=0 +γ(i) +n,1 +���(yn − µ(i) +1 ) +��� +(18) +µ(i+1) +2 += +1 +N2 +N−1 +� +n=0 +γ(i) +n,2yn +(σ2 +2)(i+1) += +1 +N2 +N−1 +� +n=0 +γ(i) +n,2(yn − µ(i) +2 )2 +where N1 = �N−1 +n=0 γ(i) +n,1 and N1 + N2 = N. The E & M +steps are iterated until the squared difference between two +successive estimates Θ(i) and Θ(i+1) converges. +D. Evaluation Methods +The parameter estimates from the EM algorithm (18) are +used to generate a fit of the LGM pdf for the sEMG samples +as follows +f(y; ˆΘ) = ˆλ1f1(y; ˆµ1, ˆσ1) + ˆλ2f2(y; ˆµ2, ˆσ2 +2) +(19) +here, ˆλ1, ˆµ1, ˆσ1, ˆλ2, ˆµ2, ˆσ2 +2 are the estimates from (18) at +convergence. The empirical pdf (mpdf) is constructed from +the histogram of the signal samples. The evaluation criteria +for the appropriateness of the model are mentioned below +Visual inspection: +The model based pdf i.e. the approx- +imate pdf fitted from a model and the mpdf are compared +visually for understanding the degree of agreement [36]. +Kullback–Leibler divergence: +Kullback–Leibler diver- +gence(KLD) [37] is a statistical metric that measures the +difference between two pdfs. Let p1 and p2 be two probability +densities then the KLD between them is +DKL(p1||p2) = +� +x +p1(x) ln +�p1(x) +p2(x) +� +(20) +in this paper, p1 is the empirical distribution and p2 is a model +based approximate pdf. If these two distributions match then +the DKL(p1||p2) equals 0. The lower the DKL(p1||p2), the +closer the approximation is to the mpdf. +A goodness of fit plot with R-squared [38]: +The rela- +tionship between the sEMG data and the model-based values +is analyzed using a goodness of fit plot. The nearer the data +points are to the line of equality, greater the model fit. On other +hand, the coefficient of determination (R-squared) is a measure +of how much the variance in the observed dependent variable +is explained by the independent variable. The closer the value +to 1 greater the correlation between the two variables. +Likelihood ratio test (LRT): The LRT is a statistical test +used to compare two different models. In order to determine + +4 +TABLE I: Basic characteristics of four benchmark sEMG datasets +Ninapro DB2 +Ninapro DB4 +Rami-khushaba DB6 +Intense Dataset +No. of Subjects +40 +10 +11 +15 +Total no. of activities +Exercise-1- 17 +Exercise-2- 23 +Exercise-3- 09 +Total 49 +Exercise-1- 12 +Exercise-2- 17 +Exercise-3- 23 +Total 52 +40 +1 +No. of activities considered +23 +17 +40 +1 +No. of repetitions +6 +6 +6 +1 +No. of channels +12 +12 +7 +8 +Type of electrode +Delsys +Cometa Mini Wave +Delsys +Myo-armband +Sampling rate +2000 samples/sec +2000 samples/sec +4000samples/sec +200 samples/sec +(a) Gestures +(b) Grasping +(c) Arm activity +(d) Intense activity +Fig. 1: Visual comparisons between mpdfs and estimated pdfs from models: LGM(green), Laplacian(blue) and Gaussian(red) +for gestures, grasping, arm and intense activities for the subjects - 10, 3, 1 and 10 with corresponding activities - 7, 18, 3 and +1 +which model is statistically significant the likelihood values +are evaluated for both the models. The LRT is defined as [39] +T = 2(log(Lp) − log(Le)) +(21) +where Lp and Le are likelihoods of the LGM model and any +existing model respectively. +III. DATA DESCRIPTION +Please note that all of the datasets analyzed in this study +are available through public sources. Their short descriptions +follow. +• Ninapro Datasets: +In Ninapro DB2 (NPDB2) [40] and DB4 (NPDB4) [41] +datasets, there are 3 exercises collected from groups of +40 and 10 subjects respectively. The exercises-1 and +2 are related to activities such as hand gestures and +grasping. The exercise-3 corresponds to finger move- +ments at various forces levels including the abduction +and adduction of the thumb. In this work, the EMG +signals corresponding to the exercise- 2 from both the +DB2 and DB4 are analyzed They consist of 23 grasping +and 17 gesture actions respectively. The sEMG signals in +this dataset have 12 channels corresponding to a set of +twelve electrodes placed at strategic muscle locations on +an arm [41]. In this dataset, a typical sEMG signal within +a activity, has a duration of 8s with a 3s rest time and 5s +activity. Each trial is repeated six times. +• Rami-khushaba DB6 (RKDB6) [42]: +This dataset consists of sEMG signals collected from +11 intact subjects (9 males and 2 females) when they +were performing 8 different movements through 5 limb +positions. The limb positions were chosen in such a way + +0.14 +Empirical +0.12 +LGM +Laplacian +Gaussian +0.1 +0.08 +P +0.06 +0.04 +0.02 +0 +-1.5 +-1 +-0.5 +0 +0.5 +1 +1.5 +SEMG +×10-70.14 +Empirical +0.12 +LGM +Laplacian +Gaussian +0.1 +0.08 +P +0.06 +0.04 +0.02 +0 +-1 +-0.5 +0 +0.5 +1 +1.5 +2 +SEMG +×10~60.14 +Empirical +0.12 +LGM +Laplacian +Gaussian +0.1 +0.08 +P +0.06 +0.04 +0.02 +-3 +-2 +-1 +0 +1 +2 +SEMG +×10~40.16 +Empirical +0.14 +LGM +Laplacian +0.12 +Gaussian +0.1 +0.08 +Q +0.06 +0.04 +0.02 +-0.01 +-0.005 +0 +0.005 +0.01 +SEMG5 +1 +5 +10 +15 +Movements +1 +5 +10 +Subjects +0.01 +0.02 +0.03 +0.04 +0.05 +0.06 +0.07 +0.08 +0.09 +(a) +1 +5 +10 +15 +Movements +1 +5 +10 +Subjects +0.1 +0.15 +0.2 +0.25 +0.3 +0.35 +0.4 +0.45 +0.5 +0.55 +(b) +1 +5 +10 +15 +Movements +1 +5 +10 +Subjects +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1 +1.1 +(c) +1 +5 +10 +15 +20 +Movements +1 +5 +10 +15 +20 +25 +30 +35 +39 +Subjects +0.01 +0.02 +0.03 +0.04 +0.05 +0.06 +0.07 +0.08 +0.09 +(d) +1 +5 +10 +15 +20 +Movements +1 +5 +10 +15 +20 +25 +30 +35 +39 +Subjects +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +(e) +1 +5 +10 +15 +20 +Movements +1 +5 +10 +15 +20 +25 +30 +35 +39 +Subjects +0.2 +0.4 +0.6 +0.8 +1 +1.2 +1.4 +1.6 +1.8 +2 +(f) +1 +5 +10 +15 +20 +25 +30 +35 +39 +Movements +1 +5 +10 +Subjects +0.01 +0.02 +0.03 +0.04 +0.05 +0.06 +0.07 +0.08 +(g) +1 +5 +10 +15 +20 +25 +30 +35 +39 +Movements +1 +5 +10 +Subjects +0.1 +0.15 +0.2 +0.25 +0.3 +0.35 +(h) +1 +5 +10 +15 +20 +25 +30 +35 +39 +Movements +1 +5 +10 +Subjects +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +(i) +Fig. 2: Heatmaps of KLD for the 3 models: (a) LGM, (b) Laplacian and (c) Gaussian corresponding to Ninapro-DB4, (d) LGM, +(e) Laplacian and (f) Gaussian from Ninapro-DB2 and (g) LGM, (h) Laplacian and (i) Gaussian from Rami-khushaba-DB6 +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 11 12 13 14 15 +Subjects +0 +0.05 +0.1 +0.15 +0.2 +0.25 +KLD +LGM +Gaussian +Laplacian +Fig. 3: KLD values of LGM, Laplacian and Gaussian models +for intense activity data +that each subject can mimic daily activities. Each activity +has six repetitions. A sEMG signal array consists of seven +channels corresponding to seven Delsys DE 2.x EMG +sensors placed across the circumference of the forearm +• Intense Action Dataset (IAD) [43]: +This dataset consists of sEMG signals acquired from 15 +healthy subjects when performing a single intense activity +i.e., each subject is instructed to hold a 6kg dumbbell +with the right hand for 120 seconds. These sEMG signals +consist of 8 channels corresponding to 8 EMG electrodes +and each activity is carried out only once. The basic +characteristics of these benchmark datasets are provided +in the table I. +IV. RESULTS AND ANALYSIS +For each of the mentioned datasets, the sEMG signals cor- +responding to each trial from each activity by each subject are +analyzed using the three models. Specifically, the sEMG signal +from the channel with the highest energy among multiple + +6 +Gestures +Grasping +Arm movements +0 +0.2 +0.4 +0.6 +0.8 +1 +(a) +Gestures +Grasping +Arm movements +0 +0.2 +0.4 +0.6 +0.8 +1 +(b) +Fig. 4: Average KLD for the 3 models (LGM-green, Laplacian-blue, Gaussian-red) for each of the trails (a) over the movements +for different subjects (b) over the subjects for different movements +channels is examined using the models based on the following +evaluation methods. +• a qualitative analysis based on visual inspection +• quantitative analyses: +1) the KL divergence analysis +2) the goodness of fit plots with R-squared and confi- +dence interval for R-squared +3) the likelihood ratio test +A. Visual Inspection +Fig. 1 illustrates the visual comparisons between the mpdf +(yellow) and the fitted pdfs from the LGM (green), the +Laplacian (blue) and the Gaussian (red) models. These pdfs +correspond to EMG signals of different activities as listed in +the following: Fig. 1(a): activity-7 i.e., pointing index finger +by subject-10, Fig. 1(b): activity-18 i.e., the quadpod grasp +by subject-3, Fig. 1(c): activity-3 i.e., a wrist supination by +subject-1 and Fig. 1(d): activity-1 i.e., lifting a dumbbell by +subject-10. Figs. 1(a), (b) and (c) correspond to pdfs of the +sEMG signal corresponding to gestures, grasping and normal +arm activities. From these it is evident that the overlap between +the mpdf and the LGM model is high compared to standalone +Laplacian and Gaussian models. Whereas Fig. 1(d) represents +the pdfs of the sEMG signal corresponding to the intense +activity, it is noticed that the overlap between the LGM model +and the mpdf is similar to that of the standalone Gaussian +model and the mpdf. In contrast, the overlap between the +standalone Laplacian model and mpdf is lower. +B. Quantitative Analysis +1) KL-divergence: For each of the datasets under consid- +eration, the KLD is evaluated between the LGM pdf and the +mpdf. For comparison purposes, the KLD computation is also +done for the Gaussian and the Laplacian pdfs against the +mpdf. The corresponding results are illustrated in Figs. 2 to +4. Specifically, the heatmaps of KLD as a function of subjects +and movements are shown in Fig. 2. Each cell in a heatmap +corresponds to the KLD for a given model for a particular +subject while performing one of the activities. Further, the +KLD represented here is an average over the given trials of an +activity. Figs. 2 (a)-(c) correspond to the KLD for the Ninapro- +DB4, Figs. 2 (d)-(f) depict the KLD for the Ninapro-DB2 +and Figs. 2 (g)-(i) represent the KLD for the Rami-khushaba- +DB6. For each of the three datasets, it is noted that in these +heatmaps, the LGM model has the lowest KLD. The lower +and upper bounds of KLD for the heatmaps in Fig. 2 are +shown in table II. The key observation is the highest KLD +value from the LGM model is the lowest KLD value for both +the Laplacian and the Gaussian models. +TABLE II: Lower and upper bounds of KLD for the proposed +and the standalone models for different datasets +Datasets +LGM +Laplacian +Gaussian +NPDB4 +[0.01 0.1] +[0.1 0.6] +[0.1 1.1] +NPDB2 +[0.01 0.1] +[0.1 0.8] +[0.1 2.2] +RKDB6 +[0.01 0.1] +[0.1 0.35] +[0.1 0.9] +The KLD values for different models in the case of the +intense activity are shown in Fig. 3. Notably, for the intense +activity dataset as well, the KLD value is the lowest for +the LGM model closely followed by the Gaussian model +and then the Laplacian model. The minimum and maximum +KLD values corresponding to the three models are: the LGM +{0.0033, 0.0301}, the Gaussian {0.0039, 0.0378} and the +Laplacian {0.0920, 0.1513}. +Fig. 4(a) shows the KLD averaged over the movements as +a function of the subjects. Fig. 4(b) shows the vice versa case. +The KLD of the LGM, Laplacian and Gaussian models are +represented in green, blue and red respectively. From Fig. +4(a) and (b), it is observed that for the activities such as the +gestures, grasping and the arm movements the average KLD +value over the movements and subjects is the lowest for the +LGM model, when compared to the other models. + +7 +(a) Gestures +(b) Grasping +(c) Normal activity +(d) Intense activity +Fig. 5: Goodness of fit plots for the models LGM(green), Laplacian(blue) and Gaussian(red) for gestures, grasping, normal +and Intense activities for the subjects-10, 3, 1 and 10 and with corresponding activities-7, 18, 3 and 1 +2) Goodness of fit plots: Fig. 5 illustrates the goodness of +fit plots between the estimates from the three models versus +the actual data. Specifically, the Figs. 5 (a) to (d) correspond to +the results on data from the gestures, grasping, normal arm and +the intense activities respectively. The LGM model, Laplacian +and Gaussian models are represented by the data points in +green, blue and red respectively. From Figs. 5 (a), (b) and (c), +in the scatter plots, the model-values of the LGM model are +found to be adjacent to the line of equality which means that +the predicted values from this model are close to the actual +values of the sEMG signal. Whereas in the case of intense +activity shown in Fig. 5(d), the model values corresponding +to both the LGM and the Gaussian models are similar and +they are adjacent to the line of equality. From Fig. 5, for +the gestures, grasping and normal arm activities, it can be +concluded that the LGM model is better compared to other +models. However, for the intense activity, both the LGM and +the Gaussian fit the EMG data quite well. The average R- +squared values are shown in the table III. For the first three +categories of activities, based on these metrics, the LGM +model is found to be superior. Additionally, for the intense +activities, the LGM and the Gaussian are again similar. The +95 percent confidence intervals(CI) [44] [45] for R-squared +corresponding to the plots in Fig. 5 are given in table IV. +3) Likelihood ratio test: The LRT given in (21) is carried +out between the LGM model and the Laplacian model as +shown below. +H0 : +The Laplacian model fits the data +H1 : +The LGM model fits the data +TABLE III: R-Squared values for four datasets from model +evaluations +Datasets +LGM +Laplacain +Gaussian +NPDB4 +0.9958 +0.94799 +0.74885 +NPDB2 +0.99491 +0.86529 +0.84151 +RKDB6 +0.9932 +0.91137 +0.82279 +IAD +0.99715 +0.54947 +0.98269 +TABLE IV: Confidence interval of R-squared for LGM, Lapla- +cian and Gaussian models +Datasets +LGM +Laplacain +Gaussian +NPDB4 +[0.9946 0.9970] +[0.9439 0.9520] +[0.7413 0.7564] +NPDB2 +[0.9937 0.9961] +[0.8598 0.8708] +[0.8357 0.8473] +RKDB6 +[0.9918 0.9946] +[0.9067 0.9160] +[0.8167 0.8289] +IAD +[0.9960 0.9983] +[0.5402 0.5587] +[0.9800 0.9854] +This test is carried out for 99% confidence interval. It is noted +that p-value is less than 0.01, which means H0 is rejected and +H1 is accepted. The test is repeated by replacing the Laplacian +with the Gaussian model for H0. In this test also the p-value +is found to be less than 0.01 and thus H1 is accepted. +C. Mixing Weights +The mixing coefficients corresponding to the Laplacian +component of the LGM model corresponding to different +activities from various datasets are shown in Fig. 6. For the +low and medium MCF levels such as the gestures, grasping +and the normal activities, it is noticed that the Laplacian + +0.07 +0.06 +lodel-Value +0.05 +0.04 +0.03 +0.02 +LGM:R2=0.99715 +Y=X Line +0.01 +Laplacian: R2 = 0.54947 +Gaussian: R? = 0.98269 +0 +0.01 +0.02 +0.03 +0.04 +0.05 +0.06 +0.07 +0.08 +Actual0.14 +LGM: R2 = 0.9932 +0.12 +Y=X Line +Laplacian: R? = 0.91137 +Gaussian: R? = 0.82279 +0.1 +on +e +0.08 +Model-V +0.06 +0.04 +0.02 +0 +0 +0.02 +0.04 +0.06 +0.08 +0.1 +Actual0.14 +LGM: R2 = 0.99491 +0.12 +Y=X Line +Laplacian: R2 = 0.86529 +Gaussian: R? = 0.84151 +0.1 +an +e +0.08 +Model-V +0.06 +0.04 +0.02 +0 +0 +0.02 +0.04 +0.06 +0.08 +0.1 +Actual0.12 +0.1 +an +lodel-Val +0.08 +0.06 +M +0.04 +LGM:R2=0.9958 +Y=X Line +0.02 +Laplacian: R2 = 0.94799 +Gaussian: R? = 0.74885 +0 +0.02 +0.04 +0.06 +0.08 +0.1 +0.12 +0.14 +Actual8 +Gestures +Grasping +Normal +Intense +0 +0.2 +0.4 +0.6 +0.8 +1 +Fig. 6: Laplacian coefficient for each trail versus subjects for +gestures, grasping, normal arm movements and intense activity +component has a stronger weighting in comparison with the +Gaussian component. Whereas in case of intense activity i.e., +at high MCF level the mixing weight corresponding to the +Gaussian component is higher and the Laplacian component +is lower. Thus from Fig. 6, it can be recognized that as the +intensity of an activity, i.e., the amount of energy required +for performing a certain action increases, the weight of the +Laplacian component reduces. Fig. 7 shows Laplacian weights +of the LGM model corresponding to the first three limb +activities under consideration. The horizontal and vertical axes +in the heatmaps correspond to the number of movements +and subjects respectively. Each cell in a heatmap denotes the +Laplacian weight in the LGM model for a particular subject +and activity. It is noticed that for most of the cases the +Laplacian weight λ1 is dominating the Gaussian weight λ2. +In some circumstances, the Laplacian weights are lower than +Gaussian weights. For example, in Fig. 7 (a) for the subject-1, +activities-4 and 9, in Fig. 7(b) for the subject-18, activity-2 and +in Fig. 7 (c), the subject-1, activities-2 and 10, the Gaussian +weights are stronger. +V. DISCUSSION +From the results presented in section IV, for the EMG +signals corresponding to the low and medium levels of muscle +recruitment i.e., for activities such as the gestures, grasping +and the normal arm movements, the LGM is found to be +a more suitable model compared to the standalone models. +This is verified in terms of 1) the visual inspection between a +model pdf and the mpdf, 2) the lowest KLD, 3) the goodness +of fit plots - the model values matching the true values, 4) +the higher R-squared values and 5) the Likelihood ratio test +accepting the alternate hypothesis. However, in the case of +intense activities, both the LGM and the Gaussian model seem +to perform quite similarly according to the four evaluation +methods described above. Hence for high levels of muscle +recruitment, the proposed LGM model behaves similar to a +standalone Gaussian model. This result is further qualified +1 +5 +10 +15 +Movements +1 +5 +10 +Subjects +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +(a) +1 +5 +10 +15 +20 +Movements +1 +5 +10 +15 +20 +25 +30 +35 +39 +Subjects +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +(b) +1 +5 +10 +15 +20 +25 +30 +35 +39 +Movements +1 +5 +10 +Subjects +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +(c) +Fig. 7: Laplacian weights of LGM model averaged over trials +as a function of subjects and movements for (a) gestures, (b) +grasping, and (C) arm activities +by the following observation, in the LGM model, the mixing +coefficient of the Laplacian component becomes very small in +comparison to that of the Gaussian component. +In the analysis on mixing weights, it is observed that for +the first three types of actions, both the Laplacian and Gaus- +sian components have significant contributions to the model. +However, for the intense activity, the Gaussian component is +much stronger. Hence, from these findings it can be postulated +that the weights of the LGM model can be related to MCF +level and motor units that are activated during an activity. For +example, for the first three activities, the Laplacian weight λ1 +is higher relating to lower MCF level and the lower number of +activated motor units. However, in the case of intense activity +the Gaussian weight λ2 is higher connecting to a higher MCF +level and a larger number of activated motor units. These +findings are in agreement with the literature on pdfs reported +in section I-B where it is noted that for the lower and medium +MCF levels, the pdfs have a sharper peak at center, hinting + +9 +a Laplacian structure, and at higher MCF levels, they have a +clear Gaussian structure. +VI. CONCLUSION +In this paper, a Laplacian Gaussian mixture model is +proposed for sEMG signals from upper limbs. The proposed +model is tested on several benchmark sEMG datasets and +compared with the existing standalone models. The suitability +of the model is validated using (1) qualitative analyses such as +visual comparison with the empirical pdf (mpdf) where it is +observed that the LGM model has the best agreement, (2) the +KL divergence between the model pdf and the mpdf, again the +KLD is lowest for the LGM model, (3) a goodness of fit plot, +comparison of coefficient of determination (CFD) - R2 and +confidence intervals for R2, here it is noted that R2 in case +of the LGM model is closest to unity and (4) the Likelihood +ratio test (LRT) that also supported the LGM model. Finally, +it is noted, for the low and medium muscle contraction force +levels, the Laplacian weight has stronger weighting than the +Gaussian. Whereas for the higher muscle contraction force +levels the Laplacian weights are lower. In the future work, we +will extend the proposed model to understand the correlations +between the sEMG signals from various muscle locations. +ACKNOWLEDGMENT +This research is funded by SERB, Govt. of India under +Project Grant No. CRG/2019/003801. +REFERENCES +[1] W. Wang, A. D. Stefano, and R. Allen, “A simulation model of the +surface EMG signal for analysis of muscle activity during the gait cycle,” +Computers in biology and medicine, vol. 36, no. 6, pp. 601–618, 2006. +[2] D. W. Stashuk, “Simulation of electromyographic signals,” Journal of +Electromyography and Kinesiology, vol. 3, no. 3, pp. 157–173, 1993. +[3] P. A. Cuddon, “Electrophysiology in neuromuscular disease,” Veterinary +Clinics: Small Animal Practice, vol. 32, no. 1, pp. 31–62, 2002. +[4] A. D. Vigotsky, I. Halperin, G. J. Lehman, G. S. Trajano, and T. M. +Vieira, “Interpreting signal amplitudes in surface electromyography +studies in sport and rehabilitation sciences,” Frontiers in physiology, +vol. 8, p. 985, 2018. +[5] C. J. De Luca, “The use of surface electromyography in biomechanics,” +Journal of applied biomechanics, vol. 13, no. 2, pp. 135–163, 1997. +[6] G. L. Soderberg and T. M. Cook, “Electromyography in biomechanics,” +Physical Therapy, vol. 64, no. 12, pp. 1813–1820, 1984. +[7] E. Hasanbelliu, “A multi-dimensional visualization tool for understand- +ing the role of EMG signals in head movement anticipation,” in ACM +SIGGRAPH 2004 Posters, 2004, p. 109. +[8] R. Merletti, L. L. Conte, E. Avignone, and P. Guglielminotti, “Mod- +eling of surface myoelectric signals. i. model implementation,” IEEE +Transactions on Biomedical Engineering, vol. 46, no. 7, pp. 810–820, +1999. +[9] J. Rodriguez-Falces, J. Navallas, and A. Malanda, “Emg modeling,” +Computational Intelligence in Electromyography Analysis-A Perspective +on Current Applications and Future Challenges, pp. 3–36, 2012. +[10] M. Hayashibe and D. Guiraud, “Voluntary EMG-to-force estimation +with a multi-scale physiological muscle model,” Biomedical engineering +online, vol. 12, no. 1, pp. 1–18, 2013. +[11] O. Paiss and G. F. Inbar, “Autoregressive modeling of surface EMG +and its spectrum with application to fatigue,” IEEE Transactions on +Biomedical Engineering, no. 10, pp. 761–770, 1987. +[12] T. Kiryu, C. J. De Luca, and Y. Saitoh, “AR modeling of myoelectric +interference signals during a ramp contraction,” IEEE Transactions on +Biomedical Engineering, vol. 41, no. 11, pp. 1031–1038, 1994. +[13] S. Shahid, J. Walker, G. M. Lyons, C. A. Byrne, and A. V. Nene, +“Application of higher order statistics techniques to EMG signals to +characterize the motor unit action potential,” IEEE Transactions on +Biomedical Engineering, vol. 52, no. 7, pp. 1195–1209, 2005. +[14] A. Furui, H. Hayashi, and T. Tsuji, “A scale mixture-based stochastic +model of surface EMG signals with variable variances,” IEEE Transac- +tions on Biomedical Engineering, vol. 66, no. 10, pp. 2780–2788, 2019. +[15] Z. O. Khokhar, Z. G. Xiao, and C. Menon, “Surface EMG pattern +recognition for real-time control of a wrist exoskeleton,” Biomedical +engineering online, vol. 9, no. 1, pp. 1–17, 2010. +[16] H. Huang, T. A. Kuiken, R. D. Lipschutz et al., “A strategy for +identifying locomotion modes using surface electromyography,” IEEE +Transactions on Biomedical Engineering, vol. 56, no. 1, pp. 65–73, +2008. +[17] A. D. Chan and K. Englehart, “Continuous classification of myoelec- +tric signals for powered prostheses using gaussian mixture models,” +in Proceedings of the 25th Annual International Conference of the +IEEE Engineering in Medicine and Biology Society (IEEE Cat. No. +03CH37439), vol. 3. +IEEE, 2003, pp. 2841–2844. +[18] A. Furui, T. Igaue, and T. Tsuji, “EMG pattern recognition via bayesian +inference with scale mixture-based stochastic generative models,” Expert +Systems with Applications, vol. 185, p. 115644, 2021. +[19] P. S. Giacomini, “Electromyography and neuromuscular disorders: clin- +ical electrophysiologic correlations,” McGill Journal of Medicine: MJM, +vol. 9, no. 2, p. 173, 2006. +[20] D. Xiong, D. Zhang, X. Zhao, and Y. Zhao, “Deep learning for EMG- +based human-machine interaction: A review,” IEEE/CAA Journal of +Automatica Sinica, vol. 8, no. 3, pp. 512–533, 2021. +[21] W. Wei, Q. Dai, Y. Wong, Y. Hu, M. Kankanhalli, and W. Geng, +“Surface-electromyography-based gesture recognition by multi-view +deep learning,” IEEE Transactions on Biomedical Engineering, vol. 66, +no. 10, pp. 2964–2973, 2019. +[22] B. Hudgins, P. Parker, and R. N. Scott, “A new strategy for multifunction +myoelectric control,” IEEE Transactions on Biomedical Engineering, +vol. 40, no. 1, pp. 82–94, 1993. +[23] H. Roesler, “Statistical analysis and evaluation of myoelectric signals +for proportional control,” The Control of upper-extremity prostheses and +orthoses, pp. 44–53, 1974. +[24] H. Milner-Brown and R. Stein, “The relation between the surface +electromyogram and muscular force.” The Journal of physiology, vol. +246, no. 3, pp. 549–569, 1975. +[25] P. A. Parker, J. A. Stuller, and R. N. Scott, “Signal processing for the +multistate myoelectric channel,” Proceedings of the IEEE, vol. 65, no. 5, +pp. 662–674, 1977. +[26] I. Hunter, R. Kearney, and L. Jones, “Estimation of the conduction +velocity of muscle action potentials using phase and impulse response +function techniques,” Medical and Biological Engineering and Comput- +ing, vol. 25, no. 2, pp. 121–126, 1987. +[27] M. Bilodeau, M. Cincera, A. B. Arsenault, and D. Gravel, “Normality +and stationarity of EMG signals of elbow flexor muscles during ramp +and step isometric contractions,” Journal of Electromyography and +Kinesiology, vol. 7, no. 2, pp. 87–96, 1997. +[28] E. A. Clancy and N. Hogan, “Probability density of the surface elec- +tromyogram and its relation to amplitude detectors,” IEEE Transactions +on Biomedical Engineering, vol. 46, no. 6, pp. 730–739, 1999. +[29] P. Kaplanis, C. S. Pattichis, L. Hadjileontiadis, and S. M. Panas, +“Bispectral analysis of surface EMG,” in 2000 10th Mediterranean Elec- +trotechnical Conference. Information Technology and Electrotechnology +for the Mediterranean Countries. Proceedings. MeleCon 2000 (Cat. No. +00CH37099), vol. 2. +IEEE, 2000, pp. 770–773. +[30] K. Nazarpour, A. Sharafat, and S. Firoozabadi, “Negentropy analysis +of surface electromyogram signal,” in IEEE/SP 13th Workshop on +Statistical Signal Processing, 2005. +IEEE, 2005, pp. 974–977. +[31] G. R. Naik and D. K. Kumar, “Evaluation of higher order statistics +parameters for multi channel sEMG using different force levels,” in 2011 +Annual International Conference of the IEEE Engineering in Medicine +and Biology Society. +IEEE, 2011, pp. 3869–3872. +[32] G. R. Naik, D. K. Kumar, and S. P. Arjunan, “Kurtosis and negentropy +investigation of myo electric signals during different MVCs,” in ISSNIP +Biosignals and Biorobotics Conference 2011. +IEEE, 2011, pp. 1–4. +[33] K. Nazarpour, A. H. Al-Timemy, G. Bugmann, and A. Jackson, “A note +on the probability distribution function of the surface electromyogram +signal,” Brain research bulletin, vol. 90, pp. 88–91, 2013. +[34] D. Kusuru, A. C. Turlapaty, and M. Thakur, “A laplacian-gaussian +mixture model for surface EMG signals from upper limbs,” in 2021 43rd +Annual International Conference of the IEEE Engineering in Medicine +& Biology Society (EMBC). +IEEE, 2021, pp. 681–685. +[35] C. M. Bishop and N. M. Nasrabadi, Pattern recognition and machine +learning. +Springer, 2006, vol. 4, no. 4. +[36] A. Spanos, Probability Theory and Statistical Inference: Empirical +Modeling with Observational Data. Cambridge University Press, 2019. + +10 +[37] S. Kullback, Information theory and statistics. +Courier Corporation, +1997. +[38] J. Cohen, P. Cohen, S. G. West, and L. S. Aiken, “Applied multiple +regression,” Correlation Analysis for the Behavioral Sciences, vol. 2, +1983. +[39] G. King, Unifying political methodology: The likelihood theory of +statistical inference. +University of Michigan Press, 1998. +[40] M. Atzori, A. Gijsberts, C. Castellini, B. Caputo, A.-G. M. Hager, +S. Elsig, G. Giatsidis, F. Bassetto, and H. M¨uller, “Electromyography +data for non-invasive naturally-controlled robotic hand prostheses,” +Scientific Data, vol. 1, no. 1, pp. 1–13, 2014. +[41] S. Pizzolato, L. Tagliapietra, M. Cognolato, M. Reggiani, H. M¨uller, +and M. Atzori, “Comparison of six electromyography acquisition setups +on hand movement classification tasks,” PloS one, vol. 12, no. 10, p. +e0186132, 2017. +[42] R. N. Khushaba, M. Takruri, J. V. Miro, and S. Kodagoda, “Towards limb +position invariant myoelectric pattern recognition using time-dependent +spectral features,” Neural Networks, vol. 55, pp. 42–58, 2014. +[43] A. Ebied, A. M. Awadallah, M. A. Abbass, and Y. El-Sharkawy, “Upper +limb muscle fatigue analysis using multi-channel surface EMG,” in +2020 2nd Novel Intelligent and Leading Emerging Sciences Conference +(NILES). +IEEE, 2020, pp. 423–427. +[44] J. D. Finn et al., “Correlations redux,” Psychological Bulletin, vol. 118, +no. 1, pp. 155–164, 1995. +[45] P. Cohen, S. G. West, and L. S. Aiken, Applied multiple regres- +sion/correlation analysis for the behavioral sciences. Psychology press, +2014. + diff --git a/TNAzT4oBgHgl3EQfJftl/content/tmp_files/load_file.txt b/TNAzT4oBgHgl3EQfJftl/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..0baa7de12aa15654215c815f73d559c436e606e7 --- /dev/null +++ b/TNAzT4oBgHgl3EQfJftl/content/tmp_files/load_file.txt @@ -0,0 +1,941 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf,len=940 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='01080v1 [eess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='SP] 3 Jan 2023 1 A Laplacian Gaussian Mixture Model for Surface EMG Signals of Human Arm Activity Durgesh Kusuru, Student Member, IEEE, Anish C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Turlapaty Member, IEEE and Mainak Thakur Member, IEEE Abstract—The probability density function (pdf) of surface Electromyography (sEMG) signals follows any one of the stan- dalone standard distributions: the Gaussian or the Laplacian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Further, the choice of the model is dependent on muscle contrac- tion force (MCF) levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Hence, a unified model is proposed which explains the statistical nature of sEMG signals at different MCF levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In this paper, we propose the Laplacian Gaussian Mixture (LGM) model for the signals recorded from upper limbs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' This model is able to explain the sEMG signals from different activities corresponding to different MCF levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The model is tested on different bench-mark sEMG data sets and is validated using both the qualitative and quantitative perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' It is determined that for low and medium contraction force levels the proposed mixture model is more accurate than both the Laplacian and the Gaussian models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Whereas for high contraction force level, the LGM model behaves as a Gaussian model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The mixing weights of the LGM model are analysed and it is observed that for low and medium MCF levels both the mixing weights of LGM model do contribute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Whereas for high contraction force levels the Laplacian weight becomes weaker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The proposed LGM model for sEMG signals from upper limbs explains sEMG signals at different MCF levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The proposed model helps in improved understanding of statistical nature of sEMG signals and better feature representation in the classification problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Index Terms—Surface electromyography (sEMG), Statistical models, Probability density function(pdf), Mixture models, Mus- cle contraction force, Parameter estimation, EM algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' INTRODUCTION A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Background Modeling of surface Electromyography (sEMG) signals has several applications such as 1) developing insights into sEMG signal generation from the constituent motor unit action potentials (MUAPs) that forms a basis for the sEMG signal synthesis [1] and simulation studies [2],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2) improving inter- pretation of the sEMG signals in clinical settings for example,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' in the diagnosis of neuromuscular disorders [3],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 3) analyzing inter-relations between the sEMG signals and the source muscle groups,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' for instance,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' in the sport sciences research [4],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [5],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [6],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' and 4) building visualization tools to support movement sciences [7],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' muscle physiology examinations and the sport science education.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The sEMG signal models can be classified based on 1) bio-electrical, 2) statistical, and 3) machine learning principles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The earliest models were based on the physiological characteristics and the electrical activity This research is funded by SERB, Govt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' of India under Project Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' CRG/2019/003801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The authors are with the Bio-signal Analysis Group, Indian Institute of Information Technology Sri City, Chittoor, Andhra Pradesh, 517646, India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' (e- mails: durgesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='k@iiits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='in, anish.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='turlapaty@iiits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='in and mainak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='thakur@iiits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='in in muscle fibers and motor units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' For example, in [8] and [9], the sEMG signal is represented as a linear combination of MUAPs, where the action potential is modeled as a cur- rent tripole propagating from the neuromuscular junction to the fiber-tendon ending.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In [10], a multi-scale physiological muscle model was used to estimate the muscle force from the sEMG signals corresponding to voluntary movements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In the statistical approach, the sEMG signal is considered as a random signal and the typical characteristics modeled are the signal strength (samples), the temporal evolution of a signal, the autocorrelation of a single channel, and the spatial cross-correlations among multiple channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The probabilistic models of the sEMG signal strength have evolved considerably during the last few decades as reviewed in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In the temporal models, sEMG signals are usually represented by a linear autoregressive process [11] [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' To estimate the MUAPs, the sEMG signals obtained from isometric contrac- tions are modeled as an output of a LTI system with non- Gaussian white noise as an input [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In the variance based model, a sEMG signal is treated as a compound random process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' For example, in a scale mixture model [14], the signal strength is modeled as a Gaussian process conditioned on the variance which is modeled as an inverse gamma variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The pattern classification of the sEMG signals plays a key role in applications such as the orthotic exoskeleton control [15], the human movement analysis [16], and the neuromus- cular disease diagnosis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' For example, they can provide suitable inputs such as motor control parameters to drive a limb ex- oskeleton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In the machine learning methods, suitable features can be extracted based on the probability density function (pdf) of the sEMG signal [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In the human movement analysis, sEMG signals can be used for discrimination among different actions, for example, hand gestures vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' grasping of objects [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In the neuormuscular disease diagnosis they can be used to study conditions such as myopathy which is related to the skeletal muscles causing them to become weaker and leading to muscle pain, weakness, fatigue and other symptoms [19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Decoding information contained in the sEMG signals is critical and requires a reliable and precise solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In human-machine interaction applications, deep learning methods play a crucial role and are used to achieve improved performance in tasks such as the movement classification, the joint angle prediction, and the force/torque estimation [20]–[22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The focus of this paper is statistical modeling of the sEMG signal strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Existing Models for pdf of sEMG strength Typical applications of a statistical signal model for sEMG 2 signals are 1) a better understanding of statistical nature of sEMG signals, 2) an improved feature representation in the classification problems, and 3) a qualitative analysis of signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Depending on the muscle contraction level and the type of muscle, the existing models of sEMG signal strength are based on any of the standalone standard distributions such as the Gaussian or the Laplacian pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Following is a summary, based on studies since 1970s, of the existing models of the sEMG signals acquired from different muscle groups of human upper limbs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In 1974, sEMG measurements were performed by Roesler [23] and it was proposed that under constant force measure- ment conditions, the sEMG signals follow a Gaussian distri- bution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Miler-Brown et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [24] observed that the distribution of the sEMG signals recorded from the first dorsal interosseus (FDI) muscle (back of a hand) at a lower force level has a sharper peak around zero than the Gaussian distribution and as the force level increases the sharpness near zero reduces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In [25], the sEMG signals collected from biceps muscles were observed to follow a Gaussian distribution for the low and medium levels of MCF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Hunter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [26] analyzed the density of the sEMG signals from the biceps under constant MCF against a Gaussian density and reported that it has a narrow peak around zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Later, Bilodeau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [27] observed that for lower MCF levels, the sEMG signals from the biceps have a non-Gaussian nature with a peak near zero and at a higher MCF level their distribution was observed to tend toward a Gaussian model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Clancy and Hogan [28] experimentally found that the density of sEMG signals at a constant MCF lies in between a Gaussian and a Laplacian pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In [29], it was noticed that the pdf of sEMG signal, 1) has a sharper peak near zero and a longer tail than a usual Gaussian distribution at the low and high levels of MCF, and 2) follows a Gaussian model at a medium MCF level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In [30], at high MCF level, the distribution of the sEMG signals was found to be a Gaussian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Based on the recent studies, the sEMG signals at higher MCF levels from the flexor digitorum superficialis [31], [32] and the biceps [33], follow a Gaussian model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Based on this review, there is no unique statistical model that explains the activity at various contraction force levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In many cases, it may not be possible to describe the data using the standard single density models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In such cases, often, modeling the data as a mixture of densities is an appropriate approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Contributions A unifying mixture model is proposed for the sEMG signals that explains the statistical nature of the signal for different levels of muscle contraction force.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The proposed model is tested on multiple benchmark sEMG datasets and the suitability of the model is com- pared against the existing models using both qualitative and quantitative methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The weights of the mixture components are analyzed for different activities and intensities and a possible inter- relation is illustrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' STATISTICAL MODEL AND PROBLEM DESCRIPTION A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Laplacian Gaussian Mixture Model In [34], a Laplacian Gaussian Mixture (LGM) model was introduced and verified on a single sEMG dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In this work, the LGM model is further analyzed and its suitability is evaluated for various benchmark datasets corresponding to distinct upper limb activities at different MCF levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' A description of the proposed model follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Let the strength of the discrete time sEMG signal be represented by a random variable Y .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The LGM model is written as fY (y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Θ) = λ1f1(y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' θ1) + λ2f2(y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' θ2) (1) y denotes a realization of Y and Θ = [λ1, λ2, θ1, θ2] is the set of unknown parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' λ1 and λ2 are the mixing weights that add to unity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' θ1 and θ2 are parameters of component densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' f1(y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' θ1) is a Laplacian density defined as f1(y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' θ1) = 1 2σ1 exp � − |y − µ1| σ1 � − ∞ < y < ∞ (2) and f2(y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' θ2) a Gaussian density given by f2(y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' θ2) = 1 � 2πσ2 2 exp � − (y − µ2)2 2σ2 2 � −∞ < y < ∞ (3) note that θ1 = [µ1, σ1] and θ2 = [µ2, σ2 2] are parameters of the respective densities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' As illustrated in (1), the mixing weights λ1 and λ2 are the hidden parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The unknown parameters of the LGM model are estimated from the sEMG data using the expectation-maximization (EM) Algorithm [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Note that the EM algorithm is commonly used for estimation of parameters of the Gaussian mixture model based on which a similar EM methodology is derived for the proposed model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Parameter Estimation Problem Consider an array y = {yn}N−1 n=0 where yn represents a discrete sample of a sEMG signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Based on the latent variable used in Gaussian mixture models [35], a discrete random vector w is defined as w = {wn}N−1 n=0 (4) here wn = [wn,1, wn,2] and has two distinct states with corresponding likelihoods (mixing weights) p(wn,1 = 1, wn,2 = 0) = λ1 (5) p(wn,1 = 0, wn,2 = 1) = λ2 and the marginal likelihood of these hidden states is given by p(wn) = λwn,1 1 λwn,2 2 (6) The conditional pdf of yn given wn and Θ is f(yn|wn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Θ) = 2 � j=1 (fj(yn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' θj))wn,j (7) Here, yn are i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The joint density of the data, the hidden states and the unknown parameters is f(y, w;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Θ) = N−1 � n=0 2 � j=1 (λjfj(yn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' θj))wn,j (8) The estimation problem can be stated as follows: given the data y which follows the LGM model (1), the objective is to estimate the parameters Θ and the related statistics in the model (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The next section describes the parameter estimation for the LGM model using the EM algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 3 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' EM-Algorithm The complete data log-likelihood is L(y, w;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Θ) = N−1 � n=0 2 � j=1 wn,j ln(λjfj(yn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' θj)) (9) 1) E-step: Given the data y and the recent estimate of Θ represented by Θ(i), Λ(y, Θ, Θ(i)) is the expectation of the full data log-likelihood evaluated with respect to the conditional likelihood of hidden variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Λ(y, Θ, Θ(i)) = Ew|y,Θ(i) � L(y, w;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Θ) � (10) The posterior probability of wn is evaluated using Bayes theorem as P(wn,j = 1|yn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Θ(i)) = f(yn|wn,j = 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' θ(i) j )P(wn,j = 1) �2 l=1 f(yn|wn,l = 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' θ(i) j )P(wn,l = 1) (11) note that the Bayesian estimate of wn is E(wn|yn, Θ(i)) = P(wn,j = 1|yn, θ(i) j ) (12) based on (7), for wn,j = 1 the conditional pdf f(yn|wn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Θ) reduces to a component density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Then the estimate (12), denoted by γ(i) n,j, can be written as γ(i) n,j = λjfj(yn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' θ(i) j ) �2 i=1 λifi(yn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' θ(i) i ) (13) Thus, the expectation on the complete data log likelihood becomes Λ(y, Θ, γ(i)) = n � i=1 2 � j=1 γ(i) n,j ln(λjfj(yn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' θj)) (14) where γ(i) = {γ(i) 0,1, γ(i) 2,1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=', γ(i) N−1,1, γ(i) 0,2, γ(i) 1,2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=', γ(i) N−1,2} (15) 2) M-step: Substituting both the Laplacian pdf (3) and the Gaussian pdf (2) in (14) leads to Λ(y, Θ, γ(i)) = N−1 � n=0 γ(i) n,j � ln λ1 − ln σ1 − |yn − µ1| σ1 ln λ2 − 1 2 ln σ2 2 − (yn − µ2)2 2σ2 2 � (16) Based on the optimization problem given below, the parame- ters are estimated iteratively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Θ(i+1) = max Θ Λ(y, Θ, γ(i)) (17) By equating the partial derivatives of Λ(y, Θ, γ(i)) in (16) to zero and solving the corresponding equations, the estimates of the parameters are obtained as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' λ(i+1) 1 = N1 N λ(i+1) 2 = N2 N µ(i+1) 1 = Median ��γ(i) n,1 N1 , yn �N−1 n=0 � (σ1)(i+1) = 1 N1 N−1 � n=0 γ(i) n,1 ���(yn − µ(i) 1 ) ��� (18) µ(i+1) 2 = 1 N2 N−1 � n=0 γ(i) n,2yn (σ2 2)(i+1) = 1 N2 N−1 � n=0 γ(i) n,2(yn − µ(i) 2 )2 where N1 = �N−1 n=0 γ(i) n,1 and N1 + N2 = N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The E & M steps are iterated until the squared difference between two successive estimates Θ(i) and Θ(i+1) converges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Evaluation Methods The parameter estimates from the EM algorithm (18) are used to generate a fit of the LGM pdf for the sEMG samples as follows f(y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' ˆΘ) = ˆλ1f1(y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' ˆµ1, ˆσ1) + ˆλ2f2(y;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' ˆµ2, ˆσ2 2) (19) here, ˆλ1, ˆµ1, ˆσ1, ˆλ2, ˆµ2, ˆσ2 2 are the estimates from (18) at convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The empirical pdf (mpdf) is constructed from the histogram of the signal samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The evaluation criteria for the appropriateness of the model are mentioned below Visual inspection: The model based pdf i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' the approx- imate pdf fitted from a model and the mpdf are compared visually for understanding the degree of agreement [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Kullback–Leibler divergence: Kullback–Leibler diver- gence(KLD) [37] is a statistical metric that measures the difference between two pdfs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Let p1 and p2 be two probability densities then the KLD between them is DKL(p1||p2) = � x p1(x) ln �p1(x) p2(x) � (20) in this paper, p1 is the empirical distribution and p2 is a model based approximate pdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' If these two distributions match then the DKL(p1||p2) equals 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The lower the DKL(p1||p2), the closer the approximation is to the mpdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' A goodness of fit plot with R-squared [38]: The rela- tionship between the sEMG data and the model-based values is analyzed using a goodness of fit plot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The nearer the data points are to the line of equality, greater the model fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' On other hand, the coefficient of determination (R-squared) is a measure of how much the variance in the observed dependent variable is explained by the independent variable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The closer the value to 1 greater the correlation between the two variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Likelihood ratio test (LRT): The LRT is a statistical test used to compare two different models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In order to determine 4 TABLE I: Basic characteristics of four benchmark sEMG datasets Ninapro DB2 Ninapro DB4 Rami-khushaba DB6 Intense Dataset No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' of Subjects 40 10 11 15 Total no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' of activities Exercise-1- 17 Exercise-2- 23 Exercise-3- 09 Total 49 Exercise-1- 12 Exercise-2- 17 Exercise-3- 23 Total 52 40 1 No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' of activities considered 23 17 40 1 No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' of repetitions 6 6 6 1 No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' of channels 12 12 7 8 Type of electrode Delsys Cometa Mini Wave Delsys Myo-armband Sampling rate 2000 samples/sec 2000 samples/sec 4000samples/sec 200 samples/sec (a) Gestures (b) Grasping (c) Arm activity (d) Intense activity Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1: Visual comparisons between mpdfs and estimated pdfs from models: LGM(green), Laplacian(blue) and Gaussian(red) for gestures, grasping, arm and intense activities for the subjects - 10, 3, 1 and 10 with corresponding activities - 7, 18, 3 and 1 which model is statistically significant the likelihood values are evaluated for both the models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The LRT is defined as [39] T = 2(log(Lp) − log(Le)) (21) where Lp and Le are likelihoods of the LGM model and any existing model respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' DATA DESCRIPTION Please note that all of the datasets analyzed in this study are available through public sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Their short descriptions follow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Ninapro Datasets: In Ninapro DB2 (NPDB2) [40] and DB4 (NPDB4) [41] datasets, there are 3 exercises collected from groups of 40 and 10 subjects respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The exercises-1 and 2 are related to activities such as hand gestures and grasping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The exercise-3 corresponds to finger move- ments at various forces levels including the abduction and adduction of the thumb.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In this work, the EMG signals corresponding to the exercise- 2 from both the DB2 and DB4 are analyzed They consist of 23 grasping and 17 gesture actions respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The sEMG signals in this dataset have 12 channels corresponding to a set of twelve electrodes placed at strategic muscle locations on an arm [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In this dataset, a typical sEMG signal within a activity, has a duration of 8s with a 3s rest time and 5s activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Each trial is repeated six times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Rami-khushaba DB6 (RKDB6) [42]: This dataset consists of sEMG signals collected from 11 intact subjects (9 males and 2 females) when they were performing 8 different movements through 5 limb positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The limb positions were chosen in such a way 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='14 Empirical 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='12 LGM Laplacian Gaussian 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='08 P 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='02 0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='5 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='5 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='5 SEMG ×10-70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='14 Empirical 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='12 LGM Laplacian Gaussian 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='08 P 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='02 0 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='5 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='5 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='5 2 SEMG ×10~60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='14 Empirical 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='12 LGM Laplacian Gaussian 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='08 P 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='02 3 2 1 0 1 2 SEMG ×10~40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='16 Empirical 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='14 LGM Laplacian 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='12 Gaussian 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='08 Q 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='005 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='005 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='01 SEMG5 1 5 10 15 Movements 1 5 10 Subjects 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='09 (a) 1 5 10 15 Movements 1 5 10 Subjects 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='55 (b) 1 5 10 15 Movements 1 5 10 Subjects 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 (c) 1 5 10 15 20 Movements 1 5 10 15 20 25 30 35 39 Subjects 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='09 (d) 1 5 10 15 20 Movements 1 5 10 15 20 25 30 35 39 Subjects 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='7 (e) 1 5 10 15 20 Movements 1 5 10 15 20 25 30 35 39 Subjects 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8 2 (f) 1 5 10 15 20 25 30 35 39 Movements 1 5 10 Subjects 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='08 (g) 1 5 10 15 20 25 30 35 39 Movements 1 5 10 Subjects 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='35 (h) 1 5 10 15 20 25 30 35 39 Movements 1 5 10 Subjects 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9 (i) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2: Heatmaps of KLD for the 3 models: (a) LGM, (b) Laplacian and (c) Gaussian corresponding to Ninapro-DB4, (d) LGM, (e) Laplacian and (f) Gaussian from Ninapro-DB2 and (g) LGM, (h) Laplacian and (i) Gaussian from Rami-khushaba-DB6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Subjects 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='25 KLD LGM Gaussian Laplacian Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 3: KLD values of LGM, Laplacian and Gaussian models for intense activity data that each subject can mimic daily activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Each activity has six repetitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' A sEMG signal array consists of seven channels corresponding to seven Delsys DE 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='x EMG sensors placed across the circumference of the forearm Intense Action Dataset (IAD) [43]: This dataset consists of sEMG signals acquired from 15 healthy subjects when performing a single intense activity i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=', each subject is instructed to hold a 6kg dumbbell with the right hand for 120 seconds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' These sEMG signals consist of 8 channels corresponding to 8 EMG electrodes and each activity is carried out only once.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The basic characteristics of these benchmark datasets are provided in the table I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' RESULTS AND ANALYSIS For each of the mentioned datasets, the sEMG signals cor- responding to each trial from each activity by each subject are analyzed using the three models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Specifically, the sEMG signal from the channel with the highest energy among multiple 6 Gestures Grasping Arm movements 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8 1 (a) Gestures Grasping Arm movements 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8 1 (b) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 4: Average KLD for the 3 models (LGM-green, Laplacian-blue, Gaussian-red) for each of the trails (a) over the movements for different subjects (b) over the subjects for different movements channels is examined using the models based on the following evaluation methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' a qualitative analysis based on visual inspection quantitative analyses: 1) the KL divergence analysis 2) the goodness of fit plots with R-squared and confi- dence interval for R-squared 3) the likelihood ratio test A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Visual Inspection Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1 illustrates the visual comparisons between the mpdf (yellow) and the fitted pdfs from the LGM (green), the Laplacian (blue) and the Gaussian (red) models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' These pdfs correspond to EMG signals of different activities as listed in the following: Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1(a): activity-7 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=', pointing index finger by subject-10, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1(b): activity-18 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=', the quadpod grasp by subject-3, Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1(c): activity-3 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=', a wrist supination by subject-1 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1(d): activity-1 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=', lifting a dumbbell by subject-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1(a), (b) and (c) correspond to pdfs of the sEMG signal corresponding to gestures, grasping and normal arm activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' From these it is evident that the overlap between the mpdf and the LGM model is high compared to standalone Laplacian and Gaussian models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Whereas Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1(d) represents the pdfs of the sEMG signal corresponding to the intense activity, it is noticed that the overlap between the LGM model and the mpdf is similar to that of the standalone Gaussian model and the mpdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In contrast, the overlap between the standalone Laplacian model and mpdf is lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Quantitative Analysis 1) KL-divergence: For each of the datasets under consid- eration, the KLD is evaluated between the LGM pdf and the mpdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' For comparison purposes, the KLD computation is also done for the Gaussian and the Laplacian pdfs against the mpdf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The corresponding results are illustrated in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2 to 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Specifically, the heatmaps of KLD as a function of subjects and movements are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Each cell in a heatmap corresponds to the KLD for a given model for a particular subject while performing one of the activities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Further, the KLD represented here is an average over the given trials of an activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2 (a)-(c) correspond to the KLD for the Ninapro- DB4, Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2 (d)-(f) depict the KLD for the Ninapro-DB2 and Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2 (g)-(i) represent the KLD for the Rami-khushaba- DB6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' For each of the three datasets, it is noted that in these heatmaps, the LGM model has the lowest KLD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The lower and upper bounds of KLD for the heatmaps in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2 are shown in table II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The key observation is the highest KLD value from the LGM model is the lowest KLD value for both the Laplacian and the Gaussian models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' TABLE II: Lower and upper bounds of KLD for the proposed and the standalone models for different datasets Datasets LGM Laplacian Gaussian NPDB4 [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='6] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1] NPDB2 [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='2] RKDB6 [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='35] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9] The KLD values for different models in the case of the intense activity are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Notably, for the intense activity dataset as well, the KLD value is the lowest for the LGM model closely followed by the Gaussian model and then the Laplacian model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The minimum and maximum KLD values corresponding to the three models are: the LGM {0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='0033, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='0301}, the Gaussian {0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='0039, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='0378} and the Laplacian {0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='0920, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1513}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 4(a) shows the KLD averaged over the movements as a function of the subjects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 4(b) shows the vice versa case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The KLD of the LGM, Laplacian and Gaussian models are represented in green, blue and red respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 4(a) and (b), it is observed that for the activities such as the gestures, grasping and the arm movements the average KLD value over the movements and subjects is the lowest for the LGM model, when compared to the other models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 7 (a) Gestures (b) Grasping (c) Normal activity (d) Intense activity Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 5: Goodness of fit plots for the models LGM(green), Laplacian(blue) and Gaussian(red) for gestures, grasping, normal and Intense activities for the subjects-10, 3, 1 and 10 and with corresponding activities-7, 18, 3 and 1 2) Goodness of fit plots: Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 5 illustrates the goodness of fit plots between the estimates from the three models versus the actual data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Specifically, the Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 5 (a) to (d) correspond to the results on data from the gestures, grasping, normal arm and the intense activities respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The LGM model, Laplacian and Gaussian models are represented by the data points in green, blue and red respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' From Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 5 (a), (b) and (c), in the scatter plots, the model-values of the LGM model are found to be adjacent to the line of equality which means that the predicted values from this model are close to the actual values of the sEMG signal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Whereas in the case of intense activity shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 5(d), the model values corresponding to both the LGM and the Gaussian models are similar and they are adjacent to the line of equality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 5, for the gestures, grasping and normal arm activities, it can be concluded that the LGM model is better compared to other models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' However, for the intense activity, both the LGM and the Gaussian fit the EMG data quite well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The average R- squared values are shown in the table III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' For the first three categories of activities, based on these metrics, the LGM model is found to be superior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Additionally, for the intense activities, the LGM and the Gaussian are again similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The 95 percent confidence intervals(CI) [44] [45] for R-squared corresponding to the plots in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 5 are given in table IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 3) Likelihood ratio test: The LRT given in (21) is carried out between the LGM model and the Laplacian model as shown below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' H0 : The Laplacian model fits the data H1 : The LGM model fits the data TABLE III: R-Squared values for four datasets from model evaluations Datasets LGM Laplacain Gaussian NPDB4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9958 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='94799 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='74885 NPDB2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='99491 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='86529 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='84151 RKDB6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9932 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='91137 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='82279 IAD 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='99715 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='54947 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='98269 TABLE IV: Confidence interval of R-squared for LGM, Lapla- cian and Gaussian models Datasets LGM Laplacain Gaussian NPDB4 [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9946 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9970] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9439 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9520] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='7413 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='7564] NPDB2 [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9937 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9961] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8598 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8708] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8357 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8473] RKDB6 [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9918 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9946] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9067 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9160] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8167 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8289] IAD [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9960 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9983] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='5402 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='5587] [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9800 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9854] This test is carried out for 99% confidence interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' It is noted that p-value is less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='01, which means H0 is rejected and H1 is accepted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The test is repeated by replacing the Laplacian with the Gaussian model for H0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In this test also the p-value is found to be less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='01 and thus H1 is accepted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Mixing Weights The mixing coefficients corresponding to the Laplacian component of the LGM model corresponding to different activities from various datasets are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' For the low and medium MCF levels such as the gestures, grasping and the normal activities, it is noticed that the Laplacian 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='06 lodel-Value 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='02 LGM:R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='99715 Y=X Line 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='01 Laplacian: R2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='54947 Gaussian: R?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='98269 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='08 Actual0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='14 LGM: R2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9932 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='12 Y=X Line Laplacian: R?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='91137 Gaussian: R?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='82279 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 on e 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='08 Model-V 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='02 0 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 Actual0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='14 LGM: R2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='99491 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='12 Y=X Line Laplacian: R2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='86529 Gaussian: R?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='84151 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 an e 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='08 Model-V 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='02 0 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 Actual0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 an lodel-Val 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='06 M 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='04 LGM:R2=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9958 Y=X Line 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='02 Laplacian: R2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='94799 Gaussian: R?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='74885 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='14 Actual8 Gestures Grasping Normal Intense 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8 1 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 6: Laplacian coefficient for each trail versus subjects for gestures, grasping, normal arm movements and intense activity component has a stronger weighting in comparison with the Gaussian component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Whereas in case of intense activity i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=', at high MCF level the mixing weight corresponding to the Gaussian component is higher and the Laplacian component is lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Thus from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 6, it can be recognized that as the intensity of an activity, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=', the amount of energy required for performing a certain action increases, the weight of the Laplacian component reduces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 7 shows Laplacian weights of the LGM model corresponding to the first three limb activities under consideration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The horizontal and vertical axes in the heatmaps correspond to the number of movements and subjects respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Each cell in a heatmap denotes the Laplacian weight in the LGM model for a particular subject and activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' It is noticed that for most of the cases the Laplacian weight λ1 is dominating the Gaussian weight λ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In some circumstances, the Laplacian weights are lower than Gaussian weights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' For example, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 7 (a) for the subject-1, activities-4 and 9, in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 7(b) for the subject-18, activity-2 and in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 7 (c), the subject-1, activities-2 and 10, the Gaussian weights are stronger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' DISCUSSION From the results presented in section IV, for the EMG signals corresponding to the low and medium levels of muscle recruitment i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=', for activities such as the gestures, grasping and the normal arm movements, the LGM is found to be a more suitable model compared to the standalone models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' This is verified in terms of 1) the visual inspection between a model pdf and the mpdf, 2) the lowest KLD, 3) the goodness of fit plots - the model values matching the true values, 4) the higher R-squared values and 5) the Likelihood ratio test accepting the alternate hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' However, in the case of intense activities, both the LGM and the Gaussian model seem to perform quite similarly according to the four evaluation methods described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Hence for high levels of muscle recruitment, the proposed LGM model behaves similar to a standalone Gaussian model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' This result is further qualified 1 5 10 15 Movements 1 5 10 Subjects 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9 (a) 1 5 10 15 20 Movements 1 5 10 15 20 25 30 35 39 Subjects 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9 (b) 1 5 10 15 20 25 30 35 39 Movements 1 5 10 Subjects 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='9 (c) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 7: Laplacian weights of LGM model averaged over trials as a function of subjects and movements for (a) gestures, (b) grasping, and (C) arm activities by the following observation, in the LGM model, the mixing coefficient of the Laplacian component becomes very small in comparison to that of the Gaussian component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In the analysis on mixing weights, it is observed that for the first three types of actions, both the Laplacian and Gaus- sian components have significant contributions to the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' However, for the intense activity, the Gaussian component is much stronger.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Hence, from these findings it can be postulated that the weights of the LGM model can be related to MCF level and motor units that are activated during an activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' For example, for the first three activities, the Laplacian weight λ1 is higher relating to lower MCF level and the lower number of activated motor units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' However, in the case of intense activity the Gaussian weight λ2 is higher connecting to a higher MCF level and a larger number of activated motor units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' These findings are in agreement with the literature on pdfs reported in section I-B where it is noted that for the lower and medium MCF levels, the pdfs have a sharper peak at center, hinting 9 a Laplacian structure, and at higher MCF levels, they have a clear Gaussian structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' CONCLUSION In this paper, a Laplacian Gaussian mixture model is proposed for sEMG signals from upper limbs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The proposed model is tested on several benchmark sEMG datasets and compared with the existing standalone models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' The suitability of the model is validated using (1) qualitative analyses such as visual comparison with the empirical pdf (mpdf) where it is observed that the LGM model has the best agreement,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' (2) the KL divergence between the model pdf and the mpdf,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' again the KLD is lowest for the LGM model,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' (3) a goodness of fit plot,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' comparison of coefficient of determination (CFD) - R2 and confidence intervals for R2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' here it is noted that R2 in case of the LGM model is closest to unity and (4) the Likelihood ratio test (LRT) that also supported the LGM model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Finally, it is noted, for the low and medium muscle contraction force levels, the Laplacian weight has stronger weighting than the Gaussian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Whereas for the higher muscle contraction force levels the Laplacian weights are lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' In the future work, we will extend the proposed model to understand the correlations between the sEMG signals from various muscle locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' ACKNOWLEDGMENT This research is funded by SERB, Govt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' of India under Project Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' CRG/2019/003801.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' REFERENCES [1] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Wang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Stefano, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Allen, “A simulation model of the surface EMG signal for analysis of muscle activity during the gait cycle,” Computers in biology and medicine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 36, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 601–618, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [2] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Stashuk, “Simulation of electromyographic signals,” Journal of Electromyography and Kinesiology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 3, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 157–173, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [3] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Cuddon, “Electrophysiology in neuromuscular disease,” Veterinary Clinics: Small Animal Practice, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 32, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 31–62, 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [4] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Vigotsky, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Halperin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Lehman, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Trajano, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Vieira, “Interpreting signal amplitudes in surface electromyography studies in sport and rehabilitation sciences,” Frontiers in physiology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 8, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 985, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [5] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' De Luca, “The use of surface electromyography in biomechanics,” Journal of applied biomechanics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 13, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 135–163, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [6] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Soderberg and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Cook, “Electromyography in biomechanics,” Physical Therapy, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 64, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1813–1820, 1984.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [7] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Hasanbelliu, “A multi-dimensional visualization tool for understand- ing the role of EMG signals in head movement anticipation,” in ACM SIGGRAPH 2004 Posters, 2004, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [8] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Merletti, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Conte, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Avignone, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Guglielminotti, “Mod- eling of surface myoelectric signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' model implementation,” IEEE Transactions on Biomedical Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 46, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 810–820, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [9] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Rodriguez-Falces, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Navallas, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Malanda, “Emg modeling,” Computational Intelligence in Electromyography Analysis-A Perspective on Current Applications and Future Challenges, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 3–36, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [10] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Hayashibe and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Guiraud, “Voluntary EMG-to-force estimation with a multi-scale physiological muscle model,” Biomedical engineering online, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 12, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1–18, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [11] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Paiss and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Inbar, “Autoregressive modeling of surface EMG and its spectrum with application to fatigue,” IEEE Transactions on Biomedical Engineering, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 761–770, 1987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [12] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Kiryu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' De Luca, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Saitoh, “AR modeling of myoelectric interference signals during a ramp contraction,” IEEE Transactions on Biomedical Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 41, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1031–1038, 1994.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [13] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Shahid, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Walker, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Lyons, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Byrne, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Nene, “Application of higher order statistics techniques to EMG signals to characterize the motor unit action potential,” IEEE Transactions on Biomedical Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 52, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1195–1209, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Furui, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Hayashi, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Tsuji, “A scale mixture-based stochastic model of surface EMG signals with variable variances,” IEEE Transac- tions on Biomedical Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 66, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2780–2788, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [15] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Khokhar, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Xiao, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Menon, “Surface EMG pattern recognition for real-time control of a wrist exoskeleton,” Biomedical engineering online, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 9, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1–17, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [16] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Huang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Kuiken, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Lipschutz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=', “A strategy for identifying locomotion modes using surface electromyography,” IEEE Transactions on Biomedical Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 56, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 65–73, 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [17] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Chan and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Englehart, “Continuous classification of myoelec- tric signals for powered prostheses using gaussian mixture models,” in Proceedings of the 25th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEEE Cat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 03CH37439), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' IEEE, 2003, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2841–2844.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [18] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Furui, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Igaue, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Tsuji, “EMG pattern recognition via bayesian inference with scale mixture-based stochastic generative models,” Expert Systems with Applications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 185, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 115644, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [19] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Giacomini, “Electromyography and neuromuscular disorders: clin- ical electrophysiologic correlations,” McGill Journal of Medicine: MJM, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 9, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 173, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [20] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Xiong, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Zhao, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Zhao, “Deep learning for EMG- based human-machine interaction: A review,” IEEE/CAA Journal of Automatica Sinica, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 8, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 512–533, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [21] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Wei, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Dai, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Wong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Hu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Kankanhalli, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Geng, “Surface-electromyography-based gesture recognition by multi-view deep learning,” IEEE Transactions on Biomedical Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 66, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2964–2973, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [22] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Hudgins, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Parker, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Scott, “A new strategy for multifunction myoelectric control,” IEEE Transactions on Biomedical Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 40, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 82–94, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [23] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Roesler, “Statistical analysis and evaluation of myoelectric signals for proportional control,” The Control of upper-extremity prostheses and orthoses, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 44–53, 1974.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [24] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Milner-Brown and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Stein, “The relation between the surface electromyogram and muscular force.” The Journal of physiology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 246, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 549–569, 1975.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [25] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Parker, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Stuller, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Scott, “Signal processing for the multistate myoelectric channel,” Proceedings of the IEEE, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 65, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 662–674, 1977.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [26] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Hunter, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Kearney, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Jones, “Estimation of the conduction velocity of muscle action potentials using phase and impulse response function techniques,” Medical and Biological Engineering and Comput- ing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 25, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 121–126, 1987.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [27] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Bilodeau, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Cincera, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Arsenault, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Gravel, “Normality and stationarity of EMG signals of elbow flexor muscles during ramp and step isometric contractions,” Journal of Electromyography and Kinesiology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 87–96, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [28] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Clancy and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Hogan, “Probability density of the surface elec- tromyogram and its relation to amplitude detectors,” IEEE Transactions on Biomedical Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 46, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 730–739, 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [29] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Kaplanis, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Pattichis, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Hadjileontiadis, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Panas, “Bispectral analysis of surface EMG,” in 2000 10th Mediterranean Elec- trotechnical Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Information Technology and Electrotechnology for the Mediterranean Countries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Proceedings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' MeleCon 2000 (Cat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 00CH37099), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' IEEE, 2000, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 770–773.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [30] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Nazarpour, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Sharafat, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Firoozabadi, “Negentropy analysis of surface electromyogram signal,” in IEEE/SP 13th Workshop on Statistical Signal Processing, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' IEEE, 2005, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 974–977.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [31] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Naik and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Kumar, “Evaluation of higher order statistics parameters for multi channel sEMG using different force levels,” in 2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' IEEE, 2011, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 3869–3872.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [32] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Naik, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Kumar, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Arjunan, “Kurtosis and negentropy investigation of myo electric signals during different MVCs,” in ISSNIP Biosignals and Biorobotics Conference 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' IEEE, 2011, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [33] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Nazarpour, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Al-Timemy, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Bugmann, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Jackson, “A note on the probability distribution function of the surface electromyogram signal,” Brain research bulletin, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 90, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 88–91, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [34] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Kusuru, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Turlapaty, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Thakur, “A laplacian-gaussian mixture model for surface EMG signals from upper limbs,” in 2021 43rd Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' IEEE, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 681–685.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [35] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Bishop and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Nasrabadi, Pattern recognition and machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Springer, 2006, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 4, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [36] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Spanos, Probability Theory and Statistical Inference: Empirical Modeling with Observational Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Cambridge University Press, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 10 [37] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Kullback, Information theory and statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Courier Corporation, 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [38] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Cohen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Cohen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' West, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Aiken, “Applied multiple regression,” Correlation Analysis for the Behavioral Sciences, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 2, 1983.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [39] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' King, Unifying political methodology: The likelihood theory of statistical inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' University of Michigan Press, 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [40] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Atzori, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Gijsberts, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Castellini, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Caputo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Hager, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Elsig, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Giatsidis, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Bassetto, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' M¨uller, “Electromyography data for non-invasive naturally-controlled robotic hand prostheses,” Scientific Data, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1–13, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [41] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Pizzolato, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Tagliapietra, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Cognolato, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Reggiani, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' M¨uller, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Atzori, “Comparison of six electromyography acquisition setups on hand movement classification tasks,” PloS one, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 12, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 10, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' e0186132, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [42] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Khushaba, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Takruri, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Miro, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Kodagoda, “Towards limb position invariant myoelectric pattern recognition using time-dependent spectral features,” Neural Networks, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 55, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 42–58, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [43] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Ebied, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Awadallah, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Abbass, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' El-Sharkawy, “Upper limb muscle fatigue analysis using multi-channel surface EMG,” in 2020 2nd Novel Intelligent and Leading Emerging Sciences Conference (NILES).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' IEEE, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 423–427.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [44] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Finn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=', “Correlations redux,” Psychological Bulletin, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 118, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' 155–164, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' [45] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Cohen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' West, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Aiken, Applied multiple regres- sion/correlation analysis for the behavioral sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} +page_content=' Psychology press, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/TNAzT4oBgHgl3EQfJftl/content/2301.01080v1.pdf'} diff --git a/UtAzT4oBgHgl3EQfX_xg/content/2301.01327v1.pdf b/UtAzT4oBgHgl3EQfX_xg/content/2301.01327v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b9ae5ecb142f246c625db93f9b9b00f653591a43 --- /dev/null +++ b/UtAzT4oBgHgl3EQfX_xg/content/2301.01327v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ef374206740b143b50f71320cd066c0857b90e063883ad867c25f47747f0d126 +size 790622 diff --git a/UtAzT4oBgHgl3EQfX_xg/vector_store/index.pkl b/UtAzT4oBgHgl3EQfX_xg/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..656be60532be93d9d41b96a48af57666289ba4e4 --- /dev/null +++ b/UtAzT4oBgHgl3EQfX_xg/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:089979d513ec9f9e19c43030d7abd9fb3906ac46425d3b82f2f7c575742ed645 +size 147036 diff --git a/VtAyT4oBgHgl3EQfV_ek/content/2301.00155v1.pdf b/VtAyT4oBgHgl3EQfV_ek/content/2301.00155v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..893305162e9f102e54957b190f3d486eeb675918 --- /dev/null +++ b/VtAyT4oBgHgl3EQfV_ek/content/2301.00155v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:58b48113022ee59f08c878b1616f8f5b0acf9167116fb1852f93bd3c36fed54c +size 720927 diff --git a/VtAyT4oBgHgl3EQfV_ek/vector_store/index.pkl b/VtAyT4oBgHgl3EQfV_ek/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..c10011f502428dc56935235de0a58697a9ed38e8 --- /dev/null +++ b/VtAyT4oBgHgl3EQfV_ek/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:be184cb7bae8170789e217b05c521e507bcc6b08ea9b57c7a0ff92b7e3b72e0c +size 114504 diff --git a/VtAzT4oBgHgl3EQfJ_ud/content/2301.01090v1.pdf b/VtAzT4oBgHgl3EQfJ_ud/content/2301.01090v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1bb411b42f863815fe6292066e661306b5abc7e9 --- /dev/null +++ b/VtAzT4oBgHgl3EQfJ_ud/content/2301.01090v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:73ec74876fc05c86876f3a3573c5a6bd7bd73f57caed0f5bc5e75fd13a0e72a3 +size 1998458 diff --git a/VtAzT4oBgHgl3EQfJ_ud/vector_store/index.faiss b/VtAzT4oBgHgl3EQfJ_ud/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..6ede98e7aa0afe6af10c261d9eb715136892d72b --- /dev/null +++ b/VtAzT4oBgHgl3EQfJ_ud/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cc59ac8292b1dd4a9debb449d06a72d57dc7b214b058feaa235372c0640cebed +size 8519725 diff --git a/WdE5T4oBgHgl3EQfCA5G/vector_store/index.faiss b/WdE5T4oBgHgl3EQfCA5G/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..5ae5e10ba16d4e470c97664abcbcc5bf0a176d09 --- /dev/null +++ b/WdE5T4oBgHgl3EQfCA5G/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1f54598d578dc9533e6b6dbfff966555d5b4d7a3942aded337be02d65181a4f9 +size 1572909 diff --git a/X9E1T4oBgHgl3EQfcARq/content/tmp_files/2301.03179v1.pdf.txt b/X9E1T4oBgHgl3EQfcARq/content/tmp_files/2301.03179v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..88b22680ff1cbb35975371be67aa5b608b21e980 --- /dev/null +++ b/X9E1T4oBgHgl3EQfcARq/content/tmp_files/2301.03179v1.pdf.txt @@ -0,0 +1,827 @@ + + +1 + +Behaviour of Ion Acoustic Soliton in a two-electron temperature +plasmas of Multi-pole line cusp Plasma Device (MPD) +Zubin Shaikh1, 3, A.D.Patel1, 4, P.K.Chattopadhyay1, 2, Joydeep Ghosh1, 2 +H.H.Joshi3 and N.Ramasubramanian1, 2 +1. Institute for Plasma Research, Gandhinagar-382428, India +2. Homi Bhabha National Institute, Anushaktinagar-400094, Mumbai, India +3. Department of Physics, Saurashtra University, Rajkot-360005, India +4. Institute of Plasma Physics and Laser Micro Fusion, Warsaw +01-497, Poland +zubin.ipr@gmail.com +ABSTRACT +This article presents the experimental observations and characterization of Ion Acoustic +Soliton (IAS) in a unique Multi-pole line cusp Plasma Device (MPD) device in which the +magnitude of the pole-cusp magnetic field can be varied. And by varying the magnitude of the +pole-cusp magnetic field, the proportions of two-electron-temperature components in the +filament-produced plasmas of MPD can be varied. The solitons are experimentally +characterized by measuring their amplitude-width relation and Mach numbers. The nature of +the solitons is further established by making two counter-propagating solitons interact with +each other. Later, the effect of the two-temperature electron population on soliton amplitude +and width is studied by varying the magnitude of the pole cusp-magnetic field. It has been +observed that different proportions of two-electron-temperature significantly influence the +propagation of IAS. The amplitude of the soliton has been found to be following inversely with +the effective electron temperature (𝑇𝑒𝑓𝑓). + +1. Introduction +Ion-Acoustic Solitons (IAS), the self-organized, non-linear localized structures that can +propagate long distances, are widely studied in astrophysical and laboratory plasmas to +understand their non-linear dynamics describing several fundamental processes of plasma + + + +2 + +physics. A solitary wave was first discovered to propagate long distances without changing its +shape and speed in shallow water in 1844 by J.S.Russels1. Korteweg-de Vries2 (KdV) +developed the mathematical formalism of soliton dynamics, which had led to significant +advances in determining the properties of solitons. The soliton dynamics for plasmas was +explained by Washimi and Taniuti3 by deriving and solving the KdV equation in plasma +medium using a novel mathematical approach. Sagdeev4 studied the arbitrary amplitude non- +linear waves in plasma, highlighting many more interesting phenomena of plasma acoustic +modes. Both these methods are used to analyze solitons in laboratory5 and space plasmas6. The +theory of solitons was further developed by Gardner7, obtaining an exact solution of the KdV +equation by treating it as an initial value problem using the inverse scattering method. +T.Taniuti8 introduced the reductive perturbation principle for solving the KdV equation, which +was also applicable for solving various non-linear equations apart from waves in plasma. The +solution to the KdV equation for non-linear ion-acoustic waves in plasma medium comprising +of negative ions had been obtained by Das and Tagare9 and Das10. A comprehensive review on +theoretical studies of solitons can be found in the references11,12. +The existence of solitary waves is ubiquitous in space plasmas. Solitary waves in the +magnetosphere were first observed by the S3-3 satellite13 and subsequently confirmed and +studied extensively by Viking Satellite14. These solitary structures were also observed in the +auroral acceleration region15 and the generation mechanism of these structures has been given +by Q.Lu16. +The existence of ion-acoustic solitons in laboratory plasmas was experimentally +demonstrated by H. Ikezi5 for the first time in a double plasma device17. In this experiment, the +solitons are excited by applying perturbation into a fine mesh grid immersed in plasma with +different waveforms having different frequencies18. Following this, ion-acoustic solitons were +excited in several devices19–22 mainly by pulsing a floating wire grid placed inside the plasma. +The experiments in the laboratory plasmas demonstrated the variations in soliton properties +with varying plasma parameters, which were successfully modeled using the theoretical +formulations mentioned above. The experimentally measured width and propagation velocity +of solitons matched very well with the solitary wave solutions, as shown by Sakanaka23. +The soliton-soliton interaction was also experimentally demonstrated by exciting two +solitons and making them propagate towards each other5,24,25. Over the years, several + + + +3 + +experiments were carried out in order to understand the excitation26,27, propagation28,29 +collisions30, etc., of ion-acoustic solitons in different plasma devices. +Although the ion-acoustic solitons in plasmas are extensively studied both theoretically and +experimentally, several open questions remain to be answered, such as the behaviour of solitons +in plasmas with two electron temperatures. The coexistence of two distinct species of electrons +at different temperatures is very common in space plasmas13,31 and laboratory plasmas32,33. +Theoretical studies by Cairns34 and Nishihara35 had shown that the presence of non-thermal +electrons or plasmas with two electron temperatures can significantly modify the ion acoustic +solitary structures. The propagation of ion-acoustic waves in two-electron temperature plasma +has been studied by Jones et al.,36 both experimentally and theoretically, and it has been shown +that a small fraction of hot electrons can affect the propagation of the wave. However, there +are very few controlled experimental studies on soliton characterization with respect to soliton +width and amplitude in plasmas with two-temperature electrons. +In the present work, the effect of two-electron temperature on the properties of ion-acoustic +solitons are studied in the Multi-pole line cusp Plasma Device (MPD)32,33. The special feature +of this device is the controllability of the magnitude of the pole magnetic fields by varying the +currents in electromagnets used for producing the cusp magnetic fields. This controllability of +cusp magnetic field strength at the poles facilitates the production of two-temperature electrons +in variable proportions. The confinement of the energetic electron population generated in the +filament-produced argon plasmas varies with varying the cusp magnetic field strengths leading +to the generation of plasmas with two-electron temperatures in variable proportions in this +device. Taking advantage of this unique feature, the effect of two-temperature electrons on ion- +acoustic soliton propagation and characteristics are studied in the MPD. The solitons are +excited using the conventional technique by pulsing a floating metal mesh grid placed inside +the plasma. Before varying the magnetic field strengths, the solitons are thoroughly +characterized by measuring the velocities and width of solitons and compared with theoretical +estimations. The solitary nature of the excited waves is also verified by inducing interactions +of two counter-propagating solitons. The cusp magnetic field strengths are then varied to vary +the hot-electron fraction. It has been observed that the soliton amplitude increases, and its width +decreases with systematically increasing the hot-electron populations in the plasma. Most +importantly, it has been found that the effective electron temperature (𝑇𝑒𝑓𝑓) controls the width +of the solitons almost proportionally. + + + +4 + +The paper is organized as follows. Section 2 describes the details of the experimental setup +and wave excitation and detection techniques. Section 3 describes the detailed experimental +results and characterization of solitons. Section 4 describes the effect of two-temperature +electrons on soliton dynamics, followed by a summary in section 5. +2. Experimental Setup +The present experiment is carried out in a Multi-pole line cusp Plasma Device +(MPD)32,33. MPD consists of six rectangular-shaped electromagnets with profiled core material +to produce the variable multi-pole line cusp magnetic field. These electromagnets provide +uniqueness in varying the magnetic field strength and configuration. These electromagnets are +placed on the periphery of the vacuum vessel, and each magnet is placed 60 degrees apart. The +majority of early experiments used permanent magnets to create the multi-cusp field. Those +devices were limited in terms of performing investigations with variable cusp magnetic fields +as the magnetic field produced by permanent magnets is fixed. The novel aspect of MPD is +that by varying the current in the electromagnets both in terms of magnitude and direction, the +magnetic field strength and configuration can be changed in a controlled way. In all +configurations, the magnetic field strength in the center always remains very small in the order +of a few gausses only. Hence, the field-free region inside the chamber does not change +appreciably. The present experiment is performed with 12 pole cusp magnetic field +configuration. The current in all six electromagnets is in the same direction; hence all six +magnets will produce one type of pole, and another virtual pole will be produced in between +two magnets; hence a total of 12 cusps will be there of six dipoles. The 12-pole cusp +configuration has a field-free region of ~20 cm37. +The MPD comprises of a non-magnetic stainless steel cylindrical vacuum vessel with +a length of 1500 mm, a diameter of 400 mm, and a wall thickness of 6mm. The chamber is +evacuated by a Turbo Molecular Pump (440 l/s) backed by a rotary pump through a conical +reducer at one side of the chamber. A base pressure of 1x10-6 mbar is achieved, measured by a +hot ionization gauge. The filamentary argon discharge plasma is produced using a hot filament- +based cathode source. The plasma source (cathode) is two dimensional (8cm x 8cm) vertical +array of five tungsten filaments; each filament has a 0.5 mm diameter and 8 cm length. These +filaments are powered by a 500 A, 15 V floating power supply, usually operated at around 16 +- 19 A and 7.5V per filament. The chamber is filled with Argon gas through a needle valve to +a working pressure of ~8 x 10- 5 m-bar. The filament source is biased negatively at a voltage of + + + +5 + +50 V with respect to the grounded chamber walls using a discharge power supply of ratings +~125V and ~25A. The electric field lines between the high-potential filament and the grounded +chamber wall accelerates the primary electrons emitted from the joule-heated filaments. These +electrons collide with the neutral argon atoms and ionize some of them. These ions and +electrons are confined by the multi-pole line cusp magnetic field. + + Figure 1: Schematic diagram of the Multi-Cusp Plasma Device (MPD) Experimental setup +The plasma thus confined in the MPD is usually reported as bi-Maxwellian, i.e., having two +temperature electrons32,38–40; one having low temperature called cold electron (𝑇𝑐) and other +having relatively larger temperature called hot electrons (𝑇ℎ). It is well known that the cusp +magnetic is an ideal configuration for the confinement of primary or hot electrons 41–44. The +cusp magnetic field confines the hot electrons by mirror effects. Due to the mirror effect in +cusp configuration, electrons will move back and forth between the poles; thus, the maximum +hot energetic electrons are confined by the cusp magnetic field45,41,46,47. +The measurement of plasma parameters have been estimated from the V-I +characteristics of Langmuir probes32,48. In the filament-produced plasmas of this device, the +typical V-I characteristic always shows the existence of two-electron temperature distributions +in the central plasma region. In bi-Maxwellian plasma, the electron current collected by a probe +in the electron retarding region is given by +𝐼𝑒 = 𝐼𝑐0𝑒𝑥𝑝 [𝑒(𝑉𝑝𝑟 − 𝑉𝑝) +𝑘𝐵𝑇𝑐 +] + 𝐼ℎ0𝑒𝑥𝑝 [𝑒(𝑉𝑝𝑟 − 𝑉𝑝) +𝑘𝐵𝑇ℎ +] +(1) + + +150cm +Magnet +Filament +Probe +array +Exciter +Disc +12V +Oscilloscope +GateValve +-50V +C +Function +Generator +Turbomolecular +dwnd + +6 + +Where, 𝐼𝑐0 = 𝐴𝑝𝑁𝑐(𝑘𝑏𝑇𝑐 2𝜋𝑚𝑒) +⁄ +1/2 and 𝐼ℎ0 = 𝐴𝑝𝑁ℎ(𝑘𝑏𝑇ℎ 2𝜋𝑚𝑒) +⁄ +1/2, 𝑁𝑐 and 𝑁ℎ are the cold +electron density and hot electron density, and 𝑉𝑝𝑟 is probe potential. 𝑁0 ≈ 𝑁𝑐 + 𝑁ℎ is the total +electron density. By deducting the 𝐼𝑖𝑠𝑎𝑡 from the total probe current(𝐼𝑝), the variation of +electron current (𝐼𝑒) drawn by the probe is determined. 𝑇ℎ and 𝑇𝑐 are then estimated from the +slope of the line of 𝑉𝑝 vs 𝑙𝑛𝐼𝑒 and 𝑉𝑝 vs ln (𝐼𝑒 − 𝐼ℎ) curves, respectively. The hot electron +density (𝑁ℎ) is defined as +𝑁ℎ = − (2𝑚𝑒𝑣ℎ +𝑒2𝐴𝑝 +) 𝑑𝐼 𝑑𝑉 +⁄ + +(2) +Where 𝑚𝑒 is the mass of an electron, 𝑣ℎ= √2𝑒 𝑉𝑑 𝑚𝑒 +⁄ + is hot electron velocity, 𝑉𝑑 is +discharge voltage, 𝐴𝑝 is probe area, and 𝑑𝐼 𝑑𝑉 +⁄ + is the slope of the tail part of V-I characteristics +of plasma. The estimation of different plasma parameters for MPD is discussed in detail by +Patel et.al32,33. Previously, we have reported that a change of the currents in the electromagnets +changes the pole cusp magnetic field, which in turn changes the leak width and mirror ratio33. +The leak width shows the opposite variation to the cusp magnetic field, i.e., as the magnetic +field increases, leak width decreases33,49,50. As a result, the high energetic electron confinement +in plasma increases, and it affects the plasma parameters. So as expected, the pole cusp +magnetic field controls the density and temperature of the plasma. Hence we varied the +𝑇𝑐, 𝑇ℎ, 𝑁𝑐, 𝑎𝑛𝑑 𝑁ℎ by +systematically +varying +the +pole +magnetic +field 𝐵𝑝. +Once 𝑇𝑐, + 𝑇ℎ, 𝑁𝑐 𝑎𝑛𝑑 𝑁ℎ are measured experimentally, effective plasma temperature 𝑇𝑒𝑓𝑓 can +be estimated, which is defined as +𝑇𝑒𝑓𝑓 = 𝑁𝑜𝑇ℎ𝑇𝑐 (𝑁ℎ𝑇𝑐 + 𝑁𝑐𝑇ℎ) +⁄ + +(3) + +Figure 2 shows the variation of 𝑁𝑐 and 𝑁ℎ, and figure 3 shows the variation of 𝑇𝑐 and 𝑇ℎ at the +center of the device (R=0 cm) with different pole cusp magnetic field(𝐵𝑝) strength for argon +plasma produced with a fill pressure of ~8 x 10-5 mbar. As 𝐵𝑝 increases, the leak width51 +𝑑 = 2(𝑟𝑙𝑒𝑟𝑙𝑖) +1 2 +⁄ changes from 11 mm for 𝐵𝑝~0.16 𝑘𝐺 to 6 mm for 𝐵𝑝~0.3 𝑘𝐺, where the pole +separation is 2πr/6 = 20 cm. as the ratio of pole width and pole separation decreases, the plasma +confinement increases leading to an increase in the density of both cold and hot (𝑁𝑐 and + 𝑁ℎ) electrons. + + + +7 + +Figure 3 shows that the temperature of cold and hot electron (𝑇𝑐 and 𝑇ℎ) initially falls up to +𝐵𝑝~0.3 𝑘𝐺 and then start increasing again. The exact nature of the variation of 𝑁𝑒 and 𝑇𝑒 +(particularly 𝑇𝑒) needs a detailed device simulation. However, the aim of the present +experiment is to study the effect of 𝑇𝑒𝑓𝑓 on the amplitude and width of the soliton. Figure 4 +shows the variation of 𝑇𝑒𝑓𝑓 with 𝐵𝑝. 𝑇𝑒𝑓𝑓 is calculated using the measured values of +𝑇𝑐, 𝑇ℎ, 𝑁𝑐, and 𝑁ℎ. It has been observed that the 𝑇𝑒𝑓𝑓 decreases initially with increasing the 𝐵𝑝 +and then starts increasing again. +Figure 2: Variation of cold electron density Nc and hot electron density Nh with various cusp magnetic +field strengths. +Figure3: Variation of cold electron temperature (𝑇𝑐) and Hot electron temperature (𝑇ℎ) with various cusp +magnetic field strength +All the basic plasma parameters, such as electron temperature (𝑇𝑒), plasma density (𝑛𝑒), plasma +potential (𝑉𝑝), floating potential (𝑉𝑓), and fluctuations 𝛿𝐼𝑖𝑠𝑎𝑡 𝐼𝑖𝑠𝑎𝑡 +⁄ + remains almost constant +over the radial extent of the plasma column32,33,37. Typical measured plasma parameters at the + +16 +14 +12 +10 +(X 1014 +8 +6 +4 +2 +0 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +1.2 +1.4 +Bp (kG)8 +6 +2 +0 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +1.2 +1.4 +Bp (kG)4.5 +4.0 +3.5 +(ev +3.0 +2.5 +2.0 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +1.2 +1.4 +Bp (kG)15.0 +14.5 +14.0 +13.5 +13.0 +(ev +12.5 +12.0 +11.5 +11.0 +10.5 +10.0 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +1.2 +1.4 +Bp (kG) + +8 + +midplane of the device are: Plasma Density (𝑛𝑒) ~ 1016 m-3, electron temperature (𝑇𝑒) ~ 4-5 +eV, Plasma potential (𝑉𝑝) ~ 4-5 V, Electron Neutral Collision frequency (𝑒𝑛) ~6 x 106 Hz and +Ion plasma frequency (𝜔𝑝𝑖) ~ 4 x106 Hz for -50V discharge voltage and 8 x10-5 bar working +pressure and at a pole magnetic field of 𝐵𝑝 = 0.6𝑘𝐺 (Magnet Current 𝐼𝑚𝑎𝑔 = 80𝐴). Pole +Magnetic field 𝐵𝑝 is the measured magnetic field at the inner wall of the device. + +Figure 4: Variation of effective temperature with various cusp magnetic field strengths. +2.1 Wave excitation and detection techniques +After measuring plasma density and temperature, experiments on wave excitation are +carried out. Soliton is excited by a floating exciter metal disk which is placed inside the plasma +at the central plane of the device, where the magnetic field is minimum, and the plasma is +uniform and quiescent37. This exciter grid is a solid disk of molybdenum with a diameter of 50 +mm and a thickness of 0.25 mm. The solid disk has been used to generate uniform sheath +thickness around it52,25. A single pulse sinusoidal voltage of ~ 20 𝑉𝑝𝑝 at 90 𝑘𝐻𝑧 frequency has +been applied to the grid to excite the soliton in the MPD plasma. The magnitude of the voltage +perturbation is chosen to be much higher than plasma potential (𝑉𝑝) for soliton excitation, and +the perturbation frequency satisfies 𝜔 𝜔𝑝𝑖 +⁄ +< 0.718. A PA-85 amplifier-based circuit with a + +6.0 +5.5 +5.0 +4.5 +4.0 +3.5 +3.0 +0.2 +0.4 +0.6 +0.8 +1.0 +1.2 +Bp(kG) + +9 + +gain of ten has been used to amplify the perturbation signal of 90 𝑘𝐻𝑧 generated by a function +generator. +A compressive pulse and a rarefactive pulse that follows the compressive pulse are +excited to perturb the plasma52,53. Plasma's response to this perturbation is detected in the +electron saturation regime (𝛿𝐼𝑒𝑠𝑎𝑡), at three different radial locations using a set of Langmuir +Probes (LP) placed at 2 cm, 6 cm, and 10 cm, respectively, from the exciter disk. All three +probes are in a uniform quiescence plasma region where all the plasma parameters are constant, +and the magnetic field is minimum37,54. + + + + + + + + + + + + + +Figure 5: Cross Section view of the experimental setup of the variable multi-cusp magnetic field plasma device +(MPD) +Figure 5 shows the cross-section view of the device with the exciter and Langmuir probe array +location. The perturbation is launched in the radial-vertical plane of the device, and a response +is also recorded along the same plane. Each LP has a probe-tip diameter of 1 mm, and a tip +length of ~5 mm. The probes are biased close to the local plasma potential ~12 V in order to +measure the electron saturation current (𝛿𝐼𝑒𝑠𝑎𝑡). The data are acquired using an 8-bit digital +oscilloscope with different sampling rates and stored for further analysis. +3. Soliton wave excitation and its characterization +In our experiment, the soliton has been excited by sinusoidal pulse5,18 as described below. The +time traces of sinusoidal perturbation signal and the plasma's response to applied perturbation +is shown in figure 6. The perturbation trace is shown on the top of the figure, and the bottom + +Diagnostics Port +ChamberWall +Dia (Φ) 40cm +it +Electro Magnets +UniformPlasma +RegionDia(@)~20cm +Exciter +P1 +P2 +P3 +- +11 + +10 + +three traces show the detector probe signals from different LPs placed at different radial +locations. These signals are normalized with their maxima, as shown in the figure; hence the +Y-axis of all subfigures is on a -1 to 1 scale. Following the application of the pulse to the grid, +two distinct pulses separated in me are recorded by the LPs. These two pulses are due to +different phenomena occurring after the application of the pulse to the grid, as described below. + + +Figure 6(a): Time evolution of single pulse sine wave perturbation recorded at the different radial locations +Figure 6(b): Time evolution of continuous sinusoidal wave perturbation recorded at different radial locations + +A near replica of the applied pulse to the grid appears on the LPs almost simultaneously with +the applied pulse. This is a signature of an Ion burst or Ballistic mode55,56,57. Although this +signal is interpreted as fast electron response, capacitive pickup, or noise. The root cause of its +appearance is due to free streaming of ions56,57. However, an elaborate explanation of this +behaviour is not the main focus of this study. After recording the ion bursts almost +simultaneously with grid applied pulse, the time traces of all the LPs shows another pulse with +a time delay of ~20 μS. This second pulse in LPs is somewhat a mirror image of the applied +pulse. The reason is simple, as plasma responses to the sinusoidal perturbation in opposite +polarity, a negative peak followed by a positive peak is detected by LPs. Note that the grid +perturbation has a positive peak followed by a positive peak. The shape of time-delayed pulses +acquired by the LPs does not remain same as that of applied perturbation. The negative half of +the time trace recorded by the LPs does not follow a sine variation and shows a shape relevant +to the hyperbolic secant. From the observed time delay in the received signal, the velocity of + +201 +Input Signal +Input Signal +d=2cm +d=2cm +Se +S +d=6cm +J=6cr +d=10cm +d=10cm +0 +10 +20 +30 +40 +50 +60 +70 +0 +5 +10 +15 +20 +25 +30 +35 +40 +45 +50 +t(μs) +t(μs) + +11 + +the wave has been calculated by the time of flight method. The width of the wave and the +velocity are compared as a function of its amplitude. To obtain this relation, the amplitude of +the grid perturbations pulse is varied from 10 𝑉𝑝𝑝 to 20 𝑉𝑝𝑝. +Figure 7: Velocity of the soliton as a function of its amplitude δn +It has been observed that as the amplitude of the perturbation pulse is increased, the amplitude +of half-cycles of the time-delayed pulses observed by the LPs increases. Simultaneously, the +velocity of the propagation also increases. However, the width of the time-delayed pulses +decreases as the perturbation amplitude increases, showing an opposite variation trend as +compared to its amplitude. +The propagation velocity of the perturbation, obtained by the time of flight technique, +has been found to be higher than the ion acoustic velocity (𝐶𝑠 = √𝐾𝐵𝑇𝑒 𝑚𝑖 +⁄ +). The Mach +number (𝑢 𝐶𝑠 +⁄ +) is plotted with respect to 𝛿𝑛 𝑛 +⁄ in figure 7 and is shown in red line having +diamond marker. Where 𝛿𝑛 is the density perturbation and 𝑛 is the unperturbed plasma density. +The measured Mach number variation with 𝛿𝑛 𝑛 +⁄ matches very well with those calculated +using the KdV equation given by Ikezi et.al5,18, as shown by the blue line with star markers in +the same figure. The spatial width of the soliton is measured experimentally using the standard +technique5,18–20,58,59, as discussed briefly below. First, the full width at half maximum of the +positive part of the time-delayed pulses of the LP has been measured from the temporal +evolution of LP data, as shown in figure 6a. This gives the temporal width of the structure. To +obtain spatial width of the soliton, the measured temporal width is multiplied by the measured +velocity of propagation. This gives the width of the soliton D, and following convention, the + +1.08 +米(1+8n/3n) +米 +( (uexp/Cg) +1.07 +exp +1.06 +1.05 +S +ulc +1.04 +1.03 +1.02 +1.01 +0.01 +0.02 +0.03 +0.04 +0.05 +0.06 +0.07 +0.08 +Sn/n + +12 + +width is normalized by 𝜆𝐷. The normalized width of the propagating structure is plotted as a +function of the amplitude of the perturbation normalized to density in figure 8. + +Figure 8: The width D of the soliton as a function of its amplitude δn. +It is observed from figure 7 that the amplitude of the propagating structures varies linearly with +𝑢 𝐶𝑠 +⁄ + (Mach number). Furthermore, it is observed from figure 8 that square of the width is +inversely proportional to its amplitude. These observations are in accordance with the +properties of small amplitude KdV 5,11,18,21,58,59 type of ion-acoustic soliton and hence indicate +the excitation of solitons in our experiments. +In order to confirm further the propagating structures to be the solitons, two similar +counter-propagating perturbations are generated in the MPD and made them interact with each +other. It is quite well known that when two solitary waves collide, they overlap and pass +through each other without losing their identity5,11,24. +To excite the two counter-propagating solitons, another exciter disc of the same shape and size +is placed on another side of the Langmuir probe set in plasma. These probes and exciters are +kept in a uniform field-free region. A perturbation amplitude of ~20𝑉𝑝𝑝 and frequency ~90𝑘𝐻𝑧 +has been applied to both the exciters simultaneously. Figure 9 shows the interaction of two +counter-propagating solitary waves. The top trace of the figure shows the two solitons, S1 and +S2, are excited from the individual exciters and propagating towards each other. S1 and S2 + + +140 +120 +100 +80 +60 +40 +20 +0.005 +0.010 +0.015 +0.020 +0.025 +0.030 +0.035 +0.040 +6n/n + +13 + +Figure 9: Interaction between two counter-propagating solitons +have the same amplitude and velocity. S1 and S2 interact at the center of the two exciters, +merge into each other linearly and generate a single soliton, shown in the mid trace. After the +interaction, they separate and travel ahead without losing their identity. The above observation +confirms that the propagating structures excited by perturbing a disk inside the MPD as soliton. +4. Effect of Two-Electron Temperature on the Propagation of Ion +Acoustic Soliton +After establishing the solitary nature of the propagating wave in MPD, the effect of +two-temperature electron distribution on the propagation of IAS is studied by varying the ratios +of the population of two-temperature electrons. As mentioned earlier, in MPD the +electromagnets produce the cusp magnetic field, which gives freedom to change the pole cusp +magnetic field strength by changing the applied currents to electromagnets. This change in cusp +magnetic field strength also controls the population of cold and hot electrons in plasma +confined by this magnetic field32,41,43,44. After exciting the IAS as described earlier, the pole +cusp magnetic field has been varied by applying different magnitudes of currents to the +electromagnets. +IAS is excited in the uniform field-free region where the ions are unmagnetized, and +plasma is uniform and quiescent32,37. The cusp magnetic field configuration provides +exceptional macroscopic plasma consistency due to U-shaped magnetic field curvature towards +the confined plasma system in the center, and plasma is also stable to large-scale + +S1 +S2 +esat +S1+S2 +S2 +-25 +-20 +-15 +-10 +-5 +0 +5 +10 +15 +20 +25 +t (μS) + +14 + +perturbation44,46 and cusp field confines the maximum primary or high energetic +electrons41,47,44. +Figure 10 shows the variation of soliton amplitude and width with different pole cusp +magnetic field values. It is observed that as the cusp magnetic field value is applied and +increased initially, the soliton amplitude increases with a magnetic field. At ~0.6 𝑘𝐺 (𝐼𝑚𝑎𝑔 = +80𝐴), the amplitude attains the maximum value. Increasing the cusp magnetic field further, the +soliton amplitude starts decreasing gradually. During the initial increase of the cusp magnetic +field where the amplitude of the soliton increases, the width has been observed to be decreasing, +and beyond ~0.6 𝑘𝐺 (𝐼𝑚𝑎𝑔 = 80 𝐴), it starts increasing gradually. The observed inverse +relation between the soliton amplitude and its width, as seen from figure 10, clearly +demonstrates that the solitary nature of the triggered perturbation structure is sustained in the +plasma at each applied cusp magnetic field value. + + +Figure 10: Amplitude and Width of soliton with increasing multi-pole cusp magnetic field. + + +0.070 +0.020 +0.065 +(A) +0.018 +e +Amplitude +0.060 +0.055 +0.014 +0.050 +0.012 +0.045 +0.010 +0.040 +6.0 +5.5 +(B) +5.0 +4.5 +4.0 +3.5 +3.0 +0.2 +0.4 +0.6 +0.8 +1.0 +1.2 +Bp(kG) + +15 + +Variation of 𝑇𝑒𝑓𝑓 with pole cusp magnetic field is also plotted in figure 10. It can be +seen from the figure that the value of 𝑇𝑒𝑓𝑓 initially decreases with the increase in the cusp +magnetic field, reaching its minimum around 𝐵𝑝 = ~0.4 − 0.6𝑘𝐺 and then increase with the +increase in the cusp magnetic field. The width of the soliton also varies in a similar fashion, +whereas the amplitude of the soliton first increases and reaches to its maximum value at 𝐵𝑝 = +~0.4 − 0.6𝑘𝐺 before decreasing with an increase in the cusp magnetic field strength. +Soliton propagation being affected by 𝑇𝑒𝑓𝑓 has not been studied much experimentally +as varying 𝑇𝑒𝑓𝑓over a range in a single device, keeping the other parameters more or less +constant, is quite difficult, and hence very few reports are available on the subject60,61. Taking +advantage of MPD’s unique feature of obtaining 𝑇𝑒𝑓𝑓, the observations of variation of soliton +amplitude and width with the 𝑇𝑒𝑓𝑓 are very helpful in understanding the behaviour of soliton +propagation in plasma having two temperature electrons in different fractions. Few theoretical +analyses have reported the effect of 𝑇𝑒𝑓𝑓 on the propagation of solitons. Goswami and Buti60 +have shown theoretically that as the 𝑇𝑒𝑓𝑓 decreases, the amplitude of soliton increases. Though +qualitatively, it agrees with the experimental results, and however, it does not explain the entire +variation of soliton properties with the 𝑇𝑒𝑓𝑓. + Lakhina61 et.al, has shown through simulations that the amplitude of IAS gets +modifies in presence of the high energetic electrons in the plasma. By solving the basic +equations of the arbitrary amplitude solitons numerically, they have shown that the amplitude +of the soliton is inversely proportional to the value of 𝑇𝑒𝑓𝑓 i.e. as 𝑇𝑒𝑓𝑓 increases (decreases), +the soliton amplitude decreases (increases). Interestingly, similar behaviour of soliton +propagation with the 𝑇𝑒𝑓𝑓 has been observed in our experiments, substantiating the fact that the +𝑇𝑒𝑓𝑓 indeed effect of the soliton propagation. + +Summary & Discussion +In this paper we report the excitation of the ion acoustic soliton in the MPD by applying +a sinusoidal perturbation to a disk placed inside the field free region of the plasma. The +propagating wave structures satisfy the relation between the amplitude, the Mach number, and +width of the solitary wave and establishes the excitation of solitons in the experiments. By +launching two counter-propagating perturbations and observing their overlapping and passing +through each other without losing their identity ascertains the wave structures to be solitons. +The maximum amplitude of the soliton generated in the present experiment is 𝐵𝑝 = + + + +16 + +0.6 𝑘𝐺(𝐼𝑚𝑎𝑔 = 80𝐴 ). After thoroughly characterizing the existence of the solitons, the effect +of two temperature electron distributions on the propagation of IAS has been explored. The +effective temperature of electron (𝑇𝑒𝑓𝑓) has been varied by varying the population ratio and +temperature of cold and hot components of electrons. It has been observed that in MPD pole +cusp magnetic field value influences the propagation of IAS significantly. The amplitude of +soliton has been found to be increasing with the field value up to 𝐵𝑝 = 0.6 𝑘𝐺 after which it +has been found to be decreasing with a further increase in the field values. The width of the +soliton shows the opposite variation to its amplitude variation as a function of the cusp +magnetic field. The soliton evolution is found to be sensitive to the effective temperature of +plasma as the amplitude and width of soliton has been observed to be significantly with 𝑇𝑒𝑓𝑓. +This observation quantitatively agrees with the theoretical study of the dependence of soliton +amplitude with effective electron temperature in two-electron temperature plasmas. + +Acknowledgments + +It is a pleasure to acknowledge Professor Abhijit Sen for fruitful discussions and +encouragements. The authors are thankful to Dr. Pintu Bandopadhyay for the critical review of +the manuscript. Z.S is indebted to University Grant Commission (UGC) and Ministry of +Minority affairs, Government of India for their support under the Maulana Azad National +Fellowship scheme award letter number 2016-17/MANF-2015-17-GUJ-67921. + + +References +1Report on Waves 14th Meeting of the British Association for the Advancement of Science +(London, 1845). +2 D.J. Korteweg and G. de Vries, London, Edinburgh, Dublin Philos. Mag. J. Sci. 39, 422 +(1895). +3 H. Washimi and T. Taniuti, Phys. Rev. Lett. 17, 996 (1966). +4 R.Z. Sagdeev, COOPERATIVE PHENOMENA AND SHOCK WAVES IN COLLISIONLESS +PLASMAS (Consultant Bureau, New York, 1966). +5 H. Ikezi, R.J. Taylor, and D.R. Baker, Phys. Rev. Lett. 25, 11 (1970). +6 D.J. Wu, G.L. Huang, D.Y. Wang, and C.G. Fälthammar, Phys. Plasmas 3, 2879 (1996). +7 C.S. Gardner, J.M. Greene, M.D. Kruskal, and R.M. Miura, Phys. Rev. Lett. 19, 1095 +(1967). + + + +17 + +8 T. Taniuti, Suppl. Prog. Theor. Phys. (1974). +9 G.C. Das and S.G. Tagare, Plasma Phys. 17, 1025 (1975). +10 G.C. Das, Plasma Phys. 19, 363 (1977). +11 M.Q. Tran, Phys. Scr. 20, 317 (1979). +12 Y. Nakamura, IEEE Trans. Plasma Sci. 10, 180 (1982). +13 M. Temerin, K. Cerny, W. Lotko, and F.S. Mozer, Phys. Rev. Lett. 48, 1175 (1982). +14 R. Boström, G. Gustafsson, B. Holback, G. Holmgren, H. Koskinen, and P. Kintner, Phys. +Rev. Lett. 61, 82 (1988). +15 A. Mälkki, A.I. Eriksson, P.-O. Dovner, R. Boström, B. Holback, G. Holmgren, and H.E.J. +Koskinen, J. Geophys. Res. 98, 15521 (1993). +16 Q.M. Lu, J. Geophys. Res. 110, A03223 (2005). +17 R.J. Taylor, K.R. MacKenzie, and H. Ikezi, Rev. Sci. Instrum. 43, 1675 (1972). +18 H. Ikezi, Phys. Fluids 16, 1668 (1973). +19 Y. Nakamura and H. Sugai, Chaos, Solitons & Fractals 7, 1023 (1996). +20 P.I. John and Y.C. Saxena, Phys. Lett. A 56, 385 (1976). +21 K.E. Lonngren, Plasma Phys. 25, 943 (1983). +22 S. Watanabe, J. Phys. Soc. Japan 53, 950 (1984). +23 P.H. Sakanaka, Phys. Fluids 15, 304 (1972). +24 N.J. Zabusky and M.D. Kruskal, Phys. Rev. Lett. 15, 240 (1965). +25 S. Watanabe, J. Plasma Phys. 14, 353 (1975). +26 D. Xiao, J.X. Ma, Y. Li, Y. Li, and M.Y. Yu, Phys. Plasmas 14, 092104 (2007). +27 H.H. Pajouh and H. Abbasi, Phys. Plasmas 15, (2008). +28 L. Schott, J. Appl. Phys. 59, 1390 (1986). +29 H.H. Kuehl, Phys. Fluids 26, 1577 (1983). +30 P. Chatterjee, M. kr. Ghorui, and C.S. Wong, Phys. Plasmas 18, 103710 (2011). +31 W.C. Feldman, J.R. Asbridge, S.J. Bame, M.D. Montgomery, and S.P. Gary, J. Geophys. +Res. 80, 4181 (1975). +32 A.D. Patel, M. Sharma, N. Ramasubramanian, R. Ganesh, and P.K. Chattopadhyay, Rev. +Sci. Instrum. 89, (2018). +33 A.D. Patel, M. Sharma, N. Ramasubramanian, J. Ghosh, and P.K. Chattopadhyay, Phys. +Scr. 95, (2020). +34 R.A. Cairns, A.A. Mamum, R. Bingham, R. Boström, R.O. Dendy, C.M.C. Nairn, and P.K. +Shukla, Geophys. Res. Lett. 22, 2709 (1995). +35 K. Nishihara and M. Tajiri, J. Phys. Soc. Japan 50, 4047 (1981). + + + +18 + +36 W.D. Jones, A. Lee, S.M. Gleman, and H.J. Doucet, Phys. Rev. Lett. 35, 1349 (1975). +37 M. Sharma, A.D. Patel, N. Ramasubramanian, Y.C. Saxena, P.K. Chattopadhyaya, and R. +Ganesh, Plasma Res. Express 2, (2020). +38 S.K. Singh, P.K. Srivastava, L.M. Awasthi, S.K. Mattoo, A.K. Sanyasi, R. Singh, and P.K. +Kaw, Rev. Sci. Instrum. 85, (2014). +39 J.P. Sheehan, Y. Raitses, N. Hershkowitz, I. Kaganovich, and N.J. Fisch, Phys. Plasmas 18, +073501 (2011). +40 C.-S. Yip, J.P. Sheehan, N. Hershkowitz, and G. Severn, Plasma Sources Sci. Technol. 22, +065002 (2013). +41 J. Berkowitz, K.O. Friedrichs, H. Goertzel, H. Grad, J. Killeen, and E. Rubin, J. Nucl. +Energy 7, 292 (1958). +42 K.N. Leung, N. Hershkowitz, and K.R. MacKenzie, Phys. Fluids 19, 1045 (1976). +43 B. Dankongkakul, S.J. Araki, and R.E. Wirz, Phys. Plasmas 21, 043506 (2014). +44 S. Aihara, M. Fujiwara, M. Hosokawa, and H. Ikegami, Nucl. Fusion 12, 45 (1972). +45 B. Dankongkakul, S.J. Araki, and R.E. Wirz, Phys. Plasmas 21, 043506 (2014). +46 J.K. and E.R. J. Berkowitz, K. O. Friedrichs, H. Goertzel, H. Grad, (n.d.). +47 J. Park, N.A. Krall, P.E. Sieck, D.T. Offermann, M. Skillicorn, A. Sanchez, K. Davis, E. +Alderson, and G. Lapenta, Phys. Rev. X 5, 1 (2015). +48 S. Bose, M. Kaur, P.K. Chattopadhyay, J. Ghosh, Y.C. Saxena, and R. Pal, J. Plasma Phys. +83, 615830201 (2017). +49 R.A. Bosch and R.L. Merlino, J. Appl. Phys. 60, 3056 (1986). +50 R.A. Bosch and R.M. Gilgenbach, Phys. Lett. A 128, 437 (1988). +51 N. Hershkowitz, K.N. Leung, and T. Romesser, Phys. Rev. Lett. 35, 277 (1975). +52 Y. Nakamura, T. Ito, and K. Koga, J. Plasma Phys. 49, 331 (1993). +53 J.L. Cooney, M.T. Gavin, and K.E. Lonngren, Phys. Fluids B 3, 2758 (1991). +54 M. Sharma, A.D. Patel, Z. Shaikh, N. Ramasubramanian, R. Ganesh, P.K. Chattopadhayay, +and Y.C. Saxena, Phys. Plasmas 27, (2020). +55 S. Watanabe, J. Plasma Phys. 14, 353 (1975). +56 G. Joyce, K. Lonngren, I. Alexeff, and W.D. Jones, Phys. Fluids 12, 2592 (1969). +57 T. Pierre, G. Bonhomme, G. Leclert, and J.R. Cussenot, Plasma Phys. Control. Fusion 27, +523 (1985). +58 Y. Nakamura, IEEE Trans. Plasma Sci. 10, 180 (1982). +59 S. Watanabe, J. Plasma Phys. 14, 353 (1975). +60 B.. Goswami and B. Buti, Phys. Lett. A 57, 149 (1976). + + + +19 + +61 G.S. Lakhina, A.P. Kakad, S. V. Singh, and F. Verheest, Phys. Plasmas 15, 062903 (2008). + + diff --git a/X9E1T4oBgHgl3EQfcARq/content/tmp_files/load_file.txt b/X9E1T4oBgHgl3EQfcARq/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..57cd8dd05ef9cbeddacb0c1915432c2879c5a9b5 --- /dev/null +++ b/X9E1T4oBgHgl3EQfcARq/content/tmp_files/load_file.txt @@ -0,0 +1,843 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf,len=842 +page_content='1 Behaviour of Ion Acoustic Soliton in a two-electron temperature plasmas of Multi-pole line cusp Plasma Device (MPD) Zubin Shaikh1, 3, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='Patel1, 4, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='Chattopadhyay1, 2, Joydeep Ghosh1, 2 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='Joshi3 and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='Ramasubramanian1, 2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Institute for Plasma Research, Gandhinagar-382428, India 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Homi Bhabha National Institute, Anushaktinagar-400094, Mumbai, India 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Department of Physics, Saurashtra University, Rajkot-360005, India 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Institute of Plasma Physics and Laser Micro Fusion, Warsaw 01-497, Poland zubin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='ipr@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='com ABSTRACT This article presents the experimental observations and characterization of Ion Acoustic Soliton (IAS) in a unique Multi-pole line cusp Plasma Device (MPD) device in which the magnitude of the pole-cusp magnetic field can be varied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' And by varying the magnitude of the pole-cusp magnetic field, the proportions of two-electron-temperature components in the filament-produced plasmas of MPD can be varied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The solitons are experimentally characterized by measuring their amplitude-width relation and Mach numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The nature of the solitons is further established by making two counter-propagating solitons interact with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Later, the effect of the two-temperature electron population on soliton amplitude and width is studied by varying the magnitude of the pole cusp-magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' It has been observed that different proportions of two-electron-temperature significantly influence the propagation of IAS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The amplitude of the soliton has been found to be following inversely with the effective electron temperature (𝑇𝑒𝑓𝑓).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Introduction Ion-Acoustic Solitons (IAS), the self-organized, non-linear localized structures that can propagate long distances, are widely studied in astrophysical and laboratory plasmas to understand their non-linear dynamics describing several fundamental processes of plasma 2 physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' A solitary wave was first discovered to propagate long distances without changing its shape and speed in shallow water in 1844 by J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='Russels1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Korteweg-de Vries2 (KdV) developed the mathematical formalism of soliton dynamics, which had led to significant advances in determining the properties of solitons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The soliton dynamics for plasmas was explained by Washimi and Taniuti3 by deriving and solving the KdV equation in plasma medium using a novel mathematical approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sagdeev4 studied the arbitrary amplitude non- linear waves in plasma, highlighting many more interesting phenomena of plasma acoustic modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Both these methods are used to analyze solitons in laboratory5 and space plasmas6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The theory of solitons was further developed by Gardner7, obtaining an exact solution of the KdV equation by treating it as an initial value problem using the inverse scattering method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='Taniuti8 introduced the reductive perturbation principle for solving the KdV equation, which was also applicable for solving various non-linear equations apart from waves in plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The solution to the KdV equation for non-linear ion-acoustic waves in plasma medium comprising of negative ions had been obtained by Das and Tagare9 and Das10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' A comprehensive review on theoretical studies of solitons can be found in the references11,12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The existence of solitary waves is ubiquitous in space plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Solitary waves in the magnetosphere were first observed by the S3-3 satellite13 and subsequently confirmed and studied extensively by Viking Satellite14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' These solitary structures were also observed in the auroral acceleration region15 and the generation mechanism of these structures has been given by Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='Lu16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The existence of ion-acoustic solitons in laboratory plasmas was experimentally demonstrated by H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ikezi5 for the first time in a double plasma device17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' In this experiment, the solitons are excited by applying perturbation into a fine mesh grid immersed in plasma with different waveforms having different frequencies18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Following this, ion-acoustic solitons were excited in several devices19–22 mainly by pulsing a floating wire grid placed inside the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The experiments in the laboratory plasmas demonstrated the variations in soliton properties with varying plasma parameters, which were successfully modeled using the theoretical formulations mentioned above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The experimentally measured width and propagation velocity of solitons matched very well with the solitary wave solutions, as shown by Sakanaka23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The soliton-soliton interaction was also experimentally demonstrated by exciting two solitons and making them propagate towards each other5,24,25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Over the years, several 3 experiments were carried out in order to understand the excitation26,27, propagation28,29 collisions30, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=', of ion-acoustic solitons in different plasma devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Although the ion-acoustic solitons in plasmas are extensively studied both theoretically and experimentally, several open questions remain to be answered, such as the behaviour of solitons in plasmas with two electron temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The coexistence of two distinct species of electrons at different temperatures is very common in space plasmas13,31 and laboratory plasmas32,33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Theoretical studies by Cairns34 and Nishihara35 had shown that the presence of non-thermal electrons or plasmas with two electron temperatures can significantly modify the ion acoustic solitary structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The propagation of ion-acoustic waves in two-electron temperature plasma has been studied by Jones et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=',36 both experimentally and theoretically, and it has been shown that a small fraction of hot electrons can affect the propagation of the wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' However, there are very few controlled experimental studies on soliton characterization with respect to soliton width and amplitude in plasmas with two-temperature electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' In the present work, the effect of two-electron temperature on the properties of ion-acoustic solitons are studied in the Multi-pole line cusp Plasma Device (MPD)32,33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The special feature of this device is the controllability of the magnitude of the pole magnetic fields by varying the currents in electromagnets used for producing the cusp magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' This controllability of cusp magnetic field strength at the poles facilitates the production of two-temperature electrons in variable proportions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The confinement of the energetic electron population generated in the filament-produced argon plasmas varies with varying the cusp magnetic field strengths leading to the generation of plasmas with two-electron temperatures in variable proportions in this device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Taking advantage of this unique feature, the effect of two-temperature electrons on ion- acoustic soliton propagation and characteristics are studied in the MPD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The solitons are excited using the conventional technique by pulsing a floating metal mesh grid placed inside the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Before varying the magnetic field strengths, the solitons are thoroughly characterized by measuring the velocities and width of solitons and compared with theoretical estimations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The solitary nature of the excited waves is also verified by inducing interactions of two counter-propagating solitons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The cusp magnetic field strengths are then varied to vary the hot-electron fraction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' It has been observed that the soliton amplitude increases, and its width decreases with systematically increasing the hot-electron populations in the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Most importantly, it has been found that the effective electron temperature (𝑇𝑒𝑓𝑓) controls the width of the solitons almost proportionally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 4 The paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Section 2 describes the details of the experimental setup and wave excitation and detection techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Section 3 describes the detailed experimental results and characterization of solitons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Section 4 describes the effect of two-temperature electrons on soliton dynamics, followed by a summary in section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Experimental Setup The present experiment is carried out in a Multi-pole line cusp Plasma Device (MPD)32,33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' MPD consists of six rectangular-shaped electromagnets with profiled core material to produce the variable multi-pole line cusp magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' These electromagnets provide uniqueness in varying the magnetic field strength and configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' These electromagnets are placed on the periphery of the vacuum vessel, and each magnet is placed 60 degrees apart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The majority of early experiments used permanent magnets to create the multi-cusp field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Those devices were limited in terms of performing investigations with variable cusp magnetic fields as the magnetic field produced by permanent magnets is fixed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The novel aspect of MPD is that by varying the current in the electromagnets both in terms of magnitude and direction, the magnetic field strength and configuration can be changed in a controlled way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' In all configurations, the magnetic field strength in the center always remains very small in the order of a few gausses only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Hence, the field-free region inside the chamber does not change appreciably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The present experiment is performed with 12 pole cusp magnetic field configuration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The current in all six electromagnets is in the same direction;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' hence all six magnets will produce one type of pole, and another virtual pole will be produced in between two magnets;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' hence a total of 12 cusps will be there of six dipoles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The 12-pole cusp configuration has a field-free region of ~20 cm37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The MPD comprises of a non-magnetic stainless steel cylindrical vacuum vessel with a length of 1500 mm, a diameter of 400 mm, and a wall thickness of 6mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The chamber is evacuated by a Turbo Molecular Pump (440 l/s) backed by a rotary pump through a conical reducer at one side of the chamber.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' A base pressure of 1x10-6 mbar is achieved, measured by a hot ionization gauge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The filamentary argon discharge plasma is produced using a hot filament- based cathode source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The plasma source (cathode) is two dimensional (8cm x 8cm) vertical array of five tungsten filaments;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' each filament has a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='5 mm diameter and 8 cm length.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' These filaments are powered by a 500 A, 15 V floating power supply, usually operated at around 16 - 19 A and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='5V per filament.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The chamber is filled with Argon gas through a needle valve to a working pressure of ~8 x 10- 5 m-bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The filament source is biased negatively at a voltage of 5 50 V with respect to the grounded chamber walls using a discharge power supply of ratings ~125V and ~25A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The electric field lines between the high-potential filament and the grounded chamber wall accelerates the primary electrons emitted from the joule-heated filaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' These electrons collide with the neutral argon atoms and ionize some of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' These ions and electrons are confined by the multi-pole line cusp magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Figure 1: Schematic diagram of the Multi-Cusp Plasma Device (MPD) Experimental setup The plasma thus confined in the MPD is usually reported as bi-Maxwellian, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=', having two temperature electrons32,38–40;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' one having low temperature called cold electron (𝑇𝑐) and other having relatively larger temperature called hot electrons (𝑇ℎ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' It is well known that the cusp magnetic is an ideal configuration for the confinement of primary or hot electrons 41–44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The cusp magnetic field confines the hot electrons by mirror effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Due to the mirror effect in cusp configuration, electrons will move back and forth between the poles;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' thus, the maximum hot energetic electrons are confined by the cusp magnetic field45,41,46,47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The measurement of plasma parameters have been estimated from the V-I characteristics of Langmuir probes32,48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' In the filament-produced plasmas of this device, the typical V-I characteristic always shows the existence of two-electron temperature distributions in the central plasma region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' In bi-Maxwellian plasma, the electron current collected by a probe in the electron retarding region is given by 𝐼𝑒 = 𝐼𝑐0𝑒𝑥𝑝 [𝑒(𝑉𝑝𝑟 − 𝑉𝑝) 𝑘𝐵𝑇𝑐 ] + 𝐼ℎ0𝑒𝑥𝑝 [𝑒(𝑉𝑝𝑟 − 𝑉𝑝) 𝑘𝐵𝑇ℎ ] (1) 150cm Magnet Filament Probe array Exciter Disc 12V Oscilloscope GateValve 50V C Function Generator Turbomolecular dwnd 6 Where, 𝐼𝑐0 = 𝐴𝑝𝑁𝑐(𝑘𝑏𝑇𝑐 2𝜋𝑚𝑒) ⁄ 1/2 and 𝐼ℎ0 = 𝐴𝑝𝑁ℎ(𝑘𝑏𝑇ℎ 2𝜋𝑚𝑒) ⁄ 1/2, 𝑁𝑐 and 𝑁ℎ are the cold electron density and hot electron density, and 𝑉𝑝𝑟 is probe potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 𝑁0 ≈ 𝑁𝑐 + 𝑁ℎ is the total electron density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' By deducting the 𝐼𝑖𝑠𝑎𝑡 from the total probe current(𝐼𝑝), the variation of electron current (𝐼𝑒) drawn by the probe is determined.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 𝑇ℎ and 𝑇𝑐 are then estimated from the slope of the line of 𝑉𝑝 vs 𝑙𝑛𝐼𝑒 and 𝑉𝑝 vs ln (𝐼𝑒 − 𝐼ℎ) curves, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The hot electron density (𝑁ℎ) is defined as 𝑁ℎ = − (2𝑚𝑒𝑣ℎ 𝑒2𝐴𝑝 ) 𝑑𝐼 𝑑𝑉 ⁄ (2) Where 𝑚𝑒 is the mass of an electron, 𝑣ℎ= √2𝑒 𝑉𝑑 𝑚𝑒 ⁄ is hot electron velocity, 𝑉𝑑 is discharge voltage, 𝐴𝑝 is probe area, and 𝑑𝐼 𝑑𝑉 ⁄ is the slope of the tail part of V-I characteristics of plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The estimation of different plasma parameters for MPD is discussed in detail by Patel et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='al32,33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Previously, we have reported that a change of the currents in the electromagnets changes the pole cusp magnetic field, which in turn changes the leak width and mirror ratio33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The leak width shows the opposite variation to the cusp magnetic field, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=', as the magnetic field increases, leak width decreases33,49,50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' As a result, the high energetic electron confinement in plasma increases, and it affects the plasma parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' So as expected, the pole cusp magnetic field controls the density and temperature of the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Hence we varied the 𝑇𝑐, 𝑇ℎ, 𝑁𝑐, 𝑎𝑛𝑑 𝑁ℎ by systematically varying the pole magnetic field 𝐵𝑝.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Once 𝑇𝑐, 𝑇ℎ, 𝑁𝑐 𝑎𝑛𝑑 𝑁ℎ are measured experimentally, effective plasma temperature 𝑇𝑒𝑓𝑓 can be estimated, which is defined as 𝑇𝑒𝑓𝑓 = 𝑁𝑜𝑇ℎ𝑇𝑐 (𝑁ℎ𝑇𝑐 + 𝑁𝑐𝑇ℎ) ⁄ (3) Figure 2 shows the variation of 𝑁𝑐 and 𝑁ℎ, and figure 3 shows the variation of 𝑇𝑐 and 𝑇ℎ at the center of the device (R=0 cm) with different pole cusp magnetic field(𝐵𝑝) strength for argon plasma produced with a fill pressure of ~8 x 10-5 mbar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' As 𝐵𝑝 increases, the leak width51 𝑑 = 2(𝑟𝑙𝑒𝑟𝑙𝑖) 1 2 ⁄ changes from 11 mm for 𝐵𝑝~0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='16 𝑘𝐺 to 6 mm for 𝐵𝑝~0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='3 𝑘𝐺, where the pole separation is 2πr/6 = 20 cm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' as the ratio of pole width and pole separation decreases, the plasma confinement increases leading to an increase in the density of both cold and hot (𝑁𝑐 and 𝑁ℎ) electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 7 Figure 3 shows that the temperature of cold and hot electron (𝑇𝑐 and 𝑇ℎ) initially falls up to 𝐵𝑝~0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='3 𝑘𝐺 and then start increasing again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The exact nature of the variation of 𝑁𝑒 and 𝑇𝑒 (particularly 𝑇𝑒) needs a detailed device simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' However, the aim of the present experiment is to study the effect of 𝑇𝑒𝑓𝑓 on the amplitude and width of the soliton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Figure 4 shows the variation of 𝑇𝑒𝑓𝑓 with 𝐵𝑝.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 𝑇𝑒𝑓𝑓 is calculated using the measured values of 𝑇𝑐, 𝑇ℎ, 𝑁𝑐, and 𝑁ℎ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' It has been observed that the 𝑇𝑒𝑓𝑓 decreases initially with increasing the 𝐵𝑝 and then starts increasing again.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Figure 2: Variation of cold electron density Nc and hot electron density Nh with various cusp magnetic field strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Figure3: Variation of cold electron temperature (𝑇𝑐) and Hot electron temperature (𝑇ℎ) with various cusp magnetic field strength All the basic plasma parameters, such as electron temperature (𝑇𝑒), plasma density (𝑛𝑒), plasma potential (𝑉𝑝), floating potential (𝑉𝑓), and fluctuations 𝛿𝐼𝑖𝑠𝑎𝑡 𝐼𝑖𝑠𝑎𝑡 ⁄ remains almost constant over the radial extent of the plasma column32,33,37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Typical measured plasma parameters at the 16 14 12 10 (X 1014 8 6 4 2 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='4 Bp (kG)8 6 2 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='4 Bp (kG)4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='5 (ev 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='4 Bp (kG)15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='5 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='5 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 (ev 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='5 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='5 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='5 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='4 Bp (kG) 8 midplane of the device are: Plasma Density (𝑛𝑒) ~ 1016 m-3, electron temperature (𝑇𝑒) ~ 4-5 eV, Plasma potential (𝑉𝑝) ~ 4-5 V, Electron Neutral Collision frequency (\uf06e𝑒𝑛) ~6 x 106 Hz and Ion plasma frequency (𝜔𝑝𝑖) ~ 4 x106 Hz for -50V discharge voltage and 8 x10-5 bar working pressure and at a pole magnetic field of 𝐵𝑝 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='6𝑘𝐺 (Magnet Current 𝐼𝑚𝑎𝑔 = 80𝐴).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Pole Magnetic field 𝐵𝑝 is the measured magnetic field at the inner wall of the device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Figure 4: Variation of effective temperature with various cusp magnetic field strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='1 Wave excitation and detection techniques After measuring plasma density and temperature, experiments on wave excitation are carried out.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Soliton is excited by a floating exciter metal disk which is placed inside the plasma at the central plane of the device, where the magnetic field is minimum, and the plasma is uniform and quiescent37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' This exciter grid is a solid disk of molybdenum with a diameter of 50 mm and a thickness of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='25 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The solid disk has been used to generate uniform sheath thickness around it52,25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' A single pulse sinusoidal voltage of ~ 20 𝑉𝑝𝑝 at 90 𝑘𝐻𝑧 frequency has been applied to the grid to excite the soliton in the MPD plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The magnitude of the voltage perturbation is chosen to be much higher than plasma potential (𝑉𝑝) for soliton excitation, and the perturbation frequency satisfies 𝜔 𝜔𝑝𝑖 ⁄ < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='718.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' A PA-85 amplifier-based circuit with a 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='2 Bp(kG) 9 gain of ten has been used to amplify the perturbation signal of 90 𝑘𝐻𝑧 generated by a function generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' A compressive pulse and a rarefactive pulse that follows the compressive pulse are excited to perturb the plasma52,53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=" Plasma's response to this perturbation is detected in the electron saturation regime (𝛿𝐼𝑒𝑠𝑎𝑡), at three different radial locations using a set of Langmuir Probes (LP) placed at 2 cm, 6 cm, and 10 cm, respectively, from the exciter disk." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' All three probes are in a uniform quiescence plasma region where all the plasma parameters are constant, and the magnetic field is minimum37,54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Figure 5: Cross Section view of the experimental setup of the variable multi-cusp magnetic field plasma device (MPD) Figure 5 shows the cross-section view of the device with the exciter and Langmuir probe array location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The perturbation is launched in the radial-vertical plane of the device, and a response is also recorded along the same plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Each LP has a probe-tip diameter of 1 mm, and a tip length of ~5 mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The probes are biased close to the local plasma potential ~12 V in order to measure the electron saturation current (𝛿𝐼𝑒𝑠𝑎𝑡).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The data are acquired using an 8-bit digital oscilloscope with different sampling rates and stored for further analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Soliton wave excitation and its characterization In our experiment, the soliton has been excited by sinusoidal pulse5,18 as described below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=" The time traces of sinusoidal perturbation signal and the plasma's response to applied perturbation is shown in figure 6." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The perturbation trace is shown on the top of the figure, and the bottom Diagnostics Port ChamberWall Dia (Φ) 40cm it Electro Magnets UniformPlasma RegionDia(@)~20cm Exciter P1 P2 P3 11 10 three traces show the detector probe signals from different LPs placed at different radial locations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' These signals are normalized with their maxima, as shown in the figure;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' hence the Y-axis of all subfigures is on a -1 to 1 scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Following the application of the pulse to the grid, two distinct pulses separated in me are recorded by the LPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' These two pulses are due to different phenomena occurring after the application of the pulse to the grid, as described below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Figure 6(a): Time evolution of single pulse sine wave perturbation recorded at the different radial locations Figure 6(b): Time evolution of continuous sinusoidal wave perturbation recorded at different radial locations A near replica of the applied pulse to the grid appears on the LPs almost simultaneously with the applied pulse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' This is a signature of an Ion burst or Ballistic mode55,56,57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Although this signal is interpreted as fast electron response, capacitive pickup, or noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The root cause of its appearance is due to free streaming of ions56,57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' However, an elaborate explanation of this behaviour is not the main focus of this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' After recording the ion bursts almost simultaneously with grid applied pulse, the time traces of all the LPs shows another pulse with a time delay of ~20 μS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' This second pulse in LPs is somewhat a mirror image of the applied pulse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The reason is simple, as plasma responses to the sinusoidal perturbation in opposite polarity, a negative peak followed by a positive peak is detected by LPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Note that the grid perturbation has a positive peak followed by a positive peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The shape of time-delayed pulses acquired by the LPs does not remain same as that of applied perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The negative half of the time trace recorded by the LPs does not follow a sine variation and shows a shape relevant to the hyperbolic secant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' From the observed time delay in the received signal, the velocity of 201 Input Signal Input Signal d=2cm d=2cm Se S d=6cm J=6cr d=10cm d=10cm 0 10 20 30 40 50 60 70 0 5 10 15 20 25 30 35 40 45 50 t(μs) t(μs) 11 the wave has been calculated by the time of flight method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The width of the wave and the velocity are compared as a function of its amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' To obtain this relation, the amplitude of the grid perturbations pulse is varied from 10 𝑉𝑝𝑝 to 20 𝑉𝑝𝑝.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Figure 7: Velocity of the soliton as a function of its amplitude δn It has been observed that as the amplitude of the perturbation pulse is increased, the amplitude of half-cycles of the time-delayed pulses observed by the LPs increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Simultaneously, the velocity of the propagation also increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' However, the width of the time-delayed pulses decreases as the perturbation amplitude increases, showing an opposite variation trend as compared to its amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The propagation velocity of the perturbation, obtained by the time of flight technique, has been found to be higher than the ion acoustic velocity (𝐶𝑠 = √𝐾𝐵𝑇𝑒 𝑚𝑖 ⁄ ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The Mach number (𝑢 𝐶𝑠 ⁄ ) is plotted with respect to 𝛿𝑛 𝑛 ⁄ in figure 7 and is shown in red line having diamond marker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Where 𝛿𝑛 is the density perturbation and 𝑛 is the unperturbed plasma density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The measured Mach number variation with 𝛿𝑛 𝑛 ⁄ matches very well with those calculated using the KdV equation given by Ikezi et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='al5,18, as shown by the blue line with star markers in the same figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The spatial width of the soliton is measured experimentally using the standard technique5,18–20,58,59, as discussed briefly below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' First, the full width at half maximum of the positive part of the time-delayed pulses of the LP has been measured from the temporal evolution of LP data, as shown in figure 6a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' This gives the temporal width of the structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' To obtain spatial width of the soliton, the measured temporal width is multiplied by the measured velocity of propagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' This gives the width of the soliton D, and following convention, the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='08 米(1+8n/3n) 米 ( (uexp/Cg) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='07 exp 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='06 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='05 S ulc 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='04 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='03 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='02 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='08 Sn/n 12 width is normalized by 𝜆𝐷.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The normalized width of the propagating structure is plotted as a function of the amplitude of the perturbation normalized to density in figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Figure 8: The width D of the soliton as a function of its amplitude δn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' It is observed from figure 7 that the amplitude of the propagating structures varies linearly with 𝑢 𝐶𝑠 ⁄ (Mach number).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Furthermore, it is observed from figure 8 that square of the width is inversely proportional to its amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' These observations are in accordance with the properties of small amplitude KdV 5,11,18,21,58,59 type of ion-acoustic soliton and hence indicate the excitation of solitons in our experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' In order to confirm further the propagating structures to be the solitons, two similar counter-propagating perturbations are generated in the MPD and made them interact with each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' It is quite well known that when two solitary waves collide, they overlap and pass through each other without losing their identity5,11,24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' To excite the two counter-propagating solitons, another exciter disc of the same shape and size is placed on another side of the Langmuir probe set in plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' These probes and exciters are kept in a uniform field-free region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' A perturbation amplitude of ~20𝑉𝑝𝑝 and frequency ~90𝑘𝐻𝑧 has been applied to both the exciters simultaneously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Figure 9 shows the interaction of two counter-propagating solitary waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The top trace of the figure shows the two solitons, S1 and S2, are excited from the individual exciters and propagating towards each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' S1 and S2 140 120 100 80 60 40 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='005 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='015 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='020 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='025 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='030 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='035 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='040 6n/n 13 Figure 9: Interaction between two counter-propagating solitons have the same amplitude and velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' S1 and S2 interact at the center of the two exciters, merge into each other linearly and generate a single soliton, shown in the mid trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' After the interaction, they separate and travel ahead without losing their identity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The above observation confirms that the propagating structures excited by perturbing a disk inside the MPD as soliton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Effect of Two-Electron Temperature on the Propagation of Ion Acoustic Soliton After establishing the solitary nature of the propagating wave in MPD, the effect of two-temperature electron distribution on the propagation of IAS is studied by varying the ratios of the population of two-temperature electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' As mentioned earlier, in MPD the electromagnets produce the cusp magnetic field, which gives freedom to change the pole cusp magnetic field strength by changing the applied currents to electromagnets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' This change in cusp magnetic field strength also controls the population of cold and hot electrons in plasma confined by this magnetic field32,41,43,44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' After exciting the IAS as described earlier, the pole cusp magnetic field has been varied by applying different magnitudes of currents to the electromagnets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' IAS is excited in the uniform field-free region where the ions are unmagnetized, and plasma is uniform and quiescent32,37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The cusp magnetic field configuration provides exceptional macroscopic plasma consistency due to U-shaped magnetic field curvature towards the confined plasma system in the center, and plasma is also stable to large-scale S1 S2 esat S1+S2 S2 25 20 15 10 5 0 5 10 15 20 25 t (μS) 14 perturbation44,46 and cusp field confines the maximum primary or high energetic electrons41,47,44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Figure 10 shows the variation of soliton amplitude and width with different pole cusp magnetic field values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' It is observed that as the cusp magnetic field value is applied and increased initially, the soliton amplitude increases with a magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' At ~0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='6 𝑘𝐺 (𝐼𝑚𝑎𝑔 = 80𝐴), the amplitude attains the maximum value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Increasing the cusp magnetic field further, the soliton amplitude starts decreasing gradually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' During the initial increase of the cusp magnetic field where the amplitude of the soliton increases, the width has been observed to be decreasing, and beyond ~0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='6 𝑘𝐺 (𝐼𝑚𝑎𝑔 = 80 𝐴), it starts increasing gradually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The observed inverse relation between the soliton amplitude and its width, as seen from figure 10, clearly demonstrates that the solitary nature of the triggered perturbation structure is sustained in the plasma at each applied cusp magnetic field value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Figure 10: Amplitude and Width of soliton with increasing multi-pole cusp magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='070 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='020 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='065 (A) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='018 e Amplitude 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='060 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='055 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='014 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='050 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='012 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='045 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='010 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='040 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='5 (B) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='2 Bp(kG) 15 Variation of 𝑇𝑒𝑓𝑓 with pole cusp magnetic field is also plotted in figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' It can be seen from the figure that the value of 𝑇𝑒𝑓𝑓 initially decreases with the increase in the cusp magnetic field, reaching its minimum around 𝐵𝑝 = ~0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='4 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='6𝑘𝐺 and then increase with the increase in the cusp magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The width of the soliton also varies in a similar fashion, whereas the amplitude of the soliton first increases and reaches to its maximum value at 𝐵𝑝 = ~0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='4 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='6𝑘𝐺 before decreasing with an increase in the cusp magnetic field strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Soliton propagation being affected by 𝑇𝑒𝑓𝑓 has not been studied much experimentally as varying 𝑇𝑒𝑓𝑓over a range in a single device, keeping the other parameters more or less constant, is quite difficult, and hence very few reports are available on the subject60,61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Taking advantage of MPD’s unique feature of obtaining 𝑇𝑒𝑓𝑓, the observations of variation of soliton amplitude and width with the 𝑇𝑒𝑓𝑓 are very helpful in understanding the behaviour of soliton propagation in plasma having two temperature electrons in different fractions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Few theoretical analyses have reported the effect of 𝑇𝑒𝑓𝑓 on the propagation of solitons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Goswami and Buti60 have shown theoretically that as the 𝑇𝑒𝑓𝑓 decreases, the amplitude of soliton increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Though qualitatively, it agrees with the experimental results, and however, it does not explain the entire variation of soliton properties with the 𝑇𝑒𝑓𝑓.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lakhina61 et.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='al, has shown through simulations that the amplitude of IAS gets modifies in presence of the high energetic electrons in the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' By solving the basic equations of the arbitrary amplitude solitons numerically, they have shown that the amplitude of the soliton is inversely proportional to the value of 𝑇𝑒𝑓𝑓 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' as 𝑇𝑒𝑓𝑓 increases (decreases), the soliton amplitude decreases (increases).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Interestingly, similar behaviour of soliton propagation with the 𝑇𝑒𝑓𝑓 has been observed in our experiments, substantiating the fact that the 𝑇𝑒𝑓𝑓 indeed effect of the soliton propagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Summary & Discussion In this paper we report the excitation of the ion acoustic soliton in the MPD by applying a sinusoidal perturbation to a disk placed inside the field free region of the plasma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The propagating wave structures satisfy the relation between the amplitude, the Mach number, and width of the solitary wave and establishes the excitation of solitons in the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' By launching two counter-propagating perturbations and observing their overlapping and passing through each other without losing their identity ascertains the wave structures to be solitons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The maximum amplitude of the soliton generated in the present experiment is 𝐵𝑝 = 16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='6 𝑘𝐺(𝐼𝑚𝑎𝑔 = 80𝐴 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' After thoroughly characterizing the existence of the solitons, the effect of two temperature electron distributions on the propagation of IAS has been explored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The effective temperature of electron (𝑇𝑒𝑓𝑓) has been varied by varying the population ratio and temperature of cold and hot components of electrons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' It has been observed that in MPD pole cusp magnetic field value influences the propagation of IAS significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The amplitude of soliton has been found to be increasing with the field value up to 𝐵𝑝 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='6 𝑘𝐺 after which it has been found to be decreasing with a further increase in the field values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The width of the soliton shows the opposite variation to its amplitude variation as a function of the cusp magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The soliton evolution is found to be sensitive to the effective temperature of plasma as the amplitude and width of soliton has been observed to be significantly with 𝑇𝑒𝑓𝑓.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' This observation quantitatively agrees with the theoretical study of the dependence of soliton amplitude with effective electron temperature in two-electron temperature plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Acknowledgments It is a pleasure to acknowledge Professor Abhijit Sen for fruitful discussions and encouragements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' The authors are thankful to Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Pintu Bandopadhyay for the critical review of the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='S is indebted to University Grant Commission (UGC) and Ministry of Minority affairs, Government of India for their support under the Maulana Azad National Fellowship scheme award letter number 2016-17/MANF-2015-17-GUJ-67921.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' References 1Report on Waves 14th Meeting of the British Association for the Advancement of Science (London, 1845).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 2 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Korteweg and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' de Vries, London, Edinburgh, Dublin Philos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Mag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 39, 422 (1895).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 3 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Washimi and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Taniuti, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 17, 996 (1966).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 4 R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sagdeev, COOPERATIVE PHENOMENA AND SHOCK WAVES IN COLLISIONLESS PLASMAS (Consultant Bureau, New York, 1966).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 5 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ikezi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Taylor, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Baker, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 25, 11 (1970).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 6 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Wu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Huang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Wang, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Fälthammar, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Plasmas 3, 2879 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 7 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Gardner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Greene, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Kruskal, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Miura, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 19, 1095 (1967).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 17 8 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Taniuti, Suppl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' (1974).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 9 G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Das and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Tagare, Plasma Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 17, 1025 (1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 10 G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Das, Plasma Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 19, 363 (1977).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 11 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Tran, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Scr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 20, 317 (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 12 Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Nakamura, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Plasma Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 10, 180 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 13 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Temerin, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Cerny, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lotko, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Mozer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 48, 1175 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 14 R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Boström, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Gustafsson, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Holback, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Holmgren, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Koskinen, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Kintner, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 61, 82 (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 15 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Mälkki, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Eriksson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='-O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Dovner, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Boström, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Holback, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Holmgren, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Koskinen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 98, 15521 (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 16 Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 110, A03223 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 17 R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Taylor, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' MacKenzie, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ikezi, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Instrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 43, 1675 (1972).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 18 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ikezi, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Fluids 16, 1668 (1973).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 19 Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Nakamura and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sugai, Chaos, Solitons & Fractals 7, 1023 (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 20 P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' John and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Saxena, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' A 56, 385 (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 21 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lonngren, Plasma Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 25, 943 (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 22 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Watanabe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Japan 53, 950 (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 23 P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sakanaka, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Fluids 15, 304 (1972).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 24 N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Zabusky and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Kruskal, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 15, 240 (1965).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 25 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Watanabe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Plasma Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 14, 353 (1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 26 D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Xiao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ma, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Li, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Yu, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Plasmas 14, 092104 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 27 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Pajouh and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Abbasi, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Plasmas 15, (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 28 L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Schott, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 59, 1390 (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 29 H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Kuehl, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Fluids 26, 1577 (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 30 P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Chatterjee, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' kr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ghorui, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Wong, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Plasmas 18, 103710 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 31 W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Feldman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Asbridge, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Bame, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Montgomery, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Gary, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 80, 4181 (1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 32 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Patel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sharma, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ramasubramanian, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ganesh, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Chattopadhyay, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Instrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 89, (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 33 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Patel, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sharma, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ramasubramanian, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ghosh, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Chattopadhyay, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Scr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 95, (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 34 R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Cairns, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Mamum, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Bingham, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Boström, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Dendy, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Nairn, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Shukla, Geophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 22, 2709 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 35 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Nishihara and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Tajiri, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Japan 50, 4047 (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 18 36 W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Jones, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Gleman, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Doucet, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 35, 1349 (1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 37 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sharma, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Patel, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ramasubramanian, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Saxena, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Chattopadhyaya, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ganesh, Plasma Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Express 2, (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 38 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Singh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Srivastava, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Awasthi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Mattoo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sanyasi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Singh, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Kaw, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Instrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 85, (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 39 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sheehan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Raitses, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Hershkowitz, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Kaganovich, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Fisch, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Plasmas 18, 073501 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 40 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Yip, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sheehan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Hershkowitz, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Severn, Plasma Sources Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 22, 065002 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 41 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Berkowitz, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Friedrichs, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Goertzel, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Grad, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Killeen, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Rubin, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Energy 7, 292 (1958).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 42 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Leung, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Hershkowitz, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' MacKenzie, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Fluids 19, 1045 (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 43 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Dankongkakul, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Araki, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Wirz, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Plasmas 21, 043506 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 44 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Aihara, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Fujiwara, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Hosokawa, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ikegami, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Fusion 12, 45 (1972).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 45 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Dankongkakul, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Araki, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Wirz, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Plasmas 21, 043506 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 46 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Berkowitz, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Friedrichs, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Goertzel, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Grad, (n.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 47 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Park, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Krall, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sieck, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Offermann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Skillicorn, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sanchez, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Davis, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Alderson, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lapenta, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' X 5, 1 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 48 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Bose, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Kaur, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Chattopadhyay, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ghosh, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Saxena, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Pal, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Plasma Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 83, 615830201 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 49 R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Bosch and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Merlino, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 60, 3056 (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 50 R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Bosch and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Gilgenbach, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' A 128, 437 (1988).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 51 N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Hershkowitz, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Leung, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Romesser, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 35, 277 (1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 52 Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Nakamura, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ito, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Koga, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Plasma Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 49, 331 (1993).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 53 J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Cooney, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Gavin, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lonngren, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Fluids B 3, 2758 (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 54 M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Sharma, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Patel, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Shaikh, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ramasubramanian, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Ganesh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Chattopadhayay, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Saxena, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Plasmas 27, (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 55 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Watanabe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Plasma Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 14, 353 (1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 56 G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Joyce, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lonngren, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Alexeff, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Jones, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Fluids 12, 2592 (1969).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 57 T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Pierre, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Bonhomme, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Leclert, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Cussenot, Plasma Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Fusion 27, 523 (1985).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 58 Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Nakamura, IEEE Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Plasma Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 10, 180 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 59 S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Watanabe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Plasma Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 14, 353 (1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 60 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='. Goswami and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Buti, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' A 57, 149 (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' 19 61 G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Lakhina, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Kakad, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Singh, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Verheest, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} +page_content=' Plasmas 15, 062903 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/X9E1T4oBgHgl3EQfcARq/content/2301.03179v1.pdf'} diff --git a/Y9AyT4oBgHgl3EQf9frR/content/2301.00877v1.pdf b/Y9AyT4oBgHgl3EQf9frR/content/2301.00877v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0a47e12602f0f52f0fc5b4258130177e4b393fb6 --- /dev/null +++ b/Y9AyT4oBgHgl3EQf9frR/content/2301.00877v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8dc484ee6f048396e2a9e93ac65c2d5740e3f38ebec0e59b43e0e8d22df1000e +size 128682 diff --git a/YNE5T4oBgHgl3EQfCw5O/content/2301.05398v1.pdf b/YNE5T4oBgHgl3EQfCw5O/content/2301.05398v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8417973aae5e9bf447f4d01083596aa45c56ddaa --- /dev/null +++ b/YNE5T4oBgHgl3EQfCw5O/content/2301.05398v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a0fcbb535cf4a2d0fc733e3b6d5e20bdd8bf4241e854b6cce41ace8e2017d9cd +size 749947 diff --git a/YNE5T4oBgHgl3EQfCw5O/vector_store/index.faiss b/YNE5T4oBgHgl3EQfCw5O/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..7e1d4d48b74c4b5aaaf8fa2e8ee11c7d0ed4f5a1 --- /dev/null +++ b/YNE5T4oBgHgl3EQfCw5O/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:70fd03477cf6d096d2a73bc75597c3337e783ba55e411031af9fa080a7419ea5 +size 5177389 diff --git a/a9E4T4oBgHgl3EQfoQ0b/vector_store/index.pkl b/a9E4T4oBgHgl3EQfoQ0b/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..70a0b08617dca7fbde5d50f95ab1ab85b69cff4e --- /dev/null +++ b/a9E4T4oBgHgl3EQfoQ0b/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f337aa1f8a7ad19aa7d3d509cf983a746115967dcea499438011ab9dc2db152e +size 292064 diff --git a/a9FLT4oBgHgl3EQfXi8l/content/2301.12061v1.pdf b/a9FLT4oBgHgl3EQfXi8l/content/2301.12061v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0c3d0c182496917ecd6a73053fc6fc4683c86528 --- /dev/null +++ b/a9FLT4oBgHgl3EQfXi8l/content/2301.12061v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:03c33259608c9224a2d6319cda699e691839f380d0d0ff8647d914d4f27c13ca +size 2056064 diff --git a/a9FLT4oBgHgl3EQfXi8l/vector_store/index.pkl b/a9FLT4oBgHgl3EQfXi8l/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..3a5e36497985e6a8b636e90d7accfa199afcdac2 --- /dev/null +++ b/a9FLT4oBgHgl3EQfXi8l/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b472d3a932f7f4a5e63189bcbdca4652bb45f5fecfda09f943a9b0308d8cf84c +size 313507 diff --git a/aNE2T4oBgHgl3EQfZgfV/content/tmp_files/2301.03866v1.pdf.txt b/aNE2T4oBgHgl3EQfZgfV/content/tmp_files/2301.03866v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..7398e4ad22dd9e503aeb50bbf63d47cc505fde48 --- /dev/null +++ b/aNE2T4oBgHgl3EQfZgfV/content/tmp_files/2301.03866v1.pdf.txt @@ -0,0 +1,1395 @@ +HEP/123-qed +Superradiant (In)stability, Greybody Radiation, and Quasinormal +Modes of Rotating Black Holes in non-linear Maxwell f(R) +Gravity +Sara Kanzi∗ +Faculty of Engineering, Final International University, +Kyrenia, North Cyprus via Mersin 10, Turkey +˙Izzet Sakallı† +Physics Department, Eastern Mediterranean University, +Famagusta, 99628 North Cyprus via Mersin 10, Turkey +(Dated: January 11, 2023; Received) +1 +arXiv:2301.03866v1 [hep-th] 10 Jan 2023 + +Abstract +The research of superradiant instability in the realm of quantum gravity is a well-known topic, +with many physicists and astronomers studying the potential impact it can have on gravitational +waves, the structure of the universe, and spacetime itself. In this work, we investigate the super- +radiant (in)stability of a rotating black hole obtained from the nonlinear Maxwell f(R) gravity +theory. In this study, the evaluation of stability/instability is going to be based on non-existence +and existence of magnetic field, when the magnetic field constant becomes c4 = 0 and c4 ̸= 0, +respectively. The analyzes of greybody factor (GF) and quasinormal modes (QNMs) are investi- +gated in the stationary black hole spacetime both in the absence and presence of the magnetic field +parameter. To this end, we first consider the Klein-Gordon equation for the complex scalar field +in the geometry of that rotating black hole. In the sequel, the obtained radial equation is reduced +to a one-dimensional Schr¨odinger-like wave equation with an effective potential energy. The effects +of the nonlinear Maxwell f(R) gravity theory parameters (q, c, and c4) on the effective potential, +GFs, and QNMs are thoroughly investigated. The obtained results show that even though the +factors q, c, and c4 all affect the effective potential, this phenomena, surprisingly, is not valid for +the GFs and QNMs. With the proper graphics and tables, all outputs are depicted, tabulated, and +interpreted. +∗Electronic address: sara.kanzi@final.edu.tr +†Electronic address: izzet.sakalli@emu.edu.tr +2 + +Contents +I. Introduction +3 +II. Rotating BHs in Nonlinear Maxwell f(R) gravity +7 +III. Scalar Perturbation +9 +IV. Superradiance Phenomenon +10 +A. For c4 = 0 +10 +B. For Infinitesimal c4 +14 +V. Semi-analytical Greybody Radiation +16 +VI. QNMs +18 +VII. Conclusion +23 +References +25 +I. +INTRODUCTION +Superradiance is a term used to describe a radiation amplification system that includes +a scattering mechanism. Superradiance plays a noteworthy role in the studies of relativity, +astrophysics, quantum mechanics, and optics [1]. This phenomenon can be considered as +a quantum aspect of black hole (BH) physics. Namely, in the context of quantum gravity +phenomenology, superradiance can play a crucial role in the study of BHs. For example, the +emission of Hawking radiation (or greybody radiation) [2, 3] from a BH can be enhanced +by the presence of surrounding matter, leading to a process known as BH superradiance. +This phenomenon has been proposed as a possible explanation for the observed properties +of BH systems, such as the large amounts of energy emitted from the centers of galaxies. +Because it is influenced by the BH’s area theorem, tidal forces, the Penrose process, and +Hawking radiation [4]. The concept of superradiance was first introduced by Dicke in 1954 +[5]. +Subsequently, in 1971, this phenomenon was further understood and developed by +Zel’dovich [6, 7] during his investigation of reflected wave amplification from a rotating BH +3 + +(Kerr metric). Zel’dovich proved that if the frequency ω of the ingoing wave having the plane +wave structure with e−iΩt+imφ (Ω represents the angular velocity, φ is the cyclic coordinate, +and m denotes the magnetic quantum number) convinces ω < mΩ, the scattered waves +amplify in such a way that the waves coming out of the BH to become more than the ones +entering to it. Namely, the dispersed wave is amplified. +Combination of superradiance with a confining procedure to force the wave to consistently +interact with the BH to undergo exponential increase known as ”BH bomb” [8], which has +been an active case since 1970s [9]. This phenomenon can be viable by considering a mirror +around the rotating body that could make the system unstable [7, 10]. +In [11], it was +mentioned that such a mirror can be recognized by applying a charged massive scalar field +breeding in the Kerr-Newman spacetime. Moreover, BHs can be transformed into efficient +particle detectors by applying strong constraints to ultralight bosons via the superradiant +instabilities of spinning BHs. On the other hand, instability formation and whether or not +its nonlinear time evolution follows the linear intuition are, nevertheless, topics that are not +well-understood, yet [12]. +A Kerr BH might be thought as a strong candidate for superradiant phenomena [13–15], +however BHs in Kerr form do not exhibit superradiant instabilities with significant growth +rates [10, 16–18]. In fact, there are various methods for using superradiance to extract energy +from BHs: 1) BH fission [19], 2) BH bombs (as mentioned above) [8, 10], 3) Accretion disks +and torus [20], 4) BH bombs in anti-de Sitter (AdS) spacetime [21, 22], 5) Massive fields, +soft bombs, and particle physics [23–25], 6) Floating orbits [26], 7) Generalized scalar-tensor +theories and superradiance [23, 27], 8) Ergoregion instability [28, 29]. On the other hand, +today, there are various theories for modified gravity, such as brane-world gravity [30], Dvali- +Gabadadze-Porrati gravity [31], Einstein-Aether theory [32], tensor-vector-scalar theory [33], +and f (R) gravity [34–37], which all attracted much attention in the literature. f(R) theories +of gravity are straightforwardly generated by replacing Ricci scalar R in the Einstein-Hilbert +action. Namely, we have a generic action for f(R) as follows +S = 1 +2k +� +d4x√−gf (R) , +(1) +where k = 8π denotes the gravitational constant and g is the determinant of met- +ric. Throughout the paper, unless otherwise noted, we shall work in natural units with +cs = G = ℏ = 1. Since general relativity (GR) has had many unresolved problems, includ- +4 + +ing the existence of dark energy and dark matter, deflection from Einstein’s theory allows +us to estimate the fundamental matters and extension of GR (modified gravity). Based on +different formalisms, there are three types of f (R) gravity models: 1) metric, 2) Palatini, +and 3) metric-affine, f(R) gravity [38–40]. The use of f(R) gravity in many contexts is +significant; for example, see its astrophysical perspective in [41–44], the cosmological models +with f(R) in [45, 46], and the derivations of novel BH solutions in [47–50]. Moreover, we +refer the reader to the monographs [51, 52] for some good reviews about f(R). In par- +ticular, spherically symmetric BH solutions in f (R) gravity have been receiving special +attentions (see for instance [53], in which the exact static spherically symmetric solutions in +f (R) gravity coupled with nonlinear electrodynamics derived by Hollestein and Lobo [54]). +Searching for alternative gravitational theories to conventional Einstein’s general relativity +(GR) is supported by difficult challenges ranging from quantum gravity to dark energy and +dark matter. Indeed, there are a lot of unresolved problems with GR, such as singularities, +the nature of dark energy and dark matter. All of these problems motivate researchers to +improve or modify GR in order to address the challenges at the UV and IR scales [55]. +However, the obtained feasible modified/extended theories should be consistent with the +present observational/experimental restrictions. With the awareness of this issue, an am- +bitious study has recently been carried out on the nonlinear Maxwell f(R) gravity [53]. +By using dynamical Ricci scalars that asymptotically converge to flat or (A)dS spacetimes, +Nashed and Saridakis [56] have derived a new charged rotating BH solutions, which will be +our main reference metrics in this study. +Due to the quantum effects, a BH can act as a blackbody object, which emits thermal +waves [2, 3]. The mass of a BH decreases during its HR, which can lead to complete BH +evaporation. As a matter of course, the emitted particles are affected by an effective potential +originating from the curvature of the spacetime. As a result, although some waves penetrate +the potential barrier and extend to infinity, the remainder is reflected back to the BH. Due +to the structure of the effective potential, the radiation spectra are altered and different from +that near the event horizon. As a result, the term GF [57] refers to a quantity that measures +the deviation of the radiation spectrum from the blackbody radiation. At the event horizon, +the BH emission rate [58] is defined as follows +γ (ω) = +� +d3k +8π3e +ω +TH +� +, +(2) +5 + +by which ω represents the wave frequency, TH and k denote the Hawking temperature +and surface gravity, respectively. The relation between emission rate and GF is given by +[59] +γ (ω) = +� +d3k |Al,m|2 +8π3e +ω +TH +� +, +(3) +where |Al,m|2 represents the GF. There are various methods to compute the GF, such as +matching technique [59–61], WKB approximation [62, 63], finding Bogoliubov coefficients +method [64–67], the Miller–Good transformation method [57, 68], and the rigorous bounds +[69]. +Teukolsky equation [70] describes an oscillation system that naturally dissipates. Such +a system generates QNMs instead of the classical normal mode solution. +Vishveshwara +was the first to identify the QNMs of a BH [71]. The QNMs are described by complex +frequencies that carry characteristic information about the BH spacetime, which is in the +ringdown phase. The QNMs have broad literature in the BH physics. Specifically, explicit +superpositions of QNMs may be utilized to estimate the gravitational wave frequencies in the +gravitational wave phenomenon [72–75]. There are many rich and excellent investigations +on the QNMs of various solutions of BHs [76–79], which are considered seminal works of the +subject [80–82]. +The paper is divided into the following sections. In Sec. (II), we introduce the metric of +the rotating BH in nonlinear Maxwell f (R) gravity and demonstrate some of its physical +features. Section (III) is devoted to the Klein-Gordon equation (KGE) for charged massive +scalar fields in that rotating BH geometry. In this section, we show that the radial wave +equation reduces a one-dimensional Schr¨odinger-like wave equation with a corresponding +effective potential. We also study the behaviors of the obtained effective potential under +the influence of charge q and magnetic field constant c4. As being two subsections, in Sec. +(IV), we examine the superradiant instability for zero and non-zero c4 values. Sections (V) +and (VI) are reserved for the analysis of the greybody radiation and QNMs, respectively. +Our results are summarized and discussed in Sec. (VII). We follow the metric convention +(+, −, −, −). +6 + +II. +ROTATING BHs IN NONLINEAR MAXWELL f(R) GRAVITY +In this section, we briefly review both new static and rotating BH solutions obtained in +nonlinear Maxwell f (R) gravity [56], whose the total action is given by +St = 1 +2k +� √−gf(R)d4x + +� √−gL(F)d4x, +(4) +where k is a gravitational constant, which can be considered as k = 1, without loss of gen- +erality, in this study. √−g represents the determinant of the metric gµν. The corresponding +gravitational field equations of the action (4) can be derived as follows +ξµν = ℜµνfℜ − 1 +2gµνf(ℜ) − 2gµνΛ + gµν∇α∇αfℜ − ∇µ∇νfℜ − 8πℑnlem +µυ +≡ 0, +(5) +by which ℑnlem +µυ +denotes the energy momentum tensor and fℜ ≡ df(ℜ) +dℜ . Using the following +ansatz for a spherically symmetric line element: +ds2 = H (r) dt2 − dr2 +H (r) − r2 � +dθ2 + sin2 θdϕ2� +, +(6) +in Eq. (5), after making some tedious calculations, the following metric function was finally +obtained by Nashed and Saridakis [56] +H(r) = c +2 − 2M +r ++ q2 +r2, +(7) +where c is a positive constant, which can take limited values: 0 < c < 2, q and M stand for +the charge and mass, respectively (see Ref. [56] for the details). In Fig. (1), we show the +behavior of the metric function H (r) under the influence of varying parameters q and c. It +is clearly seen that the spacetimes exhibit flatness at the asymptotic distances, independent +of the values of q and c. +The rotating version of the BH solution can be derived by applying the following trans- +formations [83, 84] +∼ +φ = Ξφ + at, +∼ +t = Ξt + aφ, +(8) +to the static and spherically symmetric metric (6). In Eq. (8), a is the rotating parameter +7 + +FIG. 1: Schematic plots of H(r) versus r. Solid lines represent c = 0.5 and dash lines are +for c = 1.5. The physical parameters are chosen as M = m = 1, ω = 15, a = 0.3, and λ = 2. +and Ξ = +√ +1 + a2. Thus, we have +ds2 = [Ξ2H(r) − a2r2 sin2 θ]dt2 − dr2 +H(r) − r2dθ2− +[Ξ2r2 sin2 θ − a2H(r)]dφ2 + 2aΞ[H(r) − r2 sin2 θ]dtdφ, +(9) +in which H(r) is provided by the static solution (7) previously derived. On the other hand, +the general gauge potential is defined by [56] +∼ +V = [Ξq(r) + as(r)]d +∼ +t + n(φ)dr + [aq(r) + Ξs(r)]d +∼ +φ, +(10) +where q(r), s(r), and n(φ) are 3 free functions generating the electric and magnetic charges +in the vector potential as follows +s(r) = c4r, +n(φ) = c4φ, +(11) +in which c4 represents the magnetic field constant. In the following sections, our investigation +will consider cases in which the magnetic field constant does not exist (c4 = 0) and exists +(c4 ̸= 0). +8 + +III. +SCALAR PERTURBATION +In recent decades, perturbations of BHs and stars have arisen as one of the main topics +of relativistic astrophysics. Furthermore, perturbations are hot subjects right now because +of their functions in gravitational waves. In this part, we employ the charged KGE to arrive +at the Schr¨odinger wave equation in one dimension. The effective potential to be obtained +in this section is crucial for studying superradiance, greybody radiation, and QNMs. +Let us consider the charged and massive KGE: +1 +√−g (∂µ − iQAµ) +�√−ggµν (∂µ − iQAν) Ψ +� += m2Ψ, +(12) +where Q and m are the charge and mass of the scalar field (spin-0), respectively. Moreover, +√−g represents the determinant of the metric. Here, for metric (9), we consider the following +ansatz for the spinor field: +Ψ = e−iωteikφR (r) Y (θ) . +(13) +During the derivation of the scalar wave equation, we will consider the dyonic case. Plus, +we set s(r) = n(φ) = 0 in Eq. (10). Thus, the components of the vector potential read +A∼ +t = Ξq, +and +A∼ +φ = aq. +(14) +Throughout the paper, without loss of generality, we shall consider qQ → q2. After substi- +tuting Eq. (14) and ansatz (13) into the massive charged KGE (12), one can obtain +�2H +r ++ H′ +� +R′ (r) + HR′′ (r) + +1 +H +� +Ξ2ω2 + Ξ4q4 + 2q2ωΞ3 + 2aωΞk + 2aΞ2q2k − 2a2Ξ2q4− +2ωa2q2Ξ + a2k2 + a4q4 − 2kq2a3 + m2 + λ +� +R (r) = −λ, +(15) +where λ is the eigenvalue whose value can be found with the help of the angular part: +cot θYθ (θ) + Yθθ (θ) − (aω + Ξk)2 +sin2 θ +Y = 0. +(16) +In the mean time, throughout the paper, a prime (dash) symbol is used to denote the +derivative of a function with respect to its argument. By considering the definition of the +tortoise coordinate: +r∗ = +� +dr +H (r), +(17) +9 + +and in the sequel applying the transformation R(r) = U(r) +r +to Eq. (16), one can acquire +one-dimensional Schr¨odinger like wave equation as follows: +d2U (r) +dr2 +∗ ++ +� +ϖ2 − Veff +� +U (r) = 0, +(18) +in which ϖ2 = ω2 (1 + a2) = ω2Ξ2 and the effective potential is given by +Veff = −2Ξ +� +q2 + ak +� +ω − +� +q2 + ak +�2 + HH′ +r ++ λH +r2 + m2H. +(19) +The behaviors of the effective potential (19) when the charge parameter q is changed for +various values of c are depicted in Fig. (2). , +FIG. 2: Plots of Veff versus r for the spin-0 particles in the case of zero magnetic constant. +The physical parameters are chosen as; M = m = 1, ω = 15, a = 0.3, and λ = 2. +IV. +SUPERRADIANCE PHENOMENON +A. +For c4 = 0 +Here, we investigate the stability of the rotating BH obtained from the non-linear Maxwell +f (R) gravity. To this end, we consider the method prescribed in Ref. [85, 86]. After applying +10 + +the transformation U (r) = e−iϖr∗ψ (r) to the Schr¨odinger equation seen in Eq. (18), one +gets +d2ψ (r) +dr2 +∗ +− 2iϖdψ (r) +dr∗ +− Veffψ (r) = 0. +(20) +Now, let us replace the tortoise coordinate (17) with the naive radial coordinate r +d +dr +� +H dψ +dr +� +− 2iϖdψ +dr − Veff +H ψ = 0, +(21) +and multiply Eq. (21) by ψ∗. By imposing H (r+) = 0 and ψ (∞) = 0, one can solve the +final differential equation by performing the well-known integration by parts method. Thus, +we get +� ∞ +rh +dr +� +H +���� +dψ +dr +���� +2 ++ 2iϖψ∗dψ +dr + Veff +H |ψ|2 +� += 0, +(22) +where the second term in the integrand can be expanded to +2iϖdψ +dr = ϖψ∗dψ +dr + +−ϖψdψ∗ +dr . +(23) +Therefore, the integration (22) recasts in +� ∞ +rh +dr +� +H +���� +dψ +dr +���� +2 ++ Veff +H |ψ|2 +� += −|ϖ|2 |ψ (rh)|2 +Im ω +. +(24) +It is also possible to write Eq. (24) as +� ∞ +rh +dr +� +H +���� +dψ +dr +���� +2 ++ +∼ +V eff +H +|ψ|2 − (q2 + ak)2 +H +|ψ|2 − 2Ξ (q2 + ak) ω +H +|ψ|2 +� += −|ϖ|2 |ψ (rh)|2 +Im ω +. +(25) +In Eq. (25), +∼ +V eff stands for the potential terms without q parameter in Veff. In addition, +it is discovered that the final term of Eq. +(25) has almost no impact on superradiance +calculations and the sign of expression +∼ +V eff +H +|ψ|2 − (q2+ak) +2 +H +|ψ|2 is critical for evaluating the +stability of the black hole. Meanwhile, the potential (19) is positive outside the horizon, +which means Im(ω) must be negative. Thus, in light of the Dirichlet boundary conditions, +one can conclude that the scalar field propagation will be stable. In order to assess the +superradiant instability of the rotating black hole in non-linear Maxwell f (r) gravity in a +more authentic form, we shall define the reflection/transmission coefficients to determine the +superradiant condition. To this end, we shall perform our computations in three different +regions. The first region (Region I) is the region that is close to the event horizon (r ≈ rh) , +where the potential is approximated to +Veff ≈ −2Ξ +� +q2 + ak +� +ω − +� +q2 + ak +�2 , +(26) +11 + +and correspondingly +∼ +V eff ≪ +� +ωΞ + +� +q2 + ak +��2 . +(27) +Thus, in Region I, the solution of the radial equation (18) is obtained as +U1 (r) = Ae−i(ωΞ+(q2+ak))r∗. +(28) +which slightly away from the event horizon yields [86] +U1 (r) ≈ A +� +1 − i (ωΞ + (q2 + ak)) +H′ (rh) +ln (r − rh) +� +, +(29) +where the near horizon tortoise coordinate is defined as r∗ = +� +dr +H(r) ≈ +1 +H′(rh) ln (r − rh). +Between the event horizon and the distant regions, Region II acts as an intermediate zone +and is defined as: +∼ +V eff ≫ +� +ωΞ + +� +q2 + ak +��2 . +(30) +Therefore, the radial equation (18) reads +d2U +dr2 +∗ += 0, ⇒ U (r∗) = B + C +� +dr∗. +(31) +By comparing the solutions in the first and second regions, we define the constants as as +A = B, and C = −Ai (ωΞ + (q2 + ak)). +To find the solution in Region II, we take into consideration an asymptotic series for +tortoise coordinate i.e., r ≫ rh. Hence, we get +U2 (r) = A +� +1 − i (ωΞ + (q2 + ak)) +4r4 +∼ +k +� +, +(32) +where +∼ +k = − 32 +c2r5 +� +32M 3cq2 − 3Mc2q4 − 64M 5� +. +(33) +The third region (Region III) is the asymptotic zone (r ≫ rh,), where the conducting terms +of the effective potential become +Veff ≈ −2Ξ +� +q2 + ak +� +ω − +� +q2 + ak +�2 + m2c +2 . +(34) +Thus, one can get the Region III solution as +U3 (r) = D1 + D2e−i +� +(ωΞ+(q2+ak))2+ m2c +2 +r∗. +(35) +12 + +Then, after matching the solution of Region II with the solution of Region III, we get +D2 = Ae +i +∼ +k +4r4 η, +(36) +where +η = +m2c +4(ωΣ + (q2 + ak)). +(37) +To obtain the reflection coefficient and the GFs and to complete our assessment of superra- +diant stability/instability, we employ the flux expression as follows +F = +√−ggrr +2i +(U ∗∂rU − U∂rU ∗) . +(38) +Therefore, one can obtain the near horizon flux as +Fhor ∝ −A2 � +ωΞ + +� +q2 + ak +�� +. +(39) +Similarly, the asymptotic flux at spatial infinity becomes +F∞ ∝ −ξ +� +1 + D1 +2 +� +D2e−iξ + D∗ +2eiξ�� +, +(40) +where ξ = +� +(ωΞ + (q2 + ak))2 + m2c +2 . By considering D1 = ˆ +D1 + ˆ +D2 and D2 = i( ˆ +D2 − ˆ +D1), +the asymptotic incoming and outgoing fluxes (40) can be written as follows +F∞−in ∝ −ξ +� +1 − i | D2 |2 sinh(iξ) +� +, +(41) +and +F∞−out ∝ −ξ +� +1 + i | D1 |2 sinh(iξ) +� +. +(42) +By employing the definition of the reflection coefficient and GF, we get +R =| F∞−out +F∞−in +|= +�1 + iA2 +1sinh(iξ) +1 − iA2 +1sinh(iξ) +� +, +(43) +and +γ = Fhor +F∞−in += A2 (ωξ + (q2 + ak)) +ξ (1 − iA2 +1sinh(iξ)) . +(44) +Now, based on Eqs. (43) and (44), we are able to determine the superradiant condition. +To this end, either the reflection coefficient should be greater than 1 or the GF should be +negative: +ω ≤ −(q2 + ak) +ξ +. +(45) +13 + +By taking into account superradiant instability conditions, in the relevant sub-cases, we now +review the behavior of the effective potential in Fig. (2). It is obvious from Fig. (2) that the +potential does not contain wells and hence there are no bound states, which can prevent the +accumulation of energy that might cause the instability. This indicates that the rotating BH +in non-linear Maxwell f(R) gravity can readily absorb the charged scalar wave and whence +the associated background becomes stable under the charged scalar perturbations. +B. +For Infinitesimal c4 +In this sub-section, our aim is to evaluate the superradiant stability/instability of the +stationary BH found in the non-linear Maxwell f(R) gravity with the case of c4. However, we +shall choose the magnetic field constant to be infinitesimally small to facilitate calculations. +Moreover, we shall determine the effective potential with the aid of Eq. (20), not from the +Schr¨odinger equation as it was done in the previous sub-section. So, following the steps we +did earlier, we get +d +dr(H(r)dΨ +dr ) − 2i¯ωdΨ +dr − Veff +H(r)Ψ = 0, +(46) +where ¯ω = H(ω + qc4φ) and the effective potential is determined as a complex expression. +In Region 3, its real part can be expressed as +Re[Veff] ≈ −H2ω2 + HH′ +r +− 2qc4φH2ω + (ωΞ + (q2 + ak))2 − H( λ +r2 − m2), +(47) +and its imaginary part reads +Im[Veff] ≈ −ωH′H. +(48) +In Eqs. +(47) and (48), the terms including c2 +4 and +c4 +r2 are ignored. +In addition, our +analysis has shown us that it is reasonable to consider only the real component of the +effective potential. +The wave solutions of Regions 1 and 2 for the existing magnetic fields of the BH are +the same as the non-existing ones, Eqs. (28) and (32), but the wave solution of Region 3 +(r >> rh) with c4 ̸= 0 is different than the c4 = 0 one: +U3(r) = D1 + D2 exp +� +�−i +� +Veff(3) +∼ +k +4r4 +� +� r∗, +(49) +14 + +FIG. 3: Plots of Veff versus r for the spin-0 particles and non-zero c4,. The solid lines +represent the effective potential for q = 3 and the dashed ones stand for q = 2. The +physical parameters are chosen as; M = m = c = 1, ω = 10, a = 0.1, and λ = 2. +where +Veff(3) = −ω2c4 +4 +− 1 +2(qc4φc2ω − m2c) + (ωΞ + (q2 + ak))2, +(50) +and +∼ +k is nothing but Eq. (27). Comparing Eq. (49) with the solution obtained for Region +2 +� +Eq. (32) +� +, one can determine the unknown constants as D1 = A and +D2 = A exp +� i +∼ +k +4r4 +∼η +� +, +(51) +in which +∼η = 2m2c − 2qc4φc2ω − ω2c4 +8 +� +ωΞ + (q2 + ak) +� +. +(52) +To determine the flux expressions at the horizon and spatial infinity, we apply the same +method followed in the previous sub-section. Thus, we have +Fhor ∝ −(ωΞ + (q2 + ak))|A|2, +(53) +15 + +and +F∞ ∝ − +� +1 + D1 +2 (D2e−iβ + D∗ +2eiβ) +� +, +(54) +where +β = +� +Veff(3) +∼ +k +4r4. +(55) +By substituting D1 = ˆ +D1 + ˆ +D2 and D2 = i( ˆ +D2 − ˆ +D1) in Eq. (54), one can obtain +F∞−in ∝ −β(1 − i| ˆ +D2|2 sinh(iβ)), +(56) +F∞−out ∝ −β(1 + i| ˆ +D1|2 sinh(iβ)). +(57) +Therefore, the reflection coefficient of the rotating BH with small c4 reads +|R| = |F∞−out +F∞−in +| = +� +1 + i| ˆ +D1|2 sinh(iβ) +1 − i| ˆ +D2|2 sinh(iβ) +� +, +(58) +and the corresponding GF becomes +γ = Fhor +F∞in += (ωΞ + (q2 + ak))|A|2 +β +� +1 + i| ˆ +D1|2 sinh(iβ) +�. +(59) +Since the result is almost the same as Eq.(44), Moreover, no explicit well in the effective +potential behavior in Fig.(3), the interpretation for the stability in the presence of a magnetic +field will be the same as the nonexistent one. +V. +SEMI-ANALYTICAL GREYBODY RADIATION +In this section, we shall follow the method, which was reviewed in [57] (and references +therein) to analyze the greybody radiation for both cases of cs = 0 and c4 ̸= 0. +The general semi-analytic bounds for GFs are given by [87] +σl (ω) ⩾ sec h2 +�� ∞ +−∞ +℘dr∗ +� +, +(60) +where σl represents the GF and ℘ is formulated as follows +℘ = +� +(h′)2 + [ω2 − V − h2]2 +2h +, +(61) +by which h is a positive function that satisfies the following condition: +h (−∞) = +h (+∞) = ω. Normally, one follows the method of replacing the V parameter with the +16 + +potential obtained in Eq. (34) and then employs the tortoise coordinate to evaluate the +GF (60). On the other hand, that method is not always the best course of action to take. +In fact, this method also fails in our situation. So, to overcome this discrepancy, we set +h = +√ +ω2 − V in Eq. (61). This allows us to rewrite the expression for GF (60) as +σl (ω) ⩾ sec h2 +�1 +2 +� ∞ +−∞ +���� +h′ +h +���� dr∗ +� +, +(62) +which corresponds to +σl (ω) ⩾ sec h2 +� +ln +�hpeak +h∞ +�� += sec h2 +� +ln +�� +ω2 − Vpeak +ω +�� +. +(63) +One can immediately observe that Eq. (63) is valid for ω2 > Vpeak, the peak value of the +potential [57]. Besides, Eq. (63) can be rewritten as +σl (ω) ⩾ 4ω2 (ω2 − Vpeak) +(2ω2 − Vpeak)2 . +(64) +To find the maximum or the peak of the potential, as is well-known, one should find +where the graph shifts from increasing to decreasing. To find out the rate at which the +graph shifts from increasing to decreasing, we look at the second derivative and see when +the value changes from positive to negative. Depending on the values of Vpeak, the GFs are +obtained. For instance, by setting M = m = 1 and λ = 2, in relation to the variables q and +c, the Vpeak expression is given by +Vpeak ≈ 0.00757c − (0.08987c + 2.0257) q2 + 1.18115 − 1.05389q4. +(65) +Substituting Eq. (65) to Eq. (64), we first compute the GFs of the rotating BH in non- +linear Maxwell f (R) gravity with c4 = 0 for various parameters of c and q. The behaviors +of the obtained GFs for c4 = 0 are illustrated in Fig. (4). It is worth noting that although +c values should obey 0 < c < 2 due to Ref. [56], we have used the values of c above the +relevant limit for the sake of revealing the changes in the GF behaviors. This by purpose +exaggeration is made for just exhibiting the differences in the GF behaviors that are almost +indistinguishable from each other within the theoretical limit of 0 < c < 2. Fig. (4) shows +a growth in the GF with q = 0.5 by increasing the c factor, but by increasing the charge +value q this course of action altered in the opposite direction. In a same circumstance, for +17 + +FIG. 4: Plots of σl (ω) versus ω for scalar particles.The physical parameters are chosen as; +M = m = 1, a = 0.1 and λ = 2. +infinitesimal c4 case, Vpeak is found to be +Vpeak ≈ −A2(100 + 62.80qc4) + 0.2493046A(0.1243055 − 0.0309899q2)+ +(10.150 + q2)2 + 0.439065 + 0.054427q2, +(66) +where A = 0.501391 + 0.0621528q2. After substituting Eq. (66) in Eq. (64), the obtained +greybody radiation is depicted in Fig. (5), which shows that the greybody radiation explicitly +increases with the magnetic field parameter c4. +VI. +QNMs +QNMs are important in the study of BH perturbation because they provide a way to +understand the behavior of a BH in the presence of external perturbations such as a scalar, +electromagnetic, gravitational, etc. When a BH is perturbed, it will respond by emitting +gravitational waves that have a characteristic frequency. This frequency, known as the QNM, +is determined by the properties of the BH, such as its mass, charge, and spin. QNMs of a BH +is characterized by complex numbers. The complex frequency of a QNM is given by a real +18 + +FIG. 5: Plots of σl (ω) versus ω for scalar particles. The dotted lines are represented for +q = 3 and solid lines for q = 2. The physical parameters are chosen as; +M = m = k = 1, a = 0.1, and λ = 2. +part and an imaginary part. The real part represents the oscillatory frequency of the mode, +while the imaginary part represents the rate of decay or growth of the mode. By observing +the QNMs in gravitational waves, astronomers can learn about the physical characteristics +of the object that produced the waves. +In this section, for the scalar perturbations, we consider a semi-analytical approach to +derive the frequencies of the QNMs of the charged rotating BHs in nonlinear Maxwell f (R) +gravity. +To this end, we employ the WKB (Wentzel-Kramers-Brillouin) approximation, +which is a mathematical method used to solve differential equations (DEs) with a large- +scale parameter. +This approximation allows for a simplified solution to the differential +equation and provides an estimate of the energy levels (frequency) within a certain accuracy. +Conventionally, the WKB approach is based on the assumption that the solutions can be +expressed as an exponential power series, where the coefficients of the series are determined +by solving a set of recursive equations: +Ψ (r) ≈ exp +� +1 +ϵ +∞ +� +n=0 +ϵnSn (r) +� +. +ϵ → 0 +(67) +19 + +The DE has a general form as +d2Ψ (r) +dr2 += Q (r) Ψ (r) , +(68) +where Q (r) = V (r) − ω2, which contains two turning points. +The boundary condi- +tion of waves is chosen to be Ψ (r) = ZoutΨ (r)out for outgoing waves as r∗ → +∞ and +Ψ (r) = ZinΨ (r)in for incoming waves while r∗ → −∞. First, Mashhoon [88] invented this +approach and applied it to the BHs in 1983. +Then it was developed by [89, 90]. +The +WKB approximation can be extended from the third to sixth order. The sixth-order WKB +approximation, also known as the Konoplya approximation, is a method used to approxi- +mate the solutions of differential equations with complex potentials. The sixth order WKB +approximation by Konoplya can be found in his seminals paper [82, 91]. The Konoplya +approximation uses a series expansion of the solution to the DE in powers of the small pa- +rameter ϵ, which is the wavelength of the solution. Konoplya approximation for obtaining +the complex frequencies of the QNMs is given by the following expression [82]: +ω2 = +� +V0 + +� +−2V ′′ +0 Λ (n) − i +� +n + 1 +2 +� � +−2V ′′ +0 (1 + Ω (n)) +� +, +(69) +where +Λ (n) = +1 +� +−2V ′′ +0 +� +1 +8 +� +V (4) +0 +V ′′′ +0 +� �1 +4 + α2 +� +− +1 +288 +�V ′′′ +0 +V ′′ +0 +�2 � +4 + 60α2� +� +, +(70) +and +Ω (n) = +1 +(−2V ′′ +0 ) +� +5 +6912 +�V ′′′ +0 +V ′′ +0 +�4 � +77 + 188α2� +− +1 +384 +� +V ′′′ +0 +2V (4) +0 +V ′′ +0 +(3) +� +� +51 + 100α2� ++ +1 +2304 +� +V (4) +0 +V ′′ +0 +�2 � +67 + 68α2� ++ +1 +288 +� +V ′′′ +0 V (5) +0 +V ′′ +0 +(2) +� +� +19 + 28α2� +− +1 +288 +� +V (6) +0 +V ′′ +0 +� +� +5 + 4α2� +� +. +(71) +In Eqs. (69)-(71), the primes and superscripts (4, 5, 6; for the higher order derivatives) +denote the differentiation with respect to r∗ and α = n + 1 +2, where n denotes the tone +number. By considering the effective potentials of both solutions, the results are tabulated +in Tables (I) and (II) for the zero and non-zero magnetic field constants, respectively. +The behaviors of the QNMs for c4 = 0 are illustrated in Figs. (6). One can observe that +both parts (real and imaginary) of the QNMs decrease by increasing the charge parameter, +20 + +l n c +q +ωBosons +n q +ωBosons +1 0 1.9 1.5 0.3531092772-0.4070157966i 1 1.5 0.4628156990-0.8165375596i +1.6 0.3481646244-0.3984431959i +1.6 0.4939092271-0.7872487864i +1.7 0.3419910035-0.3882796385i +1.7 0.5140501121-0.7543542970i +1.8 0.3344221195-0.3764501224i +1.8 0.5242699290-0.7181651739i +1.9 0.3252048163-0.3627849969i +1.9 0.5254316095-0.6791172459i +2 0.3139459780-0.3469628546i +2 0.5180125636-0.6375332598i +1.8 1.5 0.4171149837-0.4733886692i +1.5 0.4883526041-0.9338811423i +1.6 0.4079913458-0.4593160345i +1.6 0.5382395015-0.8962742366i +1.7 0.3965522968-0.4425772439i +1.7 0.5699039647-0.8530833387i +1.8 0.3822146829-0.4227292265i +1.8 0.5845200557-0.8033010248i +1.9 0.3639735647-0.3989634900i +1.9 0.5823209373-0.7458662456i +2 0.3398557041-0.3697577443i +2 0.5612257904-0.6787904390i +1.7 1.5 0.3852295784-0.445685725i +1.5 0.4230520984-0.9161599009i +1.6 0.3780735086-0.4337333922i +1.6 0.4903805959-0.8746300965i +1.7 0.3690969050-0.4195188351i +1.7 0.5318064233-0.8285691459i +1.8 0.3581027910-0.4029669396i +1.8 0.5522314188-0.7775780030i +1.9 0.3446888390-0.3837822213i +1.9 0.5553476661-0.7223112093i +2 0.3281070990-0.3613035399i +2 0.5432743870-0.6634326053i +TABLE I: Bosonic QNMs of rotating BH in non-linear Maxwell f(R) gravity for zero +magnetic field parameter: c4 = 0. +q. +Moreover, for n = 0, QNMs increase by growing the c parameter and then start to +decrease. In addition, when n = 1 and q increases, the oscillation frequencies rise and the +damping mode steadily declines. +On the other hand, for the case of c4 ̸= 0, both parts of the QNMs decrease by increasing +the magnetic field constant. The corresponding behaviors are depicted in Figs. (7) and (8). +21 + +FIG. 6: Plots of QNMs of the rotating BH with c4 = 0 under varying charge parameter q. +The dotted line represents c = 1.9 and dashed line stands for c = 1.7; both for n = 0 (left). +The solid line is for c = 1.9, however, the dotted line stands for c = 1.7; both for n = 1 +(right). +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +FIG. 7: Plots of QNMs of the rotating BH under varying c4 values and fix charge q = 1; +for the tones of n = 0 (left) and n = 1 (right). +22 + +l n q +c4 +ωBosons +n +c4 +ωBosons +1 0 1 0.01 +0.5689309522-0.5679607840i +1 0.01 0.9833280391-0.9857933522i +0.011 +0.5676889204-0.5667273000i +0.011 0.9811788557-0.9836281427i +0.012 +0.5664589707-0.5655057950i +0.012 0.9790776944-0.9815108377i +0.013 +0.5652237736-0.5642789170i +0.013 0.9769537380-0.9793708001i +0.014 +0.5639890661-0.5630524167i +0.014 0.9748305274-0.9772315143i +0.015 +0.5627548196-0.5618262697i +0.015 0.9727080152-0.9750929361i +0.016 +0.5615210087-0.5606004477i +0.016 0.9705861561-0.9729550175i +0.017 0.5602875984-0.559374939322i +0.017 0.9684648987-0.9708177181i +0.018 +0.5590545741-0.5581496853i +0.018 0.9663442042-0.9686809854i +2 0.01 +0.7806931526-0.7847869409i +1 0.01 +1.348548830-1.362771574i +0.011 +0.7850205043-0.7891179837i +0.011 +1.356111851-1.370209477i +0.012 +0.7891946437-0.7932951529i +0.012 +1.363406512-1.377383600i +0.013 +0.7932235382-0.7973263608i +0.013 +1.370446745-1.384307536i +0.014 +0.7971145023-0.8012189424i +0.014 +1.377245378-1.390993848i +0.015 +0.8008742877-0.8049796989i +0.015 +1.383814279-1.397454164i +0.016 +0.8045091827-0.8086149183i +0.016 +1.390164462-1.403699260i +0.017 +0.8080250159-0.8121304478i +0.017 +1.396306156-1.409739150i +0.018 +0.8114272287-0.8155317201i +0.018 +1.402248881-1.415583157i +TABLE II: Bosonic QNMs of rotating BH in non-linear Maxwell f(R) gravity for +infinitesimal magnetic field parameter c4. +, +VII. +CONCLUSION +In this paper, we have studied the superradiant instability/stability of a rotating BH +in non-linear Maxwell f(R) gravity under the influences of q, c, and c4. To examine the +(in)stability in this spacetime under the Dirichlet boundary condition, we have expanded the +solutions into three different regions; near the event horizon (Region 1), intermediate (Region +2), and asymptotic (Region 3) regions. We next used the semi-analytic method outlined in +Sec. V to determine the GFs of the BH. To this end, we have followed a less problematic +23 + +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +c +FIG. 8: Plots of QNMs of the rotating BH under varying c4 values and fix charge q = 2; +for the tones of n = 0 (left) and n = 1 (right). +method and replaced the expression h = +√ +ω2 − V with Eq. (61) to reach Eq. (63) or Eq. +(64). Then by defining the Vpeak, the GFs of the rotating BH in non-linear Maxwell f(R) +gravity with/without magnetic field constant have been computed. The results obtained +have been depicted in Fig. (4) to reveal the effects of q and c parameters on the GFs. +The supreme point in the GFs behavior belongs to the c = 1 and q = 0.5, thereafter, by +increasing the values of both c and q the GFs decrease. +To analyze the QNMs originated from the scalar perturbations of the rotating BH in +non-linear Maxwell f(R) gravity with/without magnetic field constant, we have considered +the 6th order WKB approximation or the so-called Konoplya approximation. The results +obtained have been both tabulated and illustrated in Figs. (6) and (6). Thus, we have +shown the influence of q and c parameters on the QNMs. According to the relevant results, +the QNMs with n = 0 case have more stability than n = 1 state. Similar to the real part +of the QNMs, which decrease when the charge parameter is increased, the damping rate +component (imaginary part) of the QNMs exhibits the almost same behavior, as illustrated +in Figs. (7) and (8). In addition, the obtained QNMs have been presented in Tables I and +II under different physical parameter changes and shown that the results support Figs. (7) +and (8). +24 + +In our findings, we have discovered that all unstable modes exhibit superradiance and +all stable modes do not, consistent with the superradiant condition (45). This means that +scalar waves can experience superradiant amplification by extracting charge from the BH, +indicating that the BH geometry is unstable. Additionally, superradiance can also be used +to probe the fundamental principles of quantum gravity, such as the behavior of quantum +particles in the presence of strong gravitational fields. Through the study of superradiance, +researchers can gain a better understanding of the interplay between quantum mechanics +and general relativity, leading to new insights into the nature of space, time, and gravity. +And finally, we would like to state that we plan to extend this study to the fermionic +perturbations of the rotating BH of the non-linear Maxwell f(R) gravity in the near future. +[1] M. C. Braidotti, D. Faccio and E. M. Wright, Phys. Rev. Lett. 125, 193902 (2020). +[2] S. W. Hawking, Nature 248, 30 (1974). +[3] S. W. Hawking, Commun. Math. Phys. 43, 199 (1975) [erratum: Commun. Math. Phys. 46, +206 (1976)]. +[4] E. Mc Caughey, Eur. Phys. J. C 76, 179 (2016). +[5] R. Dicke, Phys. Rev. 93, 99110 (1954). +[6] Y. B. Zel’dovich Pis’ma Zh. Eksp. Teor. Fiz. 14, 270 (1971). [JETP Lett. 14, 180 (1971)]. +[7] Y. B. Zel’dovich Zh. Eksp. Teor. Fiz 62, 2076 (1972). [Sov.Phys. JETP 35, 1085 (1972)]. +[8] W. H. Press and S. A. Teukolsky, Nature (London) 238, 211 (1972). +[9] R. Brito, V. Cardoso, and P. Pani, Lect. Notes Phys. 906, 1 (2015). +[10] V. Cardoso, O. J. C. Dias, J. P. S. Lemos, and S. Yoshida, Phys. Rev. D 70, 044039 (2004) +[erratum: Phys. Rev. D 70, 049903 (2004)]. +[11] T. Damour, N. Deruelle, and R. Ruffini, Lett. Nuovo Cim. 15, 257 (1976). +[12] R. Brito, V. Cardoso and P. Pani, Class. Quant. Grav. 32, 134001 (2015). +[13] J. M. Bardeen, W.H. Press, and S.A. Teukolsky, Astrophys. J. 178, 347 (1972). +[14] A. A. Starobinsky, Zh. Eksp. Teor. Fiz. 64, 48 (1973). +[15] S. A. Teukolsky and W.H. Press, Astrophys. J. 193, 443 (1974). +[16] S. R. Dolan, Phys. Rev. D 87, 124026 (2013). +[17] J. H. Xu, Z. H. Zheng, M. J. Luo and J. H. Huang, Eur. Phys. J. C 81, 402 (2021). +25 + +[arXiv:2012.13594 [gr-qc]]. +[18] S. Biswas, Phys. Lett. B 820, 136597 (2021). [arXiv:2106.13837 [gr-qc]]. +[19] R. Brito, V. Cardoso and P. Pani, Physics,” Lect. Notes Phys. 971, 1 (2020). +[20] J. D. Bekenstein and M. Schiffer, Phys. Rev. D 58, 064014 (1998). +[21] V. Cardoso and O. J. C. Dias, Phys. Rev. D 70, 084011 (2004). +[22] S. W. Hawking and H. S. Reall, Phys. Rev. D 61, 024014 (2000). +[23] V. Cardoso, Gen. Rel. Grav. 45, 2079 (2013). +[24] P. Pani, V. Cardoso, L. Gualtieri, E. Berti, and A. Ishibashi, Phys. Rev. Lett. 109, 131102 +(2012). +[25] A. Arvanitaki and S. Dubovsky, Phys. Rev. D 83, 044026 (2011). +[26] S. J. Kapadia, D. Kennefick and K. Glampedakis, Phys. Rev. D 87, 044050 (2013). +N. Yunes, P. Pani and V. Cardoso, Phys. Rev. D 85, 102003 (2012). +[27] V. Cardoso, I. P. Carucci, P. Pani and T. P. Sotiriou, Phys. Rev. D 88, 044056 (2013). +[28] J. L. Friedman, Commun. Math. Phys. 63, 243 (1978). +[29] G. Moschidis, Commun. Math. Phys. 358, no.2, 437-520 (2018). +[30] R. Maartens, Living Rev. Relativ. 7, 7 (2004). +[31] G. R. Dvali, G. Gabadadze, and M. Porrati, Phys. Lett. B 485, 208 (2000). +[32] T. Jacobson, D. Mattingly, Phys. Rev. D 64, 024028 (2001). +[33] J. D. Bekenstein, Phys. Rev. D 70, 083509 (2004). +[34] S. Nojiri, S. D. Odintsov, eConf C0602061 (2006) 06; Int. J. Geom. Methods Mod. Phys. 04, +115 (2007). +[35] T. P. Sotiriou and V. Faraoni, Rev. Mod. Phys. 82, 451 (2010). +[36] A. De Felice and S. Tsujikawa, Living Rev. Relativity 13, 3 (2010). +[37] S. I. Nojiri and S. D. Odintsov, Phys. Rep. 505, 59 (2011). +[38] H. A. Buchdahl, Mon. Not. R. Astron. Soc. 150, 1 (1970). +[39] T. P. Sotiriou and S. Liberati, J. Phys.: Conf. Ser. 68, 012022 (2007). +[40] T. P. Sotiriou and S. Liberati, Ann. Phys. 322, 935 (2007). +[41] A. V. Frolov, Phys. Rev. Lett. 101, 061103 (2008). +[42] A. Upadhye and W. Hu, Phys. Rev. D 80, 064002 (2009). +[43] A. Cooney, S. DeDeo, and D. Psaltis, Phys. Rev. D 82, 064033 (2010). +[44] K. Bamba, S. Nojiri, and S. D. Odintsov, JCAP 0810, 045 (2008), arXiv:0807.2575 [hep-th]. +26 + +[45] A. A. Starobinsky, JETP Lett. 86, 157 (2007), arXiv:0706.2041 [astro-ph]. +[46] S. Nojiri and S. D. Odintsov, Phys. Rev. D 74, 086005 (2006), arXiv:hep-th/0608008 [hep-th]. +[47] S. Capozziello and S. Vignolo, Class. Quant. Grav. 26, 168001 (2009), arXiv:0903.3368 [gr-qc]. +[48] V. Faraoni, Classical and Quantum Gravity 26, 168002 (2009). +[49] G. J. Olmo and P. Singh, JCAP 0901, 030 (2009), arXiv:0806.2783 [gr-qc]. +[50] V. Faraoni and N. Lanahan-Tremblay, Phys. Rev. D 78, 064017 (2008). +[51] S. Nojiri and S. D. Odintsov, Phys. Rept. 505, 59 (2011), arXiv:1011.0544 [gr-qc]. +[52] S. Nojiri, S. D. Odintsov, and V. K. Oikonomou, Phys. Rept. 692, 1 (2017), arXiv:1705.11098 +[gr-qc]. +[53] G. G. L. Nashed and S. Capozziello, Phys. Rev. D 99, 104018 (2019), [arXiv:1902.06783 +[gr-qc]]. +[54] L. Hollenstein and F. S. N. Lobo, Phys. Rev. D 78, 124007 (2008), arXiv:0807.2325 [gr-qc]. +[55] S. Capozziello and M. De Laurentis, Phys. Rept. 509, 167 (2011). +[56] G. G. Nashed and E. N. Saridakis, Phys. Rev. D 102, 124072 (2020). +[57] ˙I. Sakallı and S. Kanzi, Turk. J. Phys. 46, 51 (2022). +[58] J. V. Rocha, JHEP 08, 027 (2009). +[59] T. Harmark, J. Natario, and R. Schiappa, Adv.Theor. Math. Phys.14, 727 (2010). +[60] L. Ford, Phys. Rev.D 12, 2963 (1975). +[61] S. Creek, O. Efthimiou, P. Kanti, and K. Tamvakis, Phys. Rev. D 76, 104013 (2007). +[62] S. Iyer, Phys. Rev. D 35, 12 (1987). +[63] S. Kanzi and ˙I. Sakallı, Eur. Phys. J. Plus 137, 14 (2022), [arXiv:2107.11776 [hep-th]]. +[64] S. Shankaranarayanan, Phys.Rev. D 67, 084026 (2003). +[65] P. Boonserm and M. Visser, Annals Phys. 325, 1328-1339 (2010).[arXiv:0901.0944 [math-ph]]. +[66] S. Kanzi and ˙I. Sakallı, Nucl. Phys. B 946, 114703 (2019). [arXiv:1905.00477 [hep-th]]. +[67] A. Al-Badawi, ˙I. Sakallı, and S. Kanzi, Annals Phys. 412, 168026 (2020). [arXiv:1907.10144 +[gr-qc]]. +[68] A. Al-Badawi, S, Kanzi, and ˙I. Sakallı, Eur. Phys. J. Plus 135, 219 (2020). +[69] S. Kanzi, S. H. Mazharimousavi, and ˙I. Sakallı, Ann. Phys. 422, 168301 (2020). +[70] Teukolsky S A 1973 Astrophys. J. 185 635–647 +[71] Vishveshwara CV. Nature. 1970;227:936–938. +[72] V. Ferrari and B. Mashhoon. Phys.Rev. D 30, 295–304 (1984). +27 + +[73] G. T. Horowitz and V. E. Hubeny. Phys. Rev. D 62, 024027 (2000). +[74] E. Berti and K. D. Kokkotas, Phys. Rev. D 67, 064020 (2003). +[75] B. P. Abbott et al, Phys. Rev. Lett. 116, 061102 (2016). +[76] G. Panotopoulos, Mod. Phys. Lett. A33 (2018) 23, 1850130 [arXiv:1807.03278 [gr-qc]]. +[77] K. Destounis, R. D. B. Fontana and F. C. Mena, Phys. Rev. D102 (2020) 4, 044005 +[arXiv:2005.03028 [gr-qc]]. +[78] S. Kanzi and ˙I, Sakallı, Eur. Phys. J. C 81, 501 (2021).[arXiv:2102.06303 [hep-th]]. +[79] S. Kanzi and ˙I, Sakallı, Eur. Phys. J. C 82, 93 (2022) +[80] B.P. Abbott et al, Astrophys. J. Lett. 892, L3 (2020). +[81] E. Berti, V. Cardoso, and A. O. Starinets, Class. Quant. Grav. 26 (2009), 163001 +[arXiv:0905.2975 [gr-qc]] +[82] R. A. Konoplya, Phys. Rev. D 66, 044009 (2002). [arXiv:hep-th/0205142 [hep-th]]. +[83] J. P. S. Lemos, Phys. Lett. B 353, 46 (1995). +[84] A. M. Awad, G. G. L. Nashed and W. El Hanafy, Eur. Phys. J. C 79, 668 (2019). +[85] G. T. Horowitz and V. E. Hubeny, Phys. Rev. D 62, 024027 (2000). +[86] P. A. Gonzales, A. Rincon, J. Saavedra, and Y. Vasquez, Phys. Rev. D 104, 084047 (2021). +[87] Y. G. Miao and Z. M. Xu, Phys. Lett. B 772, 542 (2017). +[88] B. Mashhoon, B. (1983). In Ning, H., editor, Third Marcel Grossmann Meeting on General +Relativity, pages 599–608. +[89] S. Iyer and C. M. Will, Phys. Rev. D 35, 12 (1987). +[90] S. Iyer, Phys. Rev. D 35, 12 (1987). +[91] R. A. Konoplya, A. Zhidenko, and A. F. Zinhailo, Class. Quant. Grav. 36, 155002 (2019). +28 + diff --git a/aNE2T4oBgHgl3EQfZgfV/content/tmp_files/load_file.txt b/aNE2T4oBgHgl3EQfZgfV/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..8503937b5558c69b3eed6c9050dbdd77872a97a9 --- /dev/null +++ b/aNE2T4oBgHgl3EQfZgfV/content/tmp_files/load_file.txt @@ -0,0 +1,1168 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf,len=1167 +page_content='HEP/123-qed Superradiant (In)stability, Greybody Radiation, and Quasinormal Modes of Rotating Black Holes in non-linear Maxwell f(R) Gravity Sara Kanzi∗ Faculty of Engineering, Final International University, Kyrenia, North Cyprus via Mersin 10, Turkey ˙Izzet Sakallı† Physics Department, Eastern Mediterranean University, Famagusta, 99628 North Cyprus via Mersin 10, Turkey (Dated: January 11, 2023;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Received) 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='03866v1 [hep-th] 10 Jan 2023 Abstract The research of superradiant instability in the realm of quantum gravity is a well-known topic, with many physicists and astronomers studying the potential impact it can have on gravitational waves, the structure of the universe, and spacetime itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In this work, we investigate the super- radiant (in)stability of a rotating black hole obtained from the nonlinear Maxwell f(R) gravity theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In this study, the evaluation of stability/instability is going to be based on non-existence and existence of magnetic field, when the magnetic field constant becomes c4 = 0 and c4 ̸= 0, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The analyzes of greybody factor (GF) and quasinormal modes (QNMs) are investi- gated in the stationary black hole spacetime both in the absence and presence of the magnetic field parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' To this end, we first consider the Klein-Gordon equation for the complex scalar field in the geometry of that rotating black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In the sequel, the obtained radial equation is reduced to a one-dimensional Schr¨odinger-like wave equation with an effective potential energy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The effects of the nonlinear Maxwell f(R) gravity theory parameters (q, c, and c4) on the effective potential, GFs, and QNMs are thoroughly investigated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The obtained results show that even though the factors q, c, and c4 all affect the effective potential, this phenomena, surprisingly, is not valid for the GFs and QNMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' With the proper graphics and tables, all outputs are depicted, tabulated, and interpreted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' ∗Electronic address: sara.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='kanzi@final.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='tr †Electronic address: izzet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='sakalli@emu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='tr 2 Contents I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Introduction 3 II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rotating BHs in Nonlinear Maxwell f(R) gravity 7 III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Scalar Perturbation 9 IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Superradiance Phenomenon 10 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' For c4 = 0 10 B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' For Infinitesimal c4 14 V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Semi-analytical Greybody Radiation 16 VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' QNMs 18 VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Conclusion 23 References 25 I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' INTRODUCTION Superradiance is a term used to describe a radiation amplification system that includes a scattering mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Superradiance plays a noteworthy role in the studies of relativity, astrophysics, quantum mechanics, and optics [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' This phenomenon can be considered as a quantum aspect of black hole (BH) physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Namely, in the context of quantum gravity phenomenology, superradiance can play a crucial role in the study of BHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' For example, the emission of Hawking radiation (or greybody radiation) [2, 3] from a BH can be enhanced by the presence of surrounding matter, leading to a process known as BH superradiance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' This phenomenon has been proposed as a possible explanation for the observed properties of BH systems, such as the large amounts of energy emitted from the centers of galaxies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Because it is influenced by the BH’s area theorem, tidal forces, the Penrose process, and Hawking radiation [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The concept of superradiance was first introduced by Dicke in 1954 [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Subsequently, in 1971, this phenomenon was further understood and developed by Zel’dovich [6, 7] during his investigation of reflected wave amplification from a rotating BH 3 (Kerr metric).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Zel’dovich proved that if the frequency ω of the ingoing wave having the plane wave structure with e−iΩt+imφ (Ω represents the angular velocity, φ is the cyclic coordinate, and m denotes the magnetic quantum number) convinces ω < mΩ, the scattered waves amplify in such a way that the waves coming out of the BH to become more than the ones entering to it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Namely, the dispersed wave is amplified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Combination of superradiance with a confining procedure to force the wave to consistently interact with the BH to undergo exponential increase known as ”BH bomb” [8], which has been an active case since 1970s [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' This phenomenon can be viable by considering a mirror around the rotating body that could make the system unstable [7, 10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In [11], it was mentioned that such a mirror can be recognized by applying a charged massive scalar field breeding in the Kerr-Newman spacetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Moreover, BHs can be transformed into efficient particle detectors by applying strong constraints to ultralight bosons via the superradiant instabilities of spinning BHs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' On the other hand, instability formation and whether or not its nonlinear time evolution follows the linear intuition are, nevertheless, topics that are not well-understood, yet [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' A Kerr BH might be thought as a strong candidate for superradiant phenomena [13–15], however BHs in Kerr form do not exhibit superradiant instabilities with significant growth rates [10, 16–18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In fact, there are various methods for using superradiance to extract energy from BHs: 1) BH fission [19], 2) BH bombs (as mentioned above) [8, 10], 3) Accretion disks and torus [20], 4) BH bombs in anti-de Sitter (AdS) spacetime [21, 22], 5) Massive fields, soft bombs, and particle physics [23–25], 6) Floating orbits [26], 7) Generalized scalar-tensor theories and superradiance [23, 27], 8) Ergoregion instability [28, 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' On the other hand, today, there are various theories for modified gravity, such as brane-world gravity [30], Dvali- Gabadadze-Porrati gravity [31], Einstein-Aether theory [32], tensor-vector-scalar theory [33], and f (R) gravity [34–37], which all attracted much attention in the literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' f(R) theories of gravity are straightforwardly generated by replacing Ricci scalar R in the Einstein-Hilbert action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Namely, we have a generic action for f(R) as follows S = 1 2k � d4x√−gf (R) , (1) where k = 8π denotes the gravitational constant and g is the determinant of met- ric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Throughout the paper, unless otherwise noted, we shall work in natural units with cs = G = ℏ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Since general relativity (GR) has had many unresolved problems, includ- 4 ing the existence of dark energy and dark matter, deflection from Einstein’s theory allows us to estimate the fundamental matters and extension of GR (modified gravity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Based on different formalisms, there are three types of f (R) gravity models: 1) metric, 2) Palatini, and 3) metric-affine, f(R) gravity [38–40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The use of f(R) gravity in many contexts is significant;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' for example, see its astrophysical perspective in [41–44], the cosmological models with f(R) in [45, 46], and the derivations of novel BH solutions in [47–50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Moreover, we refer the reader to the monographs [51, 52] for some good reviews about f(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In par- ticular, spherically symmetric BH solutions in f (R) gravity have been receiving special attentions (see for instance [53], in which the exact static spherically symmetric solutions in f (R) gravity coupled with nonlinear electrodynamics derived by Hollestein and Lobo [54]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Searching for alternative gravitational theories to conventional Einstein’s general relativity (GR) is supported by difficult challenges ranging from quantum gravity to dark energy and dark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Indeed, there are a lot of unresolved problems with GR, such as singularities, the nature of dark energy and dark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' All of these problems motivate researchers to improve or modify GR in order to address the challenges at the UV and IR scales [55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' However, the obtained feasible modified/extended theories should be consistent with the present observational/experimental restrictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' With the awareness of this issue, an am- bitious study has recently been carried out on the nonlinear Maxwell f(R) gravity [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' By using dynamical Ricci scalars that asymptotically converge to flat or (A)dS spacetimes, Nashed and Saridakis [56] have derived a new charged rotating BH solutions, which will be our main reference metrics in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Due to the quantum effects, a BH can act as a blackbody object, which emits thermal waves [2, 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The mass of a BH decreases during its HR, which can lead to complete BH evaporation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' As a matter of course, the emitted particles are affected by an effective potential originating from the curvature of the spacetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' As a result, although some waves penetrate the potential barrier and extend to infinity, the remainder is reflected back to the BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Due to the structure of the effective potential, the radiation spectra are altered and different from that near the event horizon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' As a result, the term GF [57] refers to a quantity that measures the deviation of the radiation spectrum from the blackbody radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' At the event horizon, the BH emission rate [58] is defined as follows γ (ω) = � d3k 8π3e ω TH � , (2) 5 by which ω represents the wave frequency, TH and k denote the Hawking temperature and surface gravity, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The relation between emission rate and GF is given by [59] γ (ω) = � d3k |Al,m|2 8π3e ω TH � , (3) where |Al,m|2 represents the GF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' There are various methods to compute the GF, such as matching technique [59–61], WKB approximation [62, 63], finding Bogoliubov coefficients method [64–67], the Miller–Good transformation method [57, 68], and the rigorous bounds [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Teukolsky equation [70] describes an oscillation system that naturally dissipates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Such a system generates QNMs instead of the classical normal mode solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Vishveshwara was the first to identify the QNMs of a BH [71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The QNMs are described by complex frequencies that carry characteristic information about the BH spacetime, which is in the ringdown phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The QNMs have broad literature in the BH physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Specifically, explicit superpositions of QNMs may be utilized to estimate the gravitational wave frequencies in the gravitational wave phenomenon [72–75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' There are many rich and excellent investigations on the QNMs of various solutions of BHs [76–79], which are considered seminal works of the subject [80–82].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The paper is divided into the following sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (II), we introduce the metric of the rotating BH in nonlinear Maxwell f (R) gravity and demonstrate some of its physical features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Section (III) is devoted to the Klein-Gordon equation (KGE) for charged massive scalar fields in that rotating BH geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In this section, we show that the radial wave equation reduces a one-dimensional Schr¨odinger-like wave equation with a corresponding effective potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' We also study the behaviors of the obtained effective potential under the influence of charge q and magnetic field constant c4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' As being two subsections, in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (IV), we examine the superradiant instability for zero and non-zero c4 values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Sections (V) and (VI) are reserved for the analysis of the greybody radiation and QNMs, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Our results are summarized and discussed in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (VII).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' We follow the metric convention (+, −, −, −).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 6 II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' ROTATING BHs IN NONLINEAR MAXWELL f(R) GRAVITY In this section, we briefly review both new static and rotating BH solutions obtained in nonlinear Maxwell f (R) gravity [56], whose the total action is given by St = 1 2k � √−gf(R)d4x + � √−gL(F)d4x, (4) where k is a gravitational constant, which can be considered as k = 1, without loss of gen- erality, in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' √−g represents the determinant of the metric gµν.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The corresponding gravitational field equations of the action (4) can be derived as follows ξµν = ℜµνfℜ − 1 2gµνf(ℜ) − 2gµνΛ + gµν∇α∇αfℜ − ∇µ∇νfℜ − 8πℑnlem µυ ≡ 0, (5) by which ℑnlem µυ denotes the energy momentum tensor and fℜ ≡ df(ℜ) dℜ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Using the following ansatz for a spherically symmetric line element: ds2 = H (r) dt2 − dr2 H (r) − r2 � dθ2 + sin2 θdϕ2� , (6) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (5), after making some tedious calculations, the following metric function was finally obtained by Nashed and Saridakis [56] H(r) = c 2 − 2M r + q2 r2, (7) where c is a positive constant, which can take limited values: 0 < c < 2, q and M stand for the charge and mass, respectively (see Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [56] for the details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (1), we show the behavior of the metric function H (r) under the influence of varying parameters q and c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' It is clearly seen that the spacetimes exhibit flatness at the asymptotic distances, independent of the values of q and c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The rotating version of the BH solution can be derived by applying the following trans- formations [83, 84] ∼ φ = Ξφ + at, ∼ t = Ξt + aφ, (8) to the static and spherically symmetric metric (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (8), a is the rotating parameter 7 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 1: Schematic plots of H(r) versus r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Solid lines represent c = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5 and dash lines are for c = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The physical parameters are chosen as M = m = 1, ω = 15, a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3, and λ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' and Ξ = √ 1 + a2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Thus, we have ds2 = [Ξ2H(r) − a2r2 sin2 θ]dt2 − dr2 H(r) − r2dθ2− [Ξ2r2 sin2 θ − a2H(r)]dφ2 + 2aΞ[H(r) − r2 sin2 θ]dtdφ, (9) in which H(r) is provided by the static solution (7) previously derived.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' On the other hand, the general gauge potential is defined by [56] ∼ V = [Ξq(r) + as(r)]d ∼ t + n(φ)dr + [aq(r) + Ξs(r)]d ∼ φ, (10) where q(r), s(r), and n(φ) are 3 free functions generating the electric and magnetic charges in the vector potential as follows s(r) = c4r, n(φ) = c4φ, (11) in which c4 represents the magnetic field constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In the following sections, our investigation will consider cases in which the magnetic field constant does not exist (c4 = 0) and exists (c4 ̸= 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 8 III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' SCALAR PERTURBATION In recent decades, perturbations of BHs and stars have arisen as one of the main topics of relativistic astrophysics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Furthermore, perturbations are hot subjects right now because of their functions in gravitational waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In this part, we employ the charged KGE to arrive at the Schr¨odinger wave equation in one dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The effective potential to be obtained in this section is crucial for studying superradiance, greybody radiation, and QNMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Let us consider the charged and massive KGE: 1 √−g (∂µ − iQAµ) �√−ggµν (∂µ − iQAν) Ψ � = m2Ψ, (12) where Q and m are the charge and mass of the scalar field (spin-0), respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Moreover, √−g represents the determinant of the metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Here, for metric (9), we consider the following ansatz for the spinor field: Ψ = e−iωteikφR (r) Y (θ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (13) During the derivation of the scalar wave equation, we will consider the dyonic case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Plus, we set s(r) = n(φ) = 0 in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Thus, the components of the vector potential read A∼ t = Ξq, and A∼ φ = aq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (14) Throughout the paper, without loss of generality, we shall consider qQ → q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' After substi- tuting Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (14) and ansatz (13) into the massive charged KGE (12), one can obtain �2H r + H′ � R′ (r) + HR′′ (r) + 1 H � Ξ2ω2 + Ξ4q4 + 2q2ωΞ3 + 2aωΞk + 2aΞ2q2k − 2a2Ξ2q4− 2ωa2q2Ξ + a2k2 + a4q4 − 2kq2a3 + m2 + λ � R (r) = −λ, (15) where λ is the eigenvalue whose value can be found with the help of the angular part: cot θYθ (θ) + Yθθ (θ) − (aω + Ξk)2 sin2 θ Y = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (16) In the mean time, throughout the paper, a prime (dash) symbol is used to denote the derivative of a function with respect to its argument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' By considering the definition of the tortoise coordinate: r∗ = � dr H (r), (17) 9 and in the sequel applying the transformation R(r) = U(r) r to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (16), one can acquire one-dimensional Schr¨odinger like wave equation as follows: d2U (r) dr2 ∗ + � ϖ2 − Veff � U (r) = 0, (18) in which ϖ2 = ω2 (1 + a2) = ω2Ξ2 and the effective potential is given by Veff = −2Ξ � q2 + ak � ω − � q2 + ak �2 + HH′ r + λH r2 + m2H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (19) The behaviors of the effective potential (19) when the charge parameter q is changed for various values of c are depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' , FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 2: Plots of Veff versus r for the spin-0 particles in the case of zero magnetic constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The physical parameters are chosen as;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' M = m = 1, ω = 15, a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3, and λ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' IV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' SUPERRADIANCE PHENOMENON A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' For c4 = 0 Here, we investigate the stability of the rotating BH obtained from the non-linear Maxwell f (R) gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' To this end, we consider the method prescribed in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [85, 86].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' After applying 10 the transformation U (r) = e−iϖr∗ψ (r) to the Schr¨odinger equation seen in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (18), one gets d2ψ (r) dr2 ∗ − 2iϖdψ (r) dr∗ − Veffψ (r) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (20) Now, let us replace the tortoise coordinate (17) with the naive radial coordinate r d dr � H dψ dr � − 2iϖdψ dr − Veff H ψ = 0, (21) and multiply Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (21) by ψ∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' By imposing H (r+) = 0 and ψ (∞) = 0, one can solve the final differential equation by performing the well-known integration by parts method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Thus, we get � ∞ rh dr � H ���� dψ dr ���� 2 + 2iϖψ∗dψ dr + Veff H |ψ|2 � = 0, (22) where the second term in the integrand can be expanded to 2iϖdψ dr = ϖψ∗dψ dr + −ϖψdψ∗ dr .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (23) Therefore, the integration (22) recasts in � ∞ rh dr � H ���� dψ dr ���� 2 + Veff H |ψ|2 � = −|ϖ|2 |ψ (rh)|2 Im ω .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (24) It is also possible to write Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (24) as � ∞ rh dr � H ���� dψ dr ���� 2 + ∼ V eff H |ψ|2 − (q2 + ak)2 H |ψ|2 − 2Ξ (q2 + ak) ω H |ψ|2 � = −|ϖ|2 |ψ (rh)|2 Im ω .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (25) In Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (25), ∼ V eff stands for the potential terms without q parameter in Veff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In addition, it is discovered that the final term of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (25) has almost no impact on superradiance calculations and the sign of expression ∼ V eff H |ψ|2 − (q2+ak) 2 H |ψ|2 is critical for evaluating the stability of the black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Meanwhile, the potential (19) is positive outside the horizon, which means Im(ω) must be negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Thus, in light of the Dirichlet boundary conditions, one can conclude that the scalar field propagation will be stable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In order to assess the superradiant instability of the rotating black hole in non-linear Maxwell f (r) gravity in a more authentic form, we shall define the reflection/transmission coefficients to determine the superradiant condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' To this end, we shall perform our computations in three different regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The first region (Region I) is the region that is close to the event horizon (r ≈ rh) , where the potential is approximated to Veff ≈ −2Ξ � q2 + ak � ω − � q2 + ak �2 , (26) 11 and correspondingly ∼ V eff ≪ � ωΞ + � q2 + ak ��2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (27) Thus, in Region I, the solution of the radial equation (18) is obtained as U1 (r) = Ae−i(ωΞ+(q2+ak))r∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (28) which slightly away from the event horizon yields [86] U1 (r) ≈ A � 1 − i (ωΞ + (q2 + ak)) H′ (rh) ln (r − rh) � , (29) where the near horizon tortoise coordinate is defined as r∗ = � dr H(r) ≈ 1 H′(rh) ln (r − rh).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Between the event horizon and the distant regions, Region II acts as an intermediate zone and is defined as: ∼ V eff ≫ � ωΞ + � q2 + ak ��2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (30) Therefore, the radial equation (18) reads d2U dr2 ∗ = 0, ⇒ U (r∗) = B + C � dr∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (31) By comparing the solutions in the first and second regions, we define the constants as as A = B, and C = −Ai (ωΞ + (q2 + ak)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' To find the solution in Region II, we take into consideration an asymptotic series for tortoise coordinate i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=', r ≫ rh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Hence, we get U2 (r) = A � 1 − i (ωΞ + (q2 + ak)) 4r4 ∼ k � , (32) where ∼ k = − 32 c2r5 � 32M 3cq2 − 3Mc2q4 − 64M 5� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (33) The third region (Region III) is the asymptotic zone (r ≫ rh,), where the conducting terms of the effective potential become Veff ≈ −2Ξ � q2 + ak � ω − � q2 + ak �2 + m2c 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (34) Thus, one can get the Region III solution as U3 (r) = D1 + D2e−i � (ωΞ+(q2+ak))2+ m2c 2 r∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (35) 12 Then, after matching the solution of Region II with the solution of Region III, we get D2 = Ae i ∼ k 4r4 η, (36) where η = m2c 4(ωΣ + (q2 + ak)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (37) To obtain the reflection coefficient and the GFs and to complete our assessment of superra- diant stability/instability, we employ the flux expression as follows F = √−ggrr 2i (U ∗∂rU − U∂rU ∗) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (38) Therefore, one can obtain the near horizon flux as Fhor ∝ −A2 � ωΞ + � q2 + ak �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (39) Similarly, the asymptotic flux at spatial infinity becomes F∞ ∝ −ξ � 1 + D1 2 � D2e−iξ + D∗ 2eiξ�� , (40) where ξ = � (ωΞ + (q2 + ak))2 + m2c 2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' By considering D1 = ˆ D1 + ˆ D2 and D2 = i( ˆ D2 − ˆ D1), the asymptotic incoming and outgoing fluxes (40) can be written as follows F∞−in ∝ −ξ � 1 − i | D2 |2 sinh(iξ) � , (41) and F∞−out ∝ −ξ � 1 + i | D1 |2 sinh(iξ) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (42) By employing the definition of the reflection coefficient and GF, we get R =| F∞−out F∞−in |= �1 + iA2 1sinh(iξ) 1 − iA2 1sinh(iξ) � , (43) and γ = Fhor F∞−in = A2 (ωξ + (q2 + ak)) ξ (1 − iA2 1sinh(iξ)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (44) Now, based on Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (43) and (44), we are able to determine the superradiant condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' To this end, either the reflection coefficient should be greater than 1 or the GF should be negative: ω ≤ −(q2 + ak) ξ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (45) 13 By taking into account superradiant instability conditions, in the relevant sub-cases, we now review the behavior of the effective potential in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' It is obvious from Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (2) that the potential does not contain wells and hence there are no bound states, which can prevent the accumulation of energy that might cause the instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' This indicates that the rotating BH in non-linear Maxwell f(R) gravity can readily absorb the charged scalar wave and whence the associated background becomes stable under the charged scalar perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' For Infinitesimal c4 In this sub-section, our aim is to evaluate the superradiant stability/instability of the stationary BH found in the non-linear Maxwell f(R) gravity with the case of c4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' However, we shall choose the magnetic field constant to be infinitesimally small to facilitate calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Moreover, we shall determine the effective potential with the aid of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (20), not from the Schr¨odinger equation as it was done in the previous sub-section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' So, following the steps we did earlier, we get d dr(H(r)dΨ dr ) − 2i¯ωdΨ dr − Veff H(r)Ψ = 0, (46) where ¯ω = H(ω + qc4φ) and the effective potential is determined as a complex expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In Region 3, its real part can be expressed as Re[Veff] ≈ −H2ω2 + HH′ r − 2qc4φH2ω + (ωΞ + (q2 + ak))2 − H( λ r2 − m2), (47) and its imaginary part reads Im[Veff] ≈ −ωH′H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (48) In Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (47) and (48), the terms including c2 4 and c4 r2 are ignored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In addition, our analysis has shown us that it is reasonable to consider only the real component of the effective potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The wave solutions of Regions 1 and 2 for the existing magnetic fields of the BH are the same as the non-existing ones, Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (28) and (32), but the wave solution of Region 3 (r >> rh) with c4 ̸= 0 is different than the c4 = 0 one: U3(r) = D1 + D2 exp � �−i � Veff(3) ∼ k 4r4 � � r∗, (49) 14 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 3: Plots of Veff versus r for the spin-0 particles and non-zero c4,.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The solid lines represent the effective potential for q = 3 and the dashed ones stand for q = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The physical parameters are chosen as;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' M = m = c = 1, ω = 10, a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='1, and λ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' where Veff(3) = −ω2c4 4 − 1 2(qc4φc2ω − m2c) + (ωΞ + (q2 + ak))2, (50) and ∼ k is nothing but Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Comparing Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (49) with the solution obtained for Region 2 � Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (32) � , one can determine the unknown constants as D1 = A and D2 = A exp � i ∼ k 4r4 ∼η � , (51) in which ∼η = 2m2c − 2qc4φc2ω − ω2c4 8 � ωΞ + (q2 + ak) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (52) To determine the flux expressions at the horizon and spatial infinity, we apply the same method followed in the previous sub-section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Thus, we have Fhor ∝ −(ωΞ + (q2 + ak))|A|2, (53) 15 and F∞ ∝ − � 1 + D1 2 (D2e−iβ + D∗ 2eiβ) � , (54) where β = � Veff(3) ∼ k 4r4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (55) By substituting D1 = ˆ D1 + ˆ D2 and D2 = i( ˆ D2 − ˆ D1) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (54), one can obtain F∞−in ∝ −β(1 − i| ˆ D2|2 sinh(iβ)), (56) F∞−out ∝ −β(1 + i| ˆ D1|2 sinh(iβ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (57) Therefore, the reflection coefficient of the rotating BH with small c4 reads |R| = |F∞−out F∞−in | = � 1 + i| ˆ D1|2 sinh(iβ) 1 − i| ˆ D2|2 sinh(iβ) � , (58) and the corresponding GF becomes γ = Fhor F∞in = (ωΞ + (q2 + ak))|A|2 β � 1 + i| ˆ D1|2 sinh(iβ) �.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (59) Since the result is almost the same as Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (44), Moreover, no explicit well in the effective potential behavior in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (3), the interpretation for the stability in the presence of a magnetic field will be the same as the nonexistent one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' SEMI-ANALYTICAL GREYBODY RADIATION In this section, we shall follow the method, which was reviewed in [57] (and references therein) to analyze the greybody radiation for both cases of cs = 0 and c4 ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The general semi-analytic bounds for GFs are given by [87] σl (ω) ⩾ sec h2 �� ∞ −∞ ℘dr∗ � , (60) where σl represents the GF and ℘ is formulated as follows ℘ = � (h′)2 + [ω2 − V − h2]2 2h , (61) by which h is a positive function that satisfies the following condition: h (−∞) = h (+∞) = ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Normally, one follows the method of replacing the V parameter with the 16 potential obtained in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (34) and then employs the tortoise coordinate to evaluate the GF (60).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' On the other hand, that method is not always the best course of action to take.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In fact, this method also fails in our situation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' So, to overcome this discrepancy, we set h = √ ω2 − V in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (61).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' This allows us to rewrite the expression for GF (60) as σl (ω) ⩾ sec h2 �1 2 � ∞ −∞ ���� h′ h ���� dr∗ � , (62) which corresponds to σl (ω) ⩾ sec h2 � ln �hpeak h∞ �� = sec h2 � ln �� ω2 − Vpeak ω �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (63) One can immediately observe that Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (63) is valid for ω2 > Vpeak, the peak value of the potential [57].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Besides, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (63) can be rewritten as σl (ω) ⩾ 4ω2 (ω2 − Vpeak) (2ω2 − Vpeak)2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (64) To find the maximum or the peak of the potential, as is well-known, one should find where the graph shifts from increasing to decreasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' To find out the rate at which the graph shifts from increasing to decreasing, we look at the second derivative and see when the value changes from positive to negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Depending on the values of Vpeak, the GFs are obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' For instance, by setting M = m = 1 and λ = 2, in relation to the variables q and c, the Vpeak expression is given by Vpeak ≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='00757c − (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='08987c + 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='0257) q2 + 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='18115 − 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='05389q4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (65) Substituting Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (65) to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (64), we first compute the GFs of the rotating BH in non- linear Maxwell f (R) gravity with c4 = 0 for various parameters of c and q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The behaviors of the obtained GFs for c4 = 0 are illustrated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' It is worth noting that although c values should obey 0 < c < 2 due to Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [56], we have used the values of c above the relevant limit for the sake of revealing the changes in the GF behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' This by purpose exaggeration is made for just exhibiting the differences in the GF behaviors that are almost indistinguishable from each other within the theoretical limit of 0 < c < 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (4) shows a growth in the GF with q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5 by increasing the c factor, but by increasing the charge value q this course of action altered in the opposite direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In a same circumstance, for 17 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 4: Plots of σl (ω) versus ω for scalar particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='The physical parameters are chosen as;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' M = m = 1, a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='1 and λ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' infinitesimal c4 case, Vpeak is found to be Vpeak ≈ −A2(100 + 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='80qc4) + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='2493046A(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='1243055 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='0309899q2)+ (10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='150 + q2)2 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='439065 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='054427q2, (66) where A = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='501391 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='0621528q2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' After substituting Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (66) in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (64), the obtained greybody radiation is depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (5), which shows that the greybody radiation explicitly increases with the magnetic field parameter c4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' VI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' QNMs QNMs are important in the study of BH perturbation because they provide a way to understand the behavior of a BH in the presence of external perturbations such as a scalar, electromagnetic, gravitational, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' When a BH is perturbed, it will respond by emitting gravitational waves that have a characteristic frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' This frequency, known as the QNM, is determined by the properties of the BH, such as its mass, charge, and spin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' QNMs of a BH is characterized by complex numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The complex frequency of a QNM is given by a real 18 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 5: Plots of σl (ω) versus ω for scalar particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The dotted lines are represented for q = 3 and solid lines for q = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The physical parameters are chosen as;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' M = m = k = 1, a = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='1, and λ = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' part and an imaginary part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The real part represents the oscillatory frequency of the mode, while the imaginary part represents the rate of decay or growth of the mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' By observing the QNMs in gravitational waves, astronomers can learn about the physical characteristics of the object that produced the waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In this section, for the scalar perturbations, we consider a semi-analytical approach to derive the frequencies of the QNMs of the charged rotating BHs in nonlinear Maxwell f (R) gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' To this end, we employ the WKB (Wentzel-Kramers-Brillouin) approximation, which is a mathematical method used to solve differential equations (DEs) with a large- scale parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' This approximation allows for a simplified solution to the differential equation and provides an estimate of the energy levels (frequency) within a certain accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Conventionally, the WKB approach is based on the assumption that the solutions can be expressed as an exponential power series, where the coefficients of the series are determined by solving a set of recursive equations: Ψ (r) ≈ exp � 1 ϵ ∞ � n=0 ϵnSn (r) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' ϵ → 0 (67) 19 The DE has a general form as d2Ψ (r) dr2 = Q (r) Ψ (r) , (68) where Q (r) = V (r) − ω2, which contains two turning points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The boundary condi- tion of waves is chosen to be Ψ (r) = ZoutΨ (r)out for outgoing waves as r∗ → +∞ and Ψ (r) = ZinΨ (r)in for incoming waves while r∗ → −∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' First, Mashhoon [88] invented this approach and applied it to the BHs in 1983.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Then it was developed by [89, 90].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The WKB approximation can be extended from the third to sixth order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The sixth-order WKB approximation, also known as the Konoplya approximation, is a method used to approxi- mate the solutions of differential equations with complex potentials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The sixth order WKB approximation by Konoplya can be found in his seminals paper [82, 91].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The Konoplya approximation uses a series expansion of the solution to the DE in powers of the small pa- rameter ϵ, which is the wavelength of the solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Konoplya approximation for obtaining the complex frequencies of the QNMs is given by the following expression [82]: ω2 = � V0 + � −2V ′′ 0 Λ (n) − i � n + 1 2 � � −2V ′′ 0 (1 + Ω (n)) � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (69) where Λ (n) = 1 � −2V ′′ 0 � 1 8 � V (4) 0 V ′′′ 0 � �1 4 + α2 � − 1 288 �V ′′′ 0 V ′′ 0 �2 � 4 + 60α2� � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (70) and Ω (n) = 1 (−2V ′′ 0 ) � 5 6912 �V ′′′ 0 V ′′ 0 �4 � 77 + 188α2� − 1 384 � V ′′′ 0 2V (4) 0 V ′′ 0 (3) � � 51 + 100α2� + 1 2304 � V (4) 0 V ′′ 0 �2 � 67 + 68α2� + 1 288 � V ′′′ 0 V (5) 0 V ′′ 0 (2) � � 19 + 28α2� − 1 288 � V (6) 0 V ′′ 0 � � 5 + 4α2� � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (71) In Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (69)-(71), the primes and superscripts (4, 5, 6;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' for the higher order derivatives) denote the differentiation with respect to r∗ and α = n + 1 2, where n denotes the tone number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' By considering the effective potentials of both solutions, the results are tabulated in Tables (I) and (II) for the zero and non-zero magnetic field constants, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The behaviors of the QNMs for c4 = 0 are illustrated in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' One can observe that both parts (real and imaginary) of the QNMs decrease by increasing the charge parameter, 20 l n c q ωBosons n q ωBosons 1 0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3531092772-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='4070157966i 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='4628156990-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8165375596i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3481646244-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3984431959i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='4939092271-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7872487864i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3419910035-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3882796385i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5140501121-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7543542970i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3344221195-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3764501224i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5242699290-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7181651739i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3252048163-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3627849969i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5254316095-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='6791172459i 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3139459780-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3469628546i 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5180125636-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='6375332598i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='4171149837-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='4733886692i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='4883526041-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9338811423i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='4079913458-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='4593160345i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5382395015-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8962742366i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3965522968-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='4425772439i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5699039647-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8530833387i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3822146829-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='4227292265i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5845200557-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8033010248i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3639735647-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3989634900i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5823209373-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7458662456i 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3398557041-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3697577443i 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5612257904-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='6787904390i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3852295784-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='445685725i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='4230520984-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9161599009i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3780735086-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='4337333922i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='4903805959-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8746300965i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3690969050-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='4195188351i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5318064233-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8285691459i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3581027910-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='4029669396i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5522314188-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7775780030i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3446888390-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3837822213i 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5553476661-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7223112093i 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3281070990-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3613035399i 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5432743870-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='6634326053i TABLE I: Bosonic QNMs of rotating BH in non-linear Maxwell f(R) gravity for zero magnetic field parameter: c4 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Moreover, for n = 0, QNMs increase by growing the c parameter and then start to decrease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In addition, when n = 1 and q increases, the oscillation frequencies rise and the damping mode steadily declines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' On the other hand, for the case of c4 ̸= 0, both parts of the QNMs decrease by increasing the magnetic field constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The corresponding behaviors are depicted in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (7) and (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 21 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 6: Plots of QNMs of the rotating BH with c4 = 0 under varying charge parameter q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The dotted line represents c = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9 and dashed line stands for c = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' both for n = 0 (left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The solid line is for c = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9, however, the dotted line stands for c = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' both for n = 1 (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' c c c c c c c c c c c c c c c c c c FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 7: Plots of QNMs of the rotating BH under varying c4 values and fix charge q = 1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' for the tones of n = 0 (left) and n = 1 (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 22 l n q c4 ωBosons n c4 ωBosons 1 0 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5689309522-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5679607840i 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9833280391-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9857933522i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='011 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5676889204-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5667273000i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='011 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9811788557-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9836281427i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='012 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5664589707-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5655057950i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='012 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9790776944-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9815108377i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='013 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5652237736-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5642789170i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='013 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9769537380-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9793708001i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='014 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5639890661-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5630524167i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='014 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9748305274-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9772315143i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='015 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5627548196-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5618262697i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='015 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9727080152-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9750929361i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='016 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5615210087-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5606004477i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='016 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9705861561-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9729550175i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='017 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5602875984-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='559374939322i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='017 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9684648987-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9708177181i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='018 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5590545741-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5581496853i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='018 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9663442042-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='9686809854i 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7806931526-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7847869409i 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='01 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='348548830-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='362771574i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='011 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7850205043-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7891179837i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='011 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='356111851-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='370209477i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='012 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7891946437-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7932951529i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='012 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='363406512-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='377383600i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='013 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7932235382-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7973263608i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='013 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='370446745-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='384307536i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='014 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='7971145023-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8012189424i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='014 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='377245378-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='390993848i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='015 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8008742877-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8049796989i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='015 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='383814279-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='397454164i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='016 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8045091827-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8086149183i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='016 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='390164462-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='403699260i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='017 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8080250159-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8121304478i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='017 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='396306156-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='409739150i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='018 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8114272287-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='8155317201i 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='018 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='402248881-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='415583157i TABLE II: Bosonic QNMs of rotating BH in non-linear Maxwell f(R) gravity for infinitesimal magnetic field parameter c4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' , VII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' CONCLUSION In this paper, we have studied the superradiant instability/stability of a rotating BH in non-linear Maxwell f(R) gravity under the influences of q, c, and c4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' To examine the (in)stability in this spacetime under the Dirichlet boundary condition, we have expanded the solutions into three different regions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' near the event horizon (Region 1), intermediate (Region 2), and asymptotic (Region 3) regions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' We next used the semi-analytic method outlined in Sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' V to determine the GFs of the BH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' To this end, we have followed a less problematic 23 c c c c c c c c c c c c c c c c c c FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 8: Plots of QNMs of the rotating BH under varying c4 values and fix charge q = 2;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' for the tones of n = 0 (left) and n = 1 (right).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' method and replaced the expression h = √ ω2 − V with Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (61) to reach Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (63) or Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (64).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Then by defining the Vpeak, the GFs of the rotating BH in non-linear Maxwell f(R) gravity with/without magnetic field constant have been computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The results obtained have been depicted in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (4) to reveal the effects of q and c parameters on the GFs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The supreme point in the GFs behavior belongs to the c = 1 and q = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='5, thereafter, by increasing the values of both c and q the GFs decrease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' To analyze the QNMs originated from the scalar perturbations of the rotating BH in non-linear Maxwell f(R) gravity with/without magnetic field constant, we have considered the 6th order WKB approximation or the so-called Konoplya approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' The results obtained have been both tabulated and illustrated in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (6) and (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Thus, we have shown the influence of q and c parameters on the QNMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' According to the relevant results, the QNMs with n = 0 case have more stability than n = 1 state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Similar to the real part of the QNMs, which decrease when the charge parameter is increased, the damping rate component (imaginary part) of the QNMs exhibits the almost same behavior, as illustrated in Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (7) and (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In addition, the obtained QNMs have been presented in Tables I and II under different physical parameter changes and shown that the results support Figs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (7) and (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 24 In our findings, we have discovered that all unstable modes exhibit superradiance and all stable modes do not, consistent with the superradiant condition (45).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' This means that scalar waves can experience superradiant amplification by extracting charge from the BH, indicating that the BH geometry is unstable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Additionally, superradiance can also be used to probe the fundamental principles of quantum gravity, such as the behavior of quantum particles in the presence of strong gravitational fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Through the study of superradiance, researchers can gain a better understanding of the interplay between quantum mechanics and general relativity, leading to new insights into the nature of space, time, and gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' And finally, we would like to state that we plan to extend this study to the fermionic perturbations of the rotating BH of the non-linear Maxwell f(R) gravity in the near future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [1] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Braidotti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Faccio and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Wright, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 125, 193902 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [2] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Hawking, Nature 248, 30 (1974).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [3] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Hawking, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 43, 199 (1975) [erratum: Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 46, 206 (1976)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [4] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Mc Caughey, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' C 76, 179 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [5] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Dicke, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 93, 99110 (1954).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [6] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Zel’dovich Pis’ma Zh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Eksp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Teor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Fiz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 14, 270 (1971).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [JETP Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 14, 180 (1971)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [7] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Zel’dovich Zh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Eksp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Teor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Fiz 62, 2076 (1972).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [Sov.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' JETP 35, 1085 (1972)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [8] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Press and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Teukolsky, Nature (London) 238, 211 (1972).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [9] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Brito, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Cardoso, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Pani, Lect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Notes Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 906, 1 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [10] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Cardoso, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Dias, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Lemos, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Yoshida, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 70, 044039 (2004) [erratum: Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 70, 049903 (2004)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [11] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Damour, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Deruelle, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Ruffini, Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Nuovo Cim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 15, 257 (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [12] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Brito, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Cardoso and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Pani, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 32, 134001 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [13] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Bardeen, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Press, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Teukolsky, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 178, 347 (1972).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [14] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Starobinsky, Zh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Eksp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Teor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Fiz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 64, 48 (1973).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [15] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Teukolsky and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Press, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 193, 443 (1974).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [16] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Dolan, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 87, 124026 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [17] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Xu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Zheng, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Luo and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Huang, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' C 81, 402 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 25 [arXiv:2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='13594 [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [18] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Biswas, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' B 820, 136597 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [arXiv:2106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='13837 [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [19] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Brito, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Cardoso and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Pani, Physics,” Lect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Notes Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 971, 1 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [20] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Bekenstein and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Schiffer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 58, 064014 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [21] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Cardoso and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Dias, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 70, 084011 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [22] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Hawking and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Reall, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 61, 024014 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [23] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Cardoso, Gen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 45, 2079 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [24] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Pani, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Cardoso, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Gualtieri, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Berti, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Ishibashi, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 109, 131102 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [25] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Arvanitaki and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Dubovsky, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 83, 044026 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [26] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Kapadia, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Kennefick and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Glampedakis, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 87, 044050 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Yunes, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Pani and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Cardoso, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 85, 102003 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [27] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Cardoso, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Carucci, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Pani and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Sotiriou, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 88, 044056 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [28] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Friedman, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 63, 243 (1978).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [29] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Moschidis, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 358, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='2, 437-520 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [30] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Maartens, Living Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Relativ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 7, 7 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [31] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Dvali, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Gabadadze, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Porrati, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' B 485, 208 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [32] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Jacobson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Mattingly, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 64, 024028 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [33] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Bekenstein, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 70, 083509 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [34] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Nojiri, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Odintsov, eConf C0602061 (2006) 06;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Int.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Methods Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 04, 115 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [35] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Sotiriou and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Faraoni, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 82, 451 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [36] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' De Felice and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Tsujikawa, Living Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Relativity 13, 3 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [37] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Nojiri and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Odintsov, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 505, 59 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [38] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Buchdahl, Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 150, 1 (1970).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [39] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Sotiriou and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Liberati, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' : Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 68, 012022 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [40] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Sotiriou and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Liberati, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 322, 935 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [41] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Frolov, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 101, 061103 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [42] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Upadhye and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Hu, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 80, 064002 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [43] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Cooney, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' DeDeo, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Psaltis, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 82, 064033 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [44] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Bamba, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Nojiri, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Odintsov, JCAP 0810, 045 (2008), arXiv:0807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='2575 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 26 [45] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Starobinsky, JETP Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 86, 157 (2007), arXiv:0706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='2041 [astro-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [46] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Nojiri and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Odintsov, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 74, 086005 (2006), arXiv:hep-th/0608008 [hep-th].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [47] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Capozziello and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Vignolo, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 26, 168001 (2009), arXiv:0903.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='3368 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [48] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Faraoni, Classical and Quantum Gravity 26, 168002 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [49] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Olmo and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Singh, JCAP 0901, 030 (2009), arXiv:0806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='2783 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [50] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Faraoni and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Lanahan-Tremblay, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 78, 064017 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [51] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Nojiri and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Odintsov, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 505, 59 (2011), arXiv:1011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='0544 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [52] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Nojiri, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Odintsov, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Oikonomou, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 692, 1 (2017), arXiv:1705.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='11098 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [53] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Nashed and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Capozziello, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 99, 104018 (2019), [arXiv:1902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='06783 [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [54] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Hollenstein and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Lobo, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 78, 124007 (2008), arXiv:0807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='2325 [gr-qc].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [55] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Capozziello and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' De Laurentis, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 509, 167 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [56] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Nashed and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Saridakis, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 102, 124072 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [57] ˙I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Sakallı and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Kanzi, Turk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 46, 51 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [58] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rocha, JHEP 08, 027 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [59] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Harmark, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Natario, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Schiappa, Adv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='14, 727 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [60] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Ford, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='D 12, 2963 (1975).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [61] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Creek, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Efthimiou, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Kanti, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Tamvakis, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 76, 104013 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [62] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Iyer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 35, 12 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [63] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Kanzi and ˙I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Sakallı, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Plus 137, 14 (2022), [arXiv:2107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='11776 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [64] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Shankaranarayanan, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 67, 084026 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [65] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Boonserm and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Visser, Annals Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 325, 1328-1339 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [arXiv:0901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='0944 [math-ph]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [66] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Kanzi and ˙I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Sakallı, Nucl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' B 946, 114703 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [arXiv:1905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='00477 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [67] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Al-Badawi, ˙I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Sakallı, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Kanzi, Annals Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 412, 168026 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [arXiv:1907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='10144 [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [68] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Al-Badawi, S, Kanzi, and ˙I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Sakallı, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Plus 135, 219 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [69] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Kanzi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Mazharimousavi, and ˙I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Sakallı, Ann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 422, 168301 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [70] Teukolsky S A 1973 Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 185 635–647 [71] Vishveshwara CV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 1970;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='227:936–938.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [72] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Ferrari and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Mashhoon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 30, 295–304 (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 27 [73] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Horowitz and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Hubeny.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 62, 024027 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [74] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Berti and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Kokkotas, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 67, 064020 (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [75] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Abbott et al, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 116, 061102 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [76] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Panotopoulos, Mod.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' A33 (2018) 23, 1850130 [arXiv:1807.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='03278 [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [77] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Destounis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Fontana and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Mena, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D102 (2020) 4, 044005 [arXiv:2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='03028 [gr-qc]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [78] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Kanzi and ˙I, Sakallı, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' C 81, 501 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [arXiv:2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='06303 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [79] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Kanzi and ˙I, Sakallı, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' C 82, 93 (2022) [80] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Abbott et al, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 892, L3 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [81] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Berti, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Cardoso, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Starinets, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 26 (2009), 163001 [arXiv:0905.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content='2975 [gr-qc]] [82] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Konoplya, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 66, 044009 (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [arXiv:hep-th/0205142 [hep-th]].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [83] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Lemos, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' B 353, 46 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [84] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Awad, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Nashed and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' El Hanafy, Eur.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' C 79, 668 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [85] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Horowitz and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Hubeny, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 62, 024027 (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [86] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Gonzales, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rincon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Saavedra, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Vasquez, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 104, 084047 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [87] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Miao and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Xu, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' B 772, 542 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [88] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Mashhoon, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' (1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' In Ning, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=', editor, Third Marcel Grossmann Meeting on General Relativity, pages 599–608.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [89] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Iyer and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Will, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 35, 12 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [90] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Iyer, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' D 35, 12 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' [91] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Konoplya, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Zhidenko, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Zinhailo, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Quant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 36, 155002 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} +page_content=' 28' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/aNE2T4oBgHgl3EQfZgfV/content/2301.03866v1.pdf'} diff --git a/b9FPT4oBgHgl3EQfBTTg/vector_store/index.faiss b/b9FPT4oBgHgl3EQfBTTg/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..544d5890900cc2d98daec9733be50f37842fecd5 --- /dev/null +++ b/b9FPT4oBgHgl3EQfBTTg/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:34b92671de03c90e4931e4c8cebe4f0cb3f059745a19fa12d6672cab1afa61b9 +size 5701677 diff --git a/b9FPT4oBgHgl3EQfBTTg/vector_store/index.pkl b/b9FPT4oBgHgl3EQfBTTg/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..b2b121a9a435d62bf7552bc81f1d6d5b961999d9 --- /dev/null +++ b/b9FPT4oBgHgl3EQfBTTg/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:dae1335206125300989d41f6e6f145e300acadd9e4a322d62183474534697a54 +size 218734 diff --git a/bdE1T4oBgHgl3EQfKwMf/content/tmp_files/2301.02967v1.pdf.txt b/bdE1T4oBgHgl3EQfKwMf/content/tmp_files/2301.02967v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..b4108a2662e200824307fa166e88bda6bdd51585 --- /dev/null +++ b/bdE1T4oBgHgl3EQfKwMf/content/tmp_files/2301.02967v1.pdf.txt @@ -0,0 +1,1283 @@ +Taiji Data Challenge for Exploring Gravitational Wave Universe +A PREPRINT +Zhixiang Ren1,2∗, Tianyu Zhao1,3,2∗, Zhoujian Cao1,3,4,†, Zong-Kuan Guo1,5,6,4, +Wen-Biao Han1,4,7,8,9,10, Hong-Bo Jin1,11,8, Yue-Liang Wu1,5,4,9† +1 Taiji Laboratory for Gravitational Wave Universe, +University of Chinese Academy of Science (UCAS), Beijing 100049, China +2 Peng Cheng Laboratory, Shenzhen 518055, China +3 Department of Astronomy, Beijing Normal University, Beijing 100875, China +4 School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, +UCAS, Hangzhou 310024, China +5 CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, +Chinese Academy of Sciences, Beijing 100190, China +6 School of Physical Sciences, UCAS, Beijing 100049, China +7 Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China +8 School of Astronomy and Space Science, UCAS, Beijing 100049, China +9 International Centre for Theoretical Physics Asia-Pacific (ICTP-AP, UNESCO), UCAS, Beijing 100190, China +10 Shanghai Frontiers Science Center for Gravitational Wave Detection, Shanghai 200240, China +11 Key Laboratory of Computational Astrophysics, +National Astronomical Observatories, Beijing 100101, China +January 10, 2023 +ABSTRACT +The direct observation of gravitational waves (GWs) opens a new window for exploring new physics +from quanta to cosmos and provides a new tool for probing the evolution of universe. GWs detection +in space covers a broad spectrum ranging over more than four orders of magnitude and enables us +to study rich physical and astronomical phenomena. Taiji is a proposed space-based gravitational +wave (GW) detection mission that will be launched in the 2030s. Taiji will be exposed to numerous +overlapping and persistent GW signals buried in the foreground and background, posing various +data analysis challenges. In order to empower potential scientific discoveries, the Mock Laser +Interferometer Space Antenna (LISA) Data Challenge and the LISA Data Challenge (LDC) were +developed. While LDC provides a baseline framework, the first LDC needs to be updated with +more realistic simulations and adjusted detector responses for Taiji’s constellation. In this paper, +we review the scientific objectives and the roadmap for Taiji, as well as the technical difficulties in +data analysis and the data generation strategy, and present the associated data challenges. In contrast +to LDC, we utilize second-order Keplerian orbit and second-generation time delay interferometry +techniques. Additionally, we employ a new model for the extreme-mass-ratio inspiral waveform and +stochastic GW background spectrum, which enables us to test general relativity and measure the +non-Gaussianity of curvature perturbations. As the first data challenge for Taiji, we aim to build an +open ground for data analysis related to Taiji sources and sciences. More details can be found on the +official website http://taiji-tdc.ictp-ap.org. +Keywords gravitational wave · universe evolution · Taiji · data challenge +∗contributed equally +†Corresponding author(s); ylwu@itp.ac.cn;zjcao@amt.ac.cn +arXiv:2301.02967v1 [gr-qc] 8 Jan 2023 + +Taiji Data Challenge +A PREPRINT +1 +Introduction +Ground-based GW detectors have made remarkable achievements since the first detection of GW150914 [1], nearly +100 GW events have been observed so far [2]. The discovery of GWs not only provides a more fundamental test on +Einstein’s theory of general relativity (GR) but also leads us to study deeply on the nature of gravity and spacetime. +In particular, GWs detection in sapce enables us to probe the formation and structure of black holes from the early +Universe through the peak of star formation era and to understand how does the intermediate mass seed black hole +formed in the early universe and how the seed black hole grows into the large or extreme-large black hole. It will also +be helpful to explore whether the dark matter could form into the black hole or primordial black hole could be the +candidate of dark matter. +Due to the limitation by seismic noise and arm length, ground-based detectors are not sensitive at frequencies lower +than 10 Hz [3]. By moving the detector to space, we can eliminate the seismic and gravity-gradient noise and open up +the frequency band of the GW within [10−4, 0.1]Hz. The first planned space-based GW detection project is the laser +interferometer space antenna (LISA) [4], proposed by the European Space Agency (ESA) and the National Aeronautics +and Space Administration (NASA), which will be launched in around 2037 3. Furthermore, LISA has laid a solid +foundation for space-borne GW detection, including scientific objectives, data analysis algorithms, and instrumental +techniques. +During the early 2000s, Chinese scientists were also interested in space-borne GW detection programs and considered +developing independent missions. The feasibility of space-based GW detection was studied by the Chinese Academy of +Sciences (CAS) in 2008, followed by the initial mission proposal presented in 2011 [5]. A half-million-kilometer arm +length and a noise budget that is a hundred times more sensitive than LISA at 0.1 Hz made this instrument particularly +sensitive to intermediate mass black hole mergers [6]. In 2012, the first mission descoping attempt was reported to prefer +a constellation of three satellites separated each by about 3 million kilometers, coordinating both technical and scientific +goals, and the proposed three-step road map was first presented in which the launch time for the Chinese space GW +detector was expected to be in the 2030s [7, 6]. The CAS built prototypes that were used to conduct proof-of-principle +experiments [8–11]. Similar to LISA, Taiji consists of three spacecraft (SC), and each SC follows a heliocentric orbit. +The three SC form an approximately 3 million-kilometer-long equilateral triangle. There is a 20-degree trail between +the center of mass of the constellation and the Earth. The constellation is roughly 1AU distant from the Sun. This +caused a slight eccentricity in the orbits of the three SC. With the stable constellation, Taiji’s sensitive frequency band is +[10−4, 0.1]Hz [6]. A three-step road map of the Taiji program is: 1) launch a satellite Taiji-1 for individual technique +validation, 2) launch two satellites Taiji-2 for almost all techniques test, and 3) launch complete Taiji three satellites +[12, 13]. The Taiji program, with its three-step road map, has received priority support from the CAS’s strategic priority +research program since 2016 for its pre-experimental study. Some key technologies have been developed further in +the studies [12, 14–19]. Currently, the first phase of the Taiji-1 on-orbit experiment has been successfully completed +[20, 21]. +In this paper, we present the first Taiji Data Challenge (TDC). Specifically, we review the scientific objectives and +technical challenges during the data processing procedure. Then, we visualize all TDC datasets and explain their +scientific potential and technical obstacles. We implement time-domain time delay interferometry (TDI) 2.0 for +detector response calculation, which makes our data more realistic compared to LDC1’s original datasets. As the main +component of our data challenge, we generate datasets that contain only one source and also datasets that contain +multiple sources. We further generate an extreme-mass-ratio inspiral (EMRI) waveform constructed under the general +parameterized metric, which allows us to test GR and investigate the non-Gaussianity of curvature perturbations by +observing the GW background it induces. +The paper is organized as follows. In Section 2, we introduce the scientific objectives and technical challenge of Taiji +mission. In Section 3, we demonstrate how to simulate Taiji instrumental noise, detector response, and GW waveform +respectively. In Section 4, we show the properties of each dataset. The last section contains our discussions about future +work and features of our TDC website. +2 +Scientific objective and technical challenge of Taiji mission +Taiji detectors will receive a large amount of GW signals from different sources in the target frequency band of +[10−4, 0.1]Hz. The observatory will measure signals from a wide range of different sources relevant to the astrophysical +mechanism of the formation of black holes and galaxies, the test of GR, and the study of cosmology, including massive +black holes binaries (MBHBs) at all redshifts; EMRIs; the inspiral of stellar-origin binary black holes (SOBBHs); +galactic binaries (GB); verification galactic binaries (VGBs), and various stochastic GW background (SGWB) sources. +3https://sci.esa.int/web/lisa +2 + +Taiji Data Challenge +A PREPRINT +The mission’s primary objective is to determine how and when massive black holes have formed and grown over cosmic +time. For the purpose of reconstructing their evolution, the study will explore almost all of the mass-redshift parameter +space that is relevant. We will investigate the distribution of MBHB’s spins and masses in order to distinguish between +different formation mechanisms based on the GW signal from MBHBs. Additionally, the mission will analyze the +signals from GBs and provide information on stellar evolution. Tens of millions of binaries in our galaxy produce +stochastic foregrounds, which we can estimate by observing GBs. It is possible to constrain the evolutionary pathways +of compact binaries by examining the characteristics of the population, such as the number density of sources as a +function of frequency. It is expected that Taiji will provide exceptionally strong tests of GR predictions by observing +highly relativistic MBHBs and EMRIs. During the merger phase of a binary black hole system, BHs travel at nearly the +speed of light and interact strongly with each other, which allows the study of the full nonlinear dynamics of gravity. By +observing the signal of the EMRI system, the mass, spin, and quadrupole moment of the central massive black hole will +be measured making testing its level of Kerr-ness and proving the no-hair hypothesis possible. Finally, a space-based +GW detector will explore new physics and cosmology and seek out previously unknown GW sources. The scientific +objectives of the Taiji mission are listed in Table 1. +Table 1: Scientific objectives of Taiji mission +No. +Scientific objective +1 +Dynamical evolution and population of MBHBs, study the birth and growth of MBHs, and the astrophysical +environment of the host galaxy +2 +Precisely estimate parameters of MBH, reveals the physical nature of BHs, probe dynamics of galactic +nuclei, and the astrophysical environment at the galaxy center by EMRI +3 +Formation evolution and population of Galaxy binaries +4 +Study SOBHB formation, environment, population, and joint observation with LIGO +5 +Test GR, study the properties of GW propagation +6 +GW cosmology, i.e. measurement of the Hubble constant and cosmology constant +7 +PSD shape and upper limit of SGWB signals +8 +Detect unmodeled signals +9 +New physics and cosmology beyond GR +GWs signals are expected to be many orders of magnitude below the noise level caused by laser frequency fluctuations +[4]. A post-processing technique called TDI has been proposed to reduce laser noise to an acceptable level [22]. +The idea is to construct virtual equal-arm interference by combining the data streams in the appropriate way. The +second-generation TDI is applicable to rotating and flexing detectors with linearly varying arm lengths. The actual Taiji +orbits are affected by the gravitational field of the planets, which leads to non-periodic orbits. In science analysis, it is +necessary to extract scientific information from the various TDI data streams; in a similar manner to the procedure for +the electromagnetic case, science analysis is carried out by deconvolution of the response function from the data stream +in order to obtain the incident GW field observed by Taiji. +The main task of the data analyst is to quickly identify the signals and estimate their physical parameters precisely. +Unlike current ground-based detectors, Taiji will be sensitive to continuous sources, primarily from GBs. It is expected +that GBs will be the most numerous of the sources, the unresolved component of the galactic population produces an +effectively stochastic "confusion noise". Due to the non-Gaussianity of GB foreground noise, detecting other signals +buried in the foreground noise is a challenging task. What’s more, analysis of the foreground itself is another challenge +because of the enormous number of signals. Because of the long duration and complex morphology of their signals, +detecting and characterizing the physics of SOBBHs with LISA is a highly nontrivial challenge. Data gaps will appear +in the Taiji data stream due to maintenance, telescope realignment, and communication with Earth by a high-gain +antenna. A series of significant challenges arise when dealing with gapped data, namely the information loss, spectral +leakage, and noise correlations [23]. Another challenge for GW signal detection is the interference of instrumental +glitches, which can be separated relatively natural from signals by ground observations with multiple interferometers. +In contrast, this coherent searching approach can not be directly applied in space-based detection, so novel glitch +classification algorithms need to be developed [24]. All the technical challenges are summarized in Table 2. +3 +Method +When analyzing real detector data, it is necessary to model the signal and noise; therefore, for simplicity in the +TDC, several idealized models are utilized during data simulation. This section will introduce these models and their +respective approximations. Using the existing waveform model, we first obtain the source frame GW waveform during +3 + +Taiji Data Challenge +A PREPRINT +Table 2: Technical challenges of Taiji mission +No. +Technical challenges +1 +Foreground GB signals separation +2 +SOBBH signals separation +3 +Others Signal with non-Gaussian GB noise +4 +Overlapping MBHB signals +5 +Instrumental glitches +6 +Data gap due to maintenance, telescope re- +alignment, and communication issue +7 +TDI technique to suppress laser frequency noise +signal simulation. Then, we determine the response of each link, which is dependent upon the orbit of the Taiji SCs. In +addition, TDI is used to obtain the signal in the X, Y, and Z channels. The instrumental noise in those 3 channels is +Gaussian noise simulated by their PSD. In the final step, the signal is injected into the noise. +3.1 +Orbital motion +We use Keplerian orbit to approximate the motion of the Taiji SC [25–27]. Given the distance between the SC i.e. the +arm length L and the distance from the SC to the sun a, the eccentricity of the orbit is defined by: +e = +� +1 + 4 +√ +3α cos φ + 4 +3α2 +�1/2 +− 1, +(1) +where φ = π/3 + 5α/8 is the angle between the SC’s orbital planes and the ecliptic plane. α = L/2a is a small +parameter originally used in Ref. [25]. The specific value of φ reduces the breathing effect of the arm length [26]. +The reference position of the 3 SC is given by: +� +� +� +� +� +xref,k(t) = a cos ι(cos ψk(t) − e), +yref,k(t) = a +� +1 − e2 sin ψk(t), +zref,k(t) = −a sin ι(cos ψk(t) − e). +(2) +where ι is the orbital inclination of SC1 relative to the ecliptic plane. +tan ι = +2 +√ +3 +α sin φ +� +1 + +2 +√ +3α cos φ +�, +(3) +where ψk(t) is the eccentric anomaly of SCk, which is obtained by solving the Kepler equation to the desired order +iteratively: +ψk(t) − e sin ψk(t) = mk(t) = m0,k + Ω(t − t0) = m0,1 − 2π(k − 1) +3 ++ Ω(t − t0), +Ω = +2π +1 year. +(4) +Then, the position of 3 SC could be expressed in terms of the reference position and periastron λk = λ1 + 2π(k − 1)/3: +� +� +� +xk(t) = cos λkxref,k(t) − sin λkyref,k(t), +yk(t) = sin λkxref,k(t) + cos λkyref,k(t), +zk(t) = zref,k(t). +(5) +In summary, the orbits of 3 SCs are determined by 4 parameters: the semi-major axis a, the arm length L, SC1’s initial +mean anomaly m0,1, and SC1’s initial periastron λ1. +3.2 +Light travel time +Following Ref. [28], we could use the Taylor expansion of the position of the emitter SC to calculate the light travel +time analytically. So the light travel time could be expressed as: +LTT = LTT(0) + LTT(1) + LTT(2) + LTT(Sh) +(6) +4 + +Taiji Data Challenge +A PREPRINT +with +LTT(0)(t) = 1 +c |⃗xrecv(t) − ⃗xsend(t)| +(7) +LTT(1)(t) = ⃗vrecv(t) +c2 +· (⃗xrecv(t) − ⃗xsend(t)) +(8) +LTT(2)(t) = |⃗xrecv(t) − ⃗xsend(t)| +c3 +� +⃗v2 +recv(t) − ⃗arecv(t) · (⃗xrecv(t) − ⃗xsend(t)) +(9) ++ +�⃗vrecv(t) · (⃗xrecv(t) − ⃗xsend(t)) +|⃗xrecv(t) − ⃗xsend(t)| +�2 � +, +(10) +where the subscripts ’send’ and ’recv’ represent the emitter SC and the receiver SC respectively. Finally, we consider +the Shapiro delay caused by the Sun’s gravitational field, which is a second-order effect [29]: +LTT(Sh) = RS +c · ln |⃗xsend(t)| + |⃗xrecv(t)| + |⃗xrecv(t) − ⃗xsend(t)| +|⃗xsend(t)| + |⃗xrecv(t)| − |⃗xrecv(t) − ⃗xsend(t)|, +(11) +where RS is the Schwarzschild radius of the Sun. +3.3 +Detector response +For the data generation, we use a time domain detector response and the GPU accelerated code provided by [30], which +enables us to generate a large amount of data directly in the time domain. First, we transform the GW waveform from +the source frame to the solar-system barycenter (SSB) frame by +� +hSSB ++ +hSSB +× +� += +� +cos 2ψ +− sin 2ψ +sin 2ψ +cos 2ψ +� � +hsrc ++ +hsrc +× +� +. +(12) +Then, the length variation of one arm caused by the GW signal is: +H(t) = hSSB ++ +(t)ξ+(ˆθ, ˆφ,⃗n(t)) + hSSB +× +(t)ξ×(ˆθ, ˆφ,⃗n(t)), +(13) +where the antenna pattern ξ+ and ξ× are given by: +� +ξ+(⃗u,⃗v,⃗n) = (⃗u · ⃗n)2 − (⃗v · ⃗n)2, +ξ×(⃗u,⃗v,⃗n) = 2 (⃗u · ⃗n) (⃗v · ⃗n) , +(14) +ˆn(t) is the unit vector of the arm, ˆθ, ˆφ are polar and azimuthal angle in the SSB frame, based on the orthonormal +basis vectors (ˆer, ˆeθ, ˆeφ). ⃗u,⃗v are polarization vectors defined by ⃗u = −ˆeφ and ⃗v = −ˆeθ. The propagation vector is +⃗k = −ˆer. Light travel time along the arm affected by the GW is : +trecv ≃ tsend + LTT − 1 +2c +� L +0 +H(⃗x(λ), t(λ)) dλ, +(15) +where we use first order approximation as t(λ) = tsend +λ/c, ⃗x(λ) = ⃗xsend(tsend)+λ⃗n(tsend), ⃗xsend is the position of +the emitter SC. The parameter λ used as the integration variable describes the photon path. With those approximations, +H(⃗x(λ), t(λ)) is given by: +H(⃗x(λ), t(λ)) = H +� +t(λ) − +⃗k · ⃗x(λ) +c +� += H +� +tsend − +⃗k · ⃗xsend(tsend) +c ++ λ1 − ⃗k · ⃗n(tsend) +c +� +(16) +Combining equation. (15) and (16) and differentiating the resulting expression with respect to tsend yields the relative +frequency shift, +y(tsend) = +1 +2(1 − ⃗k · ⃗n(tsend)) +� +H +� +tsend − +⃗k · ⃗xsend(tsend) +c +� +− H +� +tsend − +⃗k · ⃗xrecv(trecv) +c ++ LTT +�� +. +(17) +We assume that ⃗n(tsend) ≃ ⃗n(trecv) since the variation of arm direction due to the SC’s motion during the light travel +time is less than 10−3rad in the case of Taiji [31] and trecv ≃ tsend + LTT. Finally, the GW strain of one arm is: +y(trecv) = +1 +2(1 − ⃗k · ⃗n(trecv)) +� +H +� +trecv − +⃗k · ⃗xsend(trecv) +c +− LTT(trecv) +� +− H +� +trecv − +⃗k · ⃗xrecv(trecv) +c +�� +. +(18) +5 + +Taiji Data Challenge +A PREPRINT +3.4 +TDI Combination +Due to the unequal arm length of the Taiji SCs, the laser frequency noise could not be canceled naturally, which will be +orders of magnitude above the GW signals. So the TDI technique was developed to cancel the noise by shifting the data +from different SCs by subtle time delays and combining them together. The TDI technique can be divided into several +generations: +• TDI 1.0 is used in the static case, which does not consider the rotation and breathing effect. In other words, the +arm lengths are constants in time, i.e. the light travel time satisfies LTTi = LTTi′ = const. +• TDI 1.5 is used in the rigid rotating case, which does not consider the breathing effect. The arm lengths are +still constants in time, i.e. LTTi = const., LTTi′ = const. but LTTi ̸= LTTi′ here. +• TDI 2.0 is used in the flexing case, the arm lengths are functions of time, i.e. LTTi = LTTi(t), LTTi′ = +LTTi′(t), and LTTi(t) ̸= LTTi′(t). +Here we adopt the notation from Ref. [22], the number in the subscript represents different links, where i ∈ {1, 2, 3} +denotes the clockwise link opposite to SCi and i′ denotes the counter-clockwise link. The first generation unequal arm +Michelson combination is: +X1(t) = (y2′:322′ + y1:22′ + y3:2′ + y1′) − (y3:2′3′3 + y1′:3′3 + y2′:3 + y1) . +(19) +The second-generation Michelson combination is +X2(t) = y1′ + y3,2′ + y1,22′ + y2′,322′ + y1,3′322′ + y2′,33′322′ ++ y1′,3′33′322′ + y3,2′3′33′322′ − y1 − y2′,3 − y1′,3′3 − y3;2′3′3 +− y1′,22′3′3 − y3,2′22′3′3 − y1;22′22′3′3 − y2′,322′22′3′3. +(20) +The variables Y and Z could be obtained by cyclic permutation of the indices. The colon denotes time delay when the +arm length is time-independent, +f(t):j := f +� +t − Lj +c +� +, +f(t):jk = f +� +t − Lk +c − Lj +c +� += f(t):kj, +(21) +which is commute for j ̸= k. Next, a comma denotes time delays with time-dependent arm lengths, here we compute +chained delays as simple sums of delays rather than nested delays, +f(t),jk = f +� +t − Lk(t) +c +− Lj(t) +c +� +. +(22) +This approximation is sufficient for computing the GW response function [30]. +3.5 +Instrumental noise +Despite the complex noise sources that will be involved in the Taiji detection data in practice, in our simulation, we +use a noise model consisting of just two components for simplicity. The first one is the high-frequency component, +which represents the overall noises that come from the optical metrology system, and the second is the low-frequency +component, which represents the test mass acceleration noise. The power spectral density (PSD) is given by: +Poms(f) = 64 × 10−24 1 +Hz +� +1 + +�2mHz +f +�4� �2πf +c +�2 +, +Pacc(f) = 9 × 10−30 1 +Hz +� +1 + +�0.4mHz +f +�2� � +1 + +� +f +8mHz +�4� � +1 +2πfc +�2 +. +(23) +Following [32], the analytic model of the one-sided noise PSD is derived from the noise components in each interfero- +metric measurement. We will explicitly show PSD for a Michelson-type TDI generator. Given the data combination +(19) and (20) with the assumption that the noise of each link has the same PSD, the noise PSD of the first and the +second generation TDI X channel is: +PSDX1 = 16 sin2(ωL) (Poms + (3 + cos(2ωL))Pacc) , +(24) +PSDX2 = 64 sin2(ωL) sin2(2ωL) (Poms + (3 + cos(2ωL))Pacc) , +(25) +where ω = 2πf/c. In this paper, we use TDI 2.0 PSD for noise generation. +6 + +Taiji Data Challenge +A PREPRINT +4 +Dataset +4.1 +Overall setting +The TDC dataset was designed based on the scientific objectives of Taiji. For most of the sources of Taiji, we do +not have well-established data analysis algorithms because they are not detected by ground-based detectors. So at +the beginning of the data challenge, we should focus on each source separately for simplicity. Each of the datasets +from TDC-1 to TDC-6 contains signals from a single source. Multiple sources are included in the last dataset TDC-7, +including MBHBs, VGBs, and GB foregrounds. Those datasets cover all the sources for the scientific objectives. +Similar to LDC, the sampling rate here in TDC is 0.1 Hz for all datasets, while this setting will be adjustable with +Taiji’s configuration accordingly. First, we generate the signal, then compute the TDI 2.0 response, and add it to the +simulated noise. For the time domain signals, we use the time domain TDI response as mentioned in 3.3 and 3.4. For +the stochastic GW signals, we generate them directly by their PSD, which considers TDI response. Next, we will +introduce the configuration and parameters used to generate the datasets. +(a) +(b) +(c) +(d) +(e) +(f) +(g) +(h) +(i) +Figure 1: Time-domain data of all the TDC datasets. The strain of TDI X channel data and signals are presented. (a), +TDC-1, the MBHB signal is zoomed in because of its duration. (b) and (c), TDC-2-1 and TDC-2-2. (d), TDC-3. (e), +TDC-4. (f), TDC-5. (g) and (h), TDC-6-1 and TDC-6-2. (i), TDC-7, signals No.8 and No.9 are zoomed in due to the +closeness of their coalescence time. +7 + +1e-19 +1.0 +Data +1e-20 +MBHB +2.5 +0.8 +0.0 +0.6 +-2.5 +TDI X Strain +0.4 +0.00000 +0.00005 +0.00010 ++9.999e-1 +0.2 +0.0 +0.2 +0.00 +0.25 +0.50 +0.75 +1.00 +1.25 +1.50 +1.75 +2.00 +Time [yr]1e-20 +Data +EMRI +TDI X Strain +0.00 +0.25 +0.50 +0.75 +1.00 +1.25 +1.50 +1.75 +2.00 +Time [yr]le-20 +Data +EMRI +TDI X Strain +-1 +-2 +0.00 +0.25 +0.50 +0.75 +1.00 +1.25 +1.50 +1.75 +2.00 +Time [yr]le-20 +Data +VGB +2 + +TDI X Strain +0 +-1 +-2 +0.00 +0.25 +0.50 +0.75 +1.00 +1.25 +1.50 +1.75 +2.00 +Time [yr]Data +GB +TDI X Strain +-3 +0.00 +0.25 +0.50 +0.75 +1.00 +1.25 +1.50 +1.75 +2.00 +Time [yr]le-20 +Data +SOBBH +TDIX Strain +-1 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Time [yr]le-20 +Data +SGWB +TDIX Strain +1 +0.00 +0.25 +0.50 +0.75 +1.00 +1.25 +1.50 +1.75 +2.00 +Time [yr]le-20 +Data +SGWB +TDIX Strain +1 +0.00 +0.25 +0.50 +0.75 +1.00 +1.25 +1.50 +1.75 +2.00 +Time [yr]1e-19 +5 +Data +1e-20 +GB +MBHB +4 +VGB +3 +I X Strain +2 +0.000 +0.001 ++1.6 +TDI +1 +0 - +-1 +-2 +0.00 +0.25 +0.50 +0.75 +1.00 +1.25 +1.50 +1.75 +2.00 +Time [yr]Taiji Data Challenge +A PREPRINT +(a) +(b) +(c) +(d) +(e) +(f) +(g) +(h) +(i) +Figure 2: Frequency domain data of all the TDC datasets. The PSD of TDI X channel data and signals are compared +with the noise PSD. (a), TDC-1. (b) and (c), TDC-2-1 and TDC-2-2. (d), TDC-3. (e), TDC-4. (f), TDC-5. (g) and (h), +TDC-6-1 and TDC-6-2. (i), TDC-7. +4.2 +Massive black hole binary +MBHBs are primary sources of Taiji, which is sensitive to MBHBs with total mass in the range of [105, 108]M⊙ [4]. It +is expected to detect 1 ∼ 20 MBHBs per year [33]. We will be able to gain valuable insight into how MBHs are formed +by measuring their spins and masses. It should be possible for us to test the hypothesis that modern galaxies are the +result of the merger of smaller "seed" galaxies in the early universe, as we will be able to detect the merger of MBHB +out to a high redshift. We use SEOBNRv4_opt [34] here to generate the MBHB signal and shift it by the coalescence +time tc. Only the l = m = 2 mode is included in the data. Both TDC-1 and TDC-7 contain MBHB signals. For TDC-1, +there is only one MBHB signal in this dataset, the time domain and the frequency domain behavior of the TDC-1 data +are shown in Fig. 1a and Fig. 2a respectively. In the time domain, we could see that the merger portion of the signal is +not buried in the noise, which has a short duration of ∼ hour. Then, in the frequency domain, the signal is below the +noise PSD. The parameter of MBHB signals injected in those two datasets are shown in Table 3, where MT is the total +mass of two black holes, q is the mass ratio with q < 1, s1, s2 is the spin parameters, ι is the inclination angle, ψ is the +polarization angle, λ and β is ecliptic longitude and ecliptic latitude characterize the sky location of the source, tc is +the coalescence time, and φc is coalescence phase. TDC-1 only contains signal No. 1 and all 10 signals are included +in TDC-7. The time domain and the frequency domain behavior of the TDC-7 data are shown in Fig. 1i and Fig. 2i +respectively. Signals No. 8 and No. 9 are close together, presenting additional challenges to data processing algorithms +that are not encountered by ground-based detectors. +8 + +10-38 +Data +Noise PSD +10~39, +MBHB +10-40 +TDI X PSD +10-41 +10~42, +10-43 , +10-44 +10~45 +10-4 +10~3 +10~2 +10-1 +f [Hz]10-38 +Data +Noise PSD +EMRI +10-39 +10-40 +I X PSD [1/Hz] +10 +-41 +TDI +10~42, +10~43, +10~44 +10~45 +10~4 +10~3 +10-2 +10-1 +f [Hz]10-38 +Data +Noise PSD +EMRI +10-39 +10-40 +TDI X PSD [1/Hz] +10 +-41 +10-42 +10-43, +10-44 +10-45 +10~4 +10~3 +10~2 +10-1 +f [Hz]Data +10-37. +Noise PSD +VGB +10-39, +PSD +X +10-41 +1043. +1045 +10~4 +10~3 +10~2 +10-1 +f [Hz]Data +10-37. +Noise PSD +GB +10~39. +X PSD +TDI +10-41. +10-43. +1045 +10~4 +10~3 +10~2 +10-1 +f [Hz]10-38 +Data +Noise PSD +10~39 +SOBBH +10-40, +I X PSD +10~41 +TDI +10-42 +1043, +10-44 +10~45 +10~4 +10-3 +10~2 +10-1 +f [Hz]10-38 +Simulated data +Noise PSD +10~39 +SGWB signal +SGWB PSD +10-40 +I X PSD +10-41 +TDI +10-42 +10-43 +10-44 +1045 +10-4 +10-3 +10~2 +10-1 +f [Hz]10-38 +Simulated data +Noise PSD +10-39, +SGWB signal +SGWB PSD +10-40 +TDI X PSD +10-41 +10-42 +10-43 +10-44, +1045 +10-4 +10-3 +10~2 +10-1 +Freq [Hz]Data +10-37 +GB +VGB +Noise PSD +MBHB +1039 +TDI X PSD [1/Hz] +10-41, +10-43. +1045 +10~4 +10~3 +10~2 +10-1 +f [Hz]Taiji Data Challenge +A PREPRINT +Table 3: Parameters of MBHB signals used in TDC-1 and TDC-7 +No. +MT (M⊙) +q +s1 +s2 +DL(Gpc) +ι +ψ +λ +β +tc(yr) +φc +1 +6 × 105 +0.5 +0.2 +0.4 +53.39 +π/3 +π/3 +π/5 +π/4 +0.2 +0.5 +2 +1.2 × 106 +0.3 +0.1 +0.2 +53.39 +2π/3 +π/3 +π/10 +π/8 +0.4 +1 +3 +1.8 × 106 +0.8 +0.14 +0.12 +16.02 +π +π/3 +π/15 +5π/4 +0.6 +0.05 +4 +2.4 × 106 +0.4 +0.18 +0.08 +21.36 +5π/6 +π/3 +π/20 +7π/4 +0.8 +0.1 +5 +1.5 × 106 +0.7 +0.14 +0.8 +53.39 +π/3 +π/3 +π/25 +3π/4 +1 +0.15 +6 +1.2 × 106 +0.6 +0.1 +0.6 +106.78 +π/6 +2π/3 +π/30 +5π/4 +1.2 +0.35 +7 +2.4 × 106 +0.1 +0.22 +0.48 +16.02 +8π/30 +5π/3 +π/35 +π/8 +1.4 +0.45 +8 +1.2 × 106 +0.05 +0.16 +0.28 +26.69 +13π/30 +π/3 +2π/5 +π/12 +1.6 +1 +9 +1.2 × 106 +0.5 +0.02 +0.08 +26.69 +14π/30 +π/3 +3π/5 +11π/40 +1.601 +0.4 +10 +1.2 × 107 +1 +0.12 +0.08 +10.68 +π/3 +π/3 +6π/5 +π/4 +1.8 +0.5 +4.3 +Extreme-mass-ratio inspiral +EMRIs are binary black hole systems consisting of a stellar-mass compact object (CO) and a massive black hole with +mass M ∼ 104M⊙ − 107M⊙. Taiji will observe few tens to hundreds EMRI events over 2 years with signal-to-noise +ratio (SNR) above 20 [35]. Because of the extremely large mass ratio, the EMRI evolves slowly, inspiraling about +104 ∼ 105 cycles in Taiji’s frequency band [36]. Since EMRI signals contain rich information about the geometry +surrounding the central black holes, they are one of the primary fundamental physics goals of the Taiji mission. It +has been suggested that detections of EMRIs could provide a highly accurate observational test of the "Kerr-ness" of +the central MBH [37].What’s more, EMRIs sample the stellar population near the central black holes.By detecting +EMRI signals, we can probe the physical properties of the central MBH and test GR [4]. +Several waveform +templates are developed for such a promising source of Taiji 1) Teukolsky-based method, [38, 39] 2) Numerical +Kludge (NK)[40], +3) Analytic Kludge (AK)[41], +4) Augmented Analytic Kludge (AAK) [42–44], and +5) XSPEG [45, 46]. +The first 2 of them are computationally expensive, and the AK waveform doesn’t suit Kerr +space-time, so we utilize the GPU-accelerated AAK waveform [44] for the TDC-2-1 dataset generation and the +XSPEG waveform for the TDC-2-2 dataset generation. There is only one EMRI signal in each dataset. Because +of the KRZ metric used in XSPEG waveform construction, TDC-2-2 could be used to test GR, which is a key +scientific objective of the Taiji mission. +The time domain and the frequency domain behavior of the data are +shown in Fig. 1b and 2c.Unlike MBHBs, the amplitude of a typical EMRI is an order of magnitude below the +instrumental noise. Detection is only possible if enough SNR is accumulated over a number of wave cycles. The +parameters of EMRI waveform injected in TDC-2-1 is (M, µ, a0, e0, p0, ι0, θS, φS, θK, φK, Φϕ,0, Φθ,0, Φr,0, DL) = +(106M⊙, 30M⊙, 0.6, 0.6, 15, 0.7, 10−6, 10−6, 10−6, 10−6, 0, 0, 0, 100Mpc), M and a are the mass and spin parameter +of the MBH, p is the semi-latus rectum, e is eccentricity, ι is the orbit’s inclination angle from the equatorial plane, +θS, and φS are the polar and azimuthal sky location angles. θK and φK are the azimuthal and polar angles describing +the orientation of the spin angular momentum vector of the MBH. Φϕ,0, Φθ,0, Φr,0, represent the phase of azimuthal, +polar, and radial modes respectively, DL is the luminosity distance. The parameters of the EMRI waveform injected in +TDC-2-2 is (M, µ, a0, e0, p0, ι0, λ, β, DL) = (106M⊙, 10M⊙, 0.9, 0.6, 15, π/4, 0, π/4, 8.3Mpc), and the KRZ metric +deformation parameter is (δ1, δ2, δ3) = (0.1, 0.1, 0.1). Compared to the existing LDC1-2 dataset for EMRI, an updated +AAK waveform template is used in TDC-2-1, and a waveform based on the KRZ metric is used in TDC-2-2. +4.4 +Galactic binary +We use the simple GB model from Ref. [30], which is expressed in the source frame as: +hsrc ++ (t) = A(1 + cos2 ι) cos Φ(t), +hsrc +× (t) = 2A sin ι sin Φ(t), +Φ(t) = φ0 + 2πf0t + π ˙f0t2 + π +3 +¨f0t3, +¨f0 = 11 +3 +˙f 2 +0 +f0 +. +(26) +where A is the overall amplitude, φ0 is the initial phase at the start of the observation, ι is the inclination of the BWD +orbit to the line of sight from the origin of the SSB frame. The intrinsic parameter is the frequency of the signal f and its +derivative ˙f. The comparison to LDC’s GB waveform ¨f0 is considered here.There are enormous GBs populated in the +9 + +Taiji Data Challenge +A PREPRINT +Milky Way [4] which form foreground noise, and disentangling those signals is a challenging task [47]. With the help of +GWs, GB foreground observations provide a key method for measuring the properties of a fraction of the galactic stellar +population that is routinely assumed but has never been directly observed. What’s more, there are some bright GBs +called LISA verified binaries [48], the latest catalog is available online4. Following the above catalog, we generate the +TDC-3 dataset, which contains 43 VGBs. The foreground GB noise is in the TDC-4 dataset, which consists of ∼ 3e7 +GB signals. The catalog of the TDC-4 dataset comes from the population study of GBs [49, 50].Both the signal and +the noise PSD of these two datasets are shown in Fig. 2d and 2e, associated with the corresponding time domain data +shown in 1d and 1e. Compared to LDC1’s dataset, we use TDI 2.0 here. That GB noise is also included in TDC-7. The +Taiji mission faces a data analysis challenge because of the presence of non-Gaussian and non-stationary astrophysical +foregrounds. Due to the presence of foreground signals, GW source separation procedures will be complicated. A +resolvable signal’s source parameter estimation will also be affected by the level of confusion noise. Therefore, it is +critical to study, understand, and predict the overall shape and amplitude of the potential foreground components of the +Taiji data. +4.5 +Stellar-origin binary black holes +Space-based detectors observe the early inspiral of SOBBH systems, whose merger will be detected by ground-based +detectors. Those systems evolve slowly in the LISA and Taiji frequency bands, which enable high-precision parameter +estimation [51]. The joint observation of SOBBH by Taiji and ground-based detectors could be used to probe low- +frequency modifications due to deviations from GR or to environmental effects, to facilitate electromagnetic joint +observations [52, 53]. By estimating coalescence time and sky location, we could forecast the signals for ground-based +detectors. We generate the TDC-5 dataset, which contains 21721 SOBBH signals, whose catalog comes from [53]. The +time domain and the frequency domain behavior of the data are shown in Fig. 1f and 2f. The SOBBH signals are +completely below the noise in the frequency domain, which are background signals. We generate the waveform using +the IMRPhenomD template, then transform it to the time domain and apply the TDI response. The main difference +between the TDC-5 and LDC1-5 datasets is that we use the TDI 2.0 response in the time domain rather than the TDI +1.0 response in the frequency domain. +4.6 +Stochastic gravitational wave background +One of the main scientific objectives of Taiji is to probe GWs from the early universe and reveal physics of GW sources +[54]. Fundamental physics and astronomy would be greatly enhanced by the detection of a cosmological background +from the early universe. The only way to obtain direct information about earlier epochs than decoupling may be through +GWs and possibly neutrinos. There are many possible astrophysical and cosmological sources that contribute to the +stochastic background, and up to now we put only upper bounds on its amplitude [55], and on parameters characterizing +its directional properties [56], by the LIGO/Virgo collaboration. For space-based detection, we just have a single +detector, cross-correlation based method is not suitable now, so a new SGWB detection algorithm is needed. +SGWBs that are Gaussian, isotropic, and stationary can be fully described by their energy density spectrum [57]: +ΩGW (f) = f +ρc +d ρGW +d f +, +(27) +where ρGW is the energy density of gravitational radiation contained in the frequency range f to f + df, ρc = 3H2 +0c2 +8πG is +the critical density of the universe, where c is the speed of light, and G is Newton’s constant, and H0 is the Hubble +constant. Typical SGWB sources include compact binary coalescence[55], cosmic phase transitions [58], reheating or +preheating after inflation [59], and primordial scalar and tensor perturbations from inflation [60]. There are 2 datasets +that contain different types of SGWB signals, TDC-6-1 is generated by the power-law spectrum: +h2ΩGW (f) = 10α +� f +f∗ +�β +, +(28) +where h is the dimensionless Hubble constant, f∗ is the pivot frequency, α characterize its amplitude at f∗ and β is the +slope of the spectrum. The SGWB signal in TDC-6-1 is generated using the parameters α = −12 and β = 2/3. +TDC-6-2 is generated by non-Gaussian scalar perturbation-induced SGWB signals. The induced GWs are generated +during the formation of primordial black holes (PBHs), providing a powerful tool to search for PBHs [61]. Typically, +curvature perturbations are assumed to have Gaussian probability density functions. There is a natural expectation +that non-Gaussianity will be present when a sharp peak appears in the power spectrum of curvature perturbations. +4https://gitlab.in2p3.fr/LISA/lisa-verification-binaries +10 + +Taiji Data Challenge +A PREPRINT +GWs induced by scalar perturbations with a second-order local-type non-Gaussianity were studied in Ref. [60]. The +formulae of the SGWB spectrum used to generate TDC-6-2 data is given in equation (7) in Ref. [60] with the parameters +FNL = 10, σ = 10−4, MPBH = 1022g, where FNL characterize the non-Gaussianity, σ is the peak width of curvature +perturbation spectrum, and MPBH is the mass of PBH with the assumption that PBHs can serve as all dark matter. +In summary, 9 datasets are designed for TDC, and their essential motivation (i.e. the scientific objective and the +technical challenge), and configurations are presented in Table. 4. The scientific objectives and the corresponding +technical challenges are shown in Tab. 1 and Tab. 2. +Table 4: Summary of Taiji Data Challenge datasets +Name +Scientific objective +Technical challenge +Signals +Waveform model +TDC-1 +1, 5, 6 +7 +1 MBHB signal +SEOBNRv4_opt +TDC-2-1 +2, 5, 6 +7 +1 EMRI signal +PN5AAK +TDC-2-2 +2, 5, 6 +7 +1 EMRI signal +XSPEG +TDC-3 +3, 5, 6 +7 +43 VGB signals +Sinusoidal +TDC-4 +3, 5, 6 +1, 7 +3e7 GB signals +Sinusoidal +TDC-5 +4, 5, 6 +2, 7 +2e5 SOBBH signals +IMRPhenomD +TDC-6-1 +5, 6, 7 +7 +SGWB +Power-law +TDC-6-2 +5, 6, 7 +7 +SGWB +Non-Gaussian curvature perturbations +TDC-7 +1, 3, 5, 6 +1, 3, 7 +10 MBHBs, 43 VGBs, 3e7 GBs +SEOBNRv4_opt, Sinusoidal +5 +Discussions +Building a data challenge is critical for scientists to develop algorithms and pipelines for future data analysis tasks. +We provide a complete workflow by constructing detection data and waveform templates within and beyond GR. The +datasets and challenges are available on the official website of TDC (http://taiji-tdc.ictp-ap.org). Scientists +are encouraged to participate in these data challenges and to submit their results. Currently, there is no deadline, and +users are free to submit their results at any time. We will rank the submitted results for each challenge. As part of +our website, we offer both data downloads and data customization services, which enable users to submit the data +configuration file suited to their requirements, and we will provide users links to download the customized dataset. +With TDC, we hope to create a community of researchers who can collaboratively contribute to the development of +Taiji’s data analysis pipelines and join the journey of exploring the universe and making new discoveries with Taiji +Collaboration. +6 +Acknowledgements +The research was supported by the Peng Cheng Laboratory Cloud Brain and by Peng Cheng Cloud-Brain . Further +funding was provided by the National Key Research and Development Program of China Grant No. 2021YFC2203001, +No. 2020YFC2201501 & No. 2021YFC2203002, as well as the NSFC (No. 11920101003, No. 12021003, No. +12173071, and No. 12147103). Z.C and W.H are supported by the CAS Project for Young Scientists in Basic Research +YSBR-006. Z.C was also supported by “the Interdiscipline Research Funds of Beijing Normal University". Z.G was +supported by the NSFC Grants No. 12235019 and No. 12075297. +References +[1] B. P. Abbott et al., Phys. Rev. Lett. 116, 061102 (2016). +[2] The LIGO Scientific Collaboration, the Virgo Collaboration, the KAGRA Collaboration, et al., “GWTC-3: +Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run,” +(2021), arXiv:2111.03606 . +[3] F. Matichard et al., Class. Quantum Grav. 32, 185003 (2015). +[4] P. Amaro-Seoane et al., “Laser Interferometer Space Antenna,” (2017), arXiv:1702.00786 . +[5] X. Gong, S. Xu, S. Bai, Z. Cao, et al., Class. Quantum Grav. 28, 094012 (2011). +[6] Z. Luo, Y. Wang, Y. Wu, W. Hu, and G. Jin, Prog. Theor. Exp. Phys. 2021, 05A108 (2021). +[7] Y.-L. Wu, in Presentation to 1st eLISA Consortium Meeting (2012). +11 + +Taiji Data Challenge +A PREPRINT +[8] Y.-Q. Li, Z.-R. Luo, H.-S. Liu, Y.-H. Dong, and G. Jin, Chin. Phys. Lett. 29, 079501 (2012). +[9] H.-S. Liu, Y.-H. Dong, Y.-Q. Li, Z.-R. Luo, and G. Jin, Rev. Sci. Instrum. 85, 024503 (2014). +[10] Y.-H. Dong, H.-S. Liu, Z.-R. Luo, Y.-Q. Li, and G. Jin, Rev. Sci. Instrum. 85, 074501 (2014). +[11] Y.-Q. Li, Z.-R. Luo, H.-S. Liu, Y.-H. Dong, and G. Jin, App. Phys. B 118, 309 (2015). +[12] W.-R. Hu and Y.-L. Wu, Natl. Sci. Rev. 4, 685 (2017). +[13] Z. Luo, Z. Guo, G. Jin, Y. Wu, and W. Hu, Results Phys. 16, 102918 (2020). +[14] Z. Luo, Q. Wang, C. Mahrdt, A. Goerth, and G. Heinzel, Appl. Opt. 56, 1495 (2017). +[15] Z. Luo, H. Liu, and G. Jin, Optics & Laser Tech. 105, 146 (2018). +[16] H. Liu, Y. Dong, R. Gao, Z. Luo, and G. Jin, Optical Eng. 57, 1 (2018). +[17] H. Liu, Z. Luo, and G. Jin, Micrograv. Sci. and Technol. 30, 775 (2018). +[18] W. Deng, T. Yang, J. Cao, E. Zang, L. Li, L. Chen, and Z. Fang, Optics Lett. 43, 1562 (2018). +[19] Z. Wang, W. Sha, Z. Chen, Y.-S. Kang, Z.-R. Luo, M. Li, and Y.-P. Li, Chinese Optics 11, 131 (2018), (in +Chinese). +[20] The Taiji Scientific Collaboration, Commun. Phys. 4, 34 (2021). +[21] The Taiji Scientific Collaboration, Int J Mod Phys A 36, 2102002 (2021). +[22] M. Otto, Time-Delay Interferometry Simulations for the Laser Interferometer Space Antenna, Ph.D. thesis, +Hannover : Gottfried Wilhelm Leibniz Universität Hannover (2015). +[23] A. Blelly, J. Bobin, and H. Moutarde, Mon. Notices Royal Astron. Soc. 509, 5902 (2021). +[24] T. Robson and N. J. Cornish, Phys. Rev. D 99, 024019 (2019). +[25] S. V. Dhurandhar, K. R. Nayak, S. Koshti, and J.-Y. Vinet, Class. Quantum Grav. 22, 481 (2005). +[26] K. R. Nayak, S. Koshti, S. V. Dhurandhar, and J.-Y. Vinet, Class. Quantum Grav. 23, 1763 (2006). +[27] B. Wu, C.-G. Huang, and C.-F. Qiao, Phys. Rev. D 100, 122001 (2019). +[28] B. Chauvineau, S. Pireaux, T. Regimbau, and J.-Y. Vinet, Phys. Rev. D 72, 122003 (2005). +[29] A. Hees, S. Bertone, and C. Le Poncin-Lafitte, Phys. Rev. D 89, 064045 (2014). +[30] M. L. Katz, J.-B. Bayle, A. J. K. Chua, and M. Vallisneri, “Assessing the data-analysis impact of LISA orbit +approximations using a GPU-accelerated response model,” (2022), arXiv:2204.06633 . +[31] N. Rijnveld and J. A. C. M. Pijnenburg, in International Conference on Space Optics — ICSO 2010, edited by +N. Kadowaki (SPIE, Rhodes Island, Greece, 2017) p. 96. +[32] S. Babak, M. Hewitson, and A. Petiteau, “LISA Sensitivity and SNR Calculations,” (2021), arXiv:2108.01167 . +[33] M. L. Katz, L. Z. Kelley, F. Dosopoulou, S. Berry, L. Blecha, and S. L. Larson, Mon. Notices Royal Astron. Soc. +491, 2301 (2019). +[34] A. Bohé, L. Shao, et al., Phys. Rev. D 95, 044028 (2017). +[35] J. R. Gair, S. Babak, A. Sesana, P. Amaro-Seoane, E. Barausse, C. P. L. Berry, E. Berti, and C. Sopuerta, J. Phys.: +Conf. Ser. 840, 012021 (2017). +[36] S. Babak, J. Gair, A. Sesana, E. Barausse, C. F. Sopuerta, C. P. L. Berry, E. Berti, P. Amaro-Seoane, A. Petiteau, +and A. Klein, Phys. Rev. D 95, 103012 (2017). +[37] L. Barack and C. Cutler, Phys. Rev. D 75, 042003 (2007). +[38] K. Glampedakis, Class. Quantum Grav. 22, S605 (2005). +[39] W.-B. Han and Z. Cao, Phys. Rev. D 84, 044014 (2011). +[40] S. Babak, H. Fang, J. R. Gair, K. Glampedakis, and S. A. Hughes, Phys. Rev. D 75, 024005 (2007). +[41] L. Barack and C. Cutler, Phys. Rev. D 69, 082005 (2004). +[42] A. J. K. Chua and J. R. Gair, Class. Quantum Grav. 32, 232002 (2015). +[43] A. J. K. Chua, C. J. Moore, and J. R. Gair, Phys. Rev. D 96, 044005 (2017). +[44] M. L. Katz, A. J. K. Chua, L. Speri, N. Warburton, and S. A. Hughes, Phys. Rev. D 104, 064047 (2021), +arXiv:2104.04582 . +[45] S. Xin, W.-B. Han, and S.-C. Yang, Phys. Rev. D 100, 084055 (2019). +12 + +Taiji Data Challenge +A PREPRINT +[46] C. Zhang, W.-B. Han, and S.-C. Yang, Commun. Theor. Phys. 73, 085401 (2021). +[47] X.-H. Zhang, S. D. Mohanty, X.-B. Zou, and Y.-X. Liu, Phys. Rev. D 104, 024023 (2021). +[48] Kupfer et al., Mon. Notices Royal Astron. Soc. 480, 302 (2018). +[49] G. Nelemans, L. R. Yungelson, and S. F. Portegies Zwart, Astron. Astrophys. 375, 890 (2001). +[50] G. Nelemans and C. A. Tout, Mon. Notices Royal Astron. Soc. 356, 753 (2005). +[51] J. Gair, M. Hewitson, A. Petiteau, and G. Mueller, in Handbook of Gravitational Wave Astronomy, edited by +C. Bambi, S. Katsanevas, and K. D. Kokkotas (Springer Singapore, Singapore, 2021) pp. 1–71. +[52] A. Toubiana, S. Marsat, S. Babak, J. Baker, and T. D. Canton, Phys. Rev. D 102, 124037 (2020). +[53] A. Sesana, Phys. Rev. Lett. 116, 231102 (2016). +[54] N. Bartolo, D. Bertacca, R. Caldwell, C. R. Contaldi, G. Cusin, V. De Luca, E. Dimastrogiovanni, M. Fasiello, +D. G. Figueroa, G. Franciolini, A. C. Jenkins, M. Peloso, M. Pieroni, A. Renzini, A. Ricciardone, A. Riotto, +M. Sakellariadou, L. Sorbo, G. Tasinato, J. Torrado, S. Clesse, and S. Kuroyanagi, “Probing Anisotropies of the +Stochastic Gravitational Wave Background with LISA,” (2022), arXiv:2201.08782 . +[55] R. Abbott et al. (LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration), Phys. Rev. D +104, 022004 (2021). +[56] The LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration, Phys. Rev. D 105, +122001 (2022). +[57] C. Caprini, D. G. Figueroa, R. Flauger, G. Nardini, M. Peloso, M. Pieroni, A. Ricciardone, and G. Tasinato, J. +Cosmol. Astropart. Phys. 2019, 017 (2019), arXiv:1906.09244 . +[58] M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir, Phys. Rev. Lett. 112, 041301 (2014). +[59] J. Liu, Z.-K. Guo, R.-G. Cai, and G. Shiu, Phys. Rev. Lett. 120, 031301 (2018). +[60] R.-G. Cai, S. Pi, and M. Sasaki, Phys. Rev. Lett. 122, 201101 (2019). +[61] C. Yuan and Q.-G. Huang, Phys. Lett. B 821, 136606 (2021). +13 + diff --git a/bdE1T4oBgHgl3EQfKwMf/content/tmp_files/load_file.txt b/bdE1T4oBgHgl3EQfKwMf/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..308df8190a7ebd4f2b28f99a4a99202d30fc35eb --- /dev/null +++ b/bdE1T4oBgHgl3EQfKwMf/content/tmp_files/load_file.txt @@ -0,0 +1,1133 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf,len=1132 +page_content='Taiji Data Challenge for Exploring Gravitational Wave Universe A PREPRINT Zhixiang Ren1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Tianyu Zhao1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2∗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Zhoujian Cao1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='†,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Zong-Kuan Guo1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='6,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Wen-Biao Han1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='7,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='8,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='9,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='10,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Hong-Bo Jin1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='11,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='8,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Yue-Liang Wu1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='9† 1 Taiji Laboratory for Gravitational Wave Universe,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' University of Chinese Academy of Science (UCAS),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Beijing 100049,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' China 2 Peng Cheng Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Shenzhen 518055,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' China 3 Department of Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Beijing Normal University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Beijing 100875,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' China 4 School of Fundamental Physics and Mathematical Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Hangzhou Institute for Advanced Study,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' UCAS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Hangzhou 310024,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' China 5 CAS Key Laboratory of Theoretical Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Institute of Theoretical Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Chinese Academy of Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Beijing 100190,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' China 6 School of Physical Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' UCAS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Beijing 100049,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' China 7 Shanghai Astronomical Observatory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Chinese Academy of Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Shanghai 200030,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' China 8 School of Astronomy and Space Science,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' UCAS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Beijing 100049,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' China 9 International Centre for Theoretical Physics Asia-Pacific (ICTP-AP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' UNESCO),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' UCAS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Beijing 100190,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' China 10 Shanghai Frontiers Science Center for Gravitational Wave Detection,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Shanghai 200240,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' China 11 Key Laboratory of Computational Astrophysics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' National Astronomical Observatories,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Beijing 100101,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' China January 10,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 2023 ABSTRACT The direct observation of gravitational waves (GWs) opens a new window for exploring new physics from quanta to cosmos and provides a new tool for probing the evolution of universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' GWs detection in space covers a broad spectrum ranging over more than four orders of magnitude and enables us to study rich physical and astronomical phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Taiji is a proposed space-based gravitational wave (GW) detection mission that will be launched in the 2030s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Taiji will be exposed to numerous overlapping and persistent GW signals buried in the foreground and background, posing various data analysis challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In order to empower potential scientific discoveries, the Mock Laser Interferometer Space Antenna (LISA) Data Challenge and the LISA Data Challenge (LDC) were developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' While LDC provides a baseline framework, the first LDC needs to be updated with more realistic simulations and adjusted detector responses for Taiji’s constellation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In this paper, we review the scientific objectives and the roadmap for Taiji, as well as the technical difficulties in data analysis and the data generation strategy, and present the associated data challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In contrast to LDC, we utilize second-order Keplerian orbit and second-generation time delay interferometry techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Additionally, we employ a new model for the extreme-mass-ratio inspiral waveform and stochastic GW background spectrum, which enables us to test general relativity and measure the non-Gaussianity of curvature perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' As the first data challenge for Taiji, we aim to build an open ground for data analysis related to Taiji sources and sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' More details can be found on the official website http://taiji-tdc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='ictp-ap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Keywords gravitational wave · universe evolution · Taiji · data challenge ∗contributed equally †Corresponding author(s);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' ylwu@itp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='cn;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='zjcao@amt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='cn arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='02967v1 [gr-qc] 8 Jan 2023 Taiji Data Challenge A PREPRINT 1 Introduction Ground-based GW detectors have made remarkable achievements since the first detection of GW150914 [1], nearly 100 GW events have been observed so far [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The discovery of GWs not only provides a more fundamental test on Einstein’s theory of general relativity (GR) but also leads us to study deeply on the nature of gravity and spacetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In particular, GWs detection in sapce enables us to probe the formation and structure of black holes from the early Universe through the peak of star formation era and to understand how does the intermediate mass seed black hole formed in the early universe and how the seed black hole grows into the large or extreme-large black hole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' It will also be helpful to explore whether the dark matter could form into the black hole or primordial black hole could be the candidate of dark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Due to the limitation by seismic noise and arm length, ground-based detectors are not sensitive at frequencies lower than 10 Hz [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' By moving the detector to space, we can eliminate the seismic and gravity-gradient noise and open up the frequency band of the GW within [10−4, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='1]Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The first planned space-based GW detection project is the laser interferometer space antenna (LISA) [4], proposed by the European Space Agency (ESA) and the National Aeronautics and Space Administration (NASA), which will be launched in around 2037 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Furthermore, LISA has laid a solid foundation for space-borne GW detection, including scientific objectives, data analysis algorithms, and instrumental techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' During the early 2000s, Chinese scientists were also interested in space-borne GW detection programs and considered developing independent missions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The feasibility of space-based GW detection was studied by the Chinese Academy of Sciences (CAS) in 2008, followed by the initial mission proposal presented in 2011 [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' A half-million-kilometer arm length and a noise budget that is a hundred times more sensitive than LISA at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='1 Hz made this instrument particularly sensitive to intermediate mass black hole mergers [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In 2012, the first mission descoping attempt was reported to prefer a constellation of three satellites separated each by about 3 million kilometers, coordinating both technical and scientific goals, and the proposed three-step road map was first presented in which the launch time for the Chinese space GW detector was expected to be in the 2030s [7, 6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The CAS built prototypes that were used to conduct proof-of-principle experiments [8–11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Similar to LISA, Taiji consists of three spacecraft (SC), and each SC follows a heliocentric orbit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The three SC form an approximately 3 million-kilometer-long equilateral triangle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' There is a 20-degree trail between the center of mass of the constellation and the Earth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The constellation is roughly 1AU distant from the Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' This caused a slight eccentricity in the orbits of the three SC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' With the stable constellation, Taiji’s sensitive frequency band is [10−4, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='1]Hz [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' A three-step road map of the Taiji program is: 1) launch a satellite Taiji-1 for individual technique validation, 2) launch two satellites Taiji-2 for almost all techniques test, and 3) launch complete Taiji three satellites [12, 13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The Taiji program, with its three-step road map, has received priority support from the CAS’s strategic priority research program since 2016 for its pre-experimental study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Some key technologies have been developed further in the studies [12, 14–19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Currently, the first phase of the Taiji-1 on-orbit experiment has been successfully completed [20, 21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In this paper, we present the first Taiji Data Challenge (TDC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Specifically, we review the scientific objectives and technical challenges during the data processing procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Then, we visualize all TDC datasets and explain their scientific potential and technical obstacles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' We implement time-domain time delay interferometry (TDI) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='0 for detector response calculation, which makes our data more realistic compared to LDC1’s original datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' As the main component of our data challenge, we generate datasets that contain only one source and also datasets that contain multiple sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' We further generate an extreme-mass-ratio inspiral (EMRI) waveform constructed under the general parameterized metric, which allows us to test GR and investigate the non-Gaussianity of curvature perturbations by observing the GW background it induces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In Section 2, we introduce the scientific objectives and technical challenge of Taiji mission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In Section 3, we demonstrate how to simulate Taiji instrumental noise, detector response, and GW waveform respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In Section 4, we show the properties of each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The last section contains our discussions about future work and features of our TDC website.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 2 Scientific objective and technical challenge of Taiji mission Taiji detectors will receive a large amount of GW signals from different sources in the target frequency band of [10−4, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='1]Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The observatory will measure signals from a wide range of different sources relevant to the astrophysical mechanism of the formation of black holes and galaxies, the test of GR, and the study of cosmology, including massive black holes binaries (MBHBs) at all redshifts;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' EMRIs;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' the inspiral of stellar-origin binary black holes (SOBBHs);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' galactic binaries (GB);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' verification galactic binaries (VGBs), and various stochastic GW background (SGWB) sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 3https://sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='esa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='int/web/lisa 2 Taiji Data Challenge A PREPRINT The mission’s primary objective is to determine how and when massive black holes have formed and grown over cosmic time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' For the purpose of reconstructing their evolution, the study will explore almost all of the mass-redshift parameter space that is relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' We will investigate the distribution of MBHB’s spins and masses in order to distinguish between different formation mechanisms based on the GW signal from MBHBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Additionally, the mission will analyze the signals from GBs and provide information on stellar evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Tens of millions of binaries in our galaxy produce stochastic foregrounds, which we can estimate by observing GBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' It is possible to constrain the evolutionary pathways of compact binaries by examining the characteristics of the population, such as the number density of sources as a function of frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' It is expected that Taiji will provide exceptionally strong tests of GR predictions by observing highly relativistic MBHBs and EMRIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' During the merger phase of a binary black hole system, BHs travel at nearly the speed of light and interact strongly with each other, which allows the study of the full nonlinear dynamics of gravity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' By observing the signal of the EMRI system, the mass, spin, and quadrupole moment of the central massive black hole will be measured making testing its level of Kerr-ness and proving the no-hair hypothesis possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Finally, a space-based GW detector will explore new physics and cosmology and seek out previously unknown GW sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The scientific objectives of the Taiji mission are listed in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Table 1: Scientific objectives of Taiji mission No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Scientific objective 1 Dynamical evolution and population of MBHBs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' study the birth and growth of MBHs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' and the astrophysical environment of the host galaxy 2 Precisely estimate parameters of MBH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' reveals the physical nature of BHs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' probe dynamics of galactic nuclei,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' and the astrophysical environment at the galaxy center by EMRI 3 Formation evolution and population of Galaxy binaries 4 Study SOBHB formation,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' environment,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' population,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' and joint observation with LIGO 5 Test GR,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' study the properties of GW propagation 6 GW cosmology,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' measurement of the Hubble constant and cosmology constant 7 PSD shape and upper limit of SGWB signals 8 Detect unmodeled signals 9 New physics and cosmology beyond GR GWs signals are expected to be many orders of magnitude below the noise level caused by laser frequency fluctuations [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' A post-processing technique called TDI has been proposed to reduce laser noise to an acceptable level [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The idea is to construct virtual equal-arm interference by combining the data streams in the appropriate way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The second-generation TDI is applicable to rotating and flexing detectors with linearly varying arm lengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The actual Taiji orbits are affected by the gravitational field of the planets, which leads to non-periodic orbits.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In science analysis, it is necessary to extract scientific information from the various TDI data streams;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' in a similar manner to the procedure for the electromagnetic case, science analysis is carried out by deconvolution of the response function from the data stream in order to obtain the incident GW field observed by Taiji.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The main task of the data analyst is to quickly identify the signals and estimate their physical parameters precisely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Unlike current ground-based detectors, Taiji will be sensitive to continuous sources, primarily from GBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' It is expected that GBs will be the most numerous of the sources, the unresolved component of the galactic population produces an effectively stochastic "confusion noise".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Due to the non-Gaussianity of GB foreground noise, detecting other signals buried in the foreground noise is a challenging task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' What’s more, analysis of the foreground itself is another challenge because of the enormous number of signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Because of the long duration and complex morphology of their signals, detecting and characterizing the physics of SOBBHs with LISA is a highly nontrivial challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Data gaps will appear in the Taiji data stream due to maintenance, telescope realignment, and communication with Earth by a high-gain antenna.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' A series of significant challenges arise when dealing with gapped data, namely the information loss, spectral leakage, and noise correlations [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Another challenge for GW signal detection is the interference of instrumental glitches, which can be separated relatively natural from signals by ground observations with multiple interferometers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In contrast, this coherent searching approach can not be directly applied in space-based detection, so novel glitch classification algorithms need to be developed [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' All the technical challenges are summarized in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 3 Method When analyzing real detector data, it is necessary to model the signal and noise;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' therefore, for simplicity in the TDC, several idealized models are utilized during data simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' This section will introduce these models and their respective approximations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Using the existing waveform model, we first obtain the source frame GW waveform during 3 Taiji Data Challenge A PREPRINT Table 2: Technical challenges of Taiji mission No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Technical challenges 1 Foreground GB signals separation 2 SOBBH signals separation 3 Others Signal with non-Gaussian GB noise 4 Overlapping MBHB signals 5 Instrumental glitches 6 Data gap due to maintenance, telescope re- alignment, and communication issue 7 TDI technique to suppress laser frequency noise signal simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Then, we determine the response of each link, which is dependent upon the orbit of the Taiji SCs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In addition, TDI is used to obtain the signal in the X, Y, and Z channels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The instrumental noise in those 3 channels is Gaussian noise simulated by their PSD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In the final step, the signal is injected into the noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='1 Orbital motion We use Keplerian orbit to approximate the motion of the Taiji SC [25–27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Given the distance between the SC i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' the arm length L and the distance from the SC to the sun a, the eccentricity of the orbit is defined by: e = � 1 + 4 √ 3α cos φ + 4 3α2 �1/2 − 1, (1) where φ = π/3 + 5α/8 is the angle between the SC’s orbital planes and the ecliptic plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' α = L/2a is a small parameter originally used in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The specific value of φ reduces the breathing effect of the arm length [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The reference position of the 3 SC is given by: � � � � � xref,k(t) = a cos ι(cos ψk(t) − e), yref,k(t) = a � 1 − e2 sin ψk(t), zref,k(t) = −a sin ι(cos ψk(t) − e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (2) where ι is the orbital inclination of SC1 relative to the ecliptic plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' tan ι = 2 √ 3 α sin φ � 1 + 2 √ 3α cos φ �, (3) where ψk(t) is the eccentric anomaly of SCk, which is obtained by solving the Kepler equation to the desired order iteratively: ψk(t) − e sin ψk(t) = mk(t) = m0,k + Ω(t − t0) = m0,1 − 2π(k − 1) 3 + Ω(t − t0), Ω = 2π 1 year.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (4) Then, the position of 3 SC could be expressed in terms of the reference position and periastron λk = λ1 + 2π(k − 1)/3: � � � xk(t) = cos λkxref,k(t) − sin λkyref,k(t), yk(t) = sin λkxref,k(t) + cos λkyref,k(t), zk(t) = zref,k(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (5) In summary, the orbits of 3 SCs are determined by 4 parameters: the semi-major axis a, the arm length L, SC1’s initial mean anomaly m0,1, and SC1’s initial periastron λ1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2 Light travel time Following Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [28], we could use the Taylor expansion of the position of the emitter SC to calculate the light travel time analytically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' So the light travel time could be expressed as: LTT = LTT(0) + LTT(1) + LTT(2) + LTT(Sh) (6) 4 Taiji Data Challenge A PREPRINT with LTT(0)(t) = 1 c |⃗xrecv(t) − ⃗xsend(t)| (7) LTT(1)(t) = ⃗vrecv(t) c2 (⃗xrecv(t) − ⃗xsend(t)) (8) LTT(2)(t) = |⃗xrecv(t) − ⃗xsend(t)| c3 � ⃗v2 recv(t) − ⃗arecv(t) · (⃗xrecv(t) − ⃗xsend(t)) (9) + �⃗vrecv(t) · (⃗xrecv(t) − ⃗xsend(t)) |⃗xrecv(t) − ⃗xsend(t)| �2 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (10) where the subscripts ’send’ and ’recv’ represent the emitter SC and the receiver SC respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Finally, we consider the Shapiro delay caused by the Sun’s gravitational field, which is a second-order effect [29]: LTT(Sh) = RS c · ln |⃗xsend(t)| + |⃗xrecv(t)| + |⃗xrecv(t) − ⃗xsend(t)| |⃗xsend(t)| + |⃗xrecv(t)| − |⃗xrecv(t) − ⃗xsend(t)|, (11) where RS is the Schwarzschild radius of the Sun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='3 Detector response For the data generation, we use a time domain detector response and the GPU accelerated code provided by [30], which enables us to generate a large amount of data directly in the time domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' First, we transform the GW waveform from the source frame to the solar-system barycenter (SSB) frame by � hSSB + hSSB × � = � cos 2ψ − sin 2ψ sin 2ψ cos 2ψ � � hsrc + hsrc × � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (12) Then, the length variation of one arm caused by the GW signal is: H(t) = hSSB + (t)ξ+(ˆθ, ˆφ,⃗n(t)) + hSSB × (t)ξ×(ˆθ, ˆφ,⃗n(t)), (13) where the antenna pattern ξ+ and ξ× are given by: � ξ+(⃗u,⃗v,⃗n) = (⃗u · ⃗n)2 − (⃗v · ⃗n)2, ξ×(⃗u,⃗v,⃗n) = 2 (⃗u · ⃗n) (⃗v · ⃗n) , (14) ˆn(t) is the unit vector of the arm, ˆθ, ˆφ are polar and azimuthal angle in the SSB frame, based on the orthonormal basis vectors (ˆer, ˆeθ, ˆeφ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' ⃗u,⃗v are polarization vectors defined by ⃗u = −ˆeφ and ⃗v = −ˆeθ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The propagation vector is ⃗k = −ˆer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Light travel time along the arm affected by the GW is : trecv ≃ tsend + LTT − 1 2c � L 0 H(⃗x(λ), t(λ)) dλ, (15) where we use first order approximation as t(λ) = tsend +λ/c, ⃗x(λ) = ⃗xsend(tsend)+λ⃗n(tsend), ⃗xsend is the position of the emitter SC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The parameter λ used as the integration variable describes the photon path.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' With those approximations, H(⃗x(λ), t(λ)) is given by: H(⃗x(λ), t(λ)) = H � t(λ) − ⃗k · ⃗x(λ) c � = H � tsend − ⃗k · ⃗xsend(tsend) c + λ1 − ⃗k · ⃗n(tsend) c � (16) Combining equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (15) and (16) and differentiating the resulting expression with respect to tsend yields the relative frequency shift, y(tsend) = 1 2(1 − ⃗k · ⃗n(tsend)) � H � tsend − ⃗k · ⃗xsend(tsend) c � − H � tsend − ⃗k · ⃗xrecv(trecv) c + LTT �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (17) We assume that ⃗n(tsend) ≃ ⃗n(trecv) since the variation of arm direction due to the SC’s motion during the light travel time is less than 10−3rad in the case of Taiji [31] and trecv ≃ tsend + LTT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Finally, the GW strain of one arm is: y(trecv) = 1 2(1 − ⃗k · ⃗n(trecv)) � H � trecv − ⃗k · ⃗xsend(trecv) c − LTT(trecv) � − H � trecv − ⃗k · ⃗xrecv(trecv) c �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (18) 5 Taiji Data Challenge A PREPRINT 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4 TDI Combination Due to the unequal arm length of the Taiji SCs, the laser frequency noise could not be canceled naturally, which will be orders of magnitude above the GW signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' So the TDI technique was developed to cancel the noise by shifting the data from different SCs by subtle time delays and combining them together.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The TDI technique can be divided into several generations: TDI 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='0 is used in the static case, which does not consider the rotation and breathing effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In other words, the arm lengths are constants in time, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' the light travel time satisfies LTTi = LTTi′ = const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' TDI 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='5 is used in the rigid rotating case, which does not consider the breathing effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The arm lengths are still constants in time, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' LTTi = const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=', LTTi′ = const.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' but LTTi ̸= LTTi′ here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' TDI 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='0 is used in the flexing case, the arm lengths are functions of time, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' LTTi = LTTi(t), LTTi′ = LTTi′(t), and LTTi(t) ̸= LTTi′(t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Here we adopt the notation from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [22], the number in the subscript represents different links, where i ∈ {1, 2, 3} denotes the clockwise link opposite to SCi and i′ denotes the counter-clockwise link.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The first generation unequal arm Michelson combination is: X1(t) = (y2′:322′ + y1:22′ + y3:2′ + y1′) − (y3:2′3′3 + y1′:3′3 + y2′:3 + y1) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (19) The second-generation Michelson combination is X2(t) = y1′ + y3,2′ + y1,22′ + y2′,322′ + y1,3′322′ + y2′,33′322′ + y1′,3′33′322′ + y3,2′3′33′322′ − y1 − y2′,3 − y1′,3′3 − y3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2′3′3 − y1′,22′3′3 − y3,2′22′3′3 − y1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='22′22′3′3 − y2′,322′22′3′3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (20) The variables Y and Z could be obtained by cyclic permutation of the indices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The colon denotes time delay when the arm length is time-independent, f(t):j := f � t − Lj c � , f(t):jk = f � t − Lk c − Lj c � = f(t):kj, (21) which is commute for j ̸= k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Next, a comma denotes time delays with time-dependent arm lengths, here we compute chained delays as simple sums of delays rather than nested delays, f(t),jk = f � t − Lk(t) c − Lj(t) c � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (22) This approximation is sufficient for computing the GW response function [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='5 Instrumental noise Despite the complex noise sources that will be involved in the Taiji detection data in practice, in our simulation, we use a noise model consisting of just two components for simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The first one is the high-frequency component, which represents the overall noises that come from the optical metrology system, and the second is the low-frequency component, which represents the test mass acceleration noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The power spectral density (PSD) is given by: Poms(f) = 64 × 10−24 1 Hz � 1 + �2mHz f �4� �2πf c �2 , Pacc(f) = 9 × 10−30 1 Hz � 1 + �0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4mHz f �2� � 1 + � f 8mHz �4� � 1 2πfc �2 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (23) Following [32], the analytic model of the one-sided noise PSD is derived from the noise components in each interfero- metric measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' We will explicitly show PSD for a Michelson-type TDI generator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Given the data combination (19) and (20) with the assumption that the noise of each link has the same PSD, the noise PSD of the first and the second generation TDI X channel is: PSDX1 = 16 sin2(ωL) (Poms + (3 + cos(2ωL))Pacc) , (24) PSDX2 = 64 sin2(ωL) sin2(2ωL) (Poms + (3 + cos(2ωL))Pacc) , (25) where ω = 2πf/c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In this paper, we use TDI 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='0 PSD for noise generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 6 Taiji Data Challenge A PREPRINT 4 Dataset 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='1 Overall setting The TDC dataset was designed based on the scientific objectives of Taiji.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' For most of the sources of Taiji, we do not have well-established data analysis algorithms because they are not detected by ground-based detectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' So at the beginning of the data challenge, we should focus on each source separately for simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Each of the datasets from TDC-1 to TDC-6 contains signals from a single source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Multiple sources are included in the last dataset TDC-7, including MBHBs, VGBs, and GB foregrounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Those datasets cover all the sources for the scientific objectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Similar to LDC, the sampling rate here in TDC is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='1 Hz for all datasets, while this setting will be adjustable with Taiji’s configuration accordingly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' First, we generate the signal, then compute the TDI 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='0 response, and add it to the simulated noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' For the time domain signals, we use the time domain TDI response as mentioned in 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='3 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' For the stochastic GW signals, we generate them directly by their PSD, which considers TDI response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Next, we will introduce the configuration and parameters used to generate the datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 1: Time-domain data of all the TDC datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The strain of TDI X channel data and signals are presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (a), TDC-1, the MBHB signal is zoomed in because of its duration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (b) and (c), TDC-2-1 and TDC-2-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (d), TDC-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (e), TDC-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (f), TDC-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (g) and (h), TDC-6-1 and TDC-6-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (i), TDC-7, signals No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='8 and No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='9 are zoomed in due to the closeness of their coalescence time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 7 1e-19 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='0 Data 1e-20 MBHB 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='5 TDI X Strain 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00005 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00010 +9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='999e-1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 Time [yr]1e-20 Data EMRI TDI X Strain 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 Time [yr]le-20 Data EMRI TDI X Strain 1 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 Time [yr]le-20 Data VGB 2 TDI X Strain 0 1 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 Time [yr]Data GB TDI X Strain 3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 Time [yr]le-20 Data SOBBH TDIX Strain 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='0 Time [yr]le-20 Data SGWB TDIX Strain 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 Time [yr]le-20 Data SGWB TDIX Strain 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 Time [yr]1e-19 5 Data 1e-20 GB MBHB 4 VGB 3 I X Strain 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='001 +1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='6 TDI 1 0 - 1 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00 Time [yr]Taiji Data Challenge A PREPRINT (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 2: Frequency domain data of all the TDC datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The PSD of TDI X channel data and signals are compared with the noise PSD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (a), TDC-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (b) and (c), TDC-2-1 and TDC-2-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (d), TDC-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (e), TDC-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (f), TDC-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (g) and (h), TDC-6-1 and TDC-6-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (i), TDC-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2 Massive black hole binary MBHBs are primary sources of Taiji, which is sensitive to MBHBs with total mass in the range of [105, 108]M⊙ [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' It is expected to detect 1 ∼ 20 MBHBs per year [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' We will be able to gain valuable insight into how MBHs are formed by measuring their spins and masses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' It should be possible for us to test the hypothesis that modern galaxies are the result of the merger of smaller "seed" galaxies in the early universe, as we will be able to detect the merger of MBHB out to a high redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' We use SEOBNRv4_opt [34] here to generate the MBHB signal and shift it by the coalescence time tc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Only the l = m = 2 mode is included in the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Both TDC-1 and TDC-7 contain MBHB signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' For TDC-1, there is only one MBHB signal in this dataset, the time domain and the frequency domain behavior of the TDC-1 data are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 1a and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 2a respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In the time domain, we could see that the merger portion of the signal is not buried in the noise, which has a short duration of ∼ hour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Then, in the frequency domain, the signal is below the noise PSD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The parameter of MBHB signals injected in those two datasets are shown in Table 3, where MT is the total mass of two black holes, q is the mass ratio with q < 1, s1, s2 is the spin parameters, ι is the inclination angle, ψ is the polarization angle, λ and β is ecliptic longitude and ecliptic latitude characterize the sky location of the source, tc is the coalescence time, and φc is coalescence phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' TDC-1 only contains signal No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 1 and all 10 signals are included in TDC-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The time domain and the frequency domain behavior of the TDC-7 data are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 1i and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 2i respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Signals No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 8 and No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 9 are close together, presenting additional challenges to data processing algorithms that are not encountered by ground-based detectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 8 10-38 Data Noise PSD 10~39, MBHB 10-40 TDI X PSD 10-41 10~42, 10-43 , 10-44 10~45 10-4 10~3 10~2 10-1 f [Hz]10-38 Data Noise PSD EMRI 10-39 10-40 I X PSD [1/Hz] 10 41 TDI 10~42, 10~43, 10~44 10~45 10~4 10~3 10-2 10-1 f [Hz]10-38 Data Noise PSD EMRI 10-39 10-40 TDI X PSD [1/Hz] 10 41 10-42 10-43, 10-44 10-45 10~4 10~3 10~2 10-1 f [Hz]Data 10-37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Noise PSD VGB 10-39, PSD X 10-41 1043.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 1045 10~4 10~3 10~2 10-1 f [Hz]Data 10-37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Noise PSD GB 10~39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' X PSD TDI 10-41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 10-43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 1045 10~4 10~3 10~2 10-1 f [Hz]10-38 Data Noise PSD 10~39 SOBBH 10-40,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' I X PSD 10~41 TDI 10-42 1043,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 10-44 10~45 10~4 10-3 10~2 10-1 f [Hz]10-38 Simulated data Noise PSD 10~39 SGWB signal SGWB PSD 10-40 I X PSD 10-41 TDI 10-42 10-43 10-44 1045 10-4 10-3 10~2 10-1 f [Hz]10-38 Simulated data Noise PSD 10-39,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' SGWB signal SGWB PSD 10-40 TDI X PSD 10-41 10-42 10-43 10-44,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 1045 10-4 10-3 10~2 10-1 Freq [Hz]Data 10-37 GB VGB Noise PSD MBHB 1039 TDI X PSD [1/Hz] 10-41,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 10-43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 1045 10~4 10~3 10~2 10-1 f [Hz]Taiji Data Challenge A PREPRINT Table 3: Parameters of MBHB signals used in TDC-1 and TDC-7 No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' MT (M⊙) q s1 s2 DL(Gpc) ι ψ λ β tc(yr) φc 1 6 × 105 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='39 π/3 π/3 π/5 π/4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='5 2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2 × 106 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='39 2π/3 π/3 π/10 π/8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4 1 3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='8 × 106 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='12 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='02 π π/3 π/15 5π/4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='05 4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4 × 106 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='08 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='36 5π/6 π/3 π/20 7π/4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='1 5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='5 × 106 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='8 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='39 π/3 π/3 π/25 3π/4 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='15 6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2 × 106 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='6 106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='78 π/6 2π/3 π/30 5π/4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='35 7 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4 × 106 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='48 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='02 8π/30 5π/3 π/35 π/8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='45 8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2 × 106 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='16 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='28 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='69 13π/30 π/3 2π/5 π/12 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='6 1 9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2 × 106 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='08 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='69 14π/30 π/3 3π/5 11π/40 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='601 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4 10 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='2 × 107 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='08 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='68 π/3 π/3 6π/5 π/4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='3 Extreme-mass-ratio inspiral EMRIs are binary black hole systems consisting of a stellar-mass compact object (CO) and a massive black hole with mass M ∼ 104M⊙ − 107M⊙.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Taiji will observe few tens to hundreds EMRI events over 2 years with signal-to-noise ratio (SNR) above 20 [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Because of the extremely large mass ratio, the EMRI evolves slowly, inspiraling about 104 ∼ 105 cycles in Taiji’s frequency band [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Since EMRI signals contain rich information about the geometry surrounding the central black holes, they are one of the primary fundamental physics goals of the Taiji mission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' It has been suggested that detections of EMRIs could provide a highly accurate observational test of the "Kerr-ness" of the central MBH [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='What’s more, EMRIs sample the stellar population near the central black holes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='By detecting EMRI signals, we can probe the physical properties of the central MBH and test GR [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Several waveform templates are developed for such a promising source of Taiji 1) Teukolsky-based method, [38, 39] 2) Numerical Kludge (NK)[40], 3) Analytic Kludge (AK)[41], 4) Augmented Analytic Kludge (AAK) [42–44], and 5) XSPEG [45, 46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The first 2 of them are computationally expensive, and the AK waveform doesn’t suit Kerr space-time, so we utilize the GPU-accelerated AAK waveform [44] for the TDC-2-1 dataset generation and the XSPEG waveform for the TDC-2-2 dataset generation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' There is only one EMRI signal in each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Because of the KRZ metric used in XSPEG waveform construction, TDC-2-2 could be used to test GR, which is a key scientific objective of the Taiji mission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The time domain and the frequency domain behavior of the data are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 1b and 2c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='Unlike MBHBs, the amplitude of a typical EMRI is an order of magnitude below the instrumental noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Detection is only possible if enough SNR is accumulated over a number of wave cycles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The parameters of EMRI waveform injected in TDC-2-1 is (M, µ, a0, e0, p0, ι0, θS, φS, θK, φK, Φϕ,0, Φθ,0, Φr,0, DL) = (106M⊙, 30M⊙, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='6, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='6, 15, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='7, 10−6, 10−6, 10−6, 10−6, 0, 0, 0, 100Mpc), M and a are the mass and spin parameter of the MBH, p is the semi-latus rectum, e is eccentricity, ι is the orbit’s inclination angle from the equatorial plane, θS, and φS are the polar and azimuthal sky location angles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' θK and φK are the azimuthal and polar angles describing the orientation of the spin angular momentum vector of the MBH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Φϕ,0, Φθ,0, Φr,0, represent the phase of azimuthal, polar, and radial modes respectively, DL is the luminosity distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The parameters of the EMRI waveform injected in TDC-2-2 is (M, µ, a0, e0, p0, ι0, λ, β, DL) = (106M⊙, 10M⊙, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='9, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='6, 15, π/4, 0, π/4, 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='3Mpc), and the KRZ metric deformation parameter is (δ1, δ2, δ3) = (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Compared to the existing LDC1-2 dataset for EMRI, an updated AAK waveform template is used in TDC-2-1, and a waveform based on the KRZ metric is used in TDC-2-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='4 Galactic binary We use the simple GB model from Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [30], which is expressed in the source frame as: hsrc + (t) = A(1 + cos2 ι) cos Φ(t), hsrc × (t) = 2A sin ι sin Φ(t), Φ(t) = φ0 + 2πf0t + π ˙f0t2 + π 3 ¨f0t3, ¨f0 = 11 3 ˙f 2 0 f0 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (26) where A is the overall amplitude, φ0 is the initial phase at the start of the observation, ι is the inclination of the BWD orbit to the line of sight from the origin of the SSB frame.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The intrinsic parameter is the frequency of the signal f and its derivative ˙f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The comparison to LDC’s GB waveform ¨f0 is considered here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='There are enormous GBs populated in the 9 Taiji Data Challenge A PREPRINT Milky Way [4] which form foreground noise, and disentangling those signals is a challenging task [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' With the help of GWs, GB foreground observations provide a key method for measuring the properties of a fraction of the galactic stellar population that is routinely assumed but has never been directly observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' What’s more, there are some bright GBs called LISA verified binaries [48], the latest catalog is available online4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Following the above catalog, we generate the TDC-3 dataset, which contains 43 VGBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The foreground GB noise is in the TDC-4 dataset, which consists of ∼ 3e7 GB signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The catalog of the TDC-4 dataset comes from the population study of GBs [49, 50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='Both the signal and the noise PSD of these two datasets are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 2d and 2e, associated with the corresponding time domain data shown in 1d and 1e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Compared to LDC1’s dataset, we use TDI 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='0 here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' That GB noise is also included in TDC-7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The Taiji mission faces a data analysis challenge because of the presence of non-Gaussian and non-stationary astrophysical foregrounds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Due to the presence of foreground signals, GW source separation procedures will be complicated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' A resolvable signal’s source parameter estimation will also be affected by the level of confusion noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Therefore, it is critical to study, understand, and predict the overall shape and amplitude of the potential foreground components of the Taiji data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='5 Stellar-origin binary black holes Space-based detectors observe the early inspiral of SOBBH systems, whose merger will be detected by ground-based detectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Those systems evolve slowly in the LISA and Taiji frequency bands, which enable high-precision parameter estimation [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The joint observation of SOBBH by Taiji and ground-based detectors could be used to probe low- frequency modifications due to deviations from GR or to environmental effects, to facilitate electromagnetic joint observations [52, 53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' By estimating coalescence time and sky location, we could forecast the signals for ground-based detectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' We generate the TDC-5 dataset, which contains 21721 SOBBH signals, whose catalog comes from [53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The time domain and the frequency domain behavior of the data are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 1f and 2f.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The SOBBH signals are completely below the noise in the frequency domain, which are background signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' We generate the waveform using the IMRPhenomD template, then transform it to the time domain and apply the TDI response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The main difference between the TDC-5 and LDC1-5 datasets is that we use the TDI 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='0 response in the time domain rather than the TDI 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='0 response in the frequency domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='6 Stochastic gravitational wave background One of the main scientific objectives of Taiji is to probe GWs from the early universe and reveal physics of GW sources [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Fundamental physics and astronomy would be greatly enhanced by the detection of a cosmological background from the early universe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The only way to obtain direct information about earlier epochs than decoupling may be through GWs and possibly neutrinos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' There are many possible astrophysical and cosmological sources that contribute to the stochastic background, and up to now we put only upper bounds on its amplitude [55], and on parameters characterizing its directional properties [56], by the LIGO/Virgo collaboration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' For space-based detection, we just have a single detector, cross-correlation based method is not suitable now, so a new SGWB detection algorithm is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' SGWBs that are Gaussian, isotropic, and stationary can be fully described by their energy density spectrum [57]: ΩGW (f) = f ρc d ρGW d f , (27) where ρGW is the energy density of gravitational radiation contained in the frequency range f to f + df, ρc = 3H2 0c2 8πG is the critical density of the universe, where c is the speed of light, and G is Newton’s constant, and H0 is the Hubble constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Typical SGWB sources include compact binary coalescence[55], cosmic phase transitions [58], reheating or preheating after inflation [59], and primordial scalar and tensor perturbations from inflation [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' There are 2 datasets that contain different types of SGWB signals, TDC-6-1 is generated by the power-law spectrum: h2ΩGW (f) = 10α � f f∗ �β , (28) where h is the dimensionless Hubble constant, f∗ is the pivot frequency, α characterize its amplitude at f∗ and β is the slope of the spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The SGWB signal in TDC-6-1 is generated using the parameters α = −12 and β = 2/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' TDC-6-2 is generated by non-Gaussian scalar perturbation-induced SGWB signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The induced GWs are generated during the formation of primordial black holes (PBHs), providing a powerful tool to search for PBHs [61].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Typically, curvature perturbations are assumed to have Gaussian probability density functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' There is a natural expectation that non-Gaussianity will be present when a sharp peak appears in the power spectrum of curvature perturbations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 4https://gitlab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='in2p3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='fr/LISA/lisa-verification-binaries 10 Taiji Data Challenge A PREPRINT GWs induced by scalar perturbations with a second-order local-type non-Gaussianity were studied in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [60].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The formulae of the SGWB spectrum used to generate TDC-6-2 data is given in equation (7) in Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [60] with the parameters FNL = 10, σ = 10−4, MPBH = 1022g, where FNL characterize the non-Gaussianity, σ is the peak width of curvature perturbation spectrum, and MPBH is the mass of PBH with the assumption that PBHs can serve as all dark matter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' In summary, 9 datasets are designed for TDC, and their essential motivation (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' the scientific objective and the technical challenge), and configurations are presented in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The scientific objectives and the corresponding technical challenges are shown in Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 1 and Tab.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Table 4: Summary of Taiji Data Challenge datasets Name Scientific objective Technical challenge Signals Waveform model TDC-1 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 6 7 1 MBHB signal SEOBNRv4_opt TDC-2-1 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 6 7 1 EMRI signal PN5AAK TDC-2-2 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 6 7 1 EMRI signal XSPEG TDC-3 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 6 7 43 VGB signals Sinusoidal TDC-4 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 6 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 7 3e7 GB signals Sinusoidal TDC-5 4,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 6 2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 7 2e5 SOBBH signals IMRPhenomD TDC-6-1 5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 6,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 7 7 SGWB Power-law TDC-6-2 5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 6,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 7 7 SGWB Non-Gaussian curvature perturbations TDC-7 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 5,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 6 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 7 10 MBHBs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 43 VGBs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 3e7 GBs SEOBNRv4_opt,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Sinusoidal 5 Discussions Building a data challenge is critical for scientists to develop algorithms and pipelines for future data analysis tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' We provide a complete workflow by constructing detection data and waveform templates within and beyond GR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' The datasets and challenges are available on the official website of TDC (http://taiji-tdc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='ictp-ap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='org).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Scientists are encouraged to participate in these data challenges and to submit their results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Currently, there is no deadline, and users are free to submit their results at any time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' We will rank the submitted results for each challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' As part of our website, we offer both data downloads and data customization services, which enable users to submit the data configuration file suited to their requirements, and we will provide users links to download the customized dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' With TDC, we hope to create a community of researchers who can collaboratively contribute to the development of Taiji’s data analysis pipelines and join the journey of exploring the universe and making new discoveries with Taiji Collaboration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 6 Acknowledgements The research was supported by the Peng Cheng Laboratory Cloud Brain and by Peng Cheng Cloud-Brain .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Further funding was provided by the National Key Research and Development Program of China Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 2021YFC2203001, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 2020YFC2201501 & No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 2021YFC2203002, as well as the NSFC (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 11920101003, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 12021003, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 12173071, and No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 12147103).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='C and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='H are supported by the CAS Project for Young Scientists in Basic Research YSBR-006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='C was also supported by “the Interdiscipline Research Funds of Beijing Normal University".' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='G was supported by the NSFC Grants No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 12235019 and No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 12075297.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' References [1] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Abbott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 116, 061102 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [2] The LIGO Scientific Collaboration, the Virgo Collaboration, the KAGRA Collaboration, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=', “GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run,” (2021), arXiv:2111.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='03606 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [3] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Matichard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=', Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Quantum Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 32, 185003 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [4] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Amaro-Seoane et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=', “Laser Interferometer Space Antenna,” (2017), arXiv:1702.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='00786 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [5] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Gong, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Xu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Bai, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Cao, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=', Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Quantum Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 28, 094012 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [6] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Luo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Wu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Hu, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Jin, Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Exp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 2021, 05A108 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [7] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Wu, in Presentation to 1st eLISA Consortium Meeting (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 11 Taiji Data Challenge A PREPRINT [8] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Luo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Dong, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Jin, Chin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 29, 079501 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [9] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Dong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Luo, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Jin, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Instrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 85, 024503 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [10] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Dong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Luo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Li, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Jin, Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Instrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 85, 074501 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [11] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Luo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Dong, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Jin, App.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' B 118, 309 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [12] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Hu and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Wu, Natl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 4, 685 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [13] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Luo, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Guo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Jin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Wu, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Hu, Results Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 16, 102918 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [14] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Luo, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Mahrdt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Goerth, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Heinzel, Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Opt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 56, 1495 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [15] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Luo, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Liu, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Jin, Optics & Laser Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 105, 146 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [16] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Liu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Dong, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Gao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Luo, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Jin, Optical Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 57, 1 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [17] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Luo, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Jin, Micrograv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' and Technol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 30, 775 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [18] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Deng, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Yang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Cao, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Zang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Chen, and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Fang, Optics Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 43, 1562 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [19] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Wang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Sha, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Kang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Luo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Li, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Li, Chinese Optics 11, 131 (2018), (in Chinese).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [20] The Taiji Scientific Collaboration, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 4, 34 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [21] The Taiji Scientific Collaboration, Int J Mod Phys A 36, 2102002 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [22] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Otto, Time-Delay Interferometry Simulations for the Laser Interferometer Space Antenna, Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' thesis, Hannover : Gottfried Wilhelm Leibniz Universität Hannover (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [23] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Blelly, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Bobin, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Moutarde, Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Notices Royal Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 509, 5902 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [24] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Robson and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Cornish, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 99, 024019 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [25] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Dhurandhar, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Nayak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Koshti, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Vinet, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Quantum Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 22, 481 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [26] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Nayak, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Koshti, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Dhurandhar, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Vinet, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Quantum Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 23, 1763 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [27] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Wu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Huang, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Qiao, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 100, 122001 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [28] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Chauvineau, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Pireaux, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Regimbau, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Vinet, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 72, 122003 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [29] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Hees, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Bertone, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Le Poncin-Lafitte, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 89, 064045 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [30] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Katz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Bayle, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Chua, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Vallisneri, “Assessing the data-analysis impact of LISA orbit approximations using a GPU-accelerated response model,” (2022), arXiv:2204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='06633 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [31] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rijnveld and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Pijnenburg, in International Conference on Space Optics — ICSO 2010, edited by N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Kadowaki (SPIE, Rhodes Island, Greece, 2017) p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [32] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Babak, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Hewitson, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Petiteau, “LISA Sensitivity and SNR Calculations,” (2021), arXiv:2108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='01167 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [33] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Katz, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Kelley, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Dosopoulou, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Berry, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Blecha, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Larson, Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Notices Royal Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 491, 2301 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [34] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Bohé, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Shao, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=', Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 95, 044028 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [35] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Gair, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Babak, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Sesana, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Amaro-Seoane, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Barausse, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Berry, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Berti, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Sopuerta, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' : Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 840, 012021 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [36] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Babak, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Gair, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Sesana, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Barausse, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Sopuerta, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Berry, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Berti, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Amaro-Seoane, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Petiteau, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Klein, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 95, 103012 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [37] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Barack and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Cutler, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 75, 042003 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [38] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Glampedakis, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Quantum Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 22, S605 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [39] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Han and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Cao, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 84, 044014 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [40] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Babak, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Fang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Gair, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Glampedakis, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Hughes, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 75, 024005 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [41] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Barack and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Cutler, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 69, 082005 (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [42] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Chua and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Gair, Class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Quantum Grav.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 32, 232002 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [43] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Chua, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Moore, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Gair, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 96, 044005 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [44] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Katz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Chua, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Speri, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Warburton, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Hughes, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 104, 064047 (2021), arXiv:2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='04582 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [45] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Xin, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Han, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Yang, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 100, 084055 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 12 Taiji Data Challenge A PREPRINT [46] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Zhang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Han, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Yang, Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Theor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 73, 085401 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [47] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Mohanty, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Zou, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Liu, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 104, 024023 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [48] Kupfer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=', Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Notices Royal Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 480, 302 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [49] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Nelemans, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Yungelson, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Portegies Zwart, Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 375, 890 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [50] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Nelemans and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Tout, Mon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Notices Royal Astron.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 356, 753 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [51] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Gair, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Hewitson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Petiteau, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Mueller, in Handbook of Gravitational Wave Astronomy, edited by C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Bambi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Katsanevas, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Kokkotas (Springer Singapore, Singapore, 2021) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 1–71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [52] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Toubiana, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Marsat, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Babak, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Baker, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Canton, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 102, 124037 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [53] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Sesana, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 116, 231102 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [54] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Bartolo, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Bertacca, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Caldwell, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Contaldi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Cusin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' De Luca, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Dimastrogiovanni, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Fasiello, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Figueroa, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Franciolini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Jenkins, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Peloso, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Pieroni, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Renzini, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Ricciardone, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Riotto, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Sakellariadou, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Sorbo, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Tasinato, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Torrado, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Clesse, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Kuroyanagi, “Probing Anisotropies of the Stochastic Gravitational Wave Background with LISA,” (2022), arXiv:2201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='08782 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [55] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Abbott et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' (LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration), Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 104, 022004 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [56] The LIGO Scientific Collaboration, the Virgo Collaboration, and the KAGRA Collaboration, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' D 105, 122001 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [57] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Caprini, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Figueroa, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Flauger, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Nardini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Peloso, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Pieroni, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Ricciardone, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Tasinato, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Cosmol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 2019, 017 (2019), arXiv:1906.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='09244 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [58] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Hindmarsh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Huber, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rummukainen, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Weir, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 112, 041301 (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [59] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Liu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Guo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Cai, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Shiu, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 120, 031301 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [60] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Cai, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Pi, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Sasaki, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 122, 201101 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' [61] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Yuan and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Huang, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' B 821, 136606 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} +page_content=' 13' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/bdE1T4oBgHgl3EQfKwMf/content/2301.02967v1.pdf'} diff --git a/cdE4T4oBgHgl3EQfpA0g/content/2301.05188v1.pdf b/cdE4T4oBgHgl3EQfpA0g/content/2301.05188v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..cd3e49c7e05bfe8a8000b4cb584c09ad68caf8f7 --- /dev/null +++ b/cdE4T4oBgHgl3EQfpA0g/content/2301.05188v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d20620805e1022d6d3ef61ac3a60960d45afebfc43ad99fe3430bdda5238df17 +size 1040158 diff --git a/cdE4T4oBgHgl3EQfpA0g/vector_store/index.faiss b/cdE4T4oBgHgl3EQfpA0g/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..07071a48f84b550f0325afc470067406e09cdf0b --- /dev/null +++ b/cdE4T4oBgHgl3EQfpA0g/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d014eeff8abac346e3cb3bc59d09a8c10b9d1e1b789c616aad9275a066a93970 +size 2818093 diff --git a/d9E1T4oBgHgl3EQfLgNb/content/tmp_files/2301.02977v1.pdf.txt b/d9E1T4oBgHgl3EQfLgNb/content/tmp_files/2301.02977v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..d52fbf7a1dc0e9861da0c0912de3fbde17df2b97 --- /dev/null +++ b/d9E1T4oBgHgl3EQfLgNb/content/tmp_files/2301.02977v1.pdf.txt @@ -0,0 +1,3737 @@ +1 + +Understanding the liquid jet break-up in various regimes at elevated +pressure using a compressible VOF-LPT coupled framework +Bharat Bhatia1, Tom Johny1, and Ashoke De1,2* +1 Department of Aerospace Engineering, Indian Institute of Technology Kanpur, 208016, Kanpur, India. +2 Department of Sustainable Energy Engineering, Indian Institute of Technology Kanpur, 208016, Kanpur, India. +Abstract +The present work develops a compressible Volume of Fluid (VOF) – Lagrangian Particle Tracking +(LPT) coupled solver in OpenFOAM and utilizes it to simulate a liquid jet in crossflow (LJICF) +numerically. This methodology helps accurately predict a complex primary breakup in the Eulerian +framework and the secondary atomization of spherical droplets using a computationally efficient LPT +method. The coupled solver with Adaptive Mesh Refinement (AMR) is rigorously validated for a +liquid jet in crossflow at varying operating conditions – pressure, crossflow velocity, and inlet liquid +jet velocity. We have further carried out a thorough investigation to study the effect of momentum flux +ratio and weber number on the various flow features and liquid jet break-up phenomenon in a crossflow +while identifying the stream-wise location of the liquid jet breakup region. At low momentum flux +ratios in the bag breakup regime, the predictions reveal that the liquid jet breakup occurs due to the +growth of similar instability as usually observed in the high-speed liquid sheet atomization. The short +wavelength assumption of the inviscid dispersion relation resembles the Kelvin-Helmholtz type +instability observed in this case, as opposed to Rayleigh-Taylor instability at high momentum flux ratio +in the surface breakup regime. It is also proposed that the shear breakup along the transverse edges of +the liquid column occurs due to the shear layer instability of the air passing around the liquid column. +The simulation wavelength closely matches the Williamson correlation for shear layer instability +around cylinders – a shape similar to the cross-section of the bottom of the liquid column. The results +show a distinct streamer or bifurcation phenomenon at low momentum flux ratios and moderate weber +numbers. Further investigation suggests that the internal liquid boundary layer and the three- +dimensional flow field behind the liquid jet are responsible for streamer formation. +Keywords: Multiphase flows, Volume of Fluid (VOF), Lagrangian Particle Tracking (LPT), Sauter +mean diameter, OpenFOAM. + + +2 + +1. Introduction +Spray atomization of a liquid jet in crossflow is a complex multiphase phenomenon extensively used +in aviation engines, lean premixed prevaporized (LPP) ducts, film cooling of turbine blades, rockets, +scramjets, augmentors, and other applications. With the new environmental restrictions and regulations +to reduce NOx emissions becoming more stringent, optimizing the combustion process in these +systems has become critical. Transverse fuel injection into a crossflow enhances combustion +efficiency, cuts fuel consumption, and lowers emissions in such systems. As a result, to develop and +analyze such systems, a detailed understanding of the physics of liquid jet break-up and atomization +processes is required. Experimental investigations of the spray atomization process require precise and +expensive experimental techniques. The numerical studies can provide valuable insight into +atomization, especially when flow features close to nozzle regions are difficult to capture +experimentally. Multiphase flow modeling is inherently complex due to the wide range of scales +formed and the liquid-gas phase interaction resulting in complex structures and flow patterns. The +length scale here ranges from a few micrometers to several centimeters. +A liquid jet in a crossflow (LJICF) consists of two significant stages of break-up and atomization: +primary and secondary breakup. (1) Primary break-up results from the instabilities at the liquid-gas +interface, which grows in size due to the inertial forces and turbulence in the liquid jet, causing the +liquid core to break up into large liquid structures. (2) Secondary break-up further breaks these liquid +structures and ligaments into smaller droplets. The extent to which these droplets are disintegrated is +influenced by the external distorting forces and surface tension forces of the liquid, finally resulting in +a large number of stable spherical droplets. The break-up of a liquid jet in a cross-flow is schematically +represented in Figure 1. The crossflow atomization process involves complex flow features, mainly +the turbulent break-up, droplet deformation from the liquid-gas interaction, vortex formations, etc. It +also involves mass, momentum, and energy exchange between the liquid and gaseous phases. +Most of the early studies of spray atomization for LJICF were primarily experimental, where +researchers mainly concentrated on the liquid jet penetration, break-up and its different modes, and +their relationship with various parameters, especially the momentum flux ratio (q) and crossflow +Weber number (We) (Wu et al., 1997; Becker and Hassa, 2002; Sallam et al., 2004; 2006). Wu et al. +(1997) studied the liquid jet penetration for various test liquids (water, alcohol, and their mixtures) +under different operating conditions and plotted a transition regime between column and surface break- +up modes. They also found that the column fracture location in the streamwise direction is constant +and is equal to 8D downstream of the nozzle exit. Stenzler (2006) proposed that the aerodynamic weber +number and liquid viscosity can also affect the jet penetration and the momentum flux ratio. Ingebo + +3 + +(1957; 1967) also proposed the same by considering the effect of liquid viscosity in the spray +penetration. He also noticed that larger droplets penetrate deeply into the cross-flow and affect the +penetration. As a result, he proposed a spray trajectory correlation that includes the effect of larger +droplets by taking account of parameters (Rejet, We) other than the momentum flux ratio (q). Several +others looked into the various break-up modes, including Becker and Hassa (2002), who proposed a +qualitative and visual map for break-up and atomization. M. Eslamian (2014) proposed a similar map +based on the momentum flux ratio and crossflow weber numbers for the primary break-up and a +transition line between column and shear break-up modes. Madabhushi et al. (2004) redefined the +break-up regime based on the turbulent transition jet Reynolds number and cross-flow Weber number. +Since the momentum flux ratio does not provide the turbulence details of a liquid jet, they defined a +borderline based on the Reynolds number of the jet in addition to the break-up map to include the +effect of liquid jet turbulence. Sallam et al. (2006) classified the break-up mechanisms for non- +turbulent liquid jets into four based on the aerodynamic weber number: column, bag, multimode, and +shear break-up. There are few studies available in the literature regarding the droplet size +characteristics. +Several computational techniques have been developed to simulate the spray atomization process +numerically. Computing interface motion in complex multiphase flows such as spray atomization +requires accurate interface tracking and reconstruction techniques. The interface capturing approaches +such as the Volume of Fluid (VOF) (Hirt and Nichols, 1981), Front tracking methods (Tryggvason et +al., 2001) or CLSVOF (Sussman et al., 2000; 2013; Menard et al., 2007) are typically used modeling +approaches for the primary breakup. VOF methods are based on the volume fraction (α) of phases in +a computational cell. An additional transport equation is solved for volume fraction (α), which is then +used to track the location of the liquid-gas interface. Many VOF interface capturing techniques are +utilized to capture the interface, classified as algebraic or geometric. Older methods for interface +capture include algebraic approximations such as Compressive schemes and THINC (Tangent of +hyperbola for interface capturing) schemes. Geometric approaches are more recent, complicated, and +precise (Mirjalili, S. 2019). An interface within a computational cell is geometrically reconstructed +using a plane in three-dimensional (3D) simulations using methods such as Simple Line Interface +Calculation (SLIC) (Noh & Woodward, 1976) or the more recent Piecewise Linear Interface +Calculation (PLIC). Nonetheless, using these techniques for commercial use does have a disadvantage: +high computational cost and time. The grid resolution must be good enough in a VOF approach to +sufficiently resolve the liquid structures, droplets, and ligaments. Therefore, the computational cost of +simulating a complete spray break-up using the only VOF method is very high (Heinrich and +Schwarze, 2020). The Lagrangian Particle Tracking (LPT) methods are more suitable for secondary + +4 + +atomization involving a cloud of dispersed droplets, owing to lower computational cost and better +droplet predictions. Thus, the VOF approach can efficiently resolve the primary break-up, while the +dispersed cloud uses the LPT method. Therefore, an Eulerian-Lagrangian coupled approach could +significantly reduce the computational cost of simulating the whole spray atomization process while +still capturing the underlying physics to a high degree. +A coupling algorithm is an intermediate between the Eulerian and Lagrangian frameworks, which +tracks all the Eulerian-phase droplets throughout the computational domain and replaces them with a +Lagrangian substitute using transformation criteria. Several coupling algorithms (Hermann et al., 2008; +2010; H. Grosshans, 2014; Heinrich and Schwarze, 2020; H. Yu et al., 2017) have been proposed for +the Eulerian-Lagrangian droplet transformation. H. Grosshans (2014) performed a statistical coupling +approach by defining a coupling layer between VOF and LPT frameworks. The drawback associated +with this method is that the 2-D coupling layer is fixed in space. Also, the shearing action generates +smaller droplets from the sides of the liquid column. Since these droplets lie before the coupling layer, +they are resolved using VOF only, even though these are more appropriate to be tracked using LPT. +So the transformation into Lagrangian droplets may not be realistic as it seems. H. Yu et al. (2017) +proposed a region coupling method (RCM) with a droplet identification and extraction technique. This +method is more realistic since the transformation happens smoothly in the coupling region defined in +three-dimensional (3-D) space. One drawback of this method is the placement of the coupling region, +which has to be determined previously from another Eulerian simulation. Hermann et al. (2008; 2010) +used their band generation algorithm to couple the Lagrangian framework with a refined level-set grid +method. Heinrich and Schwarze (2020) employed an image processing algorithm called Connected +Component Labelling (CCL) to couple the VOF with LPT for incompressible flows. Such a coupled +methodology eliminates solutions through stochastic methods such as the ELSA model (Hoyas et al., +2013) or other models that use a Lagrangian droplet ejection out of a primary jet core calculated using +the VOF method (Saeedipour et al., 2016), ignoring the critical phenomenon of the primary breakup. +One assumption involved in the LPT method is that the droplet volume is minimal compared to the +local cell volume. For the LPT approach to be numerically stable, it is generally advised that the grid +size be larger by ten times the size of the droplets (Vallier et al., 2011). While Arlov et al. (2007) +proved that the LPT theory is valid even if the cell size is more than the droplet size by five times. +Multiple grid cells comprising the Eulerian droplet are required for an Eulerian framework to resolve +the small-scale features adequately. To overcome the imbalance of larger grid size requirement for the +LPT method and smaller grid size for VOF, we can either use: the (i) Adaptive Mesh Refinement +(AMR) technique based on the liquid volume fraction (α) or (ii) a static grid with a highly refined + +5 + +region for Eulerian framework and a separate coarser grid for the lagrangian framework (Herrmann +2010). The former option is preferable as the latter may cause larger lagrangian droplets on a smaller +local mesh volume. +In this work, a compressible VOF-LPT coupled solver is developed in OpenFOAM along with the +evaporation models for Eulerian and Lagrangian fields, which is also capable of simulating atomization +involving high temperature evaporating sprays. It uses a VOF-LPT coupling algorithm based on the +previous works of Heinrich and Schwarze (2020). The liquid-gas interface is reconstructed +geometrically using the isoAdvection concept developed by Roenby et al. (2016). Such a coupled +model and an additional method for interface capturing would help capture the flow physics to a high +degree in the near-nozzle region and the far downstream region while keeping the computational cost +to a minimum. The developed model is validated under elevated pressure and room temperature +conditions for a liquid jet-in-crossflow case based on the experimental works of Amighi and Ashgriz +(2019) in terms of droplet size characteristics and the Sauter mean diameter, the standard deviation of +droplets, and the jet trajectory. And further, we have carried out a detailed investigation using the same +framework for a wide range of parameters (q, We) and its effect on spray droplet sizes (D32, STD), +liquid jet penetration, and other flow features (vortex formation, break-up behavior, and deformation) +for a liquid JICF under different operating conditions. +2. Methodology +This section describes the methodologies employed in our current investigation, mainly the VOF +Eulerian formulation, the LPT formulation, and the coupling algorithm. + +Fig. 1: Schematic of the break-up of a Liquid Jet in Crossflow (LJICF) + +Column breakup +Liquid jet core +Ligaments +Windward side +Surface breakup +Leeward side +Primary breakup +Secondary breakup6 + +2.1 Eulerian framework +The VOF method tracks the interface between the two phases in the Eulerian framework. The mass, +momentum, species mass fraction, and energy equations are solved for a two-phase compressible and +immiscible system. VOF method uses the volume fraction  , defined as a step function, to distinguish +between the two phases. A volume fraction value of +1 + =1 indicates cell volume fully occupied by +liquid, and +1 + =0 indicates cell volume fully occupied by gas. A volume fraction value +1 +0 +1 + + + shows +the liquid-gas interface within the cell control volume. + +1 +1 +0 +0 +1 +1 +2 +1 +pha +phase +interface +se + + + + += + + + + + + + + + + +(1) +The step function α makes it possible to solve only one set of governing equations for both phases, +eliminating the need for separate equations for each phase. The VOF method without any interface +reconstruction method results in smearing the liquid surface. To overcome the smearing of the profile +at the interface, many interface-capturing methods have been developed for VOF involving the +reconstruction of the interface. Reconstruction methods may be either geometric or algebraic – like the +piecewise-linear interface calculation (PLIC) for geometric reconstruction and Compressive Interface +Capturing Scheme for Arbitrary Meshes (CICSAM) for algebraic reconstruction in Ansys Fluent +(ANSYS, Inc., 2016) or Gerris solver (Popinet, 2003), Multidimensional Universal Limiter with +Explicit Solution (MULES) scheme for algebraic reconstruction by interFoam solver in OpenFOAM +(Weller et al., 1998), etc. The volume fraction 𝛼𝑘 and the interface within a cell is reconstructed +geometrically using the iso-advection concept devised by Roenby et al. (2016). For geometric interface +reconstruction, it uses a piecewise linear interpolation calculation (PLIC) (Mencinger et al., 2011). +Although the method uses an integral form of the continuity equation to calculate the surface evolution, +it is represented here in the differential form to maintain consistency with the rest of the equations: +( ) +.( +) +L +S +t + + + + ++  += + +u + + + + + + + + + +(2) +Here  is the mixture density, u is the velocity, +L +S + is the source terms from the Lagrangian droplets +calculated as: +𝑆𝜌|𝐿 = 4𝜋 +𝑘 +𝑐𝑝 𝑟0 +1 +1+𝐺𝑓 𝐺 +⁄ 𝑙𝑛 [1 + +ℎ𝑔−ℎ𝑑𝑟𝑜𝑝,𝑠 +𝐿(𝑇𝑏) +(1 + +𝐺𝑓 +𝐺 )] + + + +(3) + +7 + +The source term denotes the heat transfer vaporization rate (Zuo et al. (2000)); 𝑘 is the thermal +conductivity of gas, 𝑐𝑝 is the specific heat of the gas; ℎ𝑔 and ℎ𝑑𝑟𝑜𝑝,𝑠 denotes the enthalpy of the gas +and at the droplet surface, respectively; 𝐿(𝑇𝑏) is the latent heat of vaporization at the boiling +temperature, 𝐺𝑓 is the flash-boiled vapor mass flow rate, which reduces to zero at temperatures less +than or equal to the boiling point. In the integral form of the equation, the instantaneous rate of change +of the total mass within a volume is equal to the instantaneous flux of mass through its boundary in +addition to the mass evaporated from the lagrangian particles. In the differential form, the mass +conservation equation for phase i is: +( +) +.( +) +k +k +k +k +L +E +S +S +t + + +  +  + ++  += ++ + +u + + + + + + + +(4) +While the source term from liquid to the gas phase, it is: +𝑆𝜌|𝐸 = 2 ∗ (1 − 𝛼2) ∗ M𝑡𝑐 ∗ D𝑎𝑏 ∗ 𝑑𝑌. + + + + + +(5) +Here, M𝑡𝑐 and D𝑎𝑏 are the mass transfer and diffusion coefficients between two phases, and 𝑑𝑌 is the +species gradient near the interface for liquid species. While the volume fractions are constrained, this +equation evolved in two steps. Firstly, the reconstruction step is where the distribution of fluids inside +the computational cells is estimated using an efficient iso-surface calculation methodology. Secondly, +a face-interface intersection line sweeping the face for a sub-time interval approximates the time +evolution of the submerged part of a general polygon face (belonging to a computational cell). The +sub-time interval is defined by the time a line passes the face vertices. It makes the analytical +calculation possible for the passage of a fluid across the cell face during this sub-time interval. This +reconstruction technique applies to structure as well as unstructured grids. +For cells having liquid-gas calculations, the fluid properties are calculated from the weighted average +of the phase fraction α for each computational cell. +1 +1 +2 +2 + +  +  += ++ + + + + + + +(6a) +1 +1 +2 +2 + +  +  += ++ + + + + + + +(6b) +where +1 + , +2 + and +1 + , +2 + are the dynamic viscosity and density of phases 1 and 2, respectively. Phases +1 and 2 represent the liquid and gas phases for a two-phase compressible system. A single momentum +transport equation is solved for the velocity field in both phases: + +8 + +. +( +) +( +. +) +( +) +d +ef +E +f +S +u +u +L +T +u +p +t +S +F +S + + + + + + + ++  +− += − +−  ++ ++ + ++ +uu +x +g + +(7) +where the piezometric pressure +. +dp +p + += +− g x and +( +) +2 +T +3 +( +) +eff +eff +tr + + + + + + + + += + +  +− + +u +u +u ; here, +eff + + the +effective viscosity is volume averaged as: +1 +1 +2 +2 +4( +) +3 +eff +  +  + ++ += +, and  in all the combined equations is +the mixture density for each computational cell. +, +u +u +L +E +S +S + + + are the Lagrangian and Eulerian source +terms for momentum equations, which are generated because of the atomization and the evaporation +of droplets in the domain. 𝐹𝑆𝑇 is the surface tension force calculated using the Continuum Surface +Force (CSF-model) formulation proposed by Brackbill et al. (1992). The surface tension force is +defined at the interface where a pressure jump occurs and is specified as a source term to the +momentum equation. It is calculated as follows: +( ) +( ) ( ) ( +) +ST +S +F +x +y n y +x +y dS +  + += +− + + + + + + +(8) +where  is the surface tension of the liquid phase,  is the local interface curvature, n is the unit +interface normal, and  the Dirac-delta function. x and y are the position vectors where the forces +are calculated. These are calculated using: +.n + = − + , +n +n +n += + where n = normal surface vector, defined +as n + +=  . The surface tension force source term can be expressed as: +1 ( +) +2 +ST +l +g +F +  + + + + += ++ + + + + + + + +(9) +The equation of state is used to solve densities from pressure and temperature conditions. Considering +an isentropic gas phase, the equation of state is defined as (Miller et al., 2013): +constant +c +p +a + + += += + + + + + + + +(10) +where +ca is the isentropic constant and  is the ratio of specific heat. The total derivative of  with +respect to pressure gives: +( +) +1 +1 +c +c +s +p +p +a +a + + + + +− + + + + + += + + + + + + + + + + + + + + + +(11) + +9 + +The speed of the sound wave in a liquid medium is computed as follows (Miller et al., 2013): + + +2 +1 +s +d +dp +c + + + = + + + + + + + + + + + + +(12) +where c is the speed of the sound. Integration of the above equation at a constant speed of sound yields: + +( +) +o +o +p +p + + + +− += +− + , where +2 +1 +c + = + + + + + +(13) +and +, +o +op + + are the reference density and pressure, respectively. +The species mass fraction equation is solved by assuming the liquid phase as a single component +system and the gaseous phase as a multi-component system. +2 +2 +2 +2 +2 +( +) +.( +) +.( +) +k +k +k +k +Yk +Yk +L +E +Y +Y +D +Y +S +S +t + + +  +  + + ++  +− + += ++ + +u + + +(14) +Here, 𝑌𝑘 is the species mass fraction and 𝐷𝑘 is the diffusion coefficient for the kth species for the +gaseous phase. The energy equation is also solved since our system is compressible. +1 +2 +, +,1 +,2 +( +) +( +) +.( +) +.( +) +.( +) +.( +) +T eff +T +T +L +E +v +v +T +K +T +T +p +K +S +S +t +t +c +c + + + + + + + + + + + + + + + ++  +− + ++  ++ ++  ++ += ++ + + + + + + + + + + +u +u +u + +(15) +Here, T is the temperature in the Eulerian frame at any location, 𝛼𝑇,𝑒𝑓𝑓 is the effective thermal +diffusivity, 𝐾 is the kinetic energy (𝐾 = 0.5 ∗ |𝐮|2), 𝑐𝑣1 and 𝑐𝑣2 are specific heat capacities at constant +volume for phases 1 and 2, respectively. 𝑆𝜌𝑇|𝐿 , 𝑆𝜌𝑇|𝐸 are the lagrangian and eulerian source terms for +the energy equation, which accounts for the atomization and the evaporation of droplets. Although +evaporation does not occur in our low-temperature test conditions, the developed framework accounts +for the effect of droplet evaporation in both the Eulerian and Lagrangian frameworks. +Large-eddy simulations (LES) are used to model turbulence in the flow field. The large eddies of the +turbulent flow are computed directly in LES. Sub-grid scale (SGS) modeling is performed since the +dissipative scales of turbulence are not entirely resolved in LES. The SGS models the effect of small- +scale vortices and eddies on the resolved larger eddies. Thus, the SGS terms cannot be calculated and +require closure models. The SGS Reynolds stress ( +ij + ) and the SGS heat flux ( +j +Q ) are the parameters +that require closure models at the sub-grid scales, as given by + +10 + +, +ij SGS +i +j +i +j +u u +u u + + + += +− + + + + + + +(16) +,j SGS +j +j +Q +u h +u h + + += +− + + + + + + + +(17) +and the molecular strain rate tensor is given by: + +2 +3 +k +i +j +ij +ij +k +j +i +u +u +u +S +x +x +x + + +  + + + + += − ++ ++ + + + + + + + + + + + + + + +(18) +The dynamicKEqn model, which is a one-equation eddy viscosity SGS model, is used for the present +study. This model was primarily developed by Kim and Menon (1995) based on the previous works +of Germano et al. (1991). In recent years, many improvements to the models have been proposed (Chai +and Mahesh, 2012, Huang and Li, 2010). The dynamicKeqn is represented as follows: +3/2 +2 +sgs +j +sgs +sgs +sgs +t +e +sgs +ij +ij +j +j +k +U k +k +k +C +S S +t +x +x +t + + + + + + + + ++ += +− +− + + + + + + + + + + + +(19) + +sgs +k +sgs +C +k + += + + + + + + + +(20) +where +sgs +k +is the sub-grid scale kinetic energy, +t is the effective kinematic viscosity (both molecular +and sub-grid viscosity). The +k +C , +e +C constants are computed based on the dynamic formulation from +Germano et al. (1991). +The partial differential equations (PDEs) are discretized using a Finite Volume Method (FVM) code +implemented in the OpenFOAM v1912. The convective flux discretization deploys a second-order +TVD (Total Variation Diminishing) scheme, while the viscous flux discretization involves a second- +order central scheme, and the temporal term deploys the first-order implicit Euler scheme with +sufficiently small time steps to maintain stability and reduce numerical diffusion. + +2.2 Lagrangian framework +In the LPT method, the liquid droplets are treated as point particles with mass and momentum but no +volume. The LPT approach uses parcels to represent a group of droplets with similar characteristics +such as droplet size, velocity, temperature, and thermophysical properties. The particle position and +velocities are updated at each time step using the Basset Boussinesq-Oseen (BBO) equation (Parmar +et al., 2011): + +11 + +p +p +d +dt += +x +u + + + + + + +(21) +p +p +D +G +d +m dt = ++ +u +F +F + + + + + +(22) +where +p +x , +p +m , +p +u is the position, mass, and velocity of each particle, respectively. +D +F and +G +F are +the drag and gravitational forces (body forces) acting on the particles. They are calculated as follows: +2 +8 +( +)| +| +p +D +D +g +g +p +g +p +D +C  + += +− +− +F +u +u +u +u + + + +(23) + + + +1 +g +G +p +p +m g + + + + += +− + + + + +F + + + + + + +(24) +G +F account for both gravity and buoyancy effects, +p +D is the diameter of the lagrangian parcel, +g +u and +p +u are the velocities of gas-phase and velocity of Lagrangian parcels. +D +C is the drag coefficient of +droplets, which is calculated from the Schiller-Naumann equation (Schiller, 1935): +0.687 +24 1 + 0.15 +/ +1000 +0.44 +10 +) +0 +( +0 +p +p +p +D +p +Re +Re +Re +C +Re + ++ + +=  + + + + +(25) +2 +2 +Re +g +p +p +p +D + + +− += +u +u + + + + + + +(26) +where +p +Re is the Reynolds number of the lagrangian droplets and +2 + is the gas phase dynamic +viscosity. +The LPT is intended to characterize every droplet feature like droplet break-up, heat transfer, and +evaporation. The Ranz-Marshal model (Ranz and Marshall, 1952) is used for heat transfer calculations. +Since the Lagrangian droplets are assumed to be spherical, the evaporation is calculated based on the +Frossling correlation (Frössling, 1938): + 𝑆ℎ = 2 + 0.552𝑅𝑒𝑝 +1 2 +⁄ 𝑆𝑐1 3 +⁄ + + + + + +(27) +𝑆ℎ is defined as the ratio ℎ𝑐𝑑𝑝 𝐷 +⁄ , where ℎ𝑐 denotes the convective mass transfer coefficient, and 𝑑𝑝 +is the droplet diameter, 𝑅𝑒𝑝 is the droplet Reynolds number, and 𝑆𝑐 is the Schmidt number. The typical + +12 + +value of the turbulent Schmidt number (Prandtl number) ranges from 0.7 to 1. A value of 0.85 was +used in this work. +Among the atomization models of TAB (O'Rourke & Amsden, 1987), ETAB (Tanner, 1997), and R- +D (Reitz and Diwakar, 1997), the Reitz-Diwakar secondary break-up model is chosen to model the +break-up of the parcels due to the aerodynamic forces. This is suitable for our high-pressure test +conditions and resulted in better droplet predictions. This takes into account the bag and the stripping +break-up of droplets. A critical Weber number is used to dictate the breakup of droplets. Droplet +collision is an important parameter that mainly affects droplet numbers, droplet sizes, droplet +evaporation, spray propagation, and distribution. To account for the collision and coalescence of the +droplets, we employ the trajectory model of Schimdt & Rutland (2000). A trajectory-based collision +model is more realistic as it models droplet collisions using droplet position and velocity vectors. +2.3 Coupling algorithm +As mentioned in the previous sub-sections, we have developed the compressible VOF-LPT coupled +solver in the OpenFOAM framework along with the evaporation models for Eulerian and Lagrangian +fields which is also capable of simulating atomization involving high-temperature evaporating sprays. +The algorithm provided by Heinrich & Schwarze (2020) is used to couple the compressible VOF +framework with LPT and facilitate the droplets’ transformation from one framework to another. This +coupling algorithm first identifies the individual droplets present throughout the three-dimensional (3- +D) domain in the Eulerian framework. The relevant properties are then calculated, and if the droplets +satisfy the transformation criteria, they are injected as Lagrangian parcels after deleting the +corresponding liquid droplet from the Eulerian framework. An image processing – Connected +Component Labelling (CCL) algorithm is used in the methodology to identify various liquid droplets +in the Eulerian domain (Heinrich & Schwarze, 2020). The liquid volume fraction ( +1 + ) is used to scan +the complete domain for the connectivity of liquid-filled cells. Two separate, detached lumps have +cells +1 +min + + + + in between them, where +min + + is the minimum value of liquid volume fraction to +distinguish two separate droplets. The details of the algorithm have been explained in Heinrich & +Schwarze (2020). +The properties of each Eulerian droplet are then calculated as follows: +𝑉𝑝 = ∑ 𝛼𝑖𝑉𝑖 +𝑖 + + + + + + +(28a) +𝒙𝑝 = +1 +𝑉𝑝 ∑ 𝛼𝑖𝑉𝑖𝒙𝑖 +𝑖 + + + + + + + +(28b) + +13 + +𝒖𝑝 = +1 +𝑉𝑝 ∑ 𝛼𝑖𝑉𝑖𝒖𝒊 +𝑖 + + + + + + + +(28c) +𝑇 = +1 +𝑉𝑝 ∑ 𝛼𝑖𝑉𝑖𝑇 +𝑖 + + + + + + + +(28d) +𝑑𝑝 = √ +6𝑉𝑝 +𝜋 +3 + + + + + + + + +(28e) +All the cells belonging to a particular Eulerian droplet are represented by the index i. The equivalent +diameter (𝑑𝑝) is the diameter of a sphere with the volume 𝑉𝑝 equal to that of the Eulerian droplet, +whereas 𝒙𝑝, 𝒖𝑝 and 𝑇 are the position, velocity, and temperature of the Eulerian droplet, respectively. +Lastly, the transformation criteria for each droplet are reviewed. If the droplets meet the transformation +criteria, they are injected as Lagrangian parcels, preserving their velocity, momentum, energy, and +position. And the corresponding Eulerian liquid droplet is deleted from the Eulerian framework. The +transformation criteria are based on the assumption of the size of droplets and their shape. Firstly, the +size of the droplet diameter (𝐷𝑝) should be smaller than a predetermined minimum diameter because +a larger droplet is more prone to deformation, which is better resolved in the Eulerian framework. The +minimum diameter criteria refer to the droplet size below which they are eligible for conversion into +Lagrangian droplets. This is also determined from the experiments where the value used is 280µm +(Amighi, 2015). On the other hand, smaller droplets are converted as they cannot be appropriately +resolved in the Eulerian framework and are better tracked in the Lagrangian framework. Secondly, if +the sphericity of the droplet is less than a threshold minimum. +In this study, we have used a sphericity of 1.47, calculated based on the circularity of droplets reported +in the experiments (Amighi and Ashgriz, 2019). Droplets with sphericity less than 1.47 will be +converted to lagrangian droplets, while those with sphericity more than 1.47 will remain as Eulerian +droplets. Heinrich & Schwarze, (2020) used a sphericity of 2 in their work. It is desirable for the +droplets with sphericity greater than the threshold to stay in the Eulerian framework as the irregular +droplets are vulnerable to deformation, which is well captured by the Eulerian method only. Here we +have performed a one-way coupling that facilitates the transformation of Eulerian droplets into +Lagrangian only, while a two-way coupling also does vice-versa. The one-way coupling assumes only +minor differences between the couplings, as observed in Ling et al. (2015) and Fontes et al. (2019). +2.4 Computational domain and flow conditions +The above-proposed model is validated using experimental data from Amighi and Ashgriz (2019) at +elevated pressure conditions for an experimental channel. Figure 2 illustrates the computational +domain with the same cross-section of 2535 mm2 (yz) as the experimental channel. The +computational domain in this study is 58.6mm in length (x-direction), which is only a part of the + +14 + +experimental channel size. Following the experimental measurements, D32, STD calculations are done +within a 52.45D distance downstream (blue sub-domain) from the point of liquid jet injection (28.6, +12.5, 0) mm. The liquid jet is injected from the nozzle placed at the bottom wall of the domain in the +z-direction (Jet direction). The exit diameter of the nozzle used is 572 μm. + +Fig. 2: Computational domain and region of calculation +The initial domain meshes with a 140 60 80 + + + cells, and the cells are additionally refined around the +injector (see Figure 3). We have performed four levels of refinement, with the finest grid size being +26 μm in the nozzle region to the coarsest level of 418 μm of the parent mesh. This results in a total +size of 0.75 million cells in the parent mesh. + +Fig. 3: Mesh generated with (a) blockMesh and (b) SnappyHexMesh (near nozzle) with four levels of refinement near the +nozzle +On our parent mesh, we have used adaptive mesh refinement (AMR) with three refinement levels to +accurately refine the liquid-gas interface region and capture the complicated dynamics of the interface. +A lower and upper refine level values ( +1 +0.1 +1 + + + ) of the volume fraction alpha are used as a criterion +to refine the cells having a liquid-gas interface. This continues refining the cell until the maximum +refinement is achieved or if the alpha values fall outside the acceptable range. The lower refine level +value of 0.1 is chosen after checking for different refinement levels as the lower values (<0.1) yield + +Walls +Inlet +Outlet +Nozzle Inlet(a) +(b)15 + +similar results. The use of AMR reduces the computational requirements considerably; thus, a coarser +mesh can be employed. With the help of AMR, the mesh resolution of 52 μm is achieved just at the +interface (refer Figure 4). + +Fig. 4: Adaptive mesh refinement (AMR) of cells using liquid volume fraction alpha field. Red droplets indicate +lagrangian droplets, which are converted from Eulerian to Lagrangian. +As the Eulerian liquid droplets move from one point to another, the cells where the interface is located +are refined continuously during the simulation. Once a Lagrangian droplet forms (from an Eulerian +framework, as shown in Figure 4), the grid is coarsened back to the parent base mesh resolution. In +this way, the Lagrangian assumption also holds for droplets, as the liquid fraction is less than 0.22 in +a computational cell (Arlov et al. (2007)). Note that Lagrangian droplets and Eulerian fields are shown +in red and blue in Figure 4, respectively, are in 3-dimensions, whereas the AMR grid in the background +is just a 2-dimensional, mid-section plane of the domain. Hence, many red (Lagrangian) droplets are +in the fine mesh while the coarse grid surrounds Eulerian ones. Nearby cells in the vicinity of Eulerian +droplets are also adjusted by adding six buffer layers to prevent excessive cell size jumps in the flow +field, which could result in considerable pressure and velocity gradients at the jump point. The Eulerian +and Lagrangian droplets in the computational domain, the AMR, and the buffer cells are shown in +Figure 4. Depending on the extent of break-up and penetration of the liquid jet, the total number of +cells in the domain increases from an initial count of 0.75 million to 3-5 million during the runtime. +The maximum Courant Friedrich Lewy number (CFL) is set to 0.12, providing an average time step +of 1.5 x 10-8 sec. +The cross-flow air inlet is fed with a fully developed turbulent velocity profile obtained from a separate +channel flow simulation. The liquid jet is provided a uniform velocity profile with negligible + +Parent cell +Eulerian droplet +Buffercells +Lagrangian droplets16 + +turbulence at the nozzle exit to avoid any early breakup due to turbulence (Li. et al., 2016). Water is +used as the liquid, and the air is used as the crossflow fluid. The liquid jet and cross-flow air +temperatures are kept at a constant room temperature of 25oC for all test conditions. Table 1 and 2 +describes the fluid properties and test conditions used for the simulations. +Fluid Property +P=2.1 bar, T=25oC +P=3.8 bar, T=25oC +jet + + (kg/m3) +997.10 +997.17 +air + +(kg/m3) +2.42 +4.44 + (N/m) +0.072 +0.072 +air + +(m2/s) +7.638 x 10-6 +4.167 x 10-6 +jet + +( m2/s) +8.927 x 10-7 +8.925 x 10-7 +air + +(N.s/m2) +1.849 x 10-5 +1.851 x 10-5 +jet + +(N.s/m2) +8.901 x 10-4 +8.900 x 10-4 +Table 1: Summary of fluid properties + +Pressure +(bar) +Crossflow velocity +(m/s) +Jet velocity +(m/s) +Case 1 +2.1 +61 +9 +Case 2 +2.1 +61 +12 +Case 3 +2.1 +61 +19 +Case 4 +2.1 +61 +24 +Case 5 +3.8 +65 +14 +Case 6 +3.8 +65 +19 +Case 7 +3.8 +41 +19 +Case 8 +3.8 +41 +9 +Case 9 +3.8 +41 +24 +Case 10 +3.8 +33 +19 +Table 2: Simulated test conditions with nozzle diameters of 572 µm. +3. Results and Discussion +This section first assesses our VOF-LPT coupled framework by performing a validation case at +elevated pressures of 2.1 and 3.8 bars, which would mimic the density ratios of actual gas turbines. A +grid test is then carried out to investigate the effect of grid sizes on droplet sizes and jet penetration. +And the following section discusses the impact of various parameters on droplet size characteristics +and compares our jet trajectory against various experimental correlations. Further, we discuss the +primary break-up behavior and flow features (vortex formations) observed in the liquid jet in + +17 + +crossflow. All the determined parameters (D32, STD) are time-averaged values calculated within the +sub-domain (blue-colored), as shown in Figure 2. +3.1 Spray Trajectory and Validation +The compressible VOF-LPT model is validated using a Liquid Jet-in Crossflow (JICF) case at elevated +pressure and room temperature conditions. The numerical results of the windward trajectory, droplet +sizes (D32), and the standard deviation (STD) are compared against the experimental results from +Amighi and Ashgriz (2019), as shown in Figure 5. The validation is performed for two cases with +nozzle diameters of 572 µm (Case A) and 457 µm (Case B). The parameters used with cases A and B +are listed in Table 3. + +Fig. 5: Comparison of liquid jet trajectory vs. experimental for cases A and B. The error margins of 2d + + are considered +based on the simulations due to the lack of error margin in experiments. + +Case A +Case B +Pressure +3.8 bar +2.1 bar +Temperature +25 oC +25 oC +Liquid jet velocity +19 m/s +19 m/s +Crossflow velocity +65 m/s +50 m/s +Nozzle diameter +572 µm +457 µm +Table 3: Parameters used for numerical simulations for case A and case B +As shown in Figure 5, the error bars represent 2d + + the margin for both cases A and B. In this work, +the error bars are considered based on the computational data because of the lack of data on error +margins in experimental results. All the trajectory calculations are employed by assuming the center +of the nozzle as the origin (0,0). As observed in Figure 5, the windward trajectory starts from -0.5D +with respect to the origin on the x-axis. For the low-pressure case of 457 µm as nozzle diameter (case +B), the predicted trajectory is closer in the near nozzle region (<20D) and deviates slightly after 20D. +The deviation observed in the region >15D for case A and >20D for case B is because the experimental + +35 +50 +Experiment +Experiment +Simulation +45 +Simulation +30 +中 +Error Margin ±2D +市 +Error Margin ±2D +40 +25 +35 +20 +30 +DN +25 +N +15 +20 +10 +15 +10 +5 +5 +0 +0 +5 +10 +15 +20 +0 +5 +10 +15 +20 +25 +X/DN18 + +trajectory data is based on the spray plume. An image averaging and thresholding technique is used to +determine the windward trajectory. This is chosen to account for the Eulerian and Lagrangian droplets' +contributions to the trajectory. For the Eulerian contribution to a trajectory, an iso-contour value is +used. The droplets are scaled to exact sizes for the lagrangian part to generate the whole spray +atomization image. For cases A and B, the trajectory is plotted by averaging liquid spray images over +time, where approximately 200 images are obtained with a time interval of 0.05 milliseconds between +each image. A threshold of 0.9 is applied to the averaged image, which is sufficient to remove the +traces of stray droplets outside the windward side of the trajectory (Gopala et al., 2010). + +Case A +Case B +D32 +(µm) +STD +(µm ) +D32 +(µm) +STD +(µm ) +Experimental +74.5 +18.0 +84.5 +22.1 +Computational +71.96 +19.9 +78.13 +20.71 +Error % +3.4 +10.5 +7.5 +6.3 +Table 4: Comparison of Sauter Mean Diameter (D32) and the Standard Deviation (STD) for computational and +experimental cases. +Table 3 presents the droplet sizes obtained numerically and experimentally for cases A and B. The D32 +values obtained for the validation cases A and B lie within a 10% error margin concerning the +experimental D32. Similarly, the error observed in the STD is also within a 12% error margin. +Regarding the error margin observed here, the numerically predicted droplet sizes and standard +deviation are much closer to the experimental results. This reveals a good agreement of the predicted +data against experiments. Thus, comparing the spray trajectory with Sauter Mean Diameter (D32) and +Standard Deviation (STD) of droplets against the experiments illustrates the accuracy of the numerical +simulation. + +Fig. 6: Comparison of trajectory for different mesh resolutions with experimental + +19 + +Three different baseline meshes are chosen to study grid independence, a coarse grid (105 x 45 x 60), +a medium grid (140 x 60 x 80), and a fine grid (175 x 75 x 100). The windward trajectory and the spray +droplet size characteristics, such as the Sauter mean diameter (SMD or D32) and standard deviation +(STD) for these grids, are compared in Figure 6 and Table 5. For the near nozzle region (<20D) +considered here, the variation in trajectories is minimal, and there isn't much difference between the +trajectories. However, for the medium and fine grids, the trajectory is traced along the same path until +10D, and later on, only a slight difference is observed. Compared to the medium and fine grids, the +trajectory is slightly underpredicted for the coarser grid. As a result, we can infer that the grid has less +impact on the trajectory near the nozzle (<20D) and that the trajectory is closer to experimental data +in this area. This could be attributed to the adaptive mesh refinement (AMR) taking care of the +refinement to some extent. + +D32 +(µm) +STD +(µm) +Error in +D32 +Error +in STD +Initial cell +count (x 106) +Final cell +count (x 106) +Experimental +74.5 +18.0 +- +- +- +- +Coarse +78.75 +21.62 +5.7 % +20.1 % +0.35 +1.27 +Medium +71.96 +19.9 +3.4 % +10.5 % +0.75 +3.2 +Fine +71.07 +20.08 +4.6 % +11.5 % +1.41 +6.75 +Table 5: Sauter Mean Diameter (D32) and the Standard Deviation (STD) and error observed for different mesh resolutions +For the medium and fine grids, the values of SMD and STD are found closer to each other and close +to experimental values. The SMD and STD values show significant overprediction for the coarser grid. +The error observed in STD for the coarser grid is twice that of medium and fine grids. Therefore, our +medium-sized grid (140 x 60 x 80) can provide sufficiently accurate and computationally less +expensive results for droplet sizes and liquid jet penetration. This medium grid will be used in all our +analyses from this point onwards. It is observed that when AMR is used, the final cell count is +approximately four-five times the initial cell count in the domain. The total cell count observed for +different simulation test cases varies between 3-5 million grid cells depending on the liquid jet +penetration and break-up behavior. +3.2 Effect of various parameters on droplet size characteristics +This section talks about the effect of various parameters, the liquid jet velocity (Vj), cross-flow velocity +(Vair), and ambient pressure (P), on the droplet size characteristics, namely the Sauter mean diameter +(D32) and the standard deviation (STD). All the test cases are carried out at constant temperatures of +25oC and high-pressure conditions of 2.1 and 3.8 bar. Table 6 summarises all the droplet size +characteristics gathered from simulations and experiments. The momentum flux ratio and crossflow + +20 + +Weber numbers of the test cases range from 8 to 80 and 38 to 150, respectively. The number of +lagrangian droplets formed ranges from 40,000 to 3,00,000 depending on the extent of penetration and +break-up for the test cases performed. + + +Momentum +flux ratio +(q) +Weber +number (air) +(We) +Experimental +Computational +Error +D32 +(µm) +STD +(µm) +D32 +(µm) +STD +(µm) +D32 +(%) +STD +(%) +Case 1 +P=2.1bar,T=25oC, +Va=61m/s, Vj=9m/s +8 +71 +88.8 +23.9 +81.93 +22.77 +7.74 +5.02 +Case 2 +P=2.1bar,T=25oC, +Va=61m/s, Vj=12m/s +16 +71 +84.3 +22.1 +79.16 +21.6 +6.09 +2.26 +Case 3 +P=2.1bar,T=25oC, +Va=61m/s, Vj=19m/s +41 +71 +78.5 +19.6 +76.15 +20.89 +2.99 +6.58 +Case 4 +P=2.1bar,T=25oC, +Va=61m/s, Vj=24m/s +66 +71 +73.9 +17.6 +72.24 +19.21 +2.24 +9.15 +Case 5 +P=3.8bar,T=25oC, +Va=65m/s, Vj=14m/s +10 +150 +78.8 +19.8 +75.49 +21.98 +4.20 +11.01 +Case 6 +P=3.8bar,T=25oC, +Va=65m/s, Vj=19m/s +19 +150 +74.5 +18.0 +71.96 +19.9 +3.4 +10.5 +Case 7 +P=3.8bar,T=25oC, +Va=41m/s, Vj=19m/s +48 +60 +79.3 +20.0 +75.48 +20.43 +4.81 +2.15 +Case 8 +P=3.8bar,T=25oC, +Va=41m/s, Vj=9m/s +10 +60 +87.6 +23.4 +82.95 +22.56 +5.31 +3.59 +Case 9 +P=3.8bar,T=25oC, +Va=41m/s, Vj=24m/s +77 +60 +75.2 +18.1 +68.83 +17.55 +8.47 +3.03 +Case 10 +P=3.8bar,T=25oC, +Va=33m/s, Vj=19m/s +77 +38 +78.6 +19.6 +78.15 +21.2 +0.57 +8.16 +Table 6: Summary of test results: Sauter Mean Diameter (D32) and the Standard deviation for all test cases (DN=572 µm) + +For all the test cases performed, the maximum error observed on D32 and STD is 8.47 % and 11.01 +%, respectively, and the average error observed on D32 and STD are 4.58 % and 6.15 %, respectively. +For all the D32 plots (Figures 7, 8, and 9), an error margin of 10 % is provided on the computational +D32 plot, which corresponds to an average error of 7.5 m + + +. Similarly, an error margin of 15% is +provided on the numerically calculated STD. All the D32 values obtained are observed to be within +this range. Since the experimental error values are unknown, the error margin is provided concerning +the numerical data. The values of D32 are found to be on the lower side for all the test cases performed +compared to the experimental observations. D32 and STD values are calculated in every simulation by +iterating over all the Lagrangian particles throughout the domain. To maintain the accuracy of results +similar to the experimental procedure, the irregular Eulerian droplets are neglected from the +calculations, including the ligaments carried out in the experiments. The sphericity and the minimum + +21 + +threshold value of the droplet undergoing conversion from one framework to another are set per the +experimental data analysis. This way, it ensures the droplets converted to Lagrangian particles are the +ones that need to be accounted for in the droplet characteristics calculations. Each data point on the +plot represents either simulation or experimental data. The following sections discuss the effect of +liquid jet velocity, crossflow velocity, and ambient pressure on the droplet size characteristics. +3.2.1 Effect of Liquid Jet Velocity/ Momentum flux ratio + +Fig. 7: Plot of Sauter Mean Diameter (D32) and Standard Deviation (STD) with Liquid jet velocity at a pressure of +2.1bar. The 10% and 15% error margins are considered for D32 and STD, respectively, based on the simulations due to +the paucity of error margin in experiments. +In all of the D32 plots, the error bars correspond to an error margin of 10% applied on the simulated +contour, and on STD plots, it corresponds to 15 %. Typically, the errors in measurements involving +particle statistics (e.g. D32, STD) vary between 10-30%. Considering this, our predictions exhibit an +excellent agreement regarding the accuracy of the droplet statistics. Figure 7 shows the effect of jet +velocity on global droplet sizes (D32 and STD) at an ambient pressure of 2.1 bar. From both the +numerical and experimental observations, the effect of liquid jet velocity is to decrease the size of the +droplets (both D32 and STD) formed. This is attributed to the increased atomization from the higher +momentum flux ratio (q). Momentum flux ratio (q) is defined as: + +2 +2 +j +j +jet +air +air +air +V +We +q +U +We + + += += + + + + + +(29) + +The droplet sizes decrease as the jet velocity increases from 9 m/s to 24 m/s. Similarly, for the standard +deviation, it is also reduced. The lower standard deviation due to increased jet velocity indicates that +the atomization is more uniform at higher jet velocities. The reduction in droplet size is attributed to +mainly two factors. (1) One is that the Reynolds number increases, and the jet becomes more turbulent +on increasing the jet velocity, resulting in an increased break-up. (2) Another factor is that as the jet +velocity increases, the jet is penetrated more into the cross-flow. This increases the exposure of the + +22 + +liquid jet with the cross-flow. These two factors combined result in the decrease of D32 and STD values. +The above plot shows that increased liquid jet velocity produces finer droplets, improving the +atomization process. +3.2.2 Effect of Cross-flow Velocity + +Fig. 8: Plot of Sauter Mean Diameter (D32) and Standard Deviation (STD) with crossflow velocity at a pressure of 3.8 +bar. The error margins of 10% and 15% are considered for D32 and STD, respectively. +Figure 8 shows the effect of cross-flow velocity on D32. The cross-flow velocity is varied from 33 m/s +to 41m/s and further to 65 m/s, where all other parameters, the pressure (P), liquid jet velocity (Vj), +temperature (T), are kept constant. As observed above, the increase in cross-flow velocity decreases +the droplet size. At low cross-flow velocity, the penetration of the liquid jet is higher. The increased +penetration is due to the increased momentum flux ratio from the reduced air velocity. The penetration +is higher for lower air velocity because the drag force exerted on the liquid jet is smaller at lower cross- +flow velocity. This reduces the width of the spray plume, resulting in the decreased interaction between +the liquid and the gas. On the other hand, at higher cross-flow velocity, the higher drag force bends +and flattens the liquid jet further, resulting in a more pronounced break-up and atomization. Another +explanation for the reduction in droplet sizes is that as the crossflow velocity increases, the Weber +number of the air increases. This also causes the break-up mode to be shifted to pure shear mode +(We>110), resulting in the production of a large number of smaller droplets, also causing a reduction +in droplet sizes. Weber number of air: + +2 +a +a +N +U +D +We + + += + + + + + + +(30) +The experimental D32 value at a crossflow velocity of 33m/s is slightly lower than the value at 41m/s. +But our computational prediction in Figure 8 shows that the D32 value increases with a decrease in the +crossflow velocity. The slight discrepancy in the experimental data could be due to any experimental + +23 + +errors, and this particular trend wasn’t observed with other experimental results pertaining to different +crossflow velocities. The general trend for the droplet sizes is to decrease with increased crossflow +velocity. Therefore, the numerically predicted trend is more acceptable here. +3.2.3 Effect of Pressure +Figure 9 shows the effect of cross-flow pressure on Sauter mean diameter. The ambient pressure varies +while the cross-flow velocity (61 & 65 are considered the same) and liquid jet velocity are kept +constant. As seen above, increasing the pressure decreases the SMD. A similar observation is also +obtained in numerical simulation. This is because an increase in pressure increases density and the +drag force on the jet and the ligaments and droplets, breaking into smaller droplets. The value of the +Sauter mean diameter depends more on the larger droplets than the smaller droplets. So a reduction in +the generation of larger droplets consequently reduced the SMD. The STD plot for increased pressure +also shows similar behavior. The increased pressure improves atomization, resulting in a more uniform +droplet size. In addition, the enhancement in the pressure decreases the penetration of the jet due to the +increased drag forces on the liquid jet. + +Fig. 9: Plot of Sauter Mean Diameter (D32) and Standard Deviation (STD) with ambient pressure at a crossflow velocity +of 65 and 61 m/s. The error margins of 10% and 15% are considered for D32 and STD, respectively. +3.2.4 Effect of Cross-flow Weber number +Here we have considered two sets of cases (case 5, 8 and case 9, 10) having the same liquid-to-gas +momentum flux ratio (q) with different cross-flow Weber numbers (We). The cross-flow and liquid jet +velocities are varied proportionately to keep the momentum flux ratio constant (q=10 for cases 5, 8 +and q=77 for cases 9, 10). The momentum flux ratio is: + +24 + +2 +2 +j +j +jet +air +air +air +V +We +q +U +We + + += += + + (31) +As the Weber number is increased (Case 8: q=10, We=60 and Case 5: q=10, We=150) from 60 to 150, +the droplet sizes are reduced (Case 8: D32=82.95, STD=22.56 and Case 5: D32=75.49, STD=21.98) +following a general trend (Lubarsky et al.,2010; Lee et al., 2007). The same observation is also made +at a higher momentum flux ratio (q=77) when the Weber number is increased from 38 to 60 (Case 10: +D32=78.15, STD=21.20 and Case 9: D32=68.83, STD=17.55). +3.2.5 Effect of parameters on liquid jet penetration, breakup region, and droplet distribution +(a) Liquid Jet Penetration – trajectory +Many researchers have proposed empirical correlations in power law, logarithmic, exponential, etc., +to predict penetration heights for a liquid jet in crossflows. Some researchers have considered the effect +of momentum flux ratio alone (Tambe et al., 2005), while several others included the effect of Weber +number, pressure, viscosity, etc., in their correlations (Amighi and Ashgriz (2019), Ragucci et al. +(2007), and Elshamy et al. (2007)). Stenzler et al. (2006) proposed a power-law correlation that +accounts for fluid viscosity and aerodynamic weber number and is among the first to assess the effect +of air viscosity on jet penetration. While Becker and Hassa (2002), Chen et al. (1993) pointed out that +there is no significant effect of aerodynamic weber number and break-up mode on liquid jet +penetration. The correlations proposed by Amighi and Ashgriz (2019), Tambe et al. (2005), Ragucci +et al. (2007), and Elshamy et al. (2007) for the windward trajectories are used to compare against our +numerically obtained trajectories. Most of the available correlations in the literature are only valid in +the near nozzle region (<25D). +Tambe : +0.53 +1.55 +ln 1 1.66 +N +N +y +z +q +D +D + + += ++ + + + + + + + + + + + + (32) +Ragucci : +0.367 +0.44 +0.012 +2.27 +aero +N +N +z +x +q +We +D +D +− + + += + + + + + and +0.186 +0.367 +0.422 +0.015 +,300 +2.28 +aero +N +air +k +N +z +x +q +We +D +D + + +− + + + + += + + + + + + + + + + + (33) +Elshamy : +0.05 +0.5 /10.46 +0.5 /4.14 +0.5 /1.39 +0.446 +0.141 +12.63 +1 +1 1.42 +1 +N +N +N +x +x +x +D +D +D +N +o +y +p +q +e +e +e +We +D +p +− + + + + + + +− ++ +− ++ +− ++ + + + + + + +− + + + + + + + + + + + + + + + + + + + + += +− + ++ + ++ + + + + + + + + + + + + + + + + + + (34) +Amighi : +0.27 +0.40 +0.14 +0.20 +0.65 +13.31 +0.5 +air +air +Jet +N +N +y +x +q +We +Oh +Oh +D +D +− + + += ++ + + + + + + + + + (35a) + + +0.27 +0.35 +0.72 +0.20 +0.65 +13.31 +0.5 +Re +Re +air +jet +air +Jet +N +x +We +We +D +− +− + + += ++ + + + + + + + + + (35b) + +25 + + + +Fig. 10. Liquid jet penetration along with correlations for (a) case 3 (P=2.1 bar), (b) case 6 (P=3.8 bar) and, (c) case 7 +(P=3.8 bar) +In Figure 10, the numerically obtained trajectories at two different pressure conditions (2.1 and 3.8 +bar) are compared against the experimental correlations of Amighi, Tambe, Ragucci, and Elshamy. In +Figure 10(a), the trajectory for case 3 with pressure 2.1 bar agrees well with the Elshamy correlation, +while the Amighi correlation under-predicts it. Figures 10(a) and 10(b) have similar crossflow +velocities of 61 m/s and 65 m/s, respectively, and the same liquid jet velocity of 19 m/s. The pressure +change has a consequent effect on the Weber number and momentum flux ratio because of the change +in crossflow air density. The weber number reduces to half while the momentum flux ratio doubles. +The Elshamy correlation underpredicts the trajectory in Figure 10(b), whereas Amighi’s correlation +closely predicts in this case. Amighi’s inverse dependence of windward side trajectory on the weber +number is why it shows minor change compared to other correlations +All correlations show similar predictions in Figure 10(a) and Figure 10(c) regarding the trajectory of +the current simulation. The weber number and momentum flux ratio are almost identical for cases 3 + +50 +40 +Simulation (case 3) +Simulation (case 6) +- Tambe +35 +- Tambe +40 +--- Amighi et al +--- Amighi et al +Ragucci +30 +... Ragucci +Elshamy +-- Elshamy +25 +30 +20 +N +20 +15 +10 +10 +5 +0× +0 +5 +10 +15 +20 +0 +5 +10 +15 +20 +ax +X/D. +N +(a) +(b) +50 +Simulation (case 7) +45 +Tambe +Amighi et al. +40 +..... Ragucci +Elshamy +35 +30 +25 +N +20 +15 +10 +5 +0x +0 +5 +10 +15 +20 +(c)26 + +and 7. Therefore, the simulated data lies between the Elshamy and Amighi’s correlation, and the +minimal change is only caused by the slight differences in the momentum flux ratio and weber number +values. Hence, the effect of change in pressure is sufficiently reflected through these non- +dimensionless numbers. The correlation of Tambe highly over-predicts the trajectory in the analysis +of all the cases, which can be attributed to the absence of the weber number in empirical correlation. +(b) Liquid jet break-up region + +Momentum +flux ratio +(q) +Weber +number (We) +(air) +Breakup Location +X (in DN) +Y (in DN) +Case 1 +P=2.1bar,T=25oC, +Va=61m/s, Vj=9m/s +8 + +71 +8.62 ± 1.37 DN +9.95 ± 0.484 DN +Case 2 +P=2.1bar,T=25oC, +Va=61m/s, Vj=12m/s +16 + +71 +8.785 ± 2.33 DN +14.161 ± 0.964 DN +Case 3 +P=2.1bar,T=25oC, +Va=61m/s, Vj=19m/s +41 +71 +9.64 ± 1.73 DN +22.69 ± 1.061 DN +Case 4 +P=2.1bar,T=25oC, +Va=61m/s, Vj=24m/s +66 +71 +9.29 ± 1.385 DN +27.84 ± 1.23 DN +Case 5 +P=3.8bar,T=25oC, +Va=65m/s, Vj=14m/s +10 +150 +8.79 ± 0.827 DN +11.5 ± 0.59 DN +Case 6 +(Case A) +P=3.8bar,T=25oC, +Va=65m/s, Vj=19m/s +19 +150 +8.67 ± 0.873 DN +15.335 ± 0.622 DN +Case 7 +P=3.8bar,T=25oC, +Va=41m/s, Vj=19m/s +48 +60 +11.3 ± 0.933 DN +26.14 ± 0.51 DN +Case 8 +P=3.8bar,T=25oC, +Va=41m/s, Vj=9m/s +10 +60 +8.85 ± 1.17 DN +11.11 ± 0.73 DN +Case 9 +P=3.8bar,T=25oC, +Va=41m/s, Vj=24m/s +77 +60 +8.40 ± 1.08 DN +30.10 ± 1.58 DN +Case 10 +P=3.8bar,T=25oC, +Va=33m/s, Vj=19m/s +77 +38 +10.22 ± 1.12 DN +31.58 ± 1.83 DN +Table 7. The streamwise and transverse location of breakup region for cases 1 to 10. +The break-up location is investigated for all the cases (Table 6), and it is observed that the break-up +does not occur precisely at a particular point. Instead, the break-up occurs in a broader region in the +streamwise direction than in the transverse direction (jet direction). Therefore, we have considered +break-up location a region rather than a particular point where the break-up occurs. The break-up +location refers to the region where the liquid core, after bending, shows excessive deformation and +discontinuities in the liquid core of the spray trajectory. This is the same as the column break-up +location, except our break-up is more in a multimode/shear break-up mode where both the bag-shear +and shear break-up are observed. The liquid jet is subjected to unsteady aerodynamic forces, causing +the windward and leeward surfaces to fluctuate, resulting in the liquid jet column's deformation, + +27 + +bending, and fracture. The break-up location is determined for several test cases, and it is found that +the x-location of the break-up is almost constant. As shown in Table 7, it does not show significant +variation in the streamwise direction. It is approximately located at 9.2D±1.2D for all the cases, +whereas the y-location seems to vary by a large magnitude. The y-location varies with the jet +penetration, dependent on the momentum flux ratio. The higher the momentum flux ratio, the more +the y-location of the jet breakup. Wu et al. (1997) also investigated the break-up location and found +the column fracture location constant at about 8D downstream of the nozzle. Compared to the break- +up location by Wu et al. (1997), our break-up is slightly delayed and in good agreement with the +experiments. Tambe et al. (2005) also made a similar observation regarding the independence of +momentum flux ratio on streamwise break-up location. While the transverse location of break-up +varies with the crossflow parameters (momentum flux ratio and crossflow weber number), the +momentum flux ratio has a more significant influence on penetration than the crossflow weber number. +(c) Droplet Distribution +In all of the test cases performed, the larger droplets or the liquid lumps are found closer to the upper +periphery of the liquid jet, i.e. in the upper half of the spray core region. These larger, irregular +fragments are formed from the liquid core break-up and are penetrated more into the crossflow due to +the higher momentum of the larger droplets, which are less affected by the crossflow. The smaller +droplets are larger in number and found more in the lower part. The smaller droplets are produced in +two ways: one from the secondary breakup of larger droplets and another due to the shear break-up +from the sides of the liquid column. At higher crossflow weber numbers, this model of a shear break- +up from the sides of the liquid column is more dominant than the other break-up modes leading to the +production of a large number of smaller droplets causing a decrease in the droplet sizes. For higher +momentum flux ratio cases (Case 4,7,9,10 – Table 6), the droplet sizes are found to peak at the upper +periphery of the spray core, while for lower momentum flux ratio cases (Case 1,5,8), the droplet sizes +peak near the spray core but still lies in the upper half region. +Figure 11 shows the Eulerian and Lagrangian droplets produced in crossflow atomization. The +droplets subjected to more deformation stay in the Eulerian field, and those earlier converted from +Eulerian to Lagrangian are visible in the zoomed-in image. This conversion is facilitated by the droplet +sphericity, which measures the deviation in droplet shape compared to that of a spherical droplet of +equivalent diameter. The Eulerian droplets visible in Figure 11 are the droplets having sphericity +>1.47, and the spherical droplets visible are Lagrangian droplets. The simulation produces as small as +10-15 µm droplets, better resolved using the LPT approach. The larger droplets are fewer in number, + +28 + +and the smaller droplets are larger in number. The droplet sizes generally follow a log-normal +distribution (Li et al. (2016)). + +Fig. 11: Crossflow jet atomization and breakup captured using VOF-Lagrangian particle tracking approach for case 5 +(P=3.8bar, Vair=65m/s, Vj=14m/s, q= 10, We=150). Spherical droplets indicate lagrangian droplets converted from +Eulerian droplets (blue color) + +Fig. 12: Crossflow jet atomization and breakup captured using VOF-Lagrangian particle tracking approach for case 6 +(P=3.8bar, Vair=65m/s, Vj=19m/s, q= 19, We=150) + +Dropletdiameter(um) +1.0e-05 +1.0e-4 +2.1e-04Droplet diameter (um) +1.0e-05 +1.0e-4 +2.1e-04 +Lagrangian droplets +Ligaments +Primary brcakup +Liquid jct corc29 + +3.3 Spray breakup and atomization +Figure 12 represents a liquid jet's break-up and atomization process in cross-flow (case 6) with Eulerian +(iso-contour α=0.5) and the Lagrangian droplets. The aerodynamic drag force experienced by the liquid +jet column forces it to bend in the crossflow direction because of a high-pressure windward and low- +pressure leeward region, as shown for case 3 (Table 6) in Figure 13(a). Another prominent feature of +LJICF is flattening the liquid jet cross-section from a circle to a crescent. This can be understood as +airflow around a deformable cylinder, as shown in Figure 13(b). The crucial factors responsible for +this deformation are – internal boundary layer flow and pressure difference. The internal boundary +layer (shown by the dashed line in the first image of Figure 13(b)) is formed in the liquid phase due to +the shear generated by the external flow of air around the liquid core, which transports the liquid from +point 2 towards point 3 and 4. Moreover, the pressure at point 2 is higher than the pressure at points 3 +and 4; it further helps this internal flow of the liquid away from the frontal region (around point 2) +towards the periphery (near points 3 and 4). It leads to the flattening of the liquid jet core cross-section +(as shown in the second image of Figure 13(b)). Both the factors continue forcing the liquid from point +2’ towards 3’ till the complete circular cross-section has been deformed into a thin sheet-like cross- +section (third image of Figure 13(b)). The liquid movement from points 2’’ to 3’’ (in the third image +of Figure 13(b)) leads to the thickening the liquid-jet core edges. This process is suspected to be one +of the deciding factors in streamer formation along the two edges of the deformed liquid jet, which +will be discussed later in detail. However, the flattening of the liquid jet core further increases the +effective frontal area, and consequently, the drag forces cause it to deflect even further. Figure 13(c) +shows this deformation of the liquid column for case 3 at varying distances from the bottom wall. +The liquid jet deformation is mainly followed by break-up through two mechanisms: column break-up +and surface break-up. The column break-up is characterized by instabilities and the growth of surface +waves on the liquid jet column, resulting in the formation of crests and troughs. These waves grow in +size, causing the liquid column to detach from one of the wave's troughs, resulting in a liquid break- +up. Large fragments separate in this break-up, leading to larger droplets observed in the liquid jet's +upper periphery. In the surface break-up, the droplets are pinched off (before the column break-up +occurs) from the sides of the liquid column due to the action of shear between the liquid and gas phases +on the periphery of the flattened/deformed liquid jet as observed at height (Z) between 8D to 12D in +Figure 13(c). +It is also proposed that the surface break-up is caused by the growth of turbulent instability on the +liquid column as the laminar liquid jet undergoes transition (Madabhushi et al., 2008). This is +commonly observed at moderate to high crossflow Weber numbers (Weair) with high momentum flux + +30 + +ratios (q). At lower to moderate Weber numbers, increasing crossflow weber number shifts the break- +up towards the shear regime of a column breakup. The shear break-up starts way before the instabilities +at the liquid-gas interface, causing the liquid core to rupture into smaller droplets. The droplets formed +from shearing action are smaller, resulting in better atomization of the liquid jet. These two break-up +processes constitute the primary atomization part. + +Fig. 13: (a) Mean pressure showing maximum and minimum values on the windward and leeward side of a liquid column, +(b) Schematics showing liquid column deformation at increasing distance (height) from the point of injection, (c) Liquid +jet cross-section deformation along with shear breakup at various heights from the point of injection (in jet direction, Z) +for case 3 (P=2.1bar, Vjet=19m/s, q=41, Weair=71). + + +High Pressure +Region +2 +Low Pressure +Region +(a) +Gaseous External +Original Cross-section +Boundary Layer +shape +Liquid Internal +Boundary +Layer +(b) +Droplet diameter (um) +1.0e-05 +1.0e-4 +2.1e-04 +Z=1D +Z-2D +Z=4D +Z=6D +7=15D +Z-12D4 +Z=8D +Z=4D +Z-8D +Z=10D +Z=12D +Z=-15D +Z-1D +(c)31 + +The primary break-up happens when the aerodynamic forces of the crossflow cause the liquid jet to +rupture into smaller ligaments and droplets. Sallam et al. (2004; 2006) classified the primary break-up +for non-turbulent liquid jets based on the aerodynamic Weber number into four modes, the column +(We<4), bag (4110). The break- +up mode is investigated for different crossflow weber numbers (38-150) and momentum flux ratios (8- +77). For the test cases performed in this study, the breakup modes involve bag/multi-mode and shear +modes of breakup and the surface breakup of the jet. For a few cases, multimode behavior is observed +where both bag and shear modes are present. As the aerodynamic weber number increases, the mode +of break-up shifts from multimode to pure shear mode (cases 5 and 6), characterized by the pinch-off +of droplets from the sides of the liquid column. The bag formation and its subsequent breakage into +ligaments and droplets for case 8 are discussed in detail in the subsequent section. Similar +characteristics of multimode and shear breakup modes are discussed later in the following sections. + +Fig. 14. The primary breakup regime map shows the varying momentum flux ratios and crossflow Weber numbers cases. +The red-colored encircled points show the cases that are analyzed in detail. + +Three tests out of ten listed in Table 6 are considered for detailed analysis. The three tests belong to +the different regimes of the liquid jet breakup, as shown in Figure. 14 – case 8 in bag breakup regime +of the column breakup, case 9 in surface breakup regime, and case 5 in shear breakup regime of the +column breakup. + + +100 +:Eslamian,Amighi and Ashgriz +90 +·Becker and Hassa +P=2.1bar.Vair=61m/s +80 +10 +P=3.8bar,Vair=65m/s +flux ratio (q) +P=3.8bar.Vair=41m/s +70 +P=3.8bar.Vair=33m/s +4 +60 +Momentum f +50 +40 +30 +20 +2 +10 +0. +0 +0 +50 +100 +150 +200 +250 +300 +Weber number (We . +air32 + +3.3.1 Bag Breakup Regime + +Fig. 15. Characteristic features of a LJICF in bag breakup regime for case 8 (q = 10 and We = 60). +Case 8 is ideal for bag breakup because of the low-value q and We. A few distinct features of this case +are the flow in the wake of the liquid jet, development of instability and its growth, bag breakup, and +bifurcated streamers formation, as shown in Figure 15. Each of these is analyzed in detail. +(a) Flow behind the liquid jet +As discussed above, the high and low-pressure region is created on the windward and leeward sides of +the liquid jet. The pressure difference plays a prominent role in the deformation of the liquid jet cross- +section, as shown in Figure 13. The pressure difference affects the flow passage around the liquid jet +column. As shown on the mid-plane in Figure 16(a), the high-pressure point (S1) is located at a +particular height on the windward side of the jet where the static pressure reaches a maximum value. +The streamlines using mean velocity with only x- and z-direction components are plotted in Figure +16(b) to estimate the flow features. +The low pressure in the liquid jet wake is dominant from the bottom wall at some height. It draws in +the flow passing through the jet column's sides, creating a counter-rotating vortex (CRV), as shown +by the yellow streamlines in Figure 16(b). Li et al. (2016) stated a saturation point on the leeward side +of the liquid column. The recirculating flow may divide at the rear surface of the liquid column to +create two circulation zones. In Figure 16(b), almost an entire leeward side of the jet column is exposed +to only one (spanwise) vortical structure, i.e. CRV. The point S2, where velocity would be zero on the +leeward side of the liquid column, lies in the region of the complete breakup of the liquid column into +ligaments. + + +Bag Formation +Ligaments +Streamers33 + + +Fig. 16. (a) Pressure contour shows high-pressure point S1 on the windward side of the liquid column, (c) Streamlines in +x-z plane show counter-rotating vortex (CRV) in yellow color, (c) counter-rotating sheet breakup vortex (SBV) pairs +(green-red color), (d) & (e) show movement of the SBV at consecutive time units following the bag of the wave. (f) The +white-colored streamlines break through the liquid sheet bags, pulled by the SBVs for case 8 (q = 10 and We = 60). + +Further, the two smaller counter-rotating vortex pairs act along the column breakup process +downstream of CRV. An interesting phenomenon is noticed where these two vortices’ centers move + +385000 +CRV +384000 +382501 +(a) +(b) +SBV +(c) +SBV +SBV +(d) +(e) +(f)34 + +with the trough/bag of the liquid column instability. The movement of these vortices is shown at +consecutive time units in Figures 16(d) and 16(e), where the vortex has shifted downstream following +the trough of the wave. A closer look at this phenomenon in Figure 16(f) shows the ‘white’ colored +streamlines passing through the ruptured liquid surface in the wave trough and mixing with outgoing +‘green’ streamlines of the vortex downstream. +Lower pressure at the vortex center pulls the flow-through ruptured liquid sheet. Wen et al. (2020) +referred to these vortices as the bag breakup vortex (BBV). Here we refer to them as sheet breakup +vortex (SBV) due to their role in the sheet-like liquid column breakup, which will be discussed in the +subsequent section of the high shear case. The vortex strength of SBVs diminishes downstream as the +liquid column disintegrates into ligaments and droplets. Though the streamlines corresponding to the +mean velocity field do not show any vortex formation (picture not shown here), the movement of +vortices downstream with diminishing strength indicates the vortex shedding phenomenon. Further, +the vortex shedding phenomenon will be discussed later for the high momentum flux ratio case. + +Fig. 17. Density contour at mid-plane of LJICF showing Kelvin-Helmholtz (KH) type instability. The typical KH type +asymmetric waves are observed. The sinuous waves are most unstable here, considering the upper part of the liquid column +behaves like a sheet (instead of varicose waves). + +Fig. 18. The contour of Y-vorticity (normal to figure plain) at mid-plane of LJICF showing Kelvin-Helmholtz (KH) type +instability. The near roll-ups are observed for this case. + +1027. +(gu) +800.0 +Sinuous Wave +Nature +Density +600.0 +400.0 +200.0 +4.2591.0e+05 +5.0e+4 +Vorticity Y (s-1) +0.0 +-5.0e+4 +-1.0e+0535 + +(b) Growth of instability on the windward side of the liquid in crossflow +The formation of bags results from instability created upstream on the windward side of the liquid +column. Earlier it was proposed that these are the Rayleigh-Taylor instability (Sallam, 2004; C.L.Ng +et al., 2008)) is caused due to the higher/lower air pressure on the windward/leeward side of denser +liquid which results in the bag formation similar to the finger/bag like structures obtained in the +experiments of Lewis (1950), Taylor (1950). Rayleigh-Taylor instability is caused by denser fluid +under acceleration towards lighter fluid. +In this case of lower q and We, visual observation of the evolution of instability and breakup at +consecutive time steps indicates that Kelvin-Helmholtz (KH) is the reason behind the instability +growth (refer to Figure 17 showing density contour). Similarly, Y-vorticity (normal to the image plane) +is also plotted to check the roll-ups of the two fluids (Figure 18). A small clip of the same has been +provided as supplementary data, clearly showing the presence of KH-type instability. +As evident in Figure 19(a), the unstable waves are developed across the windward surface with parallel +troughs/crests perpendicular to the stream direction. A cross-section of the liquid column is observed +at a location just before the wave starts to develop, and it shows that the liquid column has transformed +from a circular shape to that of a sheet (see Figure 19(a)). Hence, we treat this as a case of instability +development on a liquid sheet. Also, the liquid sheet-like structure is located at a much downstream +distance from the point S1 along the liquid column such that high pressure has a lesser effect than the +velocity shear between airflow and liquid column. +Considering inviscid, irrotational flow, the dispersion relation between wave number and wave growth +rate is used for a liquid sheet as deduced by Squire (1953). If a coordinate system moves with the sheet +interface at relative velocity U , an infinitesimal disturbance formed on it is described by: +0 +[ +exp( +)] +=  ++ +ikx +t + + + +, + + + + + + + +(36) +where +0 + is the initial wave amplitude, +2 +/ +k + + += + is the wave number, and +r +i +i + + + += ++ + is the complex +growth rate. The dispersion relation for a moving liquid sheet under inviscid conditions can be derived +as: + + +3 +2 +2 +2 +1 +tanh( +) +2 +0 +k +kh +Q +iQkU +QU k + + + + ++ ++ +− ++ += + + + + +(37) + +36 + +for the sinuous waves. Here, Q is equal to +2 +1 + + , h is the sheet thickness. The solutions to the above +Eq. 37 for the growth rate +r + are: + + +2 +2 +3 +1 +tanh( +) +tanh( +) +tanh( +) +r +kh QU k +k +kh +Q +kh +Q + + + +− ++ += ++ +. + + + + +(38) +Similar to above, Eqs. (37) and (38) corresponding to sinuous waves, the dispersion relation and the +wave growth rate for the varicose mode of the waves are also obtained by replacing tanh( +) +kh by +coth( +) +kh term in these equations. + +Fig. 19 (a) Location of a plane at which the cross-section of the liquid column is almost sheet-like, (b) three points showing +the location curve for liquid profile calculation, (c) Velocity profile along the axis perpendicular to the interface, (d) Growth +rate of different waves with wave numbers. +In the present case of LJICF, the velocities of the gas and liquid phase need to be parallel at the interface +for the calculations. For this purpose, the velocity data is extracted along with the line segments at +three points on the air-water interface, as depicted in Figure 19(b). The points are chosen at such a +location where the instability waves start to appear. The line segments are perpendicular to the interface +at their respective interface points. The magnitude of the velocity component is found along the line +segment by += + +tang +t +u +u n , where +tn is the unit direction vector tangent to the surface. This provides + +(a) +(b) +50 +0.1 +Short Wave, Inviscid +Long Wave, Inviscid +Sinuous Wave,Inviscid +40 +0.08 +Sinuous Wave,Viscous +P1 +P2 +30 +P3 +0.06 +h/U +/DN +20 +0.04 +10 +0.02 +0 +5 +10 +15 +20 +25 +30 +35 +40 +0 +0 +0.5 +I +1.5 +2 +2.5 +3 +kh +(c) +(d)37 + +us with the velocity profile at desired points (shown in Figure 19(c)) and helps us calculate accurate +velocity differences by avoiding the shear region. It is also visible that the maximum velocity increases +from P1 to P3. Therefore, an average of the velocity difference +( 17.56 +) +avg +U +m s + + + is used in our +calculation. Similarly, an average liquid core thickness +4 +( 1.5 10 ) +avg +h +− + + + is also considered because of +its variation along the liquid column, minimum at P3 and maximum at P1. The other details of +thermophysical variables regarding the calculation are provided in Table. 1. +Senecal et al. (1999) discussed that the maximum growth rate of sinuous waves will always be greater +or equal to the maximum growth rate of varicose waves in the moving liquid sheet. From the +observation of our present case (refer to Figure 17, Figure 18), the sheet-like liquid column shows +sinuous wave formation at its inception. Hence, we consider only the sinuous solution for the linear +stability analysis (LSA) in this work. Figure 19(d) compares the growth rate for sinuous wave solution +with short and long wave assumptions. Since the wavelength  of the disturbance in the present case +is slightly smaller than 2 times the sheet thickness h , short waves start to dominate over long waves. +This is evident in Figure 19(d) as well, where the short wave assumption (red curve) predicts near to +the general inviscid sinuous mode growth rate (blue) as compared to the long-wave assumption (red +curve). The long wave assumes tan( +) +kh +kh + + whereas the short wave assumes tan( +) +1 +kh  in Eq. 38. +Senecal et al. (1999) showed the dominance of long wave and short wave in low velocity/Weber +number and high velocity/Weber number liquid sheets cases, respectively. The Weber number for the +sheet-like liquid core is approximately +2.8 + + with the present parameters, which makes it a marginal +case for the distinction of long and short waves, albeit short wave is observed to dominate over a long +wave in the present situation (as shown in Figure 19(d) and also, the assumption of tan( +) +kh +kh + + not +holding true). +The +/ +N +D + + values from various correlations and linear stability analysis are compared with the +computationally observed result in Table 8. The data corresponding to correlations and Rayleigh- +Taylor breakup are calculated using the free stream air velocity of 41 m/s. The LSA error by +Chandrasekhar and the general sinuous inviscid wave is minimum. The solution of a sinuous wave +growth for a viscous sheet is very high, requiring further work to include viscosity effects. The +Rayleigh Taylor or RT-based correlations (Chandrasekhar, 1961; C.L. Ng et al., 2008) predict almost +50% higher values confirming the absence of this type of breakup. This also explains the formation of +cross-stream ligaments from the column breakup, as shown in Figure 19(a). +This case shows the development of KH instability and not the RT instability, which was considered +the only dominant instability responsible for the column breakup in the past. Li et al. (2016) proposed + +38 + +that the liquid jet in very low crossflow velocity behaves similar to a jet in a quiescent air/gas medium +and tends to develop KH instability. This is in contrast to the condition here. In the present case, air +velocity is significant enough, and the momentum flux ratio is also low. +An essential factor, in this case, is the high shear experienced by the liquid column in the direction of +liquid flow along the portion of its length where these KH waves start to develop. The high shear forces +along the liquid column seem only possible when the momentum of crossflow air needs to be +substantial compared to the momentum of liquid. The higher momentum of crossflow air bends the +liquid jet acutely to high angles, which has a two-fold effect. First, the high-pressure region on the +windward side of the liquid column is limited to the smaller area only, which faces directly into the +incoming crossflow. Second, high velocity is achieved in the region beyond point S1. Point S1 lies at +the approximately same area where the vorticity changes its sign as visible in Figure 18; the air velocity +now exceeds the liquid flow velocity beyond point S1. Thus, the high momentum of crossflow +compared to the liquid momentum (that is, low momentum flux ratio) may be considered one of the +governing reasons for the domination of KH instability. This is in contrast to Li et al. (2016). But we +will see in the following sub-sections that it is not the crossflow velocity but the momentum flux ratio +that decides the type of dominant instability. +Correlations/LSA +/ +N +D + + +Prediction error +(%) +KH – Short sinuous wave +0.86 +25.75 +KH – General sinuous wave +0.89 +22.57 +KH – Sinuous wave, viscous - Senecal et al. (1999) +15.05 +1200.0 +KH – Chandrasekhar (1961) +0.87 +23.94 +Rayleigh-Taylor – Chandrasekhar (1961) +1.73 +50.00 +C.L. Ng et al. correlation (2008) +1.83 +59.09 +Sallam et al. correlation (2006) +0.54 +53.03 +Present Simulation +1.15 +- +Table 8. Comparison of wavelength observed in the present case and the predictions from LSA and correlations. +(c) Bifurcation of liquid jet into streamers +In Figure 15 and also in Figure 20(a), we can observe two thread-like structures separating from the +sides of the liquid jet column known as streamers. This distinct phenomenon is termed bifurcation and +was observed in the experimental work of Sedarsky et al. (2010) and then in a computational study by +Wen et al. (2020). Still, many researchers did not clearly explain the cause of this phenomenon. +Sedarsky et al. (2010) suggested that it is due to the vortex formation behind the liquid jet column, and +Wen et al. (2020) indicated that it could be due to the sheet break-up vortex (SBV). This + +39 + +streamer/bifurcation is formed in the near nozzle region close to the wall. As the jet penetrates more +into crossflow (away from the wall), the liquid-gas circumference region is subjected to more shear +forces. As discussed earlier, the boundary layer is formed on either side of the interface in both phases. +An azimuthal instability develops across the liquid column, which may be responsible for the +perturbations at the liquid column base. The cause of this has been reported to be Centrifugal Rayleigh- +Taylor (CRT) instability (Behzad et al. (2015)). These instabilities grow along the liquid column axis +along the internal boundary layer, resulting in the thickening of liquid column edges. +Data is extracted on two planes along the liquid column at locations just before and after the bifurcation +– C1 and C2, respectively, as shown in Figure 20(a). Figure 20(b) shows the cross-stream (Z) +component of vorticity and pressure on C1 planes. Apart from the shear layer vorticity, the highlighted +region indicates the presence of vorticity within the liquid, along the two peripheral edges. The +vorticity is very weak compared to the boundary layer (for both air and liquid). Similarly, the pressure +contour reaches a very low value at the center of these areas, as seen in Figure 20(b). It shows the +continuous movement of liquid into its edges, which stretches the central region of the circular liquid +core cross-section into a thin sheet-like structure while at the same time thickening these liquid column +edges. Figure 20(c) presents the vorticity and pressure contours just after the detachment of the +streamers on the C2 plane, where these vortices on the liquid column periphery are absent. The +separated boundary layer of the liquid column and bifurcations now passes through their gap +(highlighted green). Also, the minimum pressure values are present in the gas phase only, outside the +liquid. +As described in the previous section, the two factors play a significant role in the deformation of the +cross-section of the liquid column – the internal boundary layer and the pressure difference driving the +flow. The transfer of liquid to the periphery by the internal boundary layer in the absence of a return +flow to the middle is majorly responsible for the thinning of the liquid column at the middle and the +thickening of the edges. +Another important factor is the flow orientation of CRV, as shown by the velocity vectors and white- +colored streamlines in Figure 20(d). A portion of the flow enters the wake of the liquid column from +the bottom and gets drawn up by the CRV, and without reaching the bottom again, it exits the CRV +from the sides. This sideward movement of air on either side of the liquid column pushes against the +thick edges of the liquid column. This is also evident on the C1 plane in Figure 20(b), labeled as CRV- +exit, the thick opposite vorticity witnessed at the peripheries. + +40 + + +Fig. 20 (a) The location of planes – C1 and C2 on the liquid column just below and above the point of bifurcation, (b) Plane +C1 – Left column: Vorticity Z contours show weak vorticity within the liquid at edges (at the tip of thick green arrows and +beside the internal boundary layer), whereas the black smaller arrows show the direction of flow along the edges; Right +column: The pressure plot showing a drop at transverse liquid column edges, (c) Plane C2 – Left column: Vorticity Z +contours after bifurcation with negligible vorticity within it; Right column: Low-pressure area vanishes from the liquid +edges just after the bifurcation; (d) The streamlines with stream vectors show the role of fluid exit from CRV in causing +bifurcation/streamer formations. + +(a) +C +374000 +C +50000 +373000 +CRV +Exit +口 +371000 +50000 +37000 +s0+a0't +369000 +LOW +Pressure +CRV +Exit +(b) +(c) +1.0e+05 +374000 +373000 +50000 +372000 +0 +-50000 +370000 +-1.0e+05 +369000 +1.0+00 +0.8 +(d) +(e) +(f)41 + +Figure 20(c) shows changes in the vorticity just after separation (on the C2 plane). The streamer is +found to follow this fluid exiting the CRV, thus, following a different trajectory than a liquid column. +Hence, it may be said that both the factors need to be present for a bifurcation to happen – moderate +but sufficient level of shear flow/boundary layer to thicken the liquid column edges and the typical +flow of CRV to separate and pull it along, away from the liquid column. +Also, Figure 15 shows two similar ligament-type structures alongside the bags of the liquid column at +the top. This essentially re-thickens the edges because of the boundary flow within the liquid column. +Hence, this phenomenon cannot occur because of shear instability but the internal boundary layer. The +bifurcation formed is found to be thicker for low penetration cases. The bifurcation starts vanishing as +the momentum flux ratio (q) increases (cases 1 to 4). This is because the primary break-up mode shifts +towards pure shear mode as the momentum flux ratio or crossflow Weber number increases, enhancing +the surface stripping process with crossflow. In cases 4, 9, and 10, where the momentum flux ratio is +high, we have observed multiple streamer formations in which the liquid jet column is split into +multiple(four) membranes. The bifurcation formed is very thin and can be considered almost nil in +these cases. + +Fig. 21. Basic figure of case 5 with We=150 and q=10. +3.3.2 Shear Regime +The LJICF shows a shear-dominated breakup at a high Weber number but a lower momentum flux +ratio in Figure 21. Case 5 out of the two high We cases is chosen for the study. The q value remains +the same as the previously analyzed case 8. Here, the flow feature behind the LJICF and the instability +at the edges are discussed. +(a) +Flow behind the liquid column +The flow feature behind the liquid jet column for We=150 (Figure 21) is similar to the previous case +with We=60. The pressure contour (Figure 22(a)) is similar to the low We case. In this case, only a + +42 + +single recirculation zone is visible, as shown by ‘yellow’ colored streamlines in Figure 22(b). The +saturation point of the leeward side of liquid column S2 lies in the region where the complete breakup +of the liquid column takes place. Similarly, the liquid shear at the edges vanishes downstream of point +S2. The shear breakup will be covered below in Section 3.2.2(b). The two opposite rotating vortex pairs +(referred to as SBV in the previous section) are also present, as shown in Figure 22(c), albeit their +center positions shift one behind the other, and one of them is weaker than the other. In Figure 22(c), +the red streamlines pass through the thin liquid sheets as it tears apart. The liquid sheet breakup is +delayed on the side of the weaker ‘green’ colored vortex. Hence, these vortices play an essential role +in the breakup of thin liquid sheets present on both sides of the thicker liquid column. These liquid +sheets break up without forming a bag-type hollow structure; hence these vortices’ name ‘sheet +breakup vortex’ (SBV). + +Fig. 22. (a) Pressure plot with stagnation point S1, (b) The mean flow on mid-plane showing same flow as the first +case with leeward stagnation point S2, (c) The two counter-rotating SBVs for case 5 (q = 10, We = 150). +(b) Growth of instability and Streamers +The two different disturbances are apparent here – one at the end liquid column and the other along +the edge of the liquid column. The density contours at the middle plane (XY), bisecting through the +liquid column, were analyzed for the first type of disturbance. It is not further analyzed here since the +breakup happens just after the inception of the not-so-prominent first or second wave or even before +that. Instead, a more dominant shear breakup is focused on. + +394000 +392000 +390000 +388000 +386000 +383623 +(a) +(b) +(c)43 + +As shown in Figure 23, the two different wavelength waves appear on the edges of the liquid jet. The +waves on the upper side are almost double the wavelength at the bottom of the liquid column, +increasing along the liquid column. Another aspect is the formation of ligaments and subsequent thick +droplets in the place of bifurcation/streamer. The region of a larger wavelength lies just above this +bifurcation point ‘B’. + +Fig. 23. Shear instability waves at liquid-core edges with different wavelengths at the top and bottom of point B. +The C.L. Ng et al. (2008) correlation from their experiment shows the dependence of +0.33 +G +N +4.3W +D +e + +− += + which predicts almost four times the wavelength observed near the bottom and +almost double the wavelength above point B. The different behavior witnessed in the two regions may +be due to the change in the size of the liquid column faced by the incoming air; that is, the bottom part +of the liquid column is analogous to the circular cylinder of size same as the jet diameter whereas, the +upper part (above point B) is similar to a shell of size larger than jet diameter. Considering the +disturbances in the lower portion, there is a similarity with the instabilities in separating shear flow +over the cylinder with Re +1000 + +. At a high Reynolds number case like this, two kinds of 3D +instabilities exist – a) streamwise vortices of separating shear layer and b) streamwise vortices of the +wake. In the present study, the instabilities of separating the shear layer are more critical in assessing +its effect on the liquid edges. Based on the results of Bernal and Roshko (1987), Williamson (1996) +proposed the following relation for the wavelength of streamwise vortices of separating shear layer: +0.5 +25 +S +N +L +e +D +R + +− + +. + + + + + + + + +(39) +The Re corresponds to the Reynolds number of airflow around the circular liquid column, which +behaves like a cylinder of diameter (DN) +8910 + +. The prediction is near the wavelength obtained from +simulation for the lower part of the liquid jet column, as shown in Table 9 for both case 5 and case 6 +with the same We, though there is some deviation for case 9. It also shows that the prediction is +independent of the momentum flux ratio; it does not depend on the liquid jet velocity. Similarly, the + +B +Large +Wavelength +1. +Small Wavelength44 + +study of instability in the upper part of the jet column can be part of future work concerning the flow +structures over hollow shells. +Correlations +/ +N +D + + +Case 5 +(q=10, We=150) +Case 6 +(q=19, We=150) +Case 9 +(q=77, We=60) +Williamson correlation (1996)** +0.26 +0.26 +0.33 +C.L. Ng et al. correlation(2008) +0.82 +0.82 +1.11 +Present Simulation +0.21 +0.26 +0.21 +Table 9. Comparison of wavelength observed in this study with the correlations. **Williamson correlation about shear +layer streamwise instability is valid, assuming that the same instability triggers the shear instability in liquid edges. +3.3.3 Surface Breakup Regime +Case 9 with the same Weber number 60 as case 8 but higher momentum flux ratio of 77 is chosen in +this regime. + +Fig. 24. (a) Pressure plot with longer and extended high-pressure zone on the windward side of LJICF, (b) Streamlines +showing two recirculation regions separated with a stagnation point S2. The two horizontal planes are the location for the +streamlined contours shown in Figure 25. +(a) +Flow field behind the liquid jet column +In this case, the flow is quite distinct from the low momentum flux ratio cases, as shown in Figure 24. +In Figure 24(a), there is an extended high-pressure region on the windward side of the liquid column +with a higher value of the maximum pressure. The existence of high pressure for most of the windward +side of the liquid owes to deeper penetration by this liquid jet. The streamlines on a plane shows two +recirculation zones (‘yellow’ colored vortex as CRV and ‘pink’ colored vortex lies above CRV) of +opposite rotations in Figure 24(b), different from previous cases. From this figure, the saturation point +can easily be found on the leeward side of the liquid jet. It is the same as the observation made by Li +et al. (2016) in their case with the momentum flux ratio of 88.2, which was kept constant for all their + +422093 +420000 +418000 +Z/D = 17.5 +415644. +Z/D = 9.6 +(a) +(b)45 + +three simulations. The variation of the Weber number was only employed. Hence the condition of the +present case nearly matches the conditions used by Li et al. (2016). +Figure 25 represents the instantaneous streamlines on horizontal planes at two planes – Z/DN= 9.6 +(Figures 25(a) – 25(f)) and 17.5 (Figures 25(g) – 25(l)) against the density contour, which helps to +locate flow features concerning the cross-section of the liquid column (green colored). The location of +planes is chosen appropriately, considering that it lies near the point of bifurcations (or streamer +formations), as shown in Figure 24(b). This allows us to observe the effect of bifurcated streamers on +the flowfield, if any. First, the streamlines at plane Z/DN =9.6 depict periodic vortex shedding. This +resembles the flow over a cylinder or, more appropriately, over the semi-spherical shell (a shape similar +to the liquid jet-core cross-section in Figures 25(a)-25(f)). One of the vortices in Figure 25(c) (shown +by red pointer) undergoes vortex tearing in Figure 25(d), during which one of them remains near the +jet column while the other convects downstream with the flow. Second, Figures 25(g)-25(l), on the +right side column, captures the bifurcation of the second streamer as shown by the green-colored +stretched liquid column at Z/DN =17.5 and the vortex shedding near its location on the leeward side. +The vortices at Z/DN =17.5 (right) are stronger and bigger than that observed at Z/DN =9.6 (left), and +thus, they are present for a longer downstream distance. Another feature is the vortex pairing, occurring +downstream of the liquid column in Figures 25(j) – VP-1 and VP-2. The two vortices prior to a pairing +process are shown in Figure 25(h)-(i). After completion of the pairing process in Figure 25(j), they +give rise to a stronger vortex, as observed in Figure 25(k). +The vortex pairing on the leeward side seems related to the liquid core and its bifurcated streamer +formations. The streamers’ formation results in the gap between the central liquid core and streamers, +affecting the vortex shedding downstream. It may be said that the different vortices shed in the +bifurcation process interacts with each other leading to the vortex pairing (as noticed in Figure 25(h)- +(j)). It further complicates the flow concerning the interaction between liquid core breakup into +streamers and the airflow development behind it, both dependent on each other. +Since the crossflow air velocity remains the same as for the low momentum flux ratio case in the bag +breakup regime (Section 3.2.1), the vortices witnessed (SRVs) resulting from vortex shedding are +similar to vortices on plane Z/DN = 9.6. However, the strength of these vortices will vary for both these +cases because of the difference in the trajectory of the liquid jet, size, and strength of CRV. Since the +SRVs are found to move along the KH waves in case 8, it may be an interesting future study to confirm +if it is always true. + +46 + + +Fig. 25. Left panel: Streamlines show vortex shedding along with a vortex tearing phenomena on plane Z = 9.6; Right +panel: Streamlines show vortex shedding and (two) pairing processes on plane Z = 17.5. + +z / D = 9.6 +z /D = 17.5 +(a) +(g) +40Densito so0 +5.011 200 +(b) +(h) +40Denst00 s00 102 +400ens600 +800 +(c) +(i) +(d) +(!) +VP- 1 +VT +VP- 2 +400 6 +008 +(e) +() +After VP- 1 +After VP - 2 +40Densi0o +800 +5.041200 +(f) +(1) +VT - Vortex Tearing +VP - Vortex Pairing47 + +(b) +Instability on the liquid column and surface edges +This case shows both the instabilities of – the liquid column and its edges. The Rayleigh-Taylor +instability is found to be dominant in the liquid column. The waves are symmetric until the breakup, +and the typical Kelvin-Helmholtz roll-ups are absent, as shown in Figure 26. The wavelength can be +predicted by using C.L.Ng et al.'s (2008) assumption of cylinder drag as acceleration for Rayleigh +Taylor instability in this case: +2 3 +D,cylinder +G +C +1 10Re− + + + + + +when +5 +G +1 +Re +2 10 + +  +. + +(40) +and, +0.26 +G +N +5.3W +D +e + +− += +. + + + + + + + + +(41) +Here +D +C is the coefficient of drag for the cylinder and +G +Re is the air Reynolds number. The wavelength +observed in the present case is compared with the LSA result by Chandrasekhar (1961) and correlation +by C.L.Ng et al. (2008) in Table 10. +This case with high momentum flux ratio further confirms the claim that as the momentum flux ratio +increases, the chances of Rayleigh-Taylor dominated instability is higher. In the case of high +momentum flux ratio and moderate (or low) Weber number, the liquid momentum is higher than +gas/air momentum. In other words, the injected liquid/water mass flow rate is also high, unlike case 5, +where the liquid jet bends acutely due to early flattening. It leads to deeper penetration of liquid jet +with almost vertical liquid jet through the crossflow. The portion of the liquid column that faces +directly into the incoming crossflow air has an extended high-pressure region. At the same time, the +air/gas cannot generate enough shear along the liquid flow direction. Hence, the effect of high pressure +on the windward side starts to have its outcome in Rayleigh-Taylor instability. +Correlations/LSA +/ +N +D + + +Rayleigh-Taylor - Chandrasekhar +1.73 +C.L. Ng et al. correlation (2008) +1.83 +Present Simulation +1.70 +Table 10. Comparison of wavelength observed in the present case and the predictions from LSA and correlations. + +48 + + +Fig. 26. (a) Density contour at mid-section of LJICF show Rayleigh-Taylor instability, (b) Shear instability for We = 10 +and high momentum flux ratio (q) = 77. +It is, thus, proposed here that the momentum flux ratio plays a vital role in deciding the type of +instability growth on the liquid column. The momentum flux ratio is lower, higher the probability of +developing KH type of instability. Since the present study primarily focuses on the rigorous validation +of compressible solver against varying parameters, further detailed analysis at varying q and We is +beyond the scope of this work. +The wavelength of surface waves along the transverse edges of the liquid column has been calculated +using the assumption discussed in the previous section. It is proposed that the same disturbance causes +this instability of a liquid column as that of the air shear layer around a cylinder. Eq. 39 is used for the +wavelength calculations in Table 9. Using this assumption, the Williamson shear layer correlation +predicts +/ +N +D + +equals 0.33, which is closer to the observed (non-dimensionalized) wavelength of 0.26 +from the simulations compared to 1.18 by C.L.Ng et al. (2008)’s correlation. C.L.Ng et al. (2008) +correlation may be based on the wavelength measurements downstream of the liquid column for cases +with much higher q. However, the empirical correlation by Williamson is only valid for the region +near the injection nozzle where the cross-section of the liquid column is nearly circular. +(c) +Bifurcations +The bifurcation increased to four but thinner and a little vaguely visible (compared to case 8) at a +higher momentum flux ratio, as shown in Figure 24(b). The parameters We (equal to 60) and q (equal +to 77) of this case are similar to case 3 (We = 68, q = 64) of Sedarsky et al. (2010), where they also +observed multiple streamers. This may be owed to the two circulation zones witnessed in the mean +flow behind the liquid core (Figure 27). Following the same explanation of Section 3.3.1(c), the CRV +exit carries along and diverts the first bifurcation/streamer liquid. Similar to the previous case, the fluid +exit also happens from the sides of these recirculation zones formed on the leeward side. As discussed + +(gw/ax) +1028. +800 +Density +600 +400 +200 +5.038 +Shear +Instability +at edges +(a) +(b)49 + +earlier, the flow is highly complex, with a mix of vortex shedding and recirculation. The vortex +shedding induces the sideward flow of air near the leeward side of the liquid column, which in turn +pushes against and separates the thick transverse edge from the liquid column. Hence, in this case, the +two crucial factors are the thickening of the edge by the internal boundary (shear) layer and the +separation of streamers from the central liquid column by the CRV/recirculation flow. + +Fig. 27. Streamlines show mean flow on plane Z/D=17.5. The clockwise rotation of the bottom vortex and anti- +clockwise of the upper vortex show the outward movement of gas/air near the leeward side of the liquid column. +This sideward movement is responsible for streamer formation. +4. Conclusion +This work numerically simulates a liquid jet's primary and secondary atomization in crossflow using +a compressible Volume of Fluid (VOF) - Lagrangian Particle Tracking (LPT) coupled solver +implemented in OpenFOAM. The iso-Advector scheme by Roenby et al. (2016) is used to capture the +droplets and sub-grid fluid distribution. In contrast, the coupling algorithm by Heinrich and Schwarze +(2020) provides flexibility in demarcating the droplets and converting them into Lagrangian particles +under satisfying conditions. The complete framework is validated against the comprehensive +experimental data of Amighi (2015). The numerically predicted data for liquid jet penetration, droplet +size characteristics D32, and STD agrees with experimental data. The effect of various parameters, +namely liquid jet velocity, crossflow velocity, and pressure, on the droplet size characteristics also +predicts similar trends as in the experiments. The comparison of liquid jet penetration with empirical +correlations shows that the predicted trajectory is closest to Elshamy’s correlation, and correlations +based on momentum flux ratio alone are found to overpredict by a large margin. In line with the +previous literature, the comparison of the stream-wise location of the breakup for each case is constant +at 9.2DN ± 1.2DN, independent of the momentum flux ratio. +Few cases are analyzed in different breakup regimes. The momentum flux ratio is a governing factor +for the instability that dominates the liquid column flow. The Kelvin-Helmholtz type instability causes + +CRV +Exit +Density (kg/m) +5.041 +200 +400 +600 +800 +1027.50 + +the liquid column to break up at a lower momentum flux ratio. The crossflow air momentum forces +the liquid column to bend to sharper angles, producing a higher shear force along the liquid flow +direction. Based on the observations of a sheet-like cross-section in the latter portion of the liquid +column, the inviscid and viscous linear stability analysis results are computed considering the thickness +of the sheet-like liquid column. It is found that the sheet Weber number is high enough so that only +the short wavelength instability dominates the breakup. The results are compared to the wavelength +detected from the simulations. +On the other hand, the Rayleigh-Taylor instability is dominant for the high momentum flux ratio case. +It is inferred that high momentum flux ratio causes high penetration, which is a reason for the extended +high-pressure zone on the windward side of the liquid column. The increased air pressure and lesser +shear results in the growth of Rayleigh-Taylor-type instability. The wavelength from the simulations +closely matches with linear stability analysis and correlations. +The shear instability along the transverse edges of the liquid column is well captured in the simulations. +It is hypothesized that the instability of the liquid column at the edges is caused due to the instability +of the air shear layer passing by around the liquid column. The wavelength measured at the bottom +part of the liquid column from simulations was compared to Williamson's empirical correlation of +shear layer instability for a flow over the cylinder (1996). It is closer to the simulated values than the +correlation results from the past literature. +The bifurcation or streamer generation, evident at lower to moderate values of momentum flux ratio +and Weber number, is another crucial aspect that has been observed. These bifurcations are caused by +the counter-rotating vortex's three-dimensional structure and internal boundary layer shear at the liquid +jet's windward side. The shear breakup at the edges causes the streamers to be mostly non-existent or +thin at a higher momentum flux ratio or Weber number. +To summarize, LJICF is a classical problem that involves complex flow physics. The present work +attempts to develop and access an accurate, robust platform (hybrid compressible VOF-LPT +framework) while investigating the break-up phenomenon in LJICF. The other aspects, like break-up +regimes and details of instability behavior, are ongoing work in the same group and beyond the scope +of the present study. +Acknowledgments +Financial support for this research is provided through the Department of Science and Technology (DST) under National +Supercomputing Mission (NSM), India. We acknowledge the National Supercomputing Mission (NSM) for providing + +51 + +computing resources of 'PARAM Sanganak' at IIT Kanpur, which is implemented by C-DAC and supported by the Ministry +of Electronics and Information Technology (MeitY) and Department of Science and Technology (DST), Government of +India. Also, we would like to thank the computer center (www.iitk.ac.in/cc) at IIT Kanpur for providing the resources to +carry out this work. +References +Amighi, A., & Ashgriz, N. (2019). Global droplet size in liquid jet in a high-temperature and high-pressure crossflow. AIAA +Journal, 57(3), 1260-1274. +Amighi, A., & Ashgriz, N. (2019). Trajectory of a liquid jet in a high temperature and pressure gaseous cross flow. Journal +of Engineering for Gas Turbines and Power, 141(6). +Amighi, Amirreza. (2015) Liquid jets in crossflow at elevated temperatures and pressures. University of Toronto, Canada. +ANSYS, Inc. (2016) ANSYS Fluent User’s Guide, Release 17.2. +Arienti, M., Li, X., Soteriou, M. C., Eckett, C. A., Sussman, M., & Jensen, R. J. (2013). Coupled level-set/volume-of-fluid +method for simulation of injector atomization. Journal of propulsion and power, 29(1), 147-157. +Arlov, D., Revstedt, J., & Fuchs, L. (2007). A different approach of handling large bubbles in a square sectioned bubble +column combining large eddy simulation with lagrangian particle tracking. In Proceedings of the 6th International +Conference on Multiphase Flow. +Bhandarkar, A., Manna, P., & Chakraborty, D. (2017). Assessment of droplet break-up models in high-speed cross- +flow. Atomization and Sprays, 27(1). +Becker, J., & Hassa, C. (2002). Break-up and atomization of a kerosene jet in crossflow at elevated pressure. Atomization +and Sprays, 12(1-3). +Behzad, M., Ashgriz, N., & Mashayek, A. (2015). Azimuthal shear instability of a liquid jet injected into a gaseous cross- +flow. Journal of Fluid Mechanics, 767, 146-172. +Brackbill, J. U., Kothe, D. B., & Zemach, C. (1992). A continuum method for modeling surface tension. Journal of +computational physics, 100(2), 335-354. +Chai, X., & Mahesh, K. (2012). Dynamic-equation model for large-eddy simulation of compressible flows. Journal of +Fluid Mechanics, 699, 385-413. +Chen, T., Smith, C., Schommer, D., & Nejad, A. (1993, January). Multi-zone behavior of transverse liquid jet in high- +speed flow. In 31st Aerospace Sciences Meeting (p. 453). +Eslamian, M., Amighi, A., & Ashgriz, N. (2014). Atomization of liquid jet in high-pressure and high-temperature subsonic +crossflow. AIAA journal, 52(7), 1374-1385. +Fric, T. F., & Roshko, A. (1994). Vortical structure in the wake of a transverse jet. Journal of Fluid Mechanics, 279, 1-47. + +52 + +Fuster, D., Bagué, A., Boeck, T., Le Moyne, L., Leboissetier, A., Popinet, S., & Zaleski, S. (2009). Simulation of primary +atomization with an octree adaptive mesh refinement and VOF method. International Journal of Multiphase Flow, 35(6), +550-565. +Frössling, N. (1938). The Evaporating of Falling Drops (in German). Gerlands Beitrage zur Geophysik, 52:170–216. +Gopala, Y., Zhang, P., Bibik, O., Lubarsky, E., & Zinn, B. (2010). Liquid fuel jet in crossflow-trajectory correlations based +on the column break-up point. In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and +Aerospace Exposition (p. 214). +Germano, M., Piomelli, U., Moin, P., & Cabot, W. H. (1991). A dynamic subgrid‐scale eddy viscosity model. Physics of +Fluids A: Fluid Dynamics, 3(7), 1760-1765. +Grosshans, H., Szász, R. Z., & Fuchs, L. (2014). Development of an efficient statistical volumes of fluid–Lagrangian +particle tracking coupling method. International Journal for Numerical Methods in Fluids, 74(12), 898-918. +Heinrich, M., & Schwarze, R. (2020). 3D-coupling of Volume-of-Fluid and Lagrangian particle tracking for spray +atomization simulation in OpenFOAM. SoftwareX, 11, 100483. +Herrmann, M. (2010). A parallel Eulerian interface tracking/Lagrangian point particle multi-scale coupling +procedure. Journal of computational physics, 229(3), 745-759. +Hirt, C. W., & Nichols, B. D. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of +computational physics, 39(1), 201-225. +Hoyas, S., Gil, A., Margot, X., Khuong-Anh, D., & Ravet, F. (2013). Evaluation of the Eulerian–Lagrangian Spray +Atomization (ELSA) model in spray simulations: 2D cases. Mathematical and Computer Modelling, 57(7-8), 1686-1693. +Huang, S., & Li, Q. S. (2010). A new dynamic one‐equation subgrid‐scale model for large eddy simulations. International +Journal for Numerical Methods in Engineering, 81(7), 835-865. +Ilak, M., Schlatter, P., Bagheri, S., & Henningson, D. S. (2012). Bifurcation and stability analysis of a jet in cross-flow: +onset of global instability at a low velocity ratio. Journal of Fluid Mechanics, 696, 94-121. +Ingebo, R. D., and Foster, H. H. (1957). Drop-size distribution for cross current breakup of liquid jets in airstreams. No. +NACA-TN-4087. +Ingebo, R. D. (1967) Penetration of drops into high-velocity airstreams. National Aeronautics and Space Administration. +Kim, W. W., & Menon, S. (1995). A new dynamic one-equation subgrid-scale model for large eddy simulations. In 33rd +Aerospace Sciences Meeting and Exhibit (p. 356). +Lee, K., Aalburg, C., Diez, F. J., Faeth, G. M., & Sallam, K. A. (2007). Primary break-up of turbulent round liquid jets in +uniform crossflows. AIAA journal, 45(8), 1907-1916. +Lewis, D. J. (1950). The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. +II. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 202.1068: 81-96. + +53 + +Li, X., & Soteriou, M.C. (2016). High fidelity simulation and analysis of liquid jet atomization in a gaseous crossflow at +intermediate Weber numbers. Physics of Fluids 28.8: 082101. +Ling, Y., Zaleski, S., & Scardovelli, R. (2015). Multiscale simulation of atomization with small droplets represented by a +Lagrangian point-particle model. International Journal of Multiphase Flow, 76, 122-143. +Lubarsky, E., Reichel, J. R., Zinn, B. T., & McAmis, R. (2010). Spray in crossflow: Dependence on Weber +number. Journal of Engineering for Gas Turbines and Power, 132(2). +Madabhushi, Ravi K., et al. (2006). On the breakup regime map of liquid jet in crossflow. ILASS Americas, 19th Annual +Conference on Liquid Atomization and Spray Systems, Toronto, Canada. +Ménard, +T., +Tanguy, +S., +& +Berlemont, +A. +(2007). +Coupling +level +set/VOF/ghost +fluid +methods: +Validation and application to 3D simulation of the primary break-up of a liquid jet. International +Journal of Multiphase Flow, 33(5), 510-524 +Mencinger, J., & Žun, I. (2011). A PLIC–VOF method suited for adaptive moving grids. Journal of Computational +Physics, 230(3), 644-663. +Miller, S. T., Jasak, H., Boger, D. A., Paterson, E. G., & Nedungadi, A. (2013). A pressure-based, compressible, two-phase +flow finite volume method for underwater explosions. Computers & Fluids, 87, 132-143. +Mirjalili, S. (2019). A Novel Diffuse Interface Method for Two-phase Flows and Application in Simulation of Micro- +bubble Entrainment. Stanford University. +M. Herrmann, A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids, +Journal of Computational Physics, 227 (4) (2008) 2674–2706 +Ng, C-L., R. Sankarakrishnan, and K. A. Sallam. (2008). Bag breakup of nonturbulent liquid jets in crossflow. International +Journal of Multiphase Flow 34.3: 241-259. +Noh, W. F., & Woodward, P. (1976). SLIC (simple line interface calculation). In Proceedings of the fifth international +conference on numerical methods in fluid dynamics June 28–July 2, 1976 Twente University, Enschede (pp. 330-340). +Springer, Berlin, Heidelberg. +O'Rourke, P. J., & Amsden, A. A. (1987). The TAB method for numerical calculation of spray droplet break-up (No. +872089). SAE technical paper. +Olsson, E. (2017). A description of isoadvector-a numerical method for improved surface sharpness in two-phase +flows. Proceedings of CFD with OpenSource Software, Edited by Nilsson. H. +Olyaei, G., & Kebriaee, A. (2020). Experimental study of liquid jets injected in crossflow. Experimental Thermal and Fluid +Science, 115, 110049. + +54 + +Parmar, M., Haselbacher, A., & Balachandar, S. (2011). Generalized Basset-Boussinesq-Oseen equation for unsteady +forces on a sphere in a compressible flow. Physical review letters, 106(8), 084501. +Popinet, S. (2003). Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. +Journal of Computational Physics, Elsevier, 2003, 190 (2), pp.572-600. +Ragucci, R., Bellofiore, A., & Cavaliere, A. (2007). Break-up and breakdown of bent kerosene jets in gas turbine +conditions. Proceedings of the Combustion Institute, 31(2), 2231-2238. +Ranz, W., Marshall, W.: Evaporation from drops, part I. Chem. Eng. Prog. 48, 141–146 (1952) +Reitz, R. D. (1987). Modeling atomization processes in high-pressure vaporizing sprays. Atomisation Spray +Technology, 3(4), 309-337. +Roenby, J., Bredmose, H., & Jasak, H. (2016). A computational method for sharp interface advection. Royal Society open +science, 3(11), 160405. +Saeedipour, M., Pirker, S., Bozorgi, S., & Schneiderbauer, S. (2016). An Eulerian–Lagrangian hybrid model for the coarse- +grid simulation of turbulent liquid jet break-up. International Journal of Multiphase Flow, 82, 17-26. +Sallam, K. A., Ng, C., Sankarakrishnan, R., Aalburg, C., & Lee, K. (2006). Break-up of turbulent and non-turbulent liquid +jets in gaseous crossflows. In 44th AIAA Aerospace Sciences Meeting and Exhibit (p. 1517). +Sallam, K. A., Aalburg, C., & Faeth, G. M. (2004). Break-up of round nonturbulent liquid jets in gaseous crossflow. AIAA +journal, 42(12), 2529-2540. +Schiller, L. (1933). A drag coefficient correlation. Zeit. Ver. Deutsch. Ing., 77, 318-320. +Schmidt, D. P., Rutland, C. J. (2000) A new droplet collision algorithm. Journal of Computational Physics 164.1: 62-80. +Sedarsky, D., Paciaroni, M., Berrocal, E. et al. Model validation image data for break-up of a liquid jet in crossflow: part +I. Exp Fluids 49, 391–408 (2010). +Senecal, P. K., Schmidt, D. P., Nouar, I., Rutland, C. J., Reitz, R. D., & Corradini, M. L. (1999). Modeling high-speed +viscous liquid sheet atomization. International Journal of Multiphase Flow 25.6-7: 1073-1097. +Squire, H. B. (1953). Investigation of the instability of a moving liquid film. British Journal of Applied Physics 4.6: 167. +Stenzler, J. N., Lee, J. G., Santavicca, D. A., & Lee, W. (2006). Penetration of liquid jets in a cross-flow. Atomization and +Sprays, 16(8). +Sussman, M., & Puckett, E. G. (2000). A coupled level set and volume-of-fluid method for computing 3D and axisymmetric +incompressible two-phase flows. Journal of computational physics, 162(2), 301-337. +Tambe, S., Jeng, S. M., Mongia, H., & Hsiao, G. (2005, January). Liquid jets in subsonic crossflow. In 43rd AIAA +Aerospace Sciences Meeting and Exhibit (p. 731). +Tambe, S., Elshamy, O., & Jeng, S. M. (2007). Spray properties of liquid jets injected transversely into a shear layer. +In 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit (p. 5695). + +55 + +Tanner, F. X. (2003). A cascade atomization and drop break-up model for the simulation of high-pressure liquid jets. SAE +transactions, 1352-1366. +Taskiran, O. O., & Ergeneman, M. (2014). Trajectory based droplet collision model for spray modeling. Fuel, 115, 896- +900. +Taylor, G.I. (1950). The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. +I. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 201.1065: 192-196. +Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., ... & Jan, Y. J. (2001). A front-tracking +method for the computations of multiphase flow. Journal of computational physics, 169(2), 708-759. +Vallier, A., Revstedt, J., & Nilsson, H. (2011). Procedure for the break-up of cavitation sheet. In 4-th International Meeting +on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, October, 26-28, 2011, Belgrade, Serbia (pp. +77-85). +Weller, H. G., Tabor, G., Jasak, H. & Fureby, C., (1998) A tensorial approach to computational continuum mechanics +using object-oriented techniques. Computers in physics 12.6: 620-631. +Wen, J., Hu, Y., Nakanishi, A., & Kurose, R. (2020). Atomization and evaporation process of liquid fuel jets in crossflows: +A numerical study using Eulerian/Lagrangian method. International Journal of Multiphase Flow, 129, 103331. +Williamson, C.H.K. (1996). Vortex dynamics in the cylinder wake. Annual review of fluid mechanics 28.1: 477-539. +Wu, P. K., Kirkendall, K. A., Fuller, R. P., & Nejad, A. S. (1997). Break-up processes of liquid jets in subsonic +crossflows. Journal of Propulsion and power, 13(1), 64-73. +Yu, H., Goldsworthy, L., Ghiji, M., Brandner, P. A., & Garaniya, V. (2017). A parallel volume of fluid-Lagrangian Parcel +Tracking coupling procedure for diesel spray modelling. Computers & Fluids, 150, 46-65. +Yoo, Y. L., Han, D. H., Hong, J. S., & Sung, H. G. (2017). A large eddy simulation of the break-up and atomization of a +liquid jet into a cross turbulent flow at various spray conditions. International Journal of Heat and Mass Transfer, 112, +97-112. +Zuo, B., Gomes, A. M., & Rutland, C. J. (2000). Modelling superheated fuel sprays and vaporization. International Journal +of Engine Research, 1(4), 321-336. + diff --git a/d9E1T4oBgHgl3EQfLgNb/content/tmp_files/load_file.txt b/d9E1T4oBgHgl3EQfLgNb/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..312dc976fa249e3ff76245c94cc50d42b2579eca --- /dev/null +++ b/d9E1T4oBgHgl3EQfLgNb/content/tmp_files/load_file.txt @@ -0,0 +1,1822 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf,len=1821 +page_content='1 Understanding the liquid jet break-up in various regimes at elevated pressure using a compressible VOF-LPT coupled framework Bharat Bhatia1, Tom Johny1, and Ashoke De1,2* 1 Department of Aerospace Engineering, Indian Institute of Technology Kanpur, 208016, Kanpur, India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 2 Department of Sustainable Energy Engineering, Indian Institute of Technology Kanpur, 208016, Kanpur, India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Abstract The present work develops a compressible Volume of Fluid (VOF) – Lagrangian Particle Tracking (LPT) coupled solver in OpenFOAM and utilizes it to simulate a liquid jet in crossflow (LJICF) numerically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This methodology helps accurately predict a complex primary breakup in the Eulerian framework and the secondary atomization of spherical droplets using a computationally efficient LPT method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The coupled solver with Adaptive Mesh Refinement (AMR) is rigorously validated for a liquid jet in crossflow at varying operating conditions – pressure, crossflow velocity, and inlet liquid jet velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' We have further carried out a thorough investigation to study the effect of momentum flux ratio and weber number on the various flow features and liquid jet break-up phenomenon in a crossflow while identifying the stream-wise location of the liquid jet breakup region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' At low momentum flux ratios in the bag breakup regime, the predictions reveal that the liquid jet breakup occurs due to the growth of similar instability as usually observed in the high-speed liquid sheet atomization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The short wavelength assumption of the inviscid dispersion relation resembles the Kelvin-Helmholtz type instability observed in this case, as opposed to Rayleigh-Taylor instability at high momentum flux ratio in the surface breakup regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It is also proposed that the shear breakup along the transverse edges of the liquid column occurs due to the shear layer instability of the air passing around the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The simulation wavelength closely matches the Williamson correlation for shear layer instability around cylinders – a shape similar to the cross-section of the bottom of the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The results show a distinct streamer or bifurcation phenomenon at low momentum flux ratios and moderate weber numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Further investigation suggests that the internal liquid boundary layer and the three- dimensional flow field behind the liquid jet are responsible for streamer formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Keywords: Multiphase flows, Volume of Fluid (VOF), Lagrangian Particle Tracking (LPT), Sauter mean diameter, OpenFOAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Introduction Spray atomization of a liquid jet in crossflow is a complex multiphase phenomenon extensively used in aviation engines, lean premixed prevaporized (LPP) ducts, film cooling of turbine blades, rockets, scramjets, augmentors, and other applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' With the new environmental restrictions and regulations to reduce NOx emissions becoming more stringent, optimizing the combustion process in these systems has become critical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Transverse fuel injection into a crossflow enhances combustion efficiency, cuts fuel consumption, and lowers emissions in such systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' As a result, to develop and analyze such systems, a detailed understanding of the physics of liquid jet break-up and atomization processes is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Experimental investigations of the spray atomization process require precise and expensive experimental techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The numerical studies can provide valuable insight into atomization, especially when flow features close to nozzle regions are difficult to capture experimentally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Multiphase flow modeling is inherently complex due to the wide range of scales formed and the liquid-gas phase interaction resulting in complex structures and flow patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The length scale here ranges from a few micrometers to several centimeters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A liquid jet in a crossflow (LJICF) consists of two significant stages of break-up and atomization: primary and secondary breakup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1) Primary break-up results from the instabilities at the liquid-gas interface, which grows in size due to the inertial forces and turbulence in the liquid jet, causing the liquid core to break up into large liquid structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2) Secondary break-up further breaks these liquid structures and ligaments into smaller droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The extent to which these droplets are disintegrated is influenced by the external distorting forces and surface tension forces of the liquid, finally resulting in a large number of stable spherical droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The break-up of a liquid jet in a cross-flow is schematically represented in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The crossflow atomization process involves complex flow features, mainly the turbulent break-up, droplet deformation from the liquid-gas interaction, vortex formations, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It also involves mass, momentum, and energy exchange between the liquid and gaseous phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Most of the early studies of spray atomization for LJICF were primarily experimental, where researchers mainly concentrated on the liquid jet penetration, break-up and its different modes, and their relationship with various parameters, especially the momentum flux ratio (q) and crossflow Weber number (We) (Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 1997;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Becker and Hassa, 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Sallam et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1997) studied the liquid jet penetration for various test liquids (water, alcohol, and their mixtures) under different operating conditions and plotted a transition regime between column and surface break- up modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' They also found that the column fracture location in the streamwise direction is constant and is equal to 8D downstream of the nozzle exit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Stenzler (2006) proposed that the aerodynamic weber number and liquid viscosity can also affect the jet penetration and the momentum flux ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ingebo 3 (1957;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 1967) also proposed the same by considering the effect of liquid viscosity in the spray penetration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' He also noticed that larger droplets penetrate deeply into the cross-flow and affect the penetration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' As a result, he proposed a spray trajectory correlation that includes the effect of larger droplets by taking account of parameters (Rejet, We) other than the momentum flux ratio (q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Several others looked into the various break-up modes, including Becker and Hassa (2002), who proposed a qualitative and visual map for break-up and atomization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Eslamian (2014) proposed a similar map based on the momentum flux ratio and crossflow weber numbers for the primary break-up and a transition line between column and shear break-up modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Madabhushi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2004) redefined the break-up regime based on the turbulent transition jet Reynolds number and cross-flow Weber number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Since the momentum flux ratio does not provide the turbulence details of a liquid jet, they defined a borderline based on the Reynolds number of the jet in addition to the break-up map to include the effect of liquid jet turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Sallam et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2006) classified the break-up mechanisms for non- turbulent liquid jets into four based on the aerodynamic weber number: column, bag, multimode, and shear break-up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' There are few studies available in the literature regarding the droplet size characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Several computational techniques have been developed to simulate the spray atomization process numerically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Computing interface motion in complex multiphase flows such as spray atomization requires accurate interface tracking and reconstruction techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The interface capturing approaches such as the Volume of Fluid (VOF) (Hirt and Nichols, 1981), Front tracking methods (Tryggvason et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2001) or CLSVOF (Sussman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Menard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2007) are typically used modeling approaches for the primary breakup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' VOF methods are based on the volume fraction (α) of phases in a computational cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' An additional transport equation is solved for volume fraction (α), which is then used to track the location of the liquid-gas interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Many VOF interface capturing techniques are utilized to capture the interface, classified as algebraic or geometric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Older methods for interface capture include algebraic approximations such as Compressive schemes and THINC (Tangent of hyperbola for interface capturing) schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Geometric approaches are more recent, complicated, and precise (Mirjalili, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' An interface within a computational cell is geometrically reconstructed using a plane in three-dimensional (3D) simulations using methods such as Simple Line Interface Calculation (SLIC) (Noh & Woodward, 1976) or the more recent Piecewise Linear Interface Calculation (PLIC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Nonetheless, using these techniques for commercial use does have a disadvantage: high computational cost and time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The grid resolution must be good enough in a VOF approach to sufficiently resolve the liquid structures, droplets, and ligaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Therefore, the computational cost of simulating a complete spray break-up using the only VOF method is very high (Heinrich and Schwarze, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The Lagrangian Particle Tracking (LPT) methods are more suitable for secondary 4 atomization involving a cloud of dispersed droplets, owing to lower computational cost and better droplet predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Thus, the VOF approach can efficiently resolve the primary break-up, while the dispersed cloud uses the LPT method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Therefore, an Eulerian-Lagrangian coupled approach could significantly reduce the computational cost of simulating the whole spray atomization process while still capturing the underlying physics to a high degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A coupling algorithm is an intermediate between the Eulerian and Lagrangian frameworks, which tracks all the Eulerian-phase droplets throughout the computational domain and replaces them with a Lagrangian substitute using transformation criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Several coupling algorithms (Hermann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Grosshans, 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Heinrich and Schwarze, 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2017) have been proposed for the Eulerian-Lagrangian droplet transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Grosshans (2014) performed a statistical coupling approach by defining a coupling layer between VOF and LPT frameworks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The drawback associated with this method is that the 2-D coupling layer is fixed in space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Also, the shearing action generates smaller droplets from the sides of the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Since these droplets lie before the coupling layer, they are resolved using VOF only, even though these are more appropriate to be tracked using LPT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' So the transformation into Lagrangian droplets may not be realistic as it seems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Yu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2017) proposed a region coupling method (RCM) with a droplet identification and extraction technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This method is more realistic since the transformation happens smoothly in the coupling region defined in three-dimensional (3-D) space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' One drawback of this method is the placement of the coupling region, which has to be determined previously from another Eulerian simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Hermann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 2010) used their band generation algorithm to couple the Lagrangian framework with a refined level-set grid method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Heinrich and Schwarze (2020) employed an image processing algorithm called Connected Component Labelling (CCL) to couple the VOF with LPT for incompressible flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Such a coupled methodology eliminates solutions through stochastic methods such as the ELSA model (Hoyas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2013) or other models that use a Lagrangian droplet ejection out of a primary jet core calculated using the VOF method (Saeedipour et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2016), ignoring the critical phenomenon of the primary breakup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' One assumption involved in the LPT method is that the droplet volume is minimal compared to the local cell volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' For the LPT approach to be numerically stable, it is generally advised that the grid size be larger by ten times the size of the droplets (Vallier et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' While Arlov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2007) proved that the LPT theory is valid even if the cell size is more than the droplet size by five times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Multiple grid cells comprising the Eulerian droplet are required for an Eulerian framework to resolve the small-scale features adequately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' To overcome the imbalance of larger grid size requirement for the LPT method and smaller grid size for VOF, we can either use: the (i) Adaptive Mesh Refinement (AMR) technique based on the liquid volume fraction (α) or (ii) a static grid with a highly refined 5 region for Eulerian framework and a separate coarser grid for the lagrangian framework (Herrmann 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The former option is preferable as the latter may cause larger lagrangian droplets on a smaller local mesh volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In this work, a compressible VOF-LPT coupled solver is developed in OpenFOAM along with the evaporation models for Eulerian and Lagrangian fields, which is also capable of simulating atomization involving high temperature evaporating sprays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It uses a VOF-LPT coupling algorithm based on the previous works of Heinrich and Schwarze (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The liquid-gas interface is reconstructed geometrically using the isoAdvection concept developed by Roenby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Such a coupled model and an additional method for interface capturing would help capture the flow physics to a high degree in the near-nozzle region and the far downstream region while keeping the computational cost to a minimum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The developed model is validated under elevated pressure and room temperature conditions for a liquid jet-in-crossflow case based on the experimental works of Amighi and Ashgriz (2019) in terms of droplet size characteristics and the Sauter mean diameter, the standard deviation of droplets, and the jet trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' And further, we have carried out a detailed investigation using the same framework for a wide range of parameters (q, We) and its effect on spray droplet sizes (D32, STD), liquid jet penetration, and other flow features (vortex formation, break-up behavior, and deformation) for a liquid JICF under different operating conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Methodology This section describes the methodologies employed in our current investigation, mainly the VOF Eulerian formulation, the LPT formulation, and the coupling algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 1: Schematic of the break-up of a Liquid Jet in Crossflow (LJICF) Column breakup Liquid jet core Ligaments Windward side Surface breakup Leeward side Primary breakup Secondary breakup6 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 Eulerian framework The VOF method tracks the interface between the two phases in the Eulerian framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The mass, momentum, species mass fraction, and energy equations are solved for a two-phase compressible and immiscible system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' VOF method uses the volume fraction \uf061 , defined as a step function, to distinguish between the two phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A volume fraction value of 1 \uf061 =1 indicates cell volume fully occupied by liquid, and 1 \uf061 =0 indicates cell volume fully occupied by gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A volume fraction value 1 0 1 \uf061 \uf03c \uf03c shows the liquid-gas interface within the cell control volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 1 1 0 0 1 1 2 1 pha phase interface se \uf061 \uf061 \uf0ec \uf0ef = \uf03c \uf03c \uf0ed \uf0ef\uf0ee (1) The step function α makes it possible to solve only one set of governing equations for both phases, eliminating the need for separate equations for each phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The VOF method without any interface reconstruction method results in smearing the liquid surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' To overcome the smearing of the profile at the interface, many interface-capturing methods have been developed for VOF involving the reconstruction of the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Reconstruction methods may be either geometric or algebraic – like the piecewise-linear interface calculation (PLIC) for geometric reconstruction and Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM) for algebraic reconstruction in Ansys Fluent (ANSYS, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2016) or Gerris solver (Popinet, 2003), Multidimensional Universal Limiter with Explicit Solution (MULES) scheme for algebraic reconstruction by interFoam solver in OpenFOAM (Weller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 1998), etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The volume fraction 𝛼𝑘 and the interface within a cell is reconstructed geometrically using the iso-advection concept devised by Roenby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' For geometric interface reconstruction, it uses a piecewise linear interpolation calculation (PLIC) (Mencinger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Although the method uses an integral form of the continuity equation to calculate the surface evolution, it is represented here in the differential form to maintain consistency with the rest of the equations: ( ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' ( ) L S t \uf072 \uf072 \uf072 \uf0b6 + \uf0d1 = \uf0b6 u (2) Here \uf072 is the mixture density, u is the velocity, L S\uf072 is the source terms from the Lagrangian droplets calculated as: 𝑆𝜌|𝐿 = 4𝜋 𝑘 𝑐𝑝 𝑟0 1 1+𝐺𝑓 𝐺 ⁄ 𝑙𝑛 [1 + ℎ𝑔−ℎ𝑑𝑟𝑜𝑝,𝑠 𝐿(𝑇𝑏) (1 + 𝐺𝑓 𝐺 )] (3) 7 The source term denotes the heat transfer vaporization rate (Zuo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2000));' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 𝑘 is the thermal conductivity of gas, 𝑐𝑝 is the specific heat of the gas;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' ℎ𝑔 and ℎ𝑑𝑟𝑜𝑝,𝑠 denotes the enthalpy of the gas and at the droplet surface, respectively;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 𝐿(𝑇𝑏) is the latent heat of vaporization at the boiling temperature, 𝐺𝑓 is the flash-boiled vapor mass flow rate, which reduces to zero at temperatures less than or equal to the boiling point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In the integral form of the equation, the instantaneous rate of change of the total mass within a volume is equal to the instantaneous flux of mass through its boundary in addition to the mass evaporated from the lagrangian particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In the differential form, the mass conservation equation for phase i is: ( ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' ( ) k k k k L E S S t \uf072 \uf072 \uf061 \uf072 \uf061 \uf072 \uf0b6 + \uf0d1 = + \uf0b6 u (4) While the source term from liquid to the gas phase, it is: 𝑆𝜌|𝐸 = 2 ∗ (1 − 𝛼2) ∗ M𝑡𝑐 ∗ D𝑎𝑏 ∗ 𝑑𝑌.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (5) Here, M𝑡𝑐 and D𝑎𝑏 are the mass transfer and diffusion coefficients between two phases, and 𝑑𝑌 is the species gradient near the interface for liquid species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' While the volume fractions are constrained, this equation evolved in two steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Firstly, the reconstruction step is where the distribution of fluids inside the computational cells is estimated using an efficient iso-surface calculation methodology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Secondly, a face-interface intersection line sweeping the face for a sub-time interval approximates the time evolution of the submerged part of a general polygon face (belonging to a computational cell).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The sub-time interval is defined by the time a line passes the face vertices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It makes the analytical calculation possible for the passage of a fluid across the cell face during this sub-time interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This reconstruction technique applies to structure as well as unstructured grids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' For cells having liquid-gas calculations, the fluid properties are calculated from the weighted average of the phase fraction α for each computational cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 1 1 2 2 \uf072 \uf061 \uf072 \uf061 \uf072 = + (6a) 1 1 2 2 \uf06d \uf061 \uf06d \uf061 \uf06d = + (6b) where 1 \uf06d , 2 \uf06d and 1 \uf072 , 2 \uf072 are the dynamic viscosity and density of phases 1 and 2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Phases 1 and 2 represent the liquid and gas phases for a two-phase compressible system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A single momentum transport equation is solved for the velocity field in both phases: 8 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' ( ) ( .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' ) ( ) d ef E f S u u L T u p t S F S \uf072 \uf072 \uf072 \uf072 \uf074 \uf072 \uf0b6 + \uf0d1 −\uf0d1 = −\uf0d1 − \uf0d1 + + \uf0b6 + uu x g (7) where the piezometric pressure .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' dp p \uf072 = − g x and ( ) 2 T 3 ( ) eff eff tr \uf074 \uf06d \uf0e9 \uf0f9 \uf0ea \uf0fa \uf0eb \uf0fb = \uf0d1 + \uf0d1 − \uf0d1 u u u ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' here, eff \uf06d the effective viscosity is volume averaged as: 1 1 2 2 4( ) 3 eff \uf061 \uf06d \uf061 \uf06d \uf06d + = , and \uf072 in all the combined equations is the mixture density for each computational cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' , u u L E S S \uf072 \uf072 are the Lagrangian and Eulerian source terms for momentum equations, which are generated because of the atomization and the evaporation of droplets in the domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 𝐹𝑆𝑇 is the surface tension force calculated using the Continuum Surface Force (CSF-model) formulation proposed by Brackbill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The surface tension force is defined at the interface where a pressure jump occurs and is specified as a source term to the momentum equation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It is calculated as follows: ( ) ( ) ( ) ( ) ST S F x y n y x y dS \uf073 \uf06b \uf064 = − \uf0f2 (8) where \uf073 is the surface tension of the liquid phase, \uf06b is the local interface curvature, n is the unit interface normal, and \uf064 the Dirac-delta function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' x and y are the position vectors where the forces are calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' These are calculated using: .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='n \uf06b = −\uf0d1 , n n n = where n = normal surface vector, defined as n \uf061 = \uf0d1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The surface tension force source term can be expressed as: 1 ( ) 2 ST l g F \uf072\uf06b \uf061 \uf073 \uf072 \uf072 \uf0d1 = + (9) The equation of state is used to solve densities from pressure and temperature conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Considering an isentropic gas phase, the equation of state is defined as (Miller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2013): constant c p a \uf067 \uf072 = = (10) where ca is the isentropic constant and \uf067 is the ratio of specific heat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The total derivative of \uf072 with respect to pressure gives: ( ) 1 1 c c s p p a a \uf067 \uf067 \uf072 \uf067 − \uf0e6 \uf0f6 \uf0e6 \uf0f6 \uf0b6 = \uf0e7 \uf0f7 \uf0e7 \uf0f7 \uf0b6 \uf0e8 \uf0f8 \uf0e8 \uf0f8 (11) 9 The speed of the sound wave in a liquid medium is computed as follows (Miller et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2013): 2 1 s d dp c \uf072 \uf0e6 \uf0f6 = \uf0e7 \uf0f7 \uf0e8 \uf0f8 (12) where c is the speed of the sound.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Integration of the above equation at a constant speed of sound yields: ( ) o o p p \uf072 \uf072 \uf079 − = − , where 2 1 c \uf079 = (13) and , o op \uf072 are the reference density and pressure, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The species mass fraction equation is solved by assuming the liquid phase as a single component system and the gaseous phase as a multi-component system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 2 2 2 2 2 ( ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' ( ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' ( ) k k k k Yk Yk L E Y Y D Y S S t \uf072 \uf072 \uf061 \uf072 \uf061 \uf072 \uf061 \uf0b6 + \uf0d1 −\uf0d1 \uf0d1 = + \uf0b6 u (14) Here, 𝑌𝑘 is the species mass fraction and 𝐷𝑘 is the diffusion coefficient for the kth species for the gaseous phase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The energy equation is also solved since our system is compressible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 1 2 , ,1 ,2 ( ) ( ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' ( ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' ( ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' ( ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' ( ) T eff T T L E v v T K T T p K S S t t c c \uf072 \uf072 \uf061 \uf061 \uf072 \uf072 \uf072 \uf061 \uf072 \uf0e6 \uf0f6 \uf0b6 \uf0b6 \uf0e6 \uf0f6 + \uf0d1 −\uf0d1 \uf0d1 + \uf0d1 + + \uf0d1 + = + \uf0e7 \uf0f7 \uf0e7 \uf0f7\uf0e7 \uf0f7 \uf0b6 \uf0b6 \uf0e8 \uf0f8\uf0e8 \uf0f8 u u u (15) Here, T is the temperature in the Eulerian frame at any location, 𝛼𝑇,𝑒𝑓𝑓 is the effective thermal diffusivity, 𝐾 is the kinetic energy (𝐾 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 ∗ |𝐮|2), 𝑐𝑣1 and 𝑐𝑣2 are specific heat capacities at constant volume for phases 1 and 2, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 𝑆𝜌𝑇|𝐿 , 𝑆𝜌𝑇|𝐸 are the lagrangian and eulerian source terms for the energy equation, which accounts for the atomization and the evaporation of droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Although evaporation does not occur in our low-temperature test conditions, the developed framework accounts for the effect of droplet evaporation in both the Eulerian and Lagrangian frameworks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Large-eddy simulations (LES) are used to model turbulence in the flow field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The large eddies of the turbulent flow are computed directly in LES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Sub-grid scale (SGS) modeling is performed since the dissipative scales of turbulence are not entirely resolved in LES.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The SGS models the effect of small- scale vortices and eddies on the resolved larger eddies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Thus, the SGS terms cannot be calculated and require closure models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The SGS Reynolds stress ( ij \uf074 ) and the SGS heat flux ( j Q ) are the parameters that require closure models at the sub-grid scales,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' as given by 10 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' ij SGS i j i j u u u u \uf074 \uf072 \uf072 = − (16) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='j SGS j j Q u h u h \uf072 \uf072 = − (17) and the molecular strain rate tensor is given by: 2 3 k i j ij ij k j i u u u S x x x \uf06d \uf064 \uf06d \uf0e6 \uf0f6 \uf0b6 \uf0b6 \uf0b6 = − + + \uf0e7 \uf0f7 \uf0e7 \uf0f7 \uf0b6 \uf0b6 \uf0b6 \uf0e8 \uf0f8 (18) The dynamicKEqn model,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' which is a one-equation eddy viscosity SGS model,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' is used for the present study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This model was primarily developed by Kim and Menon (1995) based on the previous works of Germano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In recent years, many improvements to the models have been proposed (Chai and Mahesh, 2012, Huang and Li, 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The dynamicKeqn is represented as follows: 3/2 2 sgs j sgs sgs sgs t e sgs ij ij j j k U k k k C S S t x x t \uf06e \uf06e \uf0b6 \uf0b6 \uf0b6 \uf0e6 \uf0f6 \uf0b6 + = − − \uf0e7 \uf0f7 \uf0b6 \uf0b6 \uf0b6 \uf0b6 \uf044 \uf0e8 \uf0f8 (19) sgs k sgs C k \uf06e = \uf044 (20) where sgs k is the sub-grid scale kinetic energy, t\uf06e is the effective kinematic viscosity (both molecular and sub-grid viscosity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The k C , e C constants are computed based on the dynamic formulation from Germano et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The partial differential equations (PDEs) are discretized using a Finite Volume Method (FVM) code implemented in the OpenFOAM v1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The convective flux discretization deploys a second-order TVD (Total Variation Diminishing) scheme, while the viscous flux discretization involves a second- order central scheme, and the temporal term deploys the first-order implicit Euler scheme with sufficiently small time steps to maintain stability and reduce numerical diffusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2 Lagrangian framework In the LPT method, the liquid droplets are treated as point particles with mass and momentum but no volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The LPT approach uses parcels to represent a group of droplets with similar characteristics such as droplet size, velocity, temperature, and thermophysical properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The particle position and velocities are updated at each time step using the Basset Boussinesq-Oseen (BBO) equation (Parmar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2011): 11 p p d dt = x u (21) p p D G d m dt = + u F F (22) where p x , p m , p u is the position, mass, and velocity of each particle, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' D F and G F are the drag and gravitational forces (body forces) acting on the particles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' They are calculated as follows: 2 8 ( )| | p D D g g p g p D C \uf070 \uf072 = − − F u u u u (23) 1 g G p p m g \uf072 \uf072 \uf0e6 \uf0f6 = − \uf0e7 \uf0f7 \uf0e8 \uf0f8 F (24) G F account for both gravity and buoyancy effects, p D is the diameter of the lagrangian parcel, g u and p u are the velocities of gas-phase and velocity of Lagrangian parcels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' D C is the drag coefficient of droplets, which is calculated from the Schiller-Naumann equation (Schiller, 1935): 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='687 24 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='15 / 1000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='44 10 ) 0 ( 0 p p p D p Re Re Re C Re \uf0ec + \uf0a3 = \uf0ed \uf03e \uf0ee (25) 2 2 Re g p p p D \uf072 \uf06d − = u u (26) where p Re is the Reynolds number of the lagrangian droplets and 2 \uf06d is the gas phase dynamic viscosity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The LPT is intended to characterize every droplet feature like droplet break-up, heat transfer, and evaporation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The Ranz-Marshal model (Ranz and Marshall, 1952) is used for heat transfer calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Since the Lagrangian droplets are assumed to be spherical, the evaporation is calculated based on the Frossling correlation (Frössling, 1938): 𝑆ℎ = 2 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='552𝑅𝑒𝑝 1 2 ⁄ 𝑆𝑐1 3 ⁄ (27) 𝑆ℎ is defined as the ratio ℎ𝑐𝑑𝑝 𝐷 ⁄ , where ℎ𝑐 denotes the convective mass transfer coefficient, and 𝑑𝑝 is the droplet diameter, 𝑅𝑒𝑝 is the droplet Reynolds number, and 𝑆𝑐 is the Schmidt number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The typical 12 value of the turbulent Schmidt number (Prandtl number) ranges from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='7 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='85 was used in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=" Among the atomization models of TAB (O'Rourke & Amsden, 1987), ETAB (Tanner, 1997), and R- D (Reitz and Diwakar, 1997), the Reitz-Diwakar secondary break-up model is chosen to model the break-up of the parcels due to the aerodynamic forces." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This is suitable for our high-pressure test conditions and resulted in better droplet predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This takes into account the bag and the stripping break-up of droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A critical Weber number is used to dictate the breakup of droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Droplet collision is an important parameter that mainly affects droplet numbers, droplet sizes, droplet evaporation, spray propagation, and distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' To account for the collision and coalescence of the droplets, we employ the trajectory model of Schimdt & Rutland (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A trajectory-based collision model is more realistic as it models droplet collisions using droplet position and velocity vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='3 Coupling algorithm As mentioned in the previous sub-sections, we have developed the compressible VOF-LPT coupled solver in the OpenFOAM framework along with the evaporation models for Eulerian and Lagrangian fields which is also capable of simulating atomization involving high-temperature evaporating sprays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The algorithm provided by Heinrich & Schwarze (2020) is used to couple the compressible VOF framework with LPT and facilitate the droplets’ transformation from one framework to another.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This coupling algorithm first identifies the individual droplets present throughout the three-dimensional (3- D) domain in the Eulerian framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The relevant properties are then calculated, and if the droplets satisfy the transformation criteria, they are injected as Lagrangian parcels after deleting the corresponding liquid droplet from the Eulerian framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' An image processing – Connected Component Labelling (CCL) algorithm is used in the methodology to identify various liquid droplets in the Eulerian domain (Heinrich & Schwarze, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The liquid volume fraction ( 1 \uf061 ) is used to scan the complete domain for the connectivity of liquid-filled cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Two separate, detached lumps have cells 1 min \uf061 \uf061 \uf03c in between them, where min \uf061 is the minimum value of liquid volume fraction to distinguish two separate droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The details of the algorithm have been explained in Heinrich & Schwarze (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The properties of each Eulerian droplet are then calculated as follows: 𝑉𝑝 = ∑ 𝛼𝑖𝑉𝑖 𝑖 (28a) 𝒙𝑝 = 1 𝑉𝑝 ∑ 𝛼𝑖𝑉𝑖𝒙𝑖 𝑖 (28b) 13 𝒖𝑝 = 1 𝑉𝑝 ∑ 𝛼𝑖𝑉𝑖𝒖𝒊 𝑖 (28c) 𝑇 = 1 𝑉𝑝 ∑ 𝛼𝑖𝑉𝑖𝑇 𝑖 (28d) 𝑑𝑝 = √ 6𝑉𝑝 𝜋 3 (28e) All the cells belonging to a particular Eulerian droplet are represented by the index i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The equivalent diameter (𝑑𝑝) is the diameter of a sphere with the volume 𝑉𝑝 equal to that of the Eulerian droplet, whereas 𝒙𝑝, 𝒖𝑝 and 𝑇 are the position, velocity, and temperature of the Eulerian droplet, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Lastly, the transformation criteria for each droplet are reviewed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' If the droplets meet the transformation criteria, they are injected as Lagrangian parcels, preserving their velocity, momentum, energy, and position.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' And the corresponding Eulerian liquid droplet is deleted from the Eulerian framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The transformation criteria are based on the assumption of the size of droplets and their shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Firstly, the size of the droplet diameter (𝐷𝑝) should be smaller than a predetermined minimum diameter because a larger droplet is more prone to deformation, which is better resolved in the Eulerian framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The minimum diameter criteria refer to the droplet size below which they are eligible for conversion into Lagrangian droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This is also determined from the experiments where the value used is 280µm (Amighi, 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' On the other hand, smaller droplets are converted as they cannot be appropriately resolved in the Eulerian framework and are better tracked in the Lagrangian framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Secondly, if the sphericity of the droplet is less than a threshold minimum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In this study, we have used a sphericity of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='47, calculated based on the circularity of droplets reported in the experiments (Amighi and Ashgriz, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Droplets with sphericity less than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='47 will be converted to lagrangian droplets, while those with sphericity more than 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='47 will remain as Eulerian droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Heinrich & Schwarze, (2020) used a sphericity of 2 in their work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It is desirable for the droplets with sphericity greater than the threshold to stay in the Eulerian framework as the irregular droplets are vulnerable to deformation, which is well captured by the Eulerian method only.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Here we have performed a one-way coupling that facilitates the transformation of Eulerian droplets into Lagrangian only, while a two-way coupling also does vice-versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The one-way coupling assumes only minor differences between the couplings, as observed in Ling et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2015) and Fontes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='4 Computational domain and flow conditions The above-proposed model is validated using experimental data from Amighi and Ashgriz (2019) at elevated pressure conditions for an experimental channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Figure 2 illustrates the computational domain with the same cross-section of 25\uf0b435 mm2 (y\uf0b4z) as the experimental channel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The computational domain in this study is 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6mm in length (x-direction), which is only a part of the 14 experimental channel size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Following the experimental measurements, D32, STD calculations are done within a 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='45D distance downstream (blue sub-domain) from the point of liquid jet injection (28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6, 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5, 0) mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The liquid jet is injected from the nozzle placed at the bottom wall of the domain in the z-direction (Jet direction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The exit diameter of the nozzle used is 572 μm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 2: Computational domain and region of calculation The initial domain meshes with a 140 60 80 \uf0b4 \uf0b4 cells, and the cells are additionally refined around the injector (see Figure 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' We have performed four levels of refinement, with the finest grid size being 26 μm in the nozzle region to the coarsest level of 418 μm of the parent mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This results in a total size of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='75 million cells in the parent mesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 3: Mesh generated with (a) blockMesh and (b) SnappyHexMesh (near nozzle) with four levels of refinement near the nozzle On our parent mesh, we have used adaptive mesh refinement (AMR) with three refinement levels to accurately refine the liquid-gas interface region and capture the complicated dynamics of the interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A lower and upper refine level values ( 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 1 \uf061 \uf03c \uf03c ) of the volume fraction alpha are used as a criterion to refine the cells having a liquid-gas interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This continues refining the cell until the maximum refinement is achieved or if the alpha values fall outside the acceptable range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The lower refine level value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 is chosen after checking for different refinement levels as the lower values (<0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1) yield Walls Inlet Outlet Nozzle Inlet(a) (b)15 similar results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The use of AMR reduces the computational requirements considerably;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' thus, a coarser mesh can be employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' With the help of AMR, the mesh resolution of 52 μm is achieved just at the interface (refer Figure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 4: Adaptive mesh refinement (AMR) of cells using liquid volume fraction alpha field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Red droplets indicate lagrangian droplets, which are converted from Eulerian to Lagrangian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' As the Eulerian liquid droplets move from one point to another, the cells where the interface is located are refined continuously during the simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Once a Lagrangian droplet forms (from an Eulerian framework, as shown in Figure 4), the grid is coarsened back to the parent base mesh resolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In this way, the Lagrangian assumption also holds for droplets, as the liquid fraction is less than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='22 in a computational cell (Arlov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2007)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Note that Lagrangian droplets and Eulerian fields are shown in red and blue in Figure 4, respectively, are in 3-dimensions, whereas the AMR grid in the background is just a 2-dimensional, mid-section plane of the domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Hence, many red (Lagrangian) droplets are in the fine mesh while the coarse grid surrounds Eulerian ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Nearby cells in the vicinity of Eulerian droplets are also adjusted by adding six buffer layers to prevent excessive cell size jumps in the flow field, which could result in considerable pressure and velocity gradients at the jump point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The Eulerian and Lagrangian droplets in the computational domain, the AMR, and the buffer cells are shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Depending on the extent of break-up and penetration of the liquid jet, the total number of cells in the domain increases from an initial count of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='75 million to 3-5 million during the runtime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The maximum Courant Friedrich Lewy number (CFL) is set to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='12, providing an average time step of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 x 10-8 sec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The cross-flow air inlet is fed with a fully developed turbulent velocity profile obtained from a separate channel flow simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The liquid jet is provided a uniform velocity profile with negligible Parent cell Eulerian droplet Buffercells Lagrangian droplets16 turbulence at the nozzle exit to avoid any early breakup due to turbulence (Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Water is used as the liquid, and the air is used as the crossflow fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The liquid jet and cross-flow air temperatures are kept at a constant room temperature of 25oC for all test conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Table 1 and 2 describes the fluid properties and test conditions used for the simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fluid Property P=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 bar, T=25oC P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 bar, T=25oC jet \uf072 (kg/m3) 997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='10 997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='17 air \uf072 (kg/m3) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='42 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='44 \uf073 (N/m) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='072 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='072 air \uf06e (m2/s) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='638 x 10-6 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='167 x 10-6 jet \uf06e ( m2/s) 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='927 x 10-7 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='925 x 10-7 air \uf06d (N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='s/m2) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='849 x 10-5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='851 x 10-5 jet \uf06d (N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='s/m2) 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='901 x 10-4 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='900 x 10-4 Table 1: Summary of fluid properties Pressure (bar) Crossflow velocity (m/s) Jet velocity (m/s) Case 1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 61 9 Case 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 61 12 Case 3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 61 19 Case 4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 61 24 Case 5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 65 14 Case 6 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 65 19 Case 7 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 41 19 Case 8 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 41 9 Case 9 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 41 24 Case 10 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 33 19 Table 2: Simulated test conditions with nozzle diameters of 572 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Results and Discussion This section first assesses our VOF-LPT coupled framework by performing a validation case at elevated pressures of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 bars, which would mimic the density ratios of actual gas turbines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A grid test is then carried out to investigate the effect of grid sizes on droplet sizes and jet penetration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' And the following section discusses the impact of various parameters on droplet size characteristics and compares our jet trajectory against various experimental correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Further, we discuss the primary break-up behavior and flow features (vortex formations) observed in the liquid jet in 17 crossflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' All the determined parameters (D32, STD) are time-averaged values calculated within the sub-domain (blue-colored), as shown in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 Spray Trajectory and Validation The compressible VOF-LPT model is validated using a Liquid Jet-in Crossflow (JICF) case at elevated pressure and room temperature conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The numerical results of the windward trajectory, droplet sizes (D32), and the standard deviation (STD) are compared against the experimental results from Amighi and Ashgriz (2019), as shown in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The validation is performed for two cases with nozzle diameters of 572 µm (Case A) and 457 µm (Case B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The parameters used with cases A and B are listed in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 5: Comparison of liquid jet trajectory vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' experimental for cases A and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The error margins of 2d \uf0b1 are considered based on the simulations due to the lack of error margin in experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Case A Case B Pressure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 bar 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 bar Temperature 25 oC 25 oC Liquid jet velocity 19 m/s 19 m/s Crossflow velocity 65 m/s 50 m/s Nozzle diameter 572 µm 457 µm Table 3: Parameters used for numerical simulations for case A and case B As shown in Figure 5, the error bars represent 2d \uf0b1 the margin for both cases A and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In this work, the error bars are considered based on the computational data because of the lack of data on error margins in experimental results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' All the trajectory calculations are employed by assuming the center of the nozzle as the origin (0,0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' As observed in Figure 5, the windward trajectory starts from -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5D with respect to the origin on the x-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' For the low-pressure case of 457 µm as nozzle diameter (case B), the predicted trajectory is closer in the near nozzle region (<20D) and deviates slightly after 20D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The deviation observed in the region >15D for case A and >20D for case B is because the experimental 35 50 Experiment Experiment Simulation 45 Simulation 30 中 Error Margin ±2D 市 Error Margin ±2D 40 25 35 20 30 DN 25 N 15 20 10 15 10 5 5 0 0 5 10 15 20 0 5 10 15 20 25 X/DN18 trajectory data is based on the spray plume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' An image averaging and thresholding technique is used to determine the windward trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=" This is chosen to account for the Eulerian and Lagrangian droplets' contributions to the trajectory." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' For the Eulerian contribution to a trajectory, an iso-contour value is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The droplets are scaled to exact sizes for the lagrangian part to generate the whole spray atomization image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' For cases A and B, the trajectory is plotted by averaging liquid spray images over time, where approximately 200 images are obtained with a time interval of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='05 milliseconds between each image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A threshold of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='9 is applied to the averaged image, which is sufficient to remove the traces of stray droplets outside the windward side of the trajectory (Gopala et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Case A Case B D32 (µm) STD (µm ) D32 (µm) STD (µm ) Experimental 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 Computational 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='96 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='9 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='13 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='71 Error % 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='4 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='3 Table 4: Comparison of Sauter Mean Diameter (D32) and the Standard Deviation (STD) for computational and experimental cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Table 3 presents the droplet sizes obtained numerically and experimentally for cases A and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The D32 values obtained for the validation cases A and B lie within a 10% error margin concerning the experimental D32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Similarly, the error observed in the STD is also within a 12% error margin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Regarding the error margin observed here, the numerically predicted droplet sizes and standard deviation are much closer to the experimental results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This reveals a good agreement of the predicted data against experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Thus, comparing the spray trajectory with Sauter Mean Diameter (D32) and Standard Deviation (STD) of droplets against the experiments illustrates the accuracy of the numerical simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 6: Comparison of trajectory for different mesh resolutions with experimental 19 Three different baseline meshes are chosen to study grid independence, a coarse grid (105 x 45 x 60), a medium grid (140 x 60 x 80), and a fine grid (175 x 75 x 100).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The windward trajectory and the spray droplet size characteristics, such as the Sauter mean diameter (SMD or D32) and standard deviation (STD) for these grids, are compared in Figure 6 and Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=" For the near nozzle region (<20D) considered here, the variation in trajectories is minimal, and there isn't much difference between the trajectories." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' However, for the medium and fine grids, the trajectory is traced along the same path until 10D, and later on, only a slight difference is observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Compared to the medium and fine grids, the trajectory is slightly underpredicted for the coarser grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' As a result, we can infer that the grid has less impact on the trajectory near the nozzle (<20D) and that the trajectory is closer to experimental data in this area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This could be attributed to the adaptive mesh refinement (AMR) taking care of the refinement to some extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' D32 (µm) STD (µm) Error in D32 Error in STD Initial cell count (x 106) Final cell count (x 106) Experimental 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0 - - - - Coarse 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='75 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='62 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='7 % 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 % 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='35 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='27 Medium 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='96 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='9 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='4 % 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 % 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='75 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2 Fine 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='07 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='08 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6 % 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 % 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='41 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='75 Table 5: Sauter Mean Diameter (D32) and the Standard Deviation (STD) and error observed for different mesh resolutions For the medium and fine grids, the values of SMD and STD are found closer to each other and close to experimental values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The SMD and STD values show significant overprediction for the coarser grid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The error observed in STD for the coarser grid is twice that of medium and fine grids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Therefore, our medium-sized grid (140 x 60 x 80) can provide sufficiently accurate and computationally less expensive results for droplet sizes and liquid jet penetration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This medium grid will be used in all our analyses from this point onwards.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It is observed that when AMR is used, the final cell count is approximately four-five times the initial cell count in the domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The total cell count observed for different simulation test cases varies between 3-5 million grid cells depending on the liquid jet penetration and break-up behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2 Effect of various parameters on droplet size characteristics This section talks about the effect of various parameters, the liquid jet velocity (Vj), cross-flow velocity (Vair), and ambient pressure (P), on the droplet size characteristics, namely the Sauter mean diameter (D32) and the standard deviation (STD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' All the test cases are carried out at constant temperatures of 25oC and high-pressure conditions of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Table 6 summarises all the droplet size characteristics gathered from simulations and experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The momentum flux ratio and crossflow 20 Weber numbers of the test cases range from 8 to 80 and 38 to 150, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The number of lagrangian droplets formed ranges from 40,000 to 3,00,000 depending on the extent of penetration and break-up for the test cases performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Momentum flux ratio (q) Weber number (air) (We) Experimental Computational Error D32 (µm) STD (µm) D32 (µm) STD (µm) D32 (%) STD (%) Case 1 P=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1bar,T=25oC, Va=61m/s, Vj=9m/s 8 71 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='9 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='93 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='77 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='74 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='02 Case 2 P=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1bar,T=25oC, Va=61m/s, Vj=12m/s 16 71 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='3 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='16 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='09 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='26 Case 3 P=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1bar,T=25oC, Va=61m/s, Vj=19m/s 41 71 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='15 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='89 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='99 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='58 Case 4 P=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1bar,T=25oC, Va=61m/s, Vj=24m/s 66 71 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='9 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='24 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='21 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='24 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='15 Case 5 P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar,T=25oC, Va=65m/s, Vj=14m/s 10 150 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='49 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='98 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='20 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='01 Case 6 P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar,T=25oC, Va=65m/s, Vj=19m/s 19 150 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='96 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='9 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='4 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 Case 7 P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar,T=25oC, Va=41m/s, Vj=19m/s 48 60 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='3 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='48 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='43 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='81 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='15 Case 8 P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar,T=25oC, Va=41m/s, Vj=9m/s 10 60 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='4 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='95 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='56 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='31 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='59 Case 9 P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar,T=25oC, Va=41m/s, Vj=24m/s 77 60 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='83 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='55 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='47 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='03 Case 10 P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar,T=25oC, Va=33m/s, Vj=19m/s 77 38 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='15 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='57 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='16 Table 6: Summary of test results: Sauter Mean Diameter (D32) and the Standard deviation for all test cases (DN=572 µm) For all the test cases performed, the maximum error observed on D32 and STD is 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='47 % and 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='01 %, respectively, and the average error observed on D32 and STD are 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='58 % and 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='15 %, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' For all the D32 plots (Figures 7, 8, and 9), an error margin of 10 % is provided on the computational D32 plot, which corresponds to an average error of 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 m \uf06d \uf0b1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Similarly, an error margin of 15% is provided on the numerically calculated STD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' All the D32 values obtained are observed to be within this range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Since the experimental error values are unknown, the error margin is provided concerning the numerical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The values of D32 are found to be on the lower side for all the test cases performed compared to the experimental observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' D32 and STD values are calculated in every simulation by iterating over all the Lagrangian particles throughout the domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' To maintain the accuracy of results similar to the experimental procedure, the irregular Eulerian droplets are neglected from the calculations, including the ligaments carried out in the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The sphericity and the minimum 21 threshold value of the droplet undergoing conversion from one framework to another are set per the experimental data analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This way, it ensures the droplets converted to Lagrangian particles are the ones that need to be accounted for in the droplet characteristics calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Each data point on the plot represents either simulation or experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The following sections discuss the effect of liquid jet velocity, crossflow velocity, and ambient pressure on the droplet size characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 Effect of Liquid Jet Velocity/ Momentum flux ratio Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 7: Plot of Sauter Mean Diameter (D32) and Standard Deviation (STD) with Liquid jet velocity at a pressure of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The 10% and 15% error margins are considered for D32 and STD, respectively, based on the simulations due to the paucity of error margin in experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In all of the D32 plots, the error bars correspond to an error margin of 10% applied on the simulated contour, and on STD plots, it corresponds to 15 %.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Typically, the errors in measurements involving particle statistics (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' D32, STD) vary between 10-30%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Considering this, our predictions exhibit an excellent agreement regarding the accuracy of the droplet statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Figure 7 shows the effect of jet velocity on global droplet sizes (D32 and STD) at an ambient pressure of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' From both the numerical and experimental observations, the effect of liquid jet velocity is to decrease the size of the droplets (both D32 and STD) formed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This is attributed to the increased atomization from the higher momentum flux ratio (q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Momentum flux ratio (q) is defined as: 2 2 j j jet air air air V We q U We \uf072 \uf072 = = (29) The droplet sizes decrease as the jet velocity increases from 9 m/s to 24 m/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Similarly, for the standard deviation, it is also reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The lower standard deviation due to increased jet velocity indicates that the atomization is more uniform at higher jet velocities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The reduction in droplet size is attributed to mainly two factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1) One is that the Reynolds number increases, and the jet becomes more turbulent on increasing the jet velocity, resulting in an increased break-up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2) Another factor is that as the jet velocity increases, the jet is penetrated more into the cross-flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This increases the exposure of the 22 liquid jet with the cross-flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' These two factors combined result in the decrease of D32 and STD values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The above plot shows that increased liquid jet velocity produces finer droplets, improving the atomization process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2 Effect of Cross-flow Velocity Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 8: Plot of Sauter Mean Diameter (D32) and Standard Deviation (STD) with crossflow velocity at a pressure of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The error margins of 10% and 15% are considered for D32 and STD, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Figure 8 shows the effect of cross-flow velocity on D32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The cross-flow velocity is varied from 33 m/s to 41m/s and further to 65 m/s, where all other parameters, the pressure (P), liquid jet velocity (Vj), temperature (T), are kept constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' As observed above, the increase in cross-flow velocity decreases the droplet size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' At low cross-flow velocity, the penetration of the liquid jet is higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The increased penetration is due to the increased momentum flux ratio from the reduced air velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The penetration is higher for lower air velocity because the drag force exerted on the liquid jet is smaller at lower cross- flow velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This reduces the width of the spray plume, resulting in the decreased interaction between the liquid and the gas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' On the other hand, at higher cross-flow velocity, the higher drag force bends and flattens the liquid jet further, resulting in a more pronounced break-up and atomization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Another explanation for the reduction in droplet sizes is that as the crossflow velocity increases, the Weber number of the air increases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This also causes the break-up mode to be shifted to pure shear mode (We>110), resulting in the production of a large number of smaller droplets, also causing a reduction in droplet sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Weber number of air: 2 a a N U D We \uf072 \uf073 = (30) The experimental D32 value at a crossflow velocity of 33m/s is slightly lower than the value at 41m/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' But our computational prediction in Figure 8 shows that the D32 value increases with a decrease in the crossflow velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The slight discrepancy in the experimental data could be due to any experimental 23 errors, and this particular trend wasn’t observed with other experimental results pertaining to different crossflow velocities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The general trend for the droplet sizes is to decrease with increased crossflow velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Therefore, the numerically predicted trend is more acceptable here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='3 Effect of Pressure Figure 9 shows the effect of cross-flow pressure on Sauter mean diameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The ambient pressure varies while the cross-flow velocity (61 & 65 are considered the same) and liquid jet velocity are kept constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' As seen above, increasing the pressure decreases the SMD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A similar observation is also obtained in numerical simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This is because an increase in pressure increases density and the drag force on the jet and the ligaments and droplets, breaking into smaller droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The value of the Sauter mean diameter depends more on the larger droplets than the smaller droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' So a reduction in the generation of larger droplets consequently reduced the SMD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The STD plot for increased pressure also shows similar behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The increased pressure improves atomization, resulting in a more uniform droplet size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In addition, the enhancement in the pressure decreases the penetration of the jet due to the increased drag forces on the liquid jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 9: Plot of Sauter Mean Diameter (D32) and Standard Deviation (STD) with ambient pressure at a crossflow velocity of 65 and 61 m/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The error margins of 10% and 15% are considered for D32 and STD, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='4 Effect of Cross-flow Weber number Here we have considered two sets of cases (case 5, 8 and case 9, 10) having the same liquid-to-gas momentum flux ratio (q) with different cross-flow Weber numbers (We).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The cross-flow and liquid jet velocities are varied proportionately to keep the momentum flux ratio constant (q=10 for cases 5, 8 and q=77 for cases 9, 10).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The momentum flux ratio is: 24 2 2 j j jet air air air V We q U We \uf072 \uf072 = = (31) As the Weber number is increased (Case 8: q=10, We=60 and Case 5: q=10, We=150) from 60 to 150, the droplet sizes are reduced (Case 8: D32=82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='95, STD=22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='56 and Case 5: D32=75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='49, STD=21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='98) following a general trend (Lubarsky et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=',2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The same observation is also made at a higher momentum flux ratio (q=77) when the Weber number is increased from 38 to 60 (Case 10: D32=78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='15, STD=21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='20 and Case 9: D32=68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='83, STD=17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='55).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 Effect of parameters on liquid jet penetration, breakup region, and droplet distribution (a) Liquid Jet Penetration – trajectory Many researchers have proposed empirical correlations in power law, logarithmic, exponential, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', to predict penetration heights for a liquid jet in crossflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Some researchers have considered the effect of momentum flux ratio alone (Tambe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2005), while several others included the effect of Weber number, pressure, viscosity, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', in their correlations (Amighi and Ashgriz (2019), Ragucci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2007), and Elshamy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2007)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Stenzler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2006) proposed a power-law correlation that accounts for fluid viscosity and aerodynamic weber number and is among the first to assess the effect of air viscosity on jet penetration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' While Becker and Hassa (2002), Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1993) pointed out that there is no significant effect of aerodynamic weber number and break-up mode on liquid jet penetration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The correlations proposed by Amighi and Ashgriz (2019), Tambe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2005), Ragucci et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2007), and Elshamy et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2007) for the windward trajectories are used to compare against our numerically obtained trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Most of the available correlations in the literature are only valid in the near nozzle region (<25D).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Tambe : 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='53 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='55 ln 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='66 N N y z q D D \uf0e6 \uf0f6 = + \uf0e7 \uf0f7 \uf0e8 \uf0f8 (32) Ragucci : 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='367 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='44 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='012 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='27 aero N N z x q We D D − \uf0e6 \uf0f6 = \uf0e7 \uf0f7 \uf0e8 \uf0f8 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='186 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='367 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='422 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='015 ,300 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='28 aero N air k N z x q We D D \uf06d \uf06d − \uf0e6 \uf0f6 \uf0e6 \uf0f6 = \uf0e7 \uf0f7 \uf0e7 \uf0f7 \uf0e7 \uf0f7 \uf0e8 \uf0f8 \uf0e8 \uf0f8 (33) Elshamy : 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 /10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='46 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 /4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 /1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='39 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='446 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='141 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='63 1 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='42 1 N N N x x x D D D N o y p q e e e We D p − \uf0e6 \uf0f6 \uf0e6 \uf0f6 \uf0e6 \uf0f6 − + − + − + \uf0e7 \uf0f7 \uf0e7 \uf0f7 \uf0e7 \uf0f7 − \uf0e8 \uf0f8 \uf0e8 \uf0f8 \uf0e8 \uf0f8 \uf0e9 \uf0f9 \uf0e9 \uf0f9 \uf0e9 \uf0f9 \uf0e6 \uf0f6 \uf0ea \uf0fa \uf0ea \uf0fa \uf0ea \uf0fa = − \uf0b4 + \uf0b4 + \uf0b4 \uf0e7 \uf0f7 \uf0ea \uf0fa \uf0ea \uf0fa \uf0ea \uf0fa \uf0e8 \uf0f8 \uf0eb \uf0fb \uf0eb \uf0fb \uf0eb \uf0fb (34) Amighi : 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='27 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='65 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='31 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 air air Jet N N y x q We Oh Oh D D − \uf0e6 \uf0f6 = + \uf0e7 \uf0f7 \uf0e8 \uf0f8 (35a) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='27 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='72 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='65 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='31 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 Re Re air jet air Jet N x We We D − − \uf0e6 \uf0f6 = + \uf0e7 \uf0f7 \uf0e8 \uf0f8 (35b) 25 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Liquid jet penetration along with correlations for (a) case 3 (P=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 bar), (b) case 6 (P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 bar) and, (c) case 7 (P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 bar) In Figure 10, the numerically obtained trajectories at two different pressure conditions (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 bar) are compared against the experimental correlations of Amighi, Tambe, Ragucci, and Elshamy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In Figure 10(a), the trajectory for case 3 with pressure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 bar agrees well with the Elshamy correlation, while the Amighi correlation under-predicts it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Figures 10(a) and 10(b) have similar crossflow velocities of 61 m/s and 65 m/s, respectively, and the same liquid jet velocity of 19 m/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The pressure change has a consequent effect on the Weber number and momentum flux ratio because of the change in crossflow air density.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The weber number reduces to half while the momentum flux ratio doubles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The Elshamy correlation underpredicts the trajectory in Figure 10(b), whereas Amighi’s correlation closely predicts in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Amighi’s inverse dependence of windward side trajectory on the weber number is why it shows minor change compared to other correlations All correlations show similar predictions in Figure 10(a) and Figure 10(c) regarding the trajectory of the current simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The weber number and momentum flux ratio are almost identical for cases 3 50 40 Simulation (case 3) Simulation (case 6) Tambe 35 Tambe 40 -- Amighi et al -- Amighi et al Ragucci 30 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ragucci Elshamy Elshamy 25 30 20 N 20 15 10 10 5 0× 0 5 10 15 20 0 5 10 15 20 ax X/D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' N (a) (b) 50 Simulation (case 7) 45 Tambe Amighi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 40 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ragucci Elshamy 35 30 25 N 20 15 10 5 0x 0 5 10 15 20 (c)26 and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Therefore, the simulated data lies between the Elshamy and Amighi’s correlation, and the minimal change is only caused by the slight differences in the momentum flux ratio and weber number values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Hence, the effect of change in pressure is sufficiently reflected through these non- dimensionless numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The correlation of Tambe highly over-predicts the trajectory in the analysis of all the cases, which can be attributed to the absence of the weber number in empirical correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (b) Liquid jet break-up region Momentum flux ratio (q) Weber number (We) (air) Breakup Location X (in DN) Y (in DN) Case 1 P=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1bar,T=25oC, Va=61m/s, Vj=9m/s 8 71 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='62 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='37 DN 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='95 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='484 DN Case 2 P=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1bar,T=25oC, Va=61m/s, Vj=12m/s 16 71 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='785 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='33 DN 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='161 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='964 DN Case 3 P=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1bar,T=25oC, Va=61m/s, Vj=19m/s 41 71 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='64 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='73 DN 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='69 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='061 DN Case 4 P=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1bar,T=25oC, Va=61m/s, Vj=24m/s 66 71 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='29 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='385 DN 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='84 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='23 DN Case 5 P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar,T=25oC, Va=65m/s, Vj=14m/s 10 150 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='79 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='827 DN 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='59 DN Case 6 (Case A) P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar,T=25oC, Va=65m/s, Vj=19m/s 19 150 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='67 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='873 DN 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='335 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='622 DN Case 7 P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar,T=25oC, Va=41m/s, Vj=19m/s 48 60 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='3 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='933 DN 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='14 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='51 DN Case 8 P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar,T=25oC, Va=41m/s, Vj=9m/s 10 60 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='85 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='17 DN 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='11 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='73 DN Case 9 P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar,T=25oC, Va=41m/s, Vj=24m/s 77 60 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='40 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='08 DN 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='10 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='58 DN Case 10 P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar,T=25oC, Va=33m/s, Vj=19m/s 77 38 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='22 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='12 DN 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='58 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='83 DN Table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The streamwise and transverse location of breakup region for cases 1 to 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The break-up location is investigated for all the cases (Table 6), and it is observed that the break-up does not occur precisely at a particular point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Instead, the break-up occurs in a broader region in the streamwise direction than in the transverse direction (jet direction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Therefore, we have considered break-up location a region rather than a particular point where the break-up occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The break-up location refers to the region where the liquid core, after bending, shows excessive deformation and discontinuities in the liquid core of the spray trajectory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This is the same as the column break-up location, except our break-up is more in a multimode/shear break-up mode where both the bag-shear and shear break-up are observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=" The liquid jet is subjected to unsteady aerodynamic forces, causing the windward and leeward surfaces to fluctuate, resulting in the liquid jet column's deformation, 27 bending, and fracture." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The break-up location is determined for several test cases, and it is found that the x-location of the break-up is almost constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' As shown in Table 7, it does not show significant variation in the streamwise direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It is approximately located at 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2D±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2D for all the cases, whereas the y-location seems to vary by a large magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The y-location varies with the jet penetration, dependent on the momentum flux ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The higher the momentum flux ratio, the more the y-location of the jet breakup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1997) also investigated the break-up location and found the column fracture location constant at about 8D downstream of the nozzle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Compared to the break- up location by Wu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1997), our break-up is slightly delayed and in good agreement with the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Tambe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2005) also made a similar observation regarding the independence of momentum flux ratio on streamwise break-up location.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' While the transverse location of break-up varies with the crossflow parameters (momentum flux ratio and crossflow weber number), the momentum flux ratio has a more significant influence on penetration than the crossflow weber number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (c) Droplet Distribution In all of the test cases performed, the larger droplets or the liquid lumps are found closer to the upper periphery of the liquid jet, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' in the upper half of the spray core region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' These larger, irregular fragments are formed from the liquid core break-up and are penetrated more into the crossflow due to the higher momentum of the larger droplets, which are less affected by the crossflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The smaller droplets are larger in number and found more in the lower part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The smaller droplets are produced in two ways: one from the secondary breakup of larger droplets and another due to the shear break-up from the sides of the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' At higher crossflow weber numbers, this model of a shear break- up from the sides of the liquid column is more dominant than the other break-up modes leading to the production of a large number of smaller droplets causing a decrease in the droplet sizes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' For higher momentum flux ratio cases (Case 4,7,9,10 – Table 6), the droplet sizes are found to peak at the upper periphery of the spray core, while for lower momentum flux ratio cases (Case 1,5,8), the droplet sizes peak near the spray core but still lies in the upper half region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Figure 11 shows the Eulerian and Lagrangian droplets produced in crossflow atomization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The droplets subjected to more deformation stay in the Eulerian field, and those earlier converted from Eulerian to Lagrangian are visible in the zoomed-in image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This conversion is facilitated by the droplet sphericity, which measures the deviation in droplet shape compared to that of a spherical droplet of equivalent diameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The Eulerian droplets visible in Figure 11 are the droplets having sphericity >1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='47, and the spherical droplets visible are Lagrangian droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The simulation produces as small as 10-15 µm droplets, better resolved using the LPT approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The larger droplets are fewer in number, 28 and the smaller droplets are larger in number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The droplet sizes generally follow a log-normal distribution (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2016)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 11: Crossflow jet atomization and breakup captured using VOF-Lagrangian particle tracking approach for case 5 (P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar, Vair=65m/s, Vj=14m/s, q= 10, We=150).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Spherical droplets indicate lagrangian droplets converted from Eulerian droplets (blue color) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 12: Crossflow jet atomization and breakup captured using VOF-Lagrangian particle tracking approach for case 6 (P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar, Vair=65m/s, Vj=19m/s, q= 19, We=150) Dropletdiameter(um) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0e 05 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0e 4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1e 04Droplet diameter (um) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0e 05 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0e 4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1e 04 Lagrangian droplets Ligaments Primary brcakup Liquid jct corc29 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content="3 Spray breakup and atomization Figure 12 represents a liquid jet's break-up and atomization process in cross-flow (case 6) with Eulerian (iso-contour α=0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5) and the Lagrangian droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The aerodynamic drag force experienced by the liquid jet column forces it to bend in the crossflow direction because of a high-pressure windward and low- pressure leeward region, as shown for case 3 (Table 6) in Figure 13(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Another prominent feature of LJICF is flattening the liquid jet cross-section from a circle to a crescent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This can be understood as airflow around a deformable cylinder, as shown in Figure 13(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The crucial factors responsible for this deformation are – internal boundary layer flow and pressure difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The internal boundary layer (shown by the dashed line in the first image of Figure 13(b)) is formed in the liquid phase due to the shear generated by the external flow of air around the liquid core, which transports the liquid from point 2 towards point 3 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Moreover, the pressure at point 2 is higher than the pressure at points 3 and 4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' it further helps this internal flow of the liquid away from the frontal region (around point 2) towards the periphery (near points 3 and 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It leads to the flattening of the liquid jet core cross-section (as shown in the second image of Figure 13(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Both the factors continue forcing the liquid from point 2’ towards 3’ till the complete circular cross-section has been deformed into a thin sheet-like cross- section (third image of Figure 13(b)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The liquid movement from points 2’’ to 3’’ (in the third image of Figure 13(b)) leads to the thickening the liquid-jet core edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This process is suspected to be one of the deciding factors in streamer formation along the two edges of the deformed liquid jet, which will be discussed later in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' However, the flattening of the liquid jet core further increases the effective frontal area, and consequently, the drag forces cause it to deflect even further.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Figure 13(c) shows this deformation of the liquid column for case 3 at varying distances from the bottom wall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The liquid jet deformation is mainly followed by break-up through two mechanisms: column break-up and surface break-up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The column break-up is characterized by instabilities and the growth of surface waves on the liquid jet column, resulting in the formation of crests and troughs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=" These waves grow in size, causing the liquid column to detach from one of the wave's troughs, resulting in a liquid break- up." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=" Large fragments separate in this break-up, leading to larger droplets observed in the liquid jet's upper periphery." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In the surface break-up, the droplets are pinched off (before the column break-up occurs) from the sides of the liquid column due to the action of shear between the liquid and gas phases on the periphery of the flattened/deformed liquid jet as observed at height (Z) between 8D to 12D in Figure 13(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It is also proposed that the surface break-up is caused by the growth of turbulent instability on the liquid column as the laminar liquid jet undergoes transition (Madabhushi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This is commonly observed at moderate to high crossflow Weber numbers (Weair) with high momentum flux 30 ratios (q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' At lower to moderate Weber numbers, increasing crossflow weber number shifts the break- up towards the shear regime of a column breakup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The shear break-up starts way before the instabilities at the liquid-gas interface, causing the liquid core to rupture into smaller droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The droplets formed from shearing action are smaller, resulting in better atomization of the liquid jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' These two break-up processes constitute the primary atomization part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 13: (a) Mean pressure showing maximum and minimum values on the windward and leeward side of a liquid column, (b) Schematics showing liquid column deformation at increasing distance (height) from the point of injection, (c) Liquid jet cross-section deformation along with shear breakup at various heights from the point of injection (in jet direction, Z) for case 3 (P=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1bar, Vjet=19m/s, q=41, Weair=71).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' High Pressure Region 2 Low Pressure Region (a) Gaseous External Original Cross section Boundary Layer shape Liquid Internal Boundary Layer (b) Droplet diameter (um) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0e 05 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0e 4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1e 04 Z=1D Z 2D Z=4D Z=6D 7=15D Z 12D4 Z=8D Z=4D Z 8D Z=10D Z=12D Z= 15D Z 1D (c)31 The primary break-up happens when the aerodynamic forces of the crossflow cause the liquid jet to rupture into smaller ligaments and droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Sallam et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 2006) classified the primary break-up for non-turbulent liquid jets based on the aerodynamic Weber number into four modes, the column (We<4), bag (4110).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The break- up mode is investigated for different crossflow weber numbers (38-150) and momentum flux ratios (8- 77).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' For the test cases performed in this study, the breakup modes involve bag/multi-mode and shear modes of breakup and the surface breakup of the jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' For a few cases, multimode behavior is observed where both bag and shear modes are present.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' As the aerodynamic weber number increases, the mode of break-up shifts from multimode to pure shear mode (cases 5 and 6), characterized by the pinch-off of droplets from the sides of the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The bag formation and its subsequent breakage into ligaments and droplets for case 8 are discussed in detail in the subsequent section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Similar characteristics of multimode and shear breakup modes are discussed later in the following sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The primary breakup regime map shows the varying momentum flux ratios and crossflow Weber numbers cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The red-colored encircled points show the cases that are analyzed in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Three tests out of ten listed in Table 6 are considered for detailed analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The three tests belong to the different regimes of the liquid jet breakup, as shown in Figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 14 – case 8 in bag breakup regime of the column breakup, case 9 in surface breakup regime, and case 5 in shear breakup regime of the column breakup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 100 :Eslamian,Amighi and Ashgriz 90 Becker and Hassa P=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='Vair=61m/s 80 10 P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar,Vair=65m/s flux ratio (q) P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='Vair=41m/s 70 P=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='Vair=33m/s 4 60 Momentum f 50 40 30 20 2 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 0 0 50 100 150 200 250 300 Weber number (We .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' air32 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 Bag Breakup Regime Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Characteristic features of a LJICF in bag breakup regime for case 8 (q = 10 and We = 60).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Case 8 is ideal for bag breakup because of the low-value q and We.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A few distinct features of this case are the flow in the wake of the liquid jet, development of instability and its growth, bag breakup, and bifurcated streamers formation, as shown in Figure 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Each of these is analyzed in detail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (a) Flow behind the liquid jet As discussed above, the high and low-pressure region is created on the windward and leeward sides of the liquid jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The pressure difference plays a prominent role in the deformation of the liquid jet cross- section, as shown in Figure 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The pressure difference affects the flow passage around the liquid jet column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' As shown on the mid-plane in Figure 16(a), the high-pressure point (S1) is located at a particular height on the windward side of the jet where the static pressure reaches a maximum value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The streamlines using mean velocity with only x- and z-direction components are plotted in Figure 16(b) to estimate the flow features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The low pressure in the liquid jet wake is dominant from the bottom wall at some height.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=" It draws in the flow passing through the jet column's sides, creating a counter-rotating vortex (CRV), as shown by the yellow streamlines in Figure 16(b)." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2016) stated a saturation point on the leeward side of the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The recirculating flow may divide at the rear surface of the liquid column to create two circulation zones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In Figure 16(b), almost an entire leeward side of the jet column is exposed to only one (spanwise) vortical structure, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' CRV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The point S2, where velocity would be zero on the leeward side of the liquid column, lies in the region of the complete breakup of the liquid column into ligaments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Bag Formation Ligaments Streamers33 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (a) Pressure contour shows high-pressure point S1 on the windward side of the liquid column, (c) Streamlines in x-z plane show counter-rotating vortex (CRV) in yellow color, (c) counter-rotating sheet breakup vortex (SBV) pairs (green-red color), (d) & (e) show movement of the SBV at consecutive time units following the bag of the wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (f) The white-colored streamlines break through the liquid sheet bags, pulled by the SBVs for case 8 (q = 10 and We = 60).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Further, the two smaller counter-rotating vortex pairs act along the column breakup process downstream of CRV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' An interesting phenomenon is noticed where these two vortices’ centers move 385000 CRV 384000 382501 (a) (b) SBV (c) SBV SBV (d) (e) (f)34 with the trough/bag of the liquid column instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The movement of these vortices is shown at consecutive time units in Figures 16(d) and 16(e), where the vortex has shifted downstream following the trough of the wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A closer look at this phenomenon in Figure 16(f) shows the ‘white’ colored streamlines passing through the ruptured liquid surface in the wave trough and mixing with outgoing ‘green’ streamlines of the vortex downstream.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Lower pressure at the vortex center pulls the flow-through ruptured liquid sheet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Wen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2020) referred to these vortices as the bag breakup vortex (BBV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Here we refer to them as sheet breakup vortex (SBV) due to their role in the sheet-like liquid column breakup, which will be discussed in the subsequent section of the high shear case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The vortex strength of SBVs diminishes downstream as the liquid column disintegrates into ligaments and droplets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Though the streamlines corresponding to the mean velocity field do not show any vortex formation (picture not shown here), the movement of vortices downstream with diminishing strength indicates the vortex shedding phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Further, the vortex shedding phenomenon will be discussed later for the high momentum flux ratio case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Density contour at mid-plane of LJICF showing Kelvin-Helmholtz (KH) type instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The typical KH type asymmetric waves are observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The sinuous waves are most unstable here, considering the upper part of the liquid column behaves like a sheet (instead of varicose waves).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The contour of Y-vorticity (normal to figure plain) at mid-plane of LJICF showing Kelvin-Helmholtz (KH) type instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The near roll-ups are observed for this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 1027.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (gu) 800.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0 Sinuous Wave Nature Density 600.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0 400.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0 200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2591.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0e+05 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0e+4 Vorticity Y (s 1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0e+4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0e+0535 (b) Growth of instability on the windward side of the liquid in crossflow The formation of bags results from instability created upstream on the windward side of the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Earlier it was proposed that these are the Rayleigh-Taylor instability (Sallam, 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2008)) is caused due to the higher/lower air pressure on the windward/leeward side of denser liquid which results in the bag formation similar to the finger/bag like structures obtained in the experiments of Lewis (1950), Taylor (1950).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Rayleigh-Taylor instability is caused by denser fluid under acceleration towards lighter fluid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In this case of lower q and We, visual observation of the evolution of instability and breakup at consecutive time steps indicates that Kelvin-Helmholtz (KH) is the reason behind the instability growth (refer to Figure 17 showing density contour).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Similarly, Y-vorticity (normal to the image plane) is also plotted to check the roll-ups of the two fluids (Figure 18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A small clip of the same has been provided as supplementary data, clearly showing the presence of KH-type instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' As evident in Figure 19(a), the unstable waves are developed across the windward surface with parallel troughs/crests perpendicular to the stream direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A cross-section of the liquid column is observed at a location just before the wave starts to develop, and it shows that the liquid column has transformed from a circular shape to that of a sheet (see Figure 19(a)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Hence, we treat this as a case of instability development on a liquid sheet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Also, the liquid sheet-like structure is located at a much downstream distance from the point S1 along the liquid column such that high pressure has a lesser effect than the velocity shear between airflow and liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Considering inviscid, irrotational flow, the dispersion relation between wave number and wave growth rate is used for a liquid sheet as deduced by Squire (1953).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' If a coordinate system moves with the sheet interface at relative velocity U , an infinitesimal disturbance formed on it is described by: 0 [ exp( )] = \uf0c2 + ikx t \uf068 \uf068 \uf077 , (36) where 0 \uf068 is the initial wave amplitude, 2 / k \uf070 \uf06c = is the wave number, and r i i \uf077 \uf077 \uf077 = + is the complex growth rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The dispersion relation for a moving liquid sheet under inviscid conditions can be derived as: \uf05b \uf05d 3 2 2 2 1 tanh( ) 2 0 k kh Q iQkU QU k \uf073 \uf077 \uf077 \uf072 + + − + = (37) 36 for the sinuous waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Here, Q is equal to 2 1 \uf072 \uf072 , h is the sheet thickness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The solutions to the above Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 37 for the growth rate r \uf077 are: \uf05b \uf05d 2 2 3 1 tanh( ) tanh( ) tanh( ) r kh QU k k kh Q kh Q \uf073 \uf072 \uf077 − + = + .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (38) Similar to above, Eqs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (37) and (38) corresponding to sinuous waves, the dispersion relation and the wave growth rate for the varicose mode of the waves are also obtained by replacing tanh( ) kh by coth( ) kh term in these equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 19 (a) Location of a plane at which the cross-section of the liquid column is almost sheet-like, (b) three points showing the location curve for liquid profile calculation, (c) Velocity profile along the axis perpendicular to the interface, (d) Growth rate of different waves with wave numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In the present case of LJICF, the velocities of the gas and liquid phase need to be parallel at the interface for the calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' For this purpose, the velocity data is extracted along with the line segments at three points on the air-water interface, as depicted in Figure 19(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The points are chosen at such a location where the instability waves start to appear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The line segments are perpendicular to the interface at their respective interface points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The magnitude of the velocity component is found along the line segment by = \uf0d7 tang t u u n , where tn is the unit direction vector tangent to the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This provides (a) (b) 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1 Short Wave, Inviscid Long Wave, Inviscid Sinuous Wave,Inviscid 40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='08 Sinuous Wave,Viscous P1 P2 30 P3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='06 h/U /DN 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='04 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='02 0 5 10 15 20 25 30 35 40 0 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 I 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 3 kh (c) (d)37 us with the velocity profile at desired points (shown in Figure 19(c)) and helps us calculate accurate velocity differences by avoiding the shear region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It is also visible that the maximum velocity increases from P1 to P3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Therefore, an average of the velocity difference ( 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='56 ) avg U m s \uf044 \uf0bb is used in our calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Similarly, an average liquid core thickness 4 ( 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 10 ) avg h − \uf0bb \uf0b4 is also considered because of its variation along the liquid column, minimum at P3 and maximum at P1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The other details of thermophysical variables regarding the calculation are provided in Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Senecal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1999) discussed that the maximum growth rate of sinuous waves will always be greater or equal to the maximum growth rate of varicose waves in the moving liquid sheet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' From the observation of our present case (refer to Figure 17, Figure 18), the sheet-like liquid column shows sinuous wave formation at its inception.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Hence, we consider only the sinuous solution for the linear stability analysis (LSA) in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Figure 19(d) compares the growth rate for sinuous wave solution with short and long wave assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Since the wavelength \uf06c of the disturbance in the present case is slightly smaller than 2\uf070 times the sheet thickness h , short waves start to dominate over long waves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This is evident in Figure 19(d) as well, where the short wave assumption (red curve) predicts near to the general inviscid sinuous mode growth rate (blue) as compared to the long-wave assumption (red curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The long wave assumes tan( ) kh kh \uf0bb whereas the short wave assumes tan( ) 1 kh \uf0bb in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Senecal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1999) showed the dominance of long wave and short wave in low velocity/Weber number and high velocity/Weber number liquid sheets cases, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The Weber number for the sheet-like liquid core is approximately 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 \uf0bb with the present parameters, which makes it a marginal case for the distinction of long and short waves, albeit short wave is observed to dominate over a long wave in the present situation (as shown in Figure 19(d) and also, the assumption of tan( ) kh kh \uf0bb not holding true).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The / N D \uf06c values from various correlations and linear stability analysis are compared with the computationally observed result in Table 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The data corresponding to correlations and Rayleigh- Taylor breakup are calculated using the free stream air velocity of 41 m/s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The LSA error by Chandrasekhar and the general sinuous inviscid wave is minimum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The solution of a sinuous wave growth for a viscous sheet is very high, requiring further work to include viscosity effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The Rayleigh Taylor or RT-based correlations (Chandrasekhar, 1961;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 2008) predict almost 50% higher values confirming the absence of this type of breakup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This also explains the formation of cross-stream ligaments from the column breakup, as shown in Figure 19(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This case shows the development of KH instability and not the RT instability, which was considered the only dominant instability responsible for the column breakup in the past.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2016) proposed 38 that the liquid jet in very low crossflow velocity behaves similar to a jet in a quiescent air/gas medium and tends to develop KH instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This is in contrast to the condition here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In the present case, air velocity is significant enough, and the momentum flux ratio is also low.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' An essential factor, in this case, is the high shear experienced by the liquid column in the direction of liquid flow along the portion of its length where these KH waves start to develop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The high shear forces along the liquid column seem only possible when the momentum of crossflow air needs to be substantial compared to the momentum of liquid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The higher momentum of crossflow air bends the liquid jet acutely to high angles, which has a two-fold effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' First, the high-pressure region on the windward side of the liquid column is limited to the smaller area only, which faces directly into the incoming crossflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Second, high velocity is achieved in the region beyond point S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Point S1 lies at the approximately same area where the vorticity changes its sign as visible in Figure 18;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' the air velocity now exceeds the liquid flow velocity beyond point S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Thus, the high momentum of crossflow compared to the liquid momentum (that is, low momentum flux ratio) may be considered one of the governing reasons for the domination of KH instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This is in contrast to Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' But we will see in the following sub-sections that it is not the crossflow velocity but the momentum flux ratio that decides the type of dominant instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Correlations/LSA / N D \uf06c Prediction error (%) KH – Short sinuous wave 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='86 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='75 KH – General sinuous wave 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='89 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='57 KH – Sinuous wave, viscous - Senecal et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1999) 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='05 1200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0 KH – Chandrasekhar (1961) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='87 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='94 Rayleigh-Taylor – Chandrasekhar (1961) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='73 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='00 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' correlation (2008) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='83 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='09 Sallam et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' correlation (2006) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='54 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='03 Present Simulation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='15 - Table 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Comparison of wavelength observed in the present case and the predictions from LSA and correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (c) Bifurcation of liquid jet into streamers In Figure 15 and also in Figure 20(a), we can observe two thread-like structures separating from the sides of the liquid jet column known as streamers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This distinct phenomenon is termed bifurcation and was observed in the experimental work of Sedarsky et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2010) and then in a computational study by Wen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Still, many researchers did not clearly explain the cause of this phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Sedarsky et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2010) suggested that it is due to the vortex formation behind the liquid jet column, and Wen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2020) indicated that it could be due to the sheet break-up vortex (SBV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This 39 streamer/bifurcation is formed in the near nozzle region close to the wall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' As the jet penetrates more into crossflow (away from the wall), the liquid-gas circumference region is subjected to more shear forces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' As discussed earlier, the boundary layer is formed on either side of the interface in both phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' An azimuthal instability develops across the liquid column, which may be responsible for the perturbations at the liquid column base.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The cause of this has been reported to be Centrifugal Rayleigh- Taylor (CRT) instability (Behzad et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2015)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' These instabilities grow along the liquid column axis along the internal boundary layer, resulting in the thickening of liquid column edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Data is extracted on two planes along the liquid column at locations just before and after the bifurcation – C1 and C2, respectively, as shown in Figure 20(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Figure 20(b) shows the cross-stream (Z) component of vorticity and pressure on C1 planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Apart from the shear layer vorticity, the highlighted region indicates the presence of vorticity within the liquid, along the two peripheral edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The vorticity is very weak compared to the boundary layer (for both air and liquid).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Similarly, the pressure contour reaches a very low value at the center of these areas, as seen in Figure 20(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It shows the continuous movement of liquid into its edges, which stretches the central region of the circular liquid core cross-section into a thin sheet-like structure while at the same time thickening these liquid column edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Figure 20(c) presents the vorticity and pressure contours just after the detachment of the streamers on the C2 plane, where these vortices on the liquid column periphery are absent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The separated boundary layer of the liquid column and bifurcations now passes through their gap (highlighted green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Also, the minimum pressure values are present in the gas phase only, outside the liquid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' As described in the previous section, the two factors play a significant role in the deformation of the cross-section of the liquid column – the internal boundary layer and the pressure difference driving the flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The transfer of liquid to the periphery by the internal boundary layer in the absence of a return flow to the middle is majorly responsible for the thinning of the liquid column at the middle and the thickening of the edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Another important factor is the flow orientation of CRV, as shown by the velocity vectors and white- colored streamlines in Figure 20(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A portion of the flow enters the wake of the liquid column from the bottom and gets drawn up by the CRV, and without reaching the bottom again, it exits the CRV from the sides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This sideward movement of air on either side of the liquid column pushes against the thick edges of the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This is also evident on the C1 plane in Figure 20(b), labeled as CRV- exit, the thick opposite vorticity witnessed at the peripheries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 40 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 20 (a) The location of planes – C1 and C2 on the liquid column just below and above the point of bifurcation, (b) Plane C1 – Left column: Vorticity Z contours show weak vorticity within the liquid at edges (at the tip of thick green arrows and beside the internal boundary layer), whereas the black smaller arrows show the direction of flow along the edges;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Right column: The pressure plot showing a drop at transverse liquid column edges, (c) Plane C2 – Left column: Vorticity Z contours after bifurcation with negligible vorticity within it;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Right column: Low-pressure area vanishes from the liquid edges just after the bifurcation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (d) The streamlines with stream vectors show the role of fluid exit from CRV in causing bifurcation/streamer formations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=" (a) C 374000 C 50000 373000 CRV Exit 口 371000 50000 37000 s0+a0't 369000 LOW Pressure CRV Exit (b) (c) 1." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0e+05 374000 373000 50000 372000 0 50000 370000 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0e+05 369000 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='0+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8 (d) (e) (f)41 Figure 20(c) shows changes in the vorticity just after separation (on the C2 plane).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The streamer is found to follow this fluid exiting the CRV, thus, following a different trajectory than a liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Hence, it may be said that both the factors need to be present for a bifurcation to happen – moderate but sufficient level of shear flow/boundary layer to thicken the liquid column edges and the typical flow of CRV to separate and pull it along, away from the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Also, Figure 15 shows two similar ligament-type structures alongside the bags of the liquid column at the top.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This essentially re-thickens the edges because of the boundary flow within the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Hence, this phenomenon cannot occur because of shear instability but the internal boundary layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The bifurcation formed is found to be thicker for low penetration cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The bifurcation starts vanishing as the momentum flux ratio (q) increases (cases 1 to 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This is because the primary break-up mode shifts towards pure shear mode as the momentum flux ratio or crossflow Weber number increases, enhancing the surface stripping process with crossflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In cases 4, 9, and 10, where the momentum flux ratio is high, we have observed multiple streamer formations in which the liquid jet column is split into multiple(four) membranes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The bifurcation formed is very thin and can be considered almost nil in these cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Basic figure of case 5 with We=150 and q=10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2 Shear Regime The LJICF shows a shear-dominated breakup at a high Weber number but a lower momentum flux ratio in Figure 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Case 5 out of the two high We cases is chosen for the study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The q value remains the same as the previously analyzed case 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Here, the flow feature behind the LJICF and the instability at the edges are discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (a) Flow behind the liquid column The flow feature behind the liquid jet column for We=150 (Figure 21) is similar to the previous case with We=60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The pressure contour (Figure 22(a)) is similar to the low We case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In this case, only a 42 single recirculation zone is visible, as shown by ‘yellow’ colored streamlines in Figure 22(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The saturation point of the leeward side of liquid column S2 lies in the region where the complete breakup of the liquid column takes place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Similarly, the liquid shear at the edges vanishes downstream of point S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The shear breakup will be covered below in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The two opposite rotating vortex pairs (referred to as SBV in the previous section) are also present, as shown in Figure 22(c), albeit their center positions shift one behind the other, and one of them is weaker than the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In Figure 22(c), the red streamlines pass through the thin liquid sheets as it tears apart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The liquid sheet breakup is delayed on the side of the weaker ‘green’ colored vortex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Hence, these vortices play an essential role in the breakup of thin liquid sheets present on both sides of the thicker liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' These liquid sheets break up without forming a bag-type hollow structure;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' hence these vortices’ name ‘sheet breakup vortex’ (SBV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (a) Pressure plot with stagnation point S1, (b) The mean flow on mid-plane showing same flow as the first case with leeward stagnation point S2, (c) The two counter-rotating SBVs for case 5 (q = 10, We = 150).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (b) Growth of instability and Streamers The two different disturbances are apparent here – one at the end liquid column and the other along the edge of the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The density contours at the middle plane (XY), bisecting through the liquid column, were analyzed for the first type of disturbance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It is not further analyzed here since the breakup happens just after the inception of the not-so-prominent first or second wave or even before that.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Instead, a more dominant shear breakup is focused on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 394000 392000 390000 388000 386000 383623 (a) (b) (c)43 As shown in Figure 23, the two different wavelength waves appear on the edges of the liquid jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The waves on the upper side are almost double the wavelength at the bottom of the liquid column, increasing along the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Another aspect is the formation of ligaments and subsequent thick droplets in the place of bifurcation/streamer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The region of a larger wavelength lies just above this bifurcation point ‘B’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Shear instability waves at liquid-core edges with different wavelengths at the top and bottom of point B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2008) correlation from their experiment shows the dependence of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='33 G N 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='3W D e \uf06c − = which predicts almost four times the wavelength observed near the bottom and almost double the wavelength above point B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The different behavior witnessed in the two regions may be due to the change in the size of the liquid column faced by the incoming air;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' that is, the bottom part of the liquid column is analogous to the circular cylinder of size same as the jet diameter whereas, the upper part (above point B) is similar to a shell of size larger than jet diameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Considering the disturbances in the lower portion, there is a similarity with the instabilities in separating shear flow over the cylinder with Re 1000 \uf03e .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' At a high Reynolds number case like this, two kinds of 3D instabilities exist – a) streamwise vortices of separating shear layer and b) streamwise vortices of the wake.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In the present study, the instabilities of separating the shear layer are more critical in assessing its effect on the liquid edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Based on the results of Bernal and Roshko (1987), Williamson (1996) proposed the following relation for the wavelength of streamwise vortices of separating shear layer: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 25 S N L e D R \uf06c − \uf0bb .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (39) The Re corresponds to the Reynolds number of airflow around the circular liquid column, which behaves like a cylinder of diameter (DN) 8910 \uf0bb .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The prediction is near the wavelength obtained from simulation for the lower part of the liquid jet column, as shown in Table 9 for both case 5 and case 6 with the same We, though there is some deviation for case 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It also shows that the prediction is independent of the momentum flux ratio;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' it does not depend on the liquid jet velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Similarly, the B Large Wavelength 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Small Wavelength44 study of instability in the upper part of the jet column can be part of future work concerning the flow structures over hollow shells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Correlations / N D \uf06c Case 5 (q=10, We=150) Case 6 (q=19, We=150) Case 9 (q=77, We=60) Williamson correlation (1996)** 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='26 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='26 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='33 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' correlation(2008) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='82 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='82 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='11 Present Simulation 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='21 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='26 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='21 Table 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Comparison of wavelength observed in this study with the correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' **Williamson correlation about shear layer streamwise instability is valid, assuming that the same instability triggers the shear instability in liquid edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='3 Surface Breakup Regime Case 9 with the same Weber number 60 as case 8 but higher momentum flux ratio of 77 is chosen in this regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (a) Pressure plot with longer and extended high-pressure zone on the windward side of LJICF, (b) Streamlines showing two recirculation regions separated with a stagnation point S2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The two horizontal planes are the location for the streamlined contours shown in Figure 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (a) Flow field behind the liquid jet column In this case, the flow is quite distinct from the low momentum flux ratio cases, as shown in Figure 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In Figure 24(a), there is an extended high-pressure region on the windward side of the liquid column with a higher value of the maximum pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The existence of high pressure for most of the windward side of the liquid owes to deeper penetration by this liquid jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The streamlines on a plane shows two recirculation zones (‘yellow’ colored vortex as CRV and ‘pink’ colored vortex lies above CRV) of opposite rotations in Figure 24(b), different from previous cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' From this figure, the saturation point can easily be found on the leeward side of the liquid jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It is the same as the observation made by Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2016) in their case with the momentum flux ratio of 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2, which was kept constant for all their 422093 420000 418000 Z/D = 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 415644.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Z/D = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6 (a) (b)45 three simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The variation of the Weber number was only employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Hence the condition of the present case nearly matches the conditions used by Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Figure 25 represents the instantaneous streamlines on horizontal planes at two planes – Z/DN= 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6 (Figures 25(a) – 25(f)) and 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 (Figures 25(g) – 25(l)) against the density contour, which helps to locate flow features concerning the cross-section of the liquid column (green colored).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The location of planes is chosen appropriately, considering that it lies near the point of bifurcations (or streamer formations), as shown in Figure 24(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This allows us to observe the effect of bifurcated streamers on the flowfield, if any.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' First, the streamlines at plane Z/DN =9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6 depict periodic vortex shedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This resembles the flow over a cylinder or, more appropriately, over the semi-spherical shell (a shape similar to the liquid jet-core cross-section in Figures 25(a)-25(f)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' One of the vortices in Figure 25(c) (shown by red pointer) undergoes vortex tearing in Figure 25(d), during which one of them remains near the jet column while the other convects downstream with the flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Second, Figures 25(g)-25(l), on the right side column, captures the bifurcation of the second streamer as shown by the green-colored stretched liquid column at Z/DN =17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 and the vortex shedding near its location on the leeward side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The vortices at Z/DN =17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 (right) are stronger and bigger than that observed at Z/DN =9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6 (left), and thus, they are present for a longer downstream distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Another feature is the vortex pairing, occurring downstream of the liquid column in Figures 25(j) – VP-1 and VP-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The two vortices prior to a pairing process are shown in Figure 25(h)-(i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' After completion of the pairing process in Figure 25(j), they give rise to a stronger vortex, as observed in Figure 25(k).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The vortex pairing on the leeward side seems related to the liquid core and its bifurcated streamer formations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The streamers’ formation results in the gap between the central liquid core and streamers, affecting the vortex shedding downstream.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It may be said that the different vortices shed in the bifurcation process interacts with each other leading to the vortex pairing (as noticed in Figure 25(h)- (j)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It further complicates the flow concerning the interaction between liquid core breakup into streamers and the airflow development behind it, both dependent on each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Since the crossflow air velocity remains the same as for the low momentum flux ratio case in the bag breakup regime (Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1), the vortices witnessed (SRVs) resulting from vortex shedding are similar to vortices on plane Z/DN = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' However, the strength of these vortices will vary for both these cases because of the difference in the trajectory of the liquid jet, size, and strength of CRV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Since the SRVs are found to move along the KH waves in case 8, it may be an interesting future study to confirm if it is always true.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 46 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Left panel: Streamlines show vortex shedding along with a vortex tearing phenomena on plane Z = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Right panel: Streamlines show vortex shedding and (two) pairing processes on plane Z = 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' z / D = 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6 z /D = 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5 (a) (g) 40Densito so0 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='011 200 (b) (h) 40Denst00 s00 102 400ens600 800 (c) (i) (d) (!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=') VP- 1 VT VP- 2 400 6 008 (e) () After VP- 1 After VP - 2 40Densi0o 800 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='041200 (f) (1) VT - Vortex Tearing VP - Vortex Pairing47 (b) Instability on the liquid column and surface edges This case shows both the instabilities of – the liquid column and its edges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The Rayleigh-Taylor instability is found to be dominant in the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The waves are symmetric until the breakup, and the typical Kelvin-Helmholtz roll-ups are absent, as shown in Figure 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The wavelength can be predicted by using C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=" 's (2008) assumption of cylinder drag as acceleration for Rayleigh Taylor instability in this case: 2 3 D,cylinder G C 1 10Re− \uf0bb + when 5 G 1 Re 2 10 \uf03c \uf03c \uf0b4 ." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (40) and, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='26 G N 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='3W D e \uf06c − = .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (41) Here D C is the coefficient of drag for the cylinder and G Re is the air Reynolds number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The wavelength observed in the present case is compared with the LSA result by Chandrasekhar (1961) and correlation by C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2008) in Table 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This case with high momentum flux ratio further confirms the claim that as the momentum flux ratio increases, the chances of Rayleigh-Taylor dominated instability is higher.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In the case of high momentum flux ratio and moderate (or low) Weber number, the liquid momentum is higher than gas/air momentum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In other words, the injected liquid/water mass flow rate is also high, unlike case 5, where the liquid jet bends acutely due to early flattening.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It leads to deeper penetration of liquid jet with almost vertical liquid jet through the crossflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The portion of the liquid column that faces directly into the incoming crossflow air has an extended high-pressure region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' At the same time, the air/gas cannot generate enough shear along the liquid flow direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Hence, the effect of high pressure on the windward side starts to have its outcome in Rayleigh-Taylor instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Correlations/LSA / N D \uf06c Rayleigh-Taylor - Chandrasekhar 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='73 C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' correlation (2008) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='83 Present Simulation 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='70 Table 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Comparison of wavelength observed in the present case and the predictions from LSA and correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 48 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (a) Density contour at mid-section of LJICF show Rayleigh-Taylor instability, (b) Shear instability for We = 10 and high momentum flux ratio (q) = 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It is, thus, proposed here that the momentum flux ratio plays a vital role in deciding the type of instability growth on the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The momentum flux ratio is lower, higher the probability of developing KH type of instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Since the present study primarily focuses on the rigorous validation of compressible solver against varying parameters, further detailed analysis at varying q and We is beyond the scope of this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The wavelength of surface waves along the transverse edges of the liquid column has been calculated using the assumption discussed in the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It is proposed that the same disturbance causes this instability of a liquid column as that of the air shear layer around a cylinder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 39 is used for the wavelength calculations in Table 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Using this assumption, the Williamson shear layer correlation predicts / N D \uf06c equals 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='33, which is closer to the observed (non-dimensionalized) wavelength of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='26 from the simulations compared to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='18 by C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2008)’s correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='Ng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2008) correlation may be based on the wavelength measurements downstream of the liquid column for cases with much higher q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' However, the empirical correlation by Williamson is only valid for the region near the injection nozzle where the cross-section of the liquid column is nearly circular.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (c) Bifurcations The bifurcation increased to four but thinner and a little vaguely visible (compared to case 8) at a higher momentum flux ratio, as shown in Figure 24(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The parameters We (equal to 60) and q (equal to 77) of this case are similar to case 3 (We = 68, q = 64) of Sedarsky et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2010), where they also observed multiple streamers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This may be owed to the two circulation zones witnessed in the mean flow behind the liquid core (Figure 27).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Following the same explanation of Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1(c), the CRV exit carries along and diverts the first bifurcation/streamer liquid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Similar to the previous case, the fluid exit also happens from the sides of these recirculation zones formed on the leeward side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' As discussed (gw/ax) 1028.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 800 Density 600 400 200 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='038 Shear Instability at edges (a) (b)49 earlier, the flow is highly complex, with a mix of vortex shedding and recirculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The vortex shedding induces the sideward flow of air near the leeward side of the liquid column, which in turn pushes against and separates the thick transverse edge from the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Hence, in this case, the two crucial factors are the thickening of the edge by the internal boundary (shear) layer and the separation of streamers from the central liquid column by the CRV/recirculation flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Streamlines show mean flow on plane Z/D=17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The clockwise rotation of the bottom vortex and anti- clockwise of the upper vortex show the outward movement of gas/air near the leeward side of the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' This sideward movement is responsible for streamer formation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=" Conclusion This work numerically simulates a liquid jet's primary and secondary atomization in crossflow using a compressible Volume of Fluid (VOF) - Lagrangian Particle Tracking (LPT) coupled solver implemented in OpenFOAM." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The iso-Advector scheme by Roenby et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2016) is used to capture the droplets and sub-grid fluid distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In contrast, the coupling algorithm by Heinrich and Schwarze (2020) provides flexibility in demarcating the droplets and converting them into Lagrangian particles under satisfying conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The complete framework is validated against the comprehensive experimental data of Amighi (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The numerically predicted data for liquid jet penetration, droplet size characteristics D32, and STD agrees with experimental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The effect of various parameters, namely liquid jet velocity, crossflow velocity, and pressure, on the droplet size characteristics also predicts similar trends as in the experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The comparison of liquid jet penetration with empirical correlations shows that the predicted trajectory is closest to Elshamy’s correlation, and correlations based on momentum flux ratio alone are found to overpredict by a large margin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In line with the previous literature, the comparison of the stream-wise location of the breakup for each case is constant at 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2DN ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2DN, independent of the momentum flux ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Few cases are analyzed in different breakup regimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The momentum flux ratio is a governing factor for the instability that dominates the liquid column flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The Kelvin-Helmholtz type instability causes CRV Exit Density (kg/m) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='041 200 400 600 800 1027.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='50 the liquid column to break up at a lower momentum flux ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The crossflow air momentum forces the liquid column to bend to sharper angles, producing a higher shear force along the liquid flow direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Based on the observations of a sheet-like cross-section in the latter portion of the liquid column, the inviscid and viscous linear stability analysis results are computed considering the thickness of the sheet-like liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It is found that the sheet Weber number is high enough so that only the short wavelength instability dominates the breakup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The results are compared to the wavelength detected from the simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' On the other hand, the Rayleigh-Taylor instability is dominant for the high momentum flux ratio case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It is inferred that high momentum flux ratio causes high penetration, which is a reason for the extended high-pressure zone on the windward side of the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The increased air pressure and lesser shear results in the growth of Rayleigh-Taylor-type instability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The wavelength from the simulations closely matches with linear stability analysis and correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The shear instability along the transverse edges of the liquid column is well captured in the simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It is hypothesized that the instability of the liquid column at the edges is caused due to the instability of the air shear layer passing by around the liquid column.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=" The wavelength measured at the bottom part of the liquid column from simulations was compared to Williamson's empirical correlation of shear layer instability for a flow over the cylinder (1996)." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' It is closer to the simulated values than the correlation results from the past literature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The bifurcation or streamer generation, evident at lower to moderate values of momentum flux ratio and Weber number, is another crucial aspect that has been observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=" These bifurcations are caused by the counter-rotating vortex's three-dimensional structure and internal boundary layer shear at the liquid jet's windward side." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The shear breakup at the edges causes the streamers to be mostly non-existent or thin at a higher momentum flux ratio or Weber number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' To summarize, LJICF is a classical problem that involves complex flow physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The present work attempts to develop and access an accurate, robust platform (hybrid compressible VOF-LPT framework) while investigating the break-up phenomenon in LJICF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The other aspects, like break-up regimes and details of instability behavior, are ongoing work in the same group and beyond the scope of the present study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Acknowledgments Financial support for this research is provided through the Department of Science and Technology (DST) under National Supercomputing Mission (NSM), India.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=" We acknowledge the National Supercomputing Mission (NSM) for providing 51 computing resources of 'PARAM Sanganak' at IIT Kanpur, which is implemented by C-DAC and supported by the Ministry of Electronics and Information Technology (MeitY) and Department of Science and Technology (DST), Government of India." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Also, we would like to thank the computer center (www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='iitk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='in/cc) at IIT Kanpur for providing the resources to carry out this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' References Amighi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Ashgriz, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Global droplet size in liquid jet in a high-temperature and high-pressure crossflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' AIAA Journal, 57(3), 1260-1274.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Amighi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Ashgriz, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Trajectory of a liquid jet in a high temperature and pressure gaseous cross flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Journal of Engineering for Gas Turbines and Power, 141(6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Amighi, Amirreza.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2015) Liquid jets in crossflow at elevated temperatures and pressures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' University of Toronto, Canada.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' ANSYS, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2016) ANSYS Fluent User’s Guide, Release 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Arienti, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Soteriou, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Eckett, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Sussman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Jensen, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Coupled level-set/volume-of-fluid method for simulation of injector atomization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Journal of propulsion and power, 29(1), 147-157.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Arlov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Revstedt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Fuchs, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A different approach of handling large bubbles in a square sectioned bubble column combining large eddy simulation with lagrangian particle tracking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In Proceedings of the 6th International Conference on Multiphase Flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Bhandarkar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Manna, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Chakraborty, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Assessment of droplet break-up models in high-speed cross- flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Atomization and Sprays, 27(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Becker, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Hassa, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Break-up and atomization of a kerosene jet in crossflow at elevated pressure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Atomization and Sprays, 12(1-3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Behzad, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Ashgriz, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Mashayek, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Azimuthal shear instability of a liquid jet injected into a gaseous cross- flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Journal of Fluid Mechanics, 767, 146-172.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Brackbill, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Kothe, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Zemach, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A continuum method for modeling surface tension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Journal of computational physics, 100(2), 335-354.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Chai, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Mahesh, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Dynamic-equation model for large-eddy simulation of compressible flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Journal of Fluid Mechanics, 699, 385-413.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Chen, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Smith, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Schommer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Nejad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1993, January).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Multi-zone behavior of transverse liquid jet in high- speed flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In 31st Aerospace Sciences Meeting (p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 453).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Eslamian, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Amighi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Ashgriz, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Atomization of liquid jet in high-pressure and high-temperature subsonic crossflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' AIAA journal, 52(7), 1374-1385.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fric, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Roshko, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Vortical structure in the wake of a transverse jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Journal of Fluid Mechanics, 279, 1-47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 52 Fuster, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Bagué, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Boeck, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Le Moyne, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Leboissetier, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Popinet, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Zaleski, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Simulation of primary atomization with an octree adaptive mesh refinement and VOF method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' International Journal of Multiphase Flow, 35(6), 550-565.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Frössling, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1938).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The Evaporating of Falling Drops (in German).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Gerlands Beitrage zur Geophysik, 52:170–216.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Gopala, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Zhang, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Bibik, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Lubarsky, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Zinn, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Liquid fuel jet in crossflow-trajectory correlations based on the column break-up point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 214).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Germano, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Piomelli, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Moin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Cabot, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1991).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A dynamic subgrid‐scale eddy viscosity model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Physics of Fluids A: Fluid Dynamics, 3(7), 1760-1765.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Grosshans, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Szász, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Fuchs, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Development of an efficient statistical volumes of fluid–Lagrangian particle tracking coupling method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' International Journal for Numerical Methods in Fluids, 74(12), 898-918.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Heinrich, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Schwarze, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 3D-coupling of Volume-of-Fluid and Lagrangian particle tracking for spray atomization simulation in OpenFOAM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' SoftwareX, 11, 100483.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Herrmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A parallel Eulerian interface tracking/Lagrangian point particle multi-scale coupling procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Journal of computational physics, 229(3), 745-759.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Hirt, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Nichols, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1981).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Volume of fluid (VOF) method for the dynamics of free boundaries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Journal of computational physics, 39(1), 201-225.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Hoyas, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Gil, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Margot, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Khuong-Anh, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Ravet, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Evaluation of the Eulerian–Lagrangian Spray Atomization (ELSA) model in spray simulations: 2D cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Mathematical and Computer Modelling, 57(7-8), 1686-1693.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Huang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Li, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A new dynamic one‐equation subgrid‐scale model for large eddy simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' International Journal for Numerical Methods in Engineering, 81(7), 835-865.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ilak, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Schlatter, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Bagheri, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Henningson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Bifurcation and stability analysis of a jet in cross-flow: onset of global instability at a low velocity ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Journal of Fluid Mechanics, 696, 94-121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ingebo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', and Foster, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1957).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Drop-size distribution for cross current breakup of liquid jets in airstreams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' NACA-TN-4087.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ingebo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1967) Penetration of drops into high-velocity airstreams.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' National Aeronautics and Space Administration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Kim, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Menon, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A new dynamic one-equation subgrid-scale model for large eddy simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In 33rd Aerospace Sciences Meeting and Exhibit (p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 356).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Aalburg, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Diez, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Faeth, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Sallam, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Primary break-up of turbulent round liquid jets in uniform crossflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' AIAA journal, 45(8), 1907-1916.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Lewis, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1950).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The instability of liquid surfaces when accelerated in a direction perpendicular to their planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Proceedings of the Royal Society of London.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Series A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Mathematical and Physical Sciences 202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1068: 81-96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 53 Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Soteriou, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' High fidelity simulation and analysis of liquid jet atomization in a gaseous crossflow at intermediate Weber numbers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Physics of Fluids 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='8: 082101.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ling, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Zaleski, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Scardovelli, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Multiscale simulation of atomization with small droplets represented by a Lagrangian point-particle model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' International Journal of Multiphase Flow, 76, 122-143.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Lubarsky, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Reichel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Zinn, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & McAmis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Spray in crossflow: Dependence on Weber number.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Journal of Engineering for Gas Turbines and Power, 132(2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Madabhushi, Ravi K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' On the breakup regime map of liquid jet in crossflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' ILASS Americas, 19th Annual Conference on Liquid Atomization and Spray Systems, Toronto, Canada.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ménard, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Tanguy, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Berlemont, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Coupling level set/VOF/ghost fluid methods: Validation and application to 3D simulation of the primary break-up of a liquid jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' International Journal of Multiphase Flow, 33(5), 510-524 Mencinger, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Žun, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A PLIC–VOF method suited for adaptive moving grids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Journal of Computational Physics, 230(3), 644-663.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Miller, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Jasak, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Boger, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Paterson, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Nedungadi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A pressure-based, compressible, two-phase flow finite volume method for underwater explosions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Computers & Fluids, 87, 132-143.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Mirjalili, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A Novel Diffuse Interface Method for Two-phase Flows and Application in Simulation of Micro- bubble Entrainment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Stanford University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Herrmann, A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids, Journal of Computational Physics, 227 (4) (2008) 2674–2706 Ng, C-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Sankarakrishnan, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Sallam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Bag breakup of nonturbulent liquid jets in crossflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' International Journal of Multiphase Flow 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='3: 241-259.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Noh, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Woodward, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1976).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' SLIC (simple line interface calculation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In Proceedings of the fifth international conference on numerical methods in fluid dynamics June 28–July 2, 1976 Twente University, Enschede (pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 330-340).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Springer, Berlin, Heidelberg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=" O'Rourke, P." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Amsden, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The TAB method for numerical calculation of spray droplet break-up (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 872089).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' SAE technical paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Olsson, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A description of isoadvector-a numerical method for improved surface sharpness in two-phase flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Proceedings of CFD with OpenSource Software, Edited by Nilsson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Olyaei, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Kebriaee, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Experimental study of liquid jets injected in crossflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Experimental Thermal and Fluid Science, 115, 110049.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 54 Parmar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Haselbacher, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Balachandar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Generalized Basset-Boussinesq-Oseen equation for unsteady forces on a sphere in a compressible flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Physical review letters, 106(8), 084501.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Popinet, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Journal of Computational Physics, Elsevier, 2003, 190 (2), pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='572-600.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ragucci, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Bellofiore, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Cavaliere, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Break-up and breakdown of bent kerosene jets in gas turbine conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Proceedings of the Combustion Institute, 31(2), 2231-2238.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ranz, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Marshall, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=': Evaporation from drops, part I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Chem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Eng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Prog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 48, 141–146 (1952) Reitz, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Modeling atomization processes in high-pressure vaporizing sprays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Atomisation Spray Technology, 3(4), 309-337.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Roenby, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Bredmose, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Jasak, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A computational method for sharp interface advection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Royal Society open science, 3(11), 160405.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Saeedipour, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Pirker, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Bozorgi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Schneiderbauer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' An Eulerian–Lagrangian hybrid model for the coarse- grid simulation of turbulent liquid jet break-up.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' International Journal of Multiphase Flow, 82, 17-26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Sallam, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Ng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Sankarakrishnan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Aalburg, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Break-up of turbulent and non-turbulent liquid jets in gaseous crossflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In 44th AIAA Aerospace Sciences Meeting and Exhibit (p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 1517).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Sallam, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Aalburg, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Faeth, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Break-up of round nonturbulent liquid jets in gaseous crossflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' AIAA journal, 42(12), 2529-2540.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Schiller, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1933).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A drag coefficient correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Zeit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ver.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Deutsch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', 77, 318-320.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Schmidt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Rutland, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2000) A new droplet collision algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Journal of Computational Physics 164.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1: 62-80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Sedarsky, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Paciaroni, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Berrocal, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Model validation image data for break-up of a liquid jet in crossflow: part I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Exp Fluids 49, 391–408 (2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Senecal, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Schmidt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Nouar, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Rutland, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Reitz, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Corradini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Modeling high-speed viscous liquid sheet atomization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' International Journal of Multiphase Flow 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6-7: 1073-1097.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Squire, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1953).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Investigation of the instability of a moving liquid film.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' British Journal of Applied Physics 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6: 167.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Stenzler, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Santavicca, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Lee, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Penetration of liquid jets in a cross-flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Atomization and Sprays, 16(8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Sussman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Puckett, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Journal of computational physics, 162(2), 301-337.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Tambe, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Jeng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Mongia, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Hsiao, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2005, January).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Liquid jets in subsonic crossflow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In 43rd AIAA Aerospace Sciences Meeting and Exhibit (p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 731).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Tambe, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Elshamy, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Jeng, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Spray properties of liquid jets injected transversely into a shear layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit (p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 5695).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 55 Tanner, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A cascade atomization and drop break-up model for the simulation of high-pressure liquid jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' SAE transactions, 1352-1366.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Taskiran, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Ergeneman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Trajectory based droplet collision model for spray modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Fuel, 115, 896- 900.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Taylor, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1950).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' The instability of liquid surfaces when accelerated in a direction perpendicular to their planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Proceedings of the Royal Society of London.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Series A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Mathematical and Physical Sciences 201.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1065: 192-196.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Tryggvason, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Bunner, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Esmaeeli, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Juric, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Al-Rawahi, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Tauber, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' & Jan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A front-tracking method for the computations of multiphase flow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Journal of computational physics, 169(2), 708-759.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Vallier, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Revstedt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Nilsson, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Procedure for the break-up of cavitation sheet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' In 4-th International Meeting on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, October, 26-28, 2011, Belgrade, Serbia (pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' 77-85).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Weller, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Tabor, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Jasak, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' & Fureby, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', (1998) A tensorial approach to computational continuum mechanics using object-oriented techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Computers in physics 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='6: 620-631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Wen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Hu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Nakanishi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Kurose, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Atomization and evaporation process of liquid fuel jets in crossflows: A numerical study using Eulerian/Lagrangian method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' International Journal of Multiphase Flow, 129, 103331.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Williamson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1996).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Vortex dynamics in the cylinder wake.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Annual review of fluid mechanics 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content='1: 477-539.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Wu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Kirkendall, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Fuller, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Nejad, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Break-up processes of liquid jets in subsonic crossflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Journal of Propulsion and power, 13(1), 64-73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Yu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Goldsworthy, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Ghiji, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Brandner, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Garaniya, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A parallel volume of fluid-Lagrangian Parcel Tracking coupling procedure for diesel spray modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Computers & Fluids, 150, 46-65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Yoo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Han, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Hong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Sung, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' A large eddy simulation of the break-up and atomization of a liquid jet into a cross turbulent flow at various spray conditions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' International Journal of Heat and Mass Transfer, 112, 97-112.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Zuo, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', Gomes, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=', & Rutland, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' (2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' Modelling superheated fuel sprays and vaporization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} +page_content=' International Journal of Engine Research, 1(4), 321-336.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/d9E1T4oBgHgl3EQfLgNb/content/2301.02977v1.pdf'} diff --git a/ddAyT4oBgHgl3EQfjPi0/content/2301.00412v1.pdf b/ddAyT4oBgHgl3EQfjPi0/content/2301.00412v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ddf5b018084f8a39a8f68ca60c4d72262bf5c8d2 --- /dev/null +++ b/ddAyT4oBgHgl3EQfjPi0/content/2301.00412v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:38782c3fed7eec3204f64a5885ee63b3153f037a0be4a2eca165b454fea7712e +size 653322 diff --git a/ddAyT4oBgHgl3EQfjPi0/vector_store/index.faiss b/ddAyT4oBgHgl3EQfjPi0/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..b0ec96d30c370d84e19ed8b2da18b9600337029e --- /dev/null +++ b/ddAyT4oBgHgl3EQfjPi0/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cc633a934e2af567a59eae8be1f6d8d9650b6b4c5b2b9c06debceb2e9c46acc1 +size 4784173 diff --git a/ddAyT4oBgHgl3EQfjPi0/vector_store/index.pkl b/ddAyT4oBgHgl3EQfjPi0/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..7590461838a4439cef12a409c4a4eef15b1a0b93 --- /dev/null +++ b/ddAyT4oBgHgl3EQfjPi0/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:400a2f149fed4e5f33bfb0a8b287f229b33623ab2d9865251ec4ff83ae777e2b +size 165026 diff --git a/ddAzT4oBgHgl3EQfn_0r/vector_store/index.faiss b/ddAzT4oBgHgl3EQfn_0r/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..afe8fa4350010518e28d1499ae257990fe4cf7cb --- /dev/null +++ b/ddAzT4oBgHgl3EQfn_0r/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7562fc6b17bb9711c54885fb25864ba3eff7455bc264fe099321d5230480486a +size 2883629 diff --git a/eNE4T4oBgHgl3EQfpw2r/content/tmp_files/2301.05195v1.pdf.txt b/eNE4T4oBgHgl3EQfpw2r/content/tmp_files/2301.05195v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..9eefa02cfcb6ad5f482bad31b6500781e394ea4d --- /dev/null +++ b/eNE4T4oBgHgl3EQfpw2r/content/tmp_files/2301.05195v1.pdf.txt @@ -0,0 +1,1366 @@ +A numerical study of measurement-induced phase transitions in the +Sachdev-Ye-Kitaev model +Stav Haldar1, ∗ and Anthony J. Brady2, † +1Department of Physics & Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA +2Department of Electrical and Computer Engineering, +University of Arizona, Tucson, Arizona 85721, USA +(Dated: January 13, 2023) +Continuous monitoring of an otherwise closed quantum system has been found to lead to a +measurement-induced phase transition (MIPT) characterized by abrupt changes in the entangle- +ment or purity of the many-body quantum state. For an entanglement MIPT, entangling dynamics +compete with measurement dynamics, pushing the system either to a phase with extensive entangle- +ment or to a phase with low-level entanglement. For purification MIPTs, projective measurements +effectively cool and localize the system, inducing a transition from a mixed state to an uncorrelated +pure state. In this work, we numerically simulate monitored dynamics in the all-to-all Sachdev-Ye- +Kitaev (SYK) model for finite N. We witness both entanglement and purification MIPTs in the +steady-state. It is often said that there is an equivalence between entanglement and purification +MIPTs, however we provide numerical evidence to the contrary, implying that entanglement and +purification MIPTs are indeed two distinct phenomena. The reason for such a distinction is quite +simple: entanglement can revive after a completely projective measurement—if measurements do +not occur too often in time—but impurity cannot. +I. +INTRODUCTION +Quantum statistical mechanics accurately captures +most properties of many-body quantum systems at equi- +librium where, e.g., the system can be described by a +handful of macroscopic quantities, such as the temper- +ature, total particle number etc. +However, many as- +pects of quantum many-body systems out of equilib- +rium [1]—such as entanglement growth in closed quan- +tum systems [2–4]—require more care. Tools from quan- +tum information have been employed to better under- +stand, characterize, and even construct highly correlated +quantum many-body states (or quantum matter) in and +out of equilibrium [5–7]. +The dynamics of a closed quantum system out of equi- +librium is governed by a Hamiltonian that introduces +correlations (entanglement) between the system’s con- +stituents. Starting from an initially uncorrelated state, +the entanglement in the system evolves in time, eventu- +ally saturating to some finite value; in which case, the +steady-state is a many-body entangled state. If the in- +teractions are strong and the subsystems are highly con- +nected, then the growth of entanglement is fast com- +pared to all other time scales, and entanglement satu- +rates to an extensive value. Circumstances change when +we “open” the system and externally perturb it with in- +coherent probes (i.e., non-unitary perturbations), such as +coupling the system to a heat bath or measuring parts of +the system. +In this work, we focus on continuously probing a quan- +tum system with measurement devices that we have ac- +∗ hstav1@lsu.edu +† ajbrady4123@arizona.edu +cess to—a process called continuous monitoring. In par- +ticular, we assume that the internal dynamics of the sys- +tem are spontaneously interrupted by local projective +measurements characterized by a measurement strength +pm and a measurement rate Γm; see Fig. 1 for an illus- +tration. Such monitoring dynamics have been feverishly +studied in the past several years, primarily via brickwork +circuit models [8–15] (see also the recent reviews [16, 17] +and references therein) which intersperse discrete two- +body interactions with local projective measurements. +In brickwork circuit models [8–17], it has been shown +that a competition arises between the entanglement dy- +namics of the closed system, which drives the system into +a many-body entangled state, and the decoupling dynam- +ics induced by continuous monitoring, which drives the +system in an uncorrelated product state. This competi- +tion leads to different phases of matter and to a so-called +measurement induced phase transition (MIPT), depend- +ing on whether the internal entangling dynamics or the +measurement dynamics dominates the evolution. Similar +studies with (random) Hamiltonian evolution [18–24]— +which include random Brownian circuits (continuous- +time analogs of brickwork circuit models) [20, 21, 24] and +large N analytically solvable models of coupled clusters +of SYK chains +[19, 22]—have come to similar conclu- +sions. A numerical study of the effects of decoherence +on information scrambling and growth of entanglement +for several many body quantum Hamiltonians including +the SYK model was also performed in [25]. Recent ex- +periments regarding entanglement growth and MIPTs in +brickwork circuits with Noisy Intermediate-Scale Quan- +tum (NISQ [26]) devices have also been performed [27– +29]. +MIPTs come in two flavors—an entanglement MIPT +and a purification MIPT—which are often conflated into +the singular phenomenon of a MIPT, however we later +arXiv:2301.05195v1 [quant-ph] 12 Jan 2023 + +2 +Γm +Γm +Γegr +Ψt → P (⃗r)ΨtP (⃗r) +Tr(P (⃗r)Ψt) +FIG. 1. Projective measurements sporadically interrupt the +internal, unitary time evolution of a quantum system (here, +5 spins with all-to-all connectivity). A competition between +the measurement rate Γm and the entanglement growth rate +Γegr determines the entanglement dynamics of the system. +discuss how these two phenomena are in fact distinct. +An entanglement MIPT refers to the transition from a +quantum state with extensive entanglement (volume-law +phase) to a quantum state with sub-extensive entangle- +ment (area-law phase). +Whereas a purification MIPT +refers to the transition from a highly mixed quantum +state (mixed phase) to an uncorrelated pure state (pure +phase).I.1 For discrete brickwork circuit models [9–17], +the critical point marking a MIPT depends on the prob- +ability that a local measurement will occur as well as +the circuit depth prior to a measurement round [31]. +For physical systems evolving under a Hamiltonian [24], +the measurement strength and the rate of entanglement +growth in the closed system establishes a dynamical rate +that competes against the local measurement rate and +dictates which phase the system is in (as well as the cor- +responding critical points). +In this work, we numerically study entanglement and +purification MIPTs in the all-to-all SYK model [38–40] +with finite N, where N is the number of Majorana +fermions (here, N ranges from 10 to 20). We simulate +monitored dynamics and track the entanglement or pu- +rity of the resulting quantum trajectories through time. +We witness entanglement and purification MIPTs in the +steady-state and observe a clear distinction between the +two phenomena. +II. +ENTANGLEMENT GROWTH IN THE SYK +MODEL +The SYK model [38–40] is a strongly interacting model +for many-body quantum systems without any quasipar- +I.1 Another intriguing perspective on purification MIPTs comes +from the theory of quantum error correction [30–37], whereby +interprets the open quantum system as a quantum memory that +is robust to decoherence due to measurements. +ticle excitations. +Low energy equilibrium states and +dynamics of the system cannot be described in terms +of quasiparticle excitations, as is the case for standard +Fermi liquids, and even the ground state is an entangled +quantum many-body state. Such systems are important +from several different perspectives. +From the point of +view of condensed matter physics, such models provide a +window into the fascinating world of strange metals and +high temperature superconductors which are yet to be +fully understood [40]. +A feature that underlies many interesting aspects of +the SYK model (and other strongly interacting models +without quasiparticles) is the fast scrambling of informa- +tion. From a physical point of view, fast scrambling can +be understood as a faster-than-usual equilibration of the +systemII.1 after a local perturbation. This perspective is +also important for understanding entanglement dynam- +ics and effect of measurements on it. +Fast scramblers +such as the SYK system quickly regenerate their exten- +sive, steady-state entanglement after a short lived local +perturbation (like a projective measurement) occurs on +a few sites. +Consider N all-to-all interacting Majorana fermions, +where the each interaction term includes 4 sites. +The +coupling constants are site dependent random variables +with zero mean ⟨Jijkl⟩ = 0 and finite variance ⟨J 2 +ijkl⟩ = +6J2/N 3, where J defines the strength of the interactions. +Let χi be the second-quantized Majorana field operator +at the site i. The SYK Hamiltonian is then +HJ = +� +1≤i 24. Although techniques such as random matrix +models or approximate diagonalization methods like the +density matrix renormalization group allow the handling +of larger number of sites, they do not provide the full +spectrum of the Hamiltonian, which is important for the +dynamics of strongly interacting systems. +We change our basis from Majorana operators χ +to spin-1/2 Pauli operators {σx, σy, σz} for computa- +tional purposes. This is done by the standard Jordan- +Wigner transformation. +Since two Majoranas map to +one fermion, odd and even Majoranas are related to Pauli +string operators as +χ2i−1 = +1 +√ +2σx +1σx +2...σx +i−1σz +i , +(II.2) +χ2i = +1 +√ +2σx +1σx +2...σx +i−1σy +i . +(II.3) +II.1 As compared to a weakly interacting system with well defined +slow moving quasiparticles that do not collide often. Note equi- +libration times in Fermi liquids diverges for low temperatures. + +3 +0 +5 +10 +15 +20 +Jt/ +0.0 +0.2 +0.4 +0.6 +0.8 +� +shalf +� +J = 0.1 +J = 0.32 +J = 1 +J = 3.2 +J = 10 +FIG. 2. Entanglement entropy (ensemble averaged) in a SYK +chain with N = 16 Majoranas, as a function of time. The +coupling strength J = 1. The dynamics have been averaged +over 50 runs. +As was briefly mentioned above, the fast scrambling +behaviour of an all-to-all model like the SYK can be +described via entanglement dynamics. More specifically +let us start by looking at the rate at which entangle- +ment grows in the system under the action of the SYK +Hamiltonian and without any measurements. We mea- +sure the entanglement using half-chain entanglement en- +tropy. Consider the system of N/2 spin-1/2 particles (N +Majorana fermions) on a linear chain with a fermion on +each site. Also, consider partitioning the chain into two +halves A and B, such that log |A| = log |B| = N/4. We +start with a unentangled product state at t = 0. The ini- +tial state is an all-up state ΨAB(0) = |Ψ(0)⟩ ⟨Ψ(0)| where +|Ψ(0)⟩ = |1⟩1 |1⟩2 ... |1⟩N/2. Here, |1⟩ is the eigenstate of +σz with eigenvalue +1 (|0⟩ is the eigenstate with eigen- +value −1). The SYK Hamiltonian is then “switched-on” +such that the state at time t is +ΨAB(t; J ) = e−iHJ t/ℏΨAB(0)e+iHJ t/ℏ. +(II.4) +We have included the label J into the argument of the +state since ΨAB(t; J ) corresponds to a single realization +HJ . +The half-chain entanglement entropy of the state ΨAB +at time t is, +Shalf(t; J ) = − Tr(ΨA log ΨA) +(II.5) +where ΨA ≡ TrB(ΨAB(t; J )). We normalize the entropy +by the number of particles in the half-chain (N/4) and +define the half-chain entropy density shalf ≡ 4Shalf/N, +such that 0 ≤ shalf ≤ 1. Since J is a random variable, +we average over many Hamiltonian realizations HJ to +compute the ensemble averaged entropy at time t, +⟨shalf(t)⟩J ≡ +ˆ +dJ p(J )shalf(t; J ), +(II.6) +10-1 +100 +101 +J/ +0.1 +0.2 +0.3 +0.4 +0.5 +Γegr +N = 12 +N = 16 +N = 20 +FIG. 3. Average entanglement growth rate Γegr as a function +of J, for different values of N. Dynamics have been averaged +over 50 runs. +where p(J ) is a zero-mean Gaussian distribution for the +random coupling strength J . Due to the ensemble aver- +age and the nature of the distribution p(J ), the average +half-chain entropy depends only on the standard devia- +tion J. Figure 2 shows the evolution of the half-chain +entanglement entropy as a function of time for differ- +ent values of interaction strength J for N = 16 Majo- +rana fermions. For stronger interactions (higher J), en- +tanglement growth is faster, and the saturation value of +⟨shalf(t → ∞)⟩J ≈ .8 (less than 1 due to finite N) is ap- +proached more quickly. +MITPs arise due to a competition between internal +scrambling of the system (generated by the many-body +Hamiltonian HJ ) and the rate of measurements. It is +thus important to quantify how quickly many-body cor- +relations build up within the system, which we quantify +by a so-called entanglement growth rate (EGR). We ex- +plicitly define the EGR as the rate of change of entan- +glement starting from a product state in the absence of +measurements, +EGR(t, J) ≡ d ⟨shalf(t)⟩J +dt +. +(II.7) +The EGR is a function of time, as is clear from Figure 2. +For instance, EGR is larger for small times (near t = 0) +and slowly falls to 0 as steady state is reached. Thus in +order to quantify the EGR in a time-independent way, +we define a time average EGR, +Γegr ≡ 1 +∆t +ˆ +∆t +dt EGR(t, J). +(II.8) +The time average is taken over a period ∆t = t3/4 − +t1/4, where t3/4 and t1/4 are implicitly defined by the +following relations: +shalf(t1/4) ≡ ⟨shalf(∞)⟩J /4 and +shalf(t3/4) ≡ 3 ⟨shalf(∞)⟩J /4. Here, ⟨shalf(∞)⟩J is the +saturation value of the half-chain entanglement entropy; +e.g., ⟨shalf(∞)⟩J ≈ .8 for N = 16 and for all values of J +(see Fig. 2). + +4 +In Fig. 3, we plot Γegr versus the coupling strength +J for different values of N. The EGR grows monoton- +ically (and non-linearly) with the coupling strength J +but is nearly independent of N. The N independence is +owed to the normalization in the Hamiltonian [see dis- +cussion surrounding Eqn. (II.1)]. Note that the coupling +strength J sets an effective time-scale for the interactions +whereas Γegr sets an effective time-scale for the growth of +many-body correlations which develop at a slower rate. +III. +MEASUREMENT DYNAMICS +We give a description of the monitored dynamics of the +SYK system. The measurements are done in the σz basis +at each site. Further, the measurements are independent +Markov processes in the sense that the probability that +a measurement takes place at a particular site and at a +particular time is independent of the measurements on +any other site or on the measurement history of the site +itself. +For every time step we make a binary choice of whether +to make a measurement or not. This decision is taken +through a Monte Carlo method. In other words, generate +a random number r between 0 and 1; if r ≤ rm, perform +a measurement, else do not. Here rm is determined by +the measurement rate Γm, +rm = Γmdt, +(III.1) +where dt is the simulation time step. The above equation +can also be regarded as the definition of the measurement +rate Γm. +If a measurement occurs in a time step, we randomize +over which and how many sites undergo measurements. +This is in concurrence with the assumption of perform- +ing independent and Markovian measurements at each +site. +The number of sites that get measured are cho- +sen assuming a Bernoulli distribution. Thus, given N/2 +sites (where N is the number of Majorana fermions), the +probability p(n) for n sites to be projectively measured +is +p(n) = +�N/2 +n +� +pn +m(1 − pm)N/2−n, +(III.2) +which can be considered the definition of the measure- +ment probability pm. We again take the standard Monte +Carlo approach, with bin sizes being determined by +Eqn. (III.2). The sites to be measured are also chosen +randomly with each site having an equal probability of +being measured. +The probabilities corresponding to all possible mea- +surements are calculated. Each site can be projected to +an eigenstate of σz +i via {P (ki) +i +}ki∈{0,1}, where P (ki) 2 +i += +P (ki) +i +and � +k P (ki) +i += Ii. +Here, i labels the site and +ki ∈ {0, 1} labels the eigenstates of σz +i . +Let n mea- +surements occur with outcomes listed in a measurement +record (bit string) ⃗r ≡ ⟨r1, r2, . . . , rn⟩ ∈ {0, 1}n, where +rℓ is the measurement outcome at the ℓth measured site. +We define the total projector corresponding to the mea- +surement record ⃗r as +P (⃗r) ≡ +n +� +i=1 +P (ri) +i +. +(III.3) +Consider the state Ψ(t1; J ) which has evolved under +the Hamiltonian HJ for time t1 per Eqn. (II.4) but has +not previously been measured. The state after the first +set of n local measurements with outcomes ⃗r1 is then, +Ψ(t1;⃗r1, J ) = P (⃗r1)Ψ(t1; J )P (⃗r1) +Tr +� +P (⃗r1)Ψ(t1; J ) +�. +(III.4) +The state Ψ(t1;⃗r1, J ) is a quantum trajectory associated +with the measurement result ⃗r1 at time t1 that is realized +with probability p(⃗r1|J ) ≡ Tr +� +P (⃗r1)Ψ(t1; J ) +� +; note that +this necessarily depends on the Hamiltonian realization +HJ as well. Following the first round of measurements, +the dynamics for times t > t1 depend on the previous +measurement record and are determined by interlacing +deterministic Hamiltonian evolution with further mea- +surements. If K rounds of measurements occur at times +t1, t2, . . . , tK (with average spacing ti+1−ti ≈ 1/Γm) with +outcomes ⃗r1,⃗r2, . . . ,⃗rK, then we describe the entire mea- +surement history via ⃗R ≡ �K +i=1 ⃗ri. We formally write +the associated probability for the measurement history +⃗R as p(⃗R|J ). +All things considered, the monitored dynamics of the +SYK chain has three primary parameters which dictate +global properties of the system: +1. The entanglement growth rate Γegr [Eqn. +(II.8)] +determines how fast correlations spread and how +fast the state returns to its unperturbed dynamics; +Γegr depends on the interaction strength J (Fig. 3). +2. The measurement rate Γm [Eqn. (III.1)] gives the +rate at which measurements (perturbations) occur. +3. The measurement probability pm [Eqn. +(III.2)] +conveys the strength of the measurements, in the +sense that higher values of pm leads to a larger +chunk of the SYK chain getting projected onto a +product state. +To gain more insight about the dynamics, note that we +can interpret Γm as the coupling rate between the SYK +chain and a ‘bath’ of measurement devices. Given the +likelihood of a measurement is pm, this results in an ef- +fective (average) decoherence rate Γ(eff) +m +≡ pmΓm due to +coupling to the bath. This interpretation is similar to +the Lindblad approach taken in Ref. [24] for analyzing +the open-system dynamics of a random Brownian circuit +for a chain of spin-1/2 particles. The authors of [24] in- +troduced a homodyne tuning parameter ϕ which governs +the non-unitary part of the evolution and thus the un- +raveling into particular quantum trajectories; here, the + +5 +measurement probability pm has a similar function (in +particular, pm ∼ cos2 ϕ). +To evaluate typical behavior, we generally focus on en- +semble averages of quantities, such as entropy and purity, +where the average is over the random couplings J and +measurement histories ⃗R. +Consider a particular quan- +tum trajectory Ψ(t; ⃗R, J ) at time t and a function of the +trajectory f(t; ⃗R, J ), which may be non-linear in Ψ. We +formally define the ensemble average of f as +⟨⟨f(t)⟩⟩ ≡ +� +⃗R +ˆ +dJ p +�⃗R|J +� +p(J )f +� +t; ⃗R, J +� +, +(III.5) +where the sum is over all possible measurement histories +⃗R [with history ⃗R occurring with probability p(⃗R|J )] and +the integral is over the random couplings J . We adopt +double-bracket notation throughout to convey that the +average is with respect to two random variables. Note +that the average depends on the coupling J, the mea- +surement probability pm, and the measurement rate Γm +as well as the initial state. +IV. +RESULTS +We present our numerical results of MIPTs for the +SYK chain with N = 16 Majorana fermions. Recall that +a MIPT refers to global changes of a system’s many- +body quantum state—such as many-body entanglement +or global purity of the system—induced by continuously +monitoring the system. An entanglement MIPT refers +to a transition from a state with extensive entanglement +entropy (in the volume-law phase) to a state with sub- +extensive entanglement entropy (in the area-law phase). +Whereas a purification MIPT—quantified by the purity +of the many-body state—refers to a transition from a +highly mixed state (in the mixed phase) to a pure state +(in the pure phase). As our numerical results here in- +dicate, entanglement MIPTs and purification MIPTs are +two distinct phenomena. In both cases however, a compe- +tition between internal scrambling dynamics and decou- +pling dynamics governs which phase the system relaxes +to. +Though there have been many measures to diagnose a +MIPT—such as the entropy, Renyi entropies, a reference +qubit etc. [9–15, 30–32, 34, 36]—we find the half-chain +entanglement entropy and the purity of the global state +sufficient to diagnose entanglement MIPTs and purifica- +tion MIPTs, respectively. We thus focus on these two +quantities throughout. +A. +Entanglement phase transition +We compute the half-chain entropy for a single Hamil- +tonian realization HJ and measurement history ⃗R at +time t starting from an initial pure state Ψ(0) with all +0 +20 +40 +60 +80 +100 +Jt/ +0.0 +0.2 +0.4 +0.6 +0.8 +�� +shalf +�� +N = 16, Γm/Γegr = 1 +pm = 0.1 +pm = 0.3 +pm = 0.5 +pm = 0.7 +pm = 0.9 +0 +20 +40 +60 +80 +100 +Jt/ +0.0 +0.2 +0.4 +0.6 +0.8 +�� +shalf +�� +N = 16, pm = 0.3 +Γm/Γegr = 0.2 +Γm/Γegr = 1 +Γm/Γegr = 2 +Γm/Γegr = 10 +FIG. 4. +Entanglement dynamics of the SYK chain. +(Top) +Half-chain entanglement entropy for different values of mea- +surement probabilities pm with a fixed measurement rate +Γm/Γegr = 1. (Bottom) Half-chain entanglement entropy for +different values of Γm/Γegr and fixed pm = .3. Dynamics have +been averaged over 20 batches with 50 runs each. Error bars +show the standard deviation from the batches. +spins pointing up (Ψ(0) = |1⟩⟨1|⊗N/2). The entropy cor- +responds directly to the amount of entanglement within +the system for a given J and ⃗R. We then average over +many realizations and measurement histories to quan- +tify the average entanglement entropy. Explicitly, given +a quantum trajectory Ψ(t; ⃗R, J ) at time t described +by measurement history ⃗R and Hamiltonian HJ , the +(average) half-chain entanglement entropy at time t is +⟨⟨shalf(t)⟩⟩ per Eq. (III.5). +A competition between entanglement growth and de- +coupling (due to measurements) determine the entangle- +ment dynamics of the SYK chain. If the measurements +are too frequent (large Γm/Γegr) and too strong (large +pm), then the system will have sub-extensive entangle- +ment in the steady state (area-law phase); whereas if the +converse is true, then the state will have an extensive + +6 +0.2 +0.28 +0.39 +0.55 +0.76 +1.07 +1.5 +2.09 +2.92 +4.84 +6.76 +9.45 +Γm/Γegr +1.0 +0.9 +0.8 +0.7 +0.6 +0.5 +0.4 +0.3 +0.2 +0.1 +pm +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +�� +s∞ +half +�� +FIG. 5. Entanglement phase diagram. Steady-state values of +the half-chain entanglement entropy as a function of measure- +ment probability pm and measurement rate Γm/Γegr. Here, +J = 1 (Γegr = .2), N = 16, and a steady-state time t∞ = 200 +is chosen. All dynamics have been averaged over 50 runs. +amount of entanglement (volume-law phase). In Fig. 4, +we plot the entanglement dynamics for different values +of pm and Γm. Clearly, the entanglement entropy satu- +rates to a lower values as the measurement probability +pm increases; we observe similar effects when increasing +the measurement rate Γm. For the latter, subtle hints +of an entanglement MIPT can be observed when passing +between Γm ≲ Γegr and Γm ≳ Γegr. +To more clearly highlight the emergence of an entan- +glement MIPT, we look at the steady-state entangle- +ment entropy ⟨⟨shalf(∞)⟩⟩. Practically, due to finite-time +simulations and finite-size effects, we cannot go to the +t → ∞ limit. +Instead, we pick a large enough time +t∞ ≫ (Γ−1 +m , Γ−1 +egr) to observe relaxation but not too large +so that finite-size effects become significant. +We then +compute ⟨⟨shalf(∞)⟩⟩ for various values (Γm/Γegr, pm) +with fixed EGR Γegr ≈ .2 (J = 1; see Fig. 3). +We +plot the results in a 2D phase-diagram in Fig. 5 and wit- +ness an entanglement MIPT—from extensive entangle- +ment (yellow-white) to sub-extensive entanglement (red- +black)—as Γm and pm increase. The fuzzy region in be- +tween is likely due to finite-size effects, as we only simu- +late N/2 = 8 spins. Nevertheless, from the diagram, we +see that, for each value 0 < pm ≤ 1, there exists a critical +measurement rate Γc +m where a MIPT occurs. Interest- +ingly, even at pm = 1, there is extensive entanglement +in the steady-state if Γm is low enough. +Similar phe- +nomenon was found in recent studies on random Brown- +ian circuits [24] and (randomly) coupled SYK chains in +the large N limit [21]. +This is intriguing because, for +pm = 1, the many-body state frequently (on a time scale +T ∼ 1/Γm) gets projected into a product state of the form +�N/2 +i=1 |ki⟩⟨ki|, where ki ∈ {0, 1} is the measurement out- +0 +50 +100 +150 +200 +Jt/ +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +�� +Tr(ρ2) +�� +N = 16, Γm/Γegr = 1 +pm = 0.1 +pm = 0.3 +pm = 0.5 +pm = 0.7 +pm = 0.9 +0 +50 +100 +150 +200 +Jt/ +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +�� +Tr(ρ2) +�� +N = 16, pm = 0.3 +Γm/Γegr = 10 +Γm/Γegr = 2 +Γm/Γegr = 1 +Γm/Γegr = 0.2 +FIG. 6. Purification dynamics of the SYK chain. (Top) Purity +for different values of measurement probabilities pm with a +fixed measurement rate Γm/Γegr = 1. (Bottom) Purity for +different values of Γm/Γegr and fixed pm = .3. +Dynamics +have been averaged over 20 batches with 50 runs in each. +Error bars show the standard deviation over the 20 batches. +come at the ith site, however the many-body correlations +quickly revives so that the system spends the majority of +the time in a highly entangled state. We note that such +a revival (and thus the appearance of a nontrivial Γc +m at +pm = 1) is distinct to entanglement dynamics and does +not occur in purification dynamics, as we discuss below. +B. +Purification phase transition +We now analyze the purification dynamics of an ini- +tially, maximally mixed (infinite temperature) state ρ0 = +I/2N/2; i.e., after a time t of evolution, we compute the +ensemble averaged purity +�� +Tr +� +ρ2(t) +��� +per Eqn. (III.5), +where Tr +� +ρ2(0) +� +≤ +�� +Tr +� +ρ2(t) +��� +≤ 1 and Tr +� +ρ2(0) +� += +1/2N/2. +Measurements (strictly) increase purity and localize + +7 +0.05 +0.097 +0.158 +0.281 +0.5 +0.889 +1.581 +2.812 +5.0 +Γm/Γegr +1.0 +0.9 +0.8 +0.7 +0.6 +0.5 +0.4 +0.3 +0.2 +0.1 +pm +0.2 +0.4 +0.6 +0.8 +1.0 +�� +Tr(ρ2) +�� +FIG. 7. Purification phase diagram. Steady-state values of +the purity as a function of measurement probability pm and +measurement rate Γm/Γegr. Here, J = 1 (Γegr = .2), N = 16, +and a steady-state time t∞ = 1000 is chosen. All dynamics +have been averaged over 50 runs. +the remaining impurity to complementary regions which +have not yet been measured. Internal dynamics, how- +ever, scrambles the impurity into many-body correla- +tions of the system, reducing the purifying effects of later +measurements. A competition arises between scrambling +and purification leading to different purification phases— +a mixed phase and a pure phase—depending on whether +scrambling or measurement dominates. In Fig. 6, we plot +the purification dynamics for different values of pm and +Γm. For high values of the measurement strength pm ≈ 1, +the system necessarily purifies on time-scales ∼ 1/Γm, +however for intermediate values 0 < pm < 1, the system +can either purify or remain mixed for times T ≫ 1/Γm +depending on whether Γm/Γegr ≫ 1 or Γm/Γegr ≪ 1, +as seen qualitatively in Fig. 6. +This is indicative of a +purification MIPT. +To more clearly highlight the emergence of a purifi- +cation MIPT, we compute the purity in the steady- +state +�� +Tr +� +ρ2(∞) +��� +and plot the results in 2D param- +eter space (Γm/Γegr, pm) in Fig. 7 for fixed Γegr. There +is a clear demarcation (though with a fuzzy bound- +ary due to finite-size effects) between the mixed phase +(black region) and pure phase (white region). Thus, for +a fixed measurement strength pm, we can increase the +measurement rate Γm to go from the mixed phase to +the pure phase (and likewise, we can tune pm starting +from a fixed Γm). +Unlike an entanglement MIPT, for +pm = 1, any nonzero measurement rate will necessar- +ily push the system to the pure phase within a time +∼ 1/Γm. +This is actually general for any pm and Γm +since Tr +� +ρ2(0) +� +≤ +�� +Tr +� +ρ2(t) +��� +≤ 1 for any pm, Γm, +and time t > 0. The inequality follows from the simple +fact that unitary evolution and projective measurements +cannot decrease purity. +Such an inequality cannot be +written for entangling dynamics since unitary evolution +generally leads to an in increase in the entanglement en- +tropy (for any bipartite cut across the system). +0.2 +0.4 +0.6 +0.8 +1.0 +pm +10-4 +10-3 +10-2 +10-1 +100 +λ +N = 16 +Γm/Γegr = 5 +Γm/Γegr = 0.5 +Γm/Γegr = 0.05 +FIG. +8. +Purification +rate +λ +assuming +the +ansatz +�� +Tr +� +ρ2(t) +��� .= tanh(λt + α), where tanh α = Tr +� +ρ2(0) +� += +1/2N/2. The purification rate is approximately linear in the +measurement rate Γm. Trends show a strong non-linear de- +pendence on pm. +1. +Purification time-scales +We attempt to find an intrinsic, purification time-scale +directly from the data. Figure 6 suggests that the dy- +namics of purity closely resembles a tanh-like profile. We +thus take the following ansatz +�� +Tr +� +ρ2(t) +��� .= tanh(λt + α), +(IV.1) +with tanh α = +�� +Tr +� +ρ2(0) +��� += 1/2N/2. Here, the purifi- +cation time-scale is quantified by the fitting parameter +λ, which depends on pm and Γm/Γegr. We find a good +fit with R2 values ranging between 0.996 and 0.999 for +different choices of pm when Γm/Γegr = 5, between 0.994 +and 0.999 when Γm/Γegr = 0.5 and between 0.983 and +0.997 when Γm/Γegr = 0.05. +From the fit, we extract the purification rate λ for sev- +eral values of pm and Γm and plot the results in Fig- +ure 8. We note that λ is close to linear in Γm, as intu- +itively expected, and that λ(pm = 1) ∼ Γm up to some +O(1) constant. Hence, λ ∼ Γmf(pm) for some function +f(pm) that may also depend on the critical strength pc +m +and critical rate Γc +m. From the data in Fig. 8, we see +that f(pm) shows strong non-linear behavior in pm, with +f(pm) changing over two orders of magnitude as the mea- +surement strength pm is tuned from 0 to 1. +V. +DISCUSSION +At this juncture, we point out an interesting viewpoint +on purification phases as seen through the lens of quan- +tum error correction [30–37]. We can think of the SYK +chain as a quantum memory which is entangled (e.g., +shares a large number of Bell pairs) with a quantum com- +puter. The quantum error correction properties of the + +8 +0 +10 +20 +30 +40 +50 +t +0.0 +0.2 +0.4 +0.6 +0.8 +shalf +N = 16, pm = 1.0, Γm/Γegr = 0.25 +0 +5 +10 +15 +20 +t +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Tr(ρ2) +N = 16, pm = 1.0, Γm/Γegr = 0.25 +FIG. 9. Quantum jumps in monitored dynamics. (Top) Re- +vival of entanglement entropy and (Bottom) purification tran- +sition for two distinct quantum trajectories (dark blue, light +blue) in the regime of completely projective (pm = 1) but +relatively infrequent (Γm/Γegr = .25) measurements. +memory refer to how well the memory retains entangle- +ment with the quantum computer in the face of external, +deleterious perturbations or errors from the environment +(e.g., measurement devices). +The internal unitary dy- +namics of the memory acts as a quantum error correcting +code that hides information (e.g., entanglement with the +quantum computer) from the environment by scrambling +the information non-locally into the memory’s many de- +grees of freedom. +In order to access this information, +the environment must couple to an extensive number of +memory qubits. Purification of the system is then inter- +preted as wiping the memory of its initial entanglement +with the quantum computer; see Appendix A for further +discussion on this perspective. +Entanglement dynamics does not admit an equivalent +QEC description because the half-chain entanglement en- +tropy captures both the initial information encoded in the +system as well as the many-body correlations that build +up over time, and these two quantities are not mutually +inclusive. On the other hand, it is often said in the liter- +ature that entanglement and purification MIPTs are two +sides of the same coin, but this is an over-simplification +and is misleading. +From previous discussions and by +comparing the phase diagrams of Figs. 5 and 7, we see +that entanglement MIPTs and purification MIPTs are in +fact two distinct phenomena. The reason for this distinc- +tion is quite simple. For an entanglement MIPT, there is +a revival of entanglement even after the system has been +completely projected onto a product state (pm = 1); see +Fig. 9. +We can thus have extensive entanglement en- +tropy in the steady state—even though the system has +lost all information about initial conditions—if the en- +tanglement growth is faster than the rate of measure- +ments (Γm/Γegr < 1) because the system spends most +of its time in highly entangled states and is only pro- +jected here-and-there into product states.V.1 Quantita- +tively, this leads to a non-trivial critical measurement +rate Γc +m ∼ Γegr at pm = 1; for Γm ≳ Γc +m, the system does +not have time to recover to a highly entangled state be- +fore another completely projective measurement occurs, +and the system spends the majority of the time in a prod- +uct state. Contrariwise, for a purification MIPT, there is +no such revival of the mixed phase once the system tran- +sitions to the pure phase (Fig. 9) because the purification +MIPT signals a true loss of initial conditions; i.e., once +the state is pure, it remains pure. Indeed, this follows di- +rectly from the inequality Tr +� +ρ2(0) +� +≤ +�� +Tr +� +ρ2(t) +��� +≤ 1 +which holds for monitoring dynamics. Hence the critical +measurement rate for a purification MIPT at pm = 1 is +trivial. Interpreting the system as a quantum memory, +projections effectively wipe the memory within a time +∼ 1/Γm, and there is no “rewriting” into the memory +thereafter. +ACKNOWLEDGMENTS +SH and AJB have benefited from discussions with +Vishal Katariya in the initial stages of this study. +SH acknowledges financial support from the Army +Research Office Multidisciplinary University Research +Initiative (ARO MURI) through the grant number +W911NF2120214. AJB acknowledges financial support +from the Defense Advanced Research Projects Agency +(DARPA) under the Young Faculty Award (YFA) Grant +No. N660012014029. +Appendix A: Purification from decoupling +We can qualitatively and quantitatively examine the +QEC properties of a scrambling system (e.g., SYK chain) +undergoing continuous monitoring [30–37] by applying +the so-called decoupling principle [41–43], which can be +explained by the following example. Consider a system S +initially in a mixed state τS which admits a purification +V.1 The steady-state is fluctuating (and thus not quite steady) due +to random quantum jumps induced by measurements, however +one can coarse-grain over a time-scale ∼ 1/Γm to witness steady +behavior. +This is effectively done by our averaging procedure +since the measurement process is a Poisson process here. + +9 +ΨRS such that τS = TrR(ΨRS), where R is a reference +that is entangled with S. For instance, consider a system +of N qubits (such that |S| = 2N) with some fraction γN +qubits in a maximally mixed state and the remaining +(1− γ)N qubits in some pure state—i.e., τS = πSγ ⊗ ψ ¯Sγ +where πSγ = I/|Sγ| and |Sγ| = 2γN (| ¯Sγ| = 2(1−γ)N). +Then one purification is ΨRS = +��γN +i=1 ΦRiSγi +� +⊗ ψ ¯Sγ, +where ΦRiSγi is a Bell pair consisting of the ith qubit in +Sγ and the ith qubit in R. Now consider an isometric +channel V : RS → RSE that couples the system S to an +environment E such that, +ΨRSE ≡ V(ΨRS) = V ΨRSV †, +(A.1) +where V †V = IRS and thus ΨRSE is pure. We assume +V = IR ⊗ VSE—i.e., the reference acts as a bystander; +see Fig. 10 for an illustration. An instance of this general +setup is the purification dynamics consisting of unitary +evolution and measurements starting from the initially +mixed state τS, where V encodes the internal unitary +evolution as well as (an isometric extension of) the ex- +ternal measurements by measurement devices E.A.1 +We are now in the position to state the decoupling +principle. Given the initial state ΨRS sent through the +channel V, the system S and reference R maintain the +entanglement within the state ΨRS with fidelity 1 − ϵ if +the reference R and environment E are approximately in +a product state (decoupled); i.e., +∥ρRE − ρR ⊗ ρE∥1 ≤ ϵ ∼ O(exp(−cN)), +(A.2) +where ∥σ∥1 = Tr ( +√ +σσ†) is the trace norm, ρRE = +TrS(ΨRSE), ρE = TrRS(ΨRSE), ρR = TrSE(ΨRSE) and +c is some constant independent of N. +For instance, given γN initial Bell pairs between S +and R and a random, scrambling unitary US followed by +measurements on (randomly chosen) pmN system qubits, +c = 1 − pm − γ [31]. In this case, decoupling fails as γ → +1 − pm. Observe that γ quantifies the initial purity of +the system via Tr +� +τ 2 +S +� += 1/2γN. Let γ = 1/N such that +there is initially only one bit of impurity in the system +[Tr +� +τ 2 +S +� += 1/2]. In the thermodynamic limit (N → ∞) +the system remains impure for all pm ≤ 1, whereas a +purification phase transition occurs at pc +m = 1 [31]. For +unitaries US that do not completely scramble within a +time 1/Γm, the critical point occurs at lower values pc +m < +1, which is the case for MIPTs in low-depth brickwork +circuits (for which pm ≈ .16 [9–15]). +The analysis above is for a single round of measure- +ments, however the purification phase is stable in the +steady state (i.e., after a large number of successive, iid +measurements) for reasonable time scales, as we show in +Figs. 6 and 7 of the main text for an SYK chain. To see +this from a decoupling perspective, consider K rounds of +iid measurements (interlaced with random, internal uni- +tary evolution), with each successive measurement occur- +ring at a rate Γm, and consider the associated isometric +channel V(K) : RS → RSEK, where EK denotes the +set of measurement devices for K measurement rounds. +In particular, the isometry is V (K) = IR ⊗ (�K +i=1 VSEi), +where Ei refers to the measurement devices for the ith +round. +Define the output state of the isometric chan- +nel as Ψ(K) +RSE ≡ V(K)(ΨRS) where ΨRS is a pure input. +Then, the system S and reference R maintain the en- +tanglement within the state ΨRS with fidelity 1 − Kαϵ, +where α ∼ O(1) constant, if the reference R and the +environment EK are approximately decoupled; i.e., +���ρ(K) +RE − ρR ⊗ ρ⊗K +E +��� +1 ≤ Kαϵ, +(A.3) +where ρ⊗K +E += �K +i=1 ρEi and ρEi is the state of the ith +environment (i.e., the ith set of measurement devices) af- +ter the ith measurement round. Why should we expect +Eqn. (A.3) to hold? The reason being that the total error +is bounded by the sum of errors in each step. [This can +be shown explicitly by successively applying the trian- +gle inequality ∥(a − b) + (b − c)∥1 ≤ ∥a − b∥1 + ∥b − c∥1 +to the left hand side of Eq. (A.3).] In turn, the error per +step scales as ϵ up to some O(1) constant such that the +average error is αϵ. +From Eqn. (A.3), we have that, for K ≪ 1/ϵ, the +reference R and environment E remain decoupled. +In +the context of purification phases, the system remains +in the mixed phase for all reasonable timescales T ∼ +poly(N)/Γm, where Γm dictates the frequency of mea- +surements. +This gives some credence to the long-time +stability of the mixed phase shown in Fig. 6. + +ψ ¯Sγ +ΦRSγ +US +US +US +M +M +M +E1 +E2 +EK +VRSE1 +VRSE2 +VRSEK +FIG. 10. +Quantum circuit view of purification dynamics. +Part of the system S is initially entangled with a reference +R such that the initial state of the system is in a mixed +phase. Internal, unitary evolution US entangles the system’s +constituents—spreading the initial impurity non-locally into +many-body degrees of freedom—while measurements (with +isometric extension M) decouples the systems qubits; US and +M together give full isometric extension VRSEi = IR ⊗ VSEi +for the ith measurement round, where Ei labels the set of +measurement devices. +A.1 The inclusion of measurements into the isometry is possible by +the principle of deferred measurements; i.e., we coherently cou- +ple/entangle the measurement devices to the system and projec- +tively measure the measurement devices at the end. + +10 +[1] J. Eisert, M. Friesdorf, and C. Gogolin, Quantum many- +body systems out of equilibrium, Nat. Phys. 11, 124 +(2015). +[2] P. Calabrese and J. Cardy, Evolution of entanglement +entropy in one-dimensional systems, J. Stat. Mech. 2005, +P04010 (2005). +[3] A. Nahum, J. Ruhman, S. Vijay, and J. Haah, Quantum +entanglement growth under random unitary dynamics, +Phys. Rev. X 7, 031016 (2017). +[4] C. W. von Keyserlingk, T. Rakovszky, F. Pollmann, and +S. L. Sondhi, Operator hydrodynamics, otocs, and en- +tanglement growth in systems without conservation laws, +Phys. Rev. X 8, 021013 (2018). +[5] L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Entan- +glement in many-body systems, Rev. Mod. Phys. 80, 517 +(2008). +[6] B. Zeng, X. Chen, D.-L. Zhou, X.-G. Wen, et al., +Quantum Information Meets Quantum Matter (Springer, +2019). +[7] T.-C. Lu, L. A. Lessa, I. H. Kim, and T. H. Hsieh, Mea- +surement as a Shortcut to Long-Range Entangled Quan- +tum Matter, PRX Quantum 3, 040337 (2022). +[8] A. Chan, R. M. Nandkishore, M. Pretko, and G. Smith, +Unitary-projective entanglement dynamics, Phys. Rev. B +99, 224307 (2019). +[9] Y. Li, X. Chen, and M. P. Fisher, Quantum Zeno effect +and the many-body entanglement transition, Phys. Rev. +B 98, 205136 (2018). +[10] B. Skinner, J. Ruhman, and A. Nahum, Measurement- +induced phase transitions in the dynamics of entangle- +ment, Phys. Rev. X 9, 031009 (2019). +[11] Y. Li, X. Chen, and M. P. Fisher, Measurement-driven +entanglement transition in hybrid quantum circuits, +Phys. Rev. B 100, 134306 (2019). +[12] M. Szyniszewski, A. Romito, and H. Schomerus, Entan- +glement transition from variable-strength weak measure- +ments, Phys. Rev. B 100, 064204 (2019). +[13] C.-M. Jian, Y.-Z. You, R. Vasseur, and A. W. W. Ludwig, +Measurement-induced criticality in random quantum cir- +cuits, Phys. Rev. B 101, 104302 (2020). +[14] A. Zabalo, M. J. Gullans, J. H. Wilson, S. Gopalakrish- +nan, D. A. Huse, and J. H. Pixley, Critical properties of +the measurement-induced transition in random quantum +circuits, Phys. Rev. B 101, 060301 (2020). +[15] Y. Bao, S. Choi, and E. Altman, Theory of the phase +transition in random unitary circuits with measurements, +Phys. Rev. B 101, 104301 (2020). +[16] A. C. Potter and R. Vasseur, Entanglement dynamics in +hybrid quantum circuits, in Entanglement in Spin Chains +(Springer, 2022) pp. 211–249. +[17] M. P. A. Fisher, V. Khemani, A. Nahum, and S. Vi- +jay, Random Quantum Circuits (2022), arXiv:2207.14280 +[quant-ph]. +[18] X. Cao, A. Tilloy, and A. D. Luca, Entanglement in +a fermion chain under continuous monitoring, SciPost +Phys. 7, 024 (2019). +[19] S.-K. Jian, C. Liu, X. Chen, B. Swingle, and P. Zhang, +Measurement-Induced Phase Transition in the Monitored +Sachdev-Ye-Kitaev Model, Phys. Rev. Lett. 127, 140601 +(2021). +[20] G. S. Bentsen, S. Sahu, and B. Swingle, Measurement- +induced purification in large-N hybrid Brownian circuits, +Phys. Rev. B 104, 094304 (2021). +[21] S. Sahu, S.-K. Jian, G. Bentsen, and B. Swingle, Entan- +glement phases in large-N hybrid Brownian circuits with +long-range couplings, Phys. Rev. B 106, 224305 (2022). +[22] C. Liu, P. Zhang, and X. Chen, Non-unitary dynamics of +Sachdev-Ye-Kitaev chain, SciPost Phys. 10, 048 (2021). +[23] X. Turkeshi, A. Biella, R. Fazio, M. Dalmonte, and +M. Schir´o, Measurement-induced entanglement transi- +tions in the quantum Ising chain: From infinite to zero +clicks, Phys. Rev. B 103, 224210 (2021). +[24] T. Vovk and H. Pichler, Entanglement-Optimal Trajec- +tories of Many-Body Quantum Markov Processes, Phys. +Rev. Lett. 128, 243601 (2022). +[25] A. Touil and S. Deffner, Information scrambling ver- +sus decoherence—two competing sinks for entropy, PRX +Quantum 2, 010306 (2021). +[26] J. Preskill, Quantum computing in the NISQ era and +beyond, Quantum 2, 79 (2018). +[27] X. Mi, P. Roushan, C. Quintana, S. Mandr`a, J. Mar- +shall, C. Neill, F. Arute, K. Arya, J. Atalaya, R. Bab- +bush, et al., Information scrambling in quantum circuits, +Science 374, 1479 (2021). +[28] C. Noel, P. Niroula, D. Zhu, A. Risinger, L. Egan, +D. Biswas, M. Cetina, A. V. Gorshkov, M. J. Gullans, +D. A. Huse, et al., Measurement-induced quantum phases +realized in a trapped-ion quantum computer, Nat. Phys. +18, 760–764 (2022). +[29] J. M. Koh, S.-N. Sun, M. Motta, and A. J. Minnich, +Experimental Realization of a Measurement-Induced +Entanglement Phase Transition on a Superconducting +Quantum Processor (2022), arXiv:2203.04338 [quant-ph]. +[30] M. J. Gullans and D. A. Huse, Dynamical purifica- +tion phase transition induced by quantum measurements, +Phys. Rev. X 10, 041020 (2020). +[31] S. Choi, Y. Bao, X.-L. Qi, and E. Altman, Quantum er- +ror correction in scrambling dynamics and measurement- +induced phase transition, Phys. Rev. Lett. 125, 030505 +(2020). +[32] M. J. Gullans and D. A. Huse, Scalable probes of +measurement-induced criticality, Phys. Rev. Lett. 125, +070606 (2020). +[33] M. Ippoliti and V. Khemani, Postselection-free entangle- +ment dynamics via spacetime duality, Phys. Rev. Lett. +126, 060501 (2021). +[34] R. Fan, S. Vijay, A. Vishwanath, and Y.-Z. You, Self- +organized error correction in random unitary circuits +with measurement, Phys. Rev. B 103, 174309 (2021). +[35] M. J. Gullans, S. Krastanov, D. A. Huse, L. Jiang, and +S. T. Flammia, Quantum coding with low-depth random +circuits, Phys. Rev. X 11, 031066 (2021). +[36] Y. Li and M. P. Fisher, Statistical mechanics of quantum +error correcting codes, Phys. Rev. B 103, 104306 (2021). +[37] L. Fidkowski, J. Haah, and M. B. Hastings, How dynam- +ical quantum memories forget, Quantum 5, 382 (2021). +[38] S. Sachdev and J. Ye, Gapless spin-fluid ground state in +a random quantum heisenberg magnet, Phys. Rev. Lett. +70, 3339 (1993). +[39] A. Kitaev, Hidden correlations in the Hawking radiation +and thermal noise (February 2015), talk at KITP. +[40] D. Chowdhury, A. Georges, O. Parcollet, and S. Sachdev, + +11 +Sachdev-Ye-Kitaev models and beyond: +Window into +non-Fermi liquids, Rev. Mod. Phys. 94, 035004 (2022). +[41] B. Schumacher and M. D. Westmoreland, Approximate +Quantum Error Correction, Quantum Inf. Process. 1, 5 +(2002). +[42] P. Hayden, M. Horodecki, A. Winter, and J. Yard, A +Decoupling Approach to the Quantum Capacity, Open +Syst. Inf. Dyn. 15, 7 (2008). +[43] F. Dupuis, The decoupling approach to quantum infor- +mation theory (2010), arXiv:1004.1641 [quant-ph]. + diff --git a/eNE4T4oBgHgl3EQfpw2r/content/tmp_files/load_file.txt b/eNE4T4oBgHgl3EQfpw2r/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..4afb1c8aba1e57302c71b9731ad385f18dbf685b --- /dev/null +++ b/eNE4T4oBgHgl3EQfpw2r/content/tmp_files/load_file.txt @@ -0,0 +1,894 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf,len=893 +page_content='A numerical study of measurement-induced phase transitions in the Sachdev-Ye-Kitaev model Stav Haldar1, ∗ and Anthony J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' Brady2, † 1Department of Physics & Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA 2Department of Electrical and Computer Engineering, University of Arizona, Tucson, Arizona 85721, USA (Dated: January 13, 2023) Continuous monitoring of an otherwise closed quantum system has been found to lead to a measurement-induced phase transition (MIPT) characterized by abrupt changes in the entangle- ment or purity of the many-body quantum state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' For an entanglement MIPT, entangling dynamics compete with measurement dynamics, pushing the system either to a phase with extensive entangle- ment or to a phase with low-level entanglement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' For purification MIPTs, projective measurements effectively cool and localize the system, inducing a transition from a mixed state to an uncorrelated pure state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' In this work, we numerically simulate monitored dynamics in the all-to-all Sachdev-Ye- Kitaev (SYK) model for finite N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' We witness both entanglement and purification MIPTs in the steady-state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' It is often said that there is an equivalence between entanglement and purification MIPTs, however we provide numerical evidence to the contrary, implying that entanglement and purification MIPTs are indeed two distinct phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' The reason for such a distinction is quite simple: entanglement can revive after a completely projective measurement—if measurements do not occur too often in time—but impurity cannot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' INTRODUCTION Quantum statistical mechanics accurately captures most properties of many-body quantum systems at equi- librium where, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=', the system can be described by a handful of macroscopic quantities, such as the temper- ature, total particle number etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' However, many as- pects of quantum many-body systems out of equilib- rium [1]—such as entanglement growth in closed quan- tum systems [2–4]—require more care.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' Tools from quan- tum information have been employed to better under- stand, characterize, and even construct highly correlated quantum many-body states (or quantum matter) in and out of equilibrium [5–7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' The dynamics of a closed quantum system out of equi- librium is governed by a Hamiltonian that introduces correlations (entanglement) between the system’s con- stituents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' Starting from an initially uncorrelated state, the entanglement in the system evolves in time, eventu- ally saturating to some finite value;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' in which case, the steady-state is a many-body entangled state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' If the in- teractions are strong and the subsystems are highly con- nected, then the growth of entanglement is fast com- pared to all other time scales, and entanglement satu- rates to an extensive value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' Circumstances change when we “open” the system and externally perturb it with in- coherent probes (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=', non-unitary perturbations), such as coupling the system to a heat bath or measuring parts of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' In this work, we focus on continuously probing a quan- tum system with measurement devices that we have ac- ∗ hstav1@lsu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content='edu † ajbrady4123@arizona.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content='edu cess to—a process called continuous monitoring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' In par- ticular, we assume that the internal dynamics of the sys- tem are spontaneously interrupted by local projective measurements characterized by a measurement strength pm and a measurement rate Γm;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' 1 for an illus- tration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' Such monitoring dynamics have been feverishly studied in the past several years, primarily via brickwork circuit models [8–15] (see also the recent reviews [16, 17] and references therein) which intersperse discrete two- body interactions with local projective measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' In brickwork circuit models [8–17], it has been shown that a competition arises between the entanglement dy- namics of the closed system, which drives the system into a many-body entangled state, and the decoupling dynam- ics induced by continuous monitoring, which drives the system in an uncorrelated product state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' This competi- tion leads to different phases of matter and to a so-called measurement induced phase transition (MIPT), depend- ing on whether the internal entangling dynamics or the measurement dynamics dominates the evolution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' Similar studies with (random) Hamiltonian evolution [18–24]— which include random Brownian circuits (continuous- time analogs of brickwork circuit models) [20, 21, 24] and large N analytically solvable models of coupled clusters of SYK chains [19, 22]—have come to similar conclu- sions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' A numerical study of the effects of decoherence on information scrambling and growth of entanglement for several many body quantum Hamiltonians including the SYK model was also performed in [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' Recent ex- periments regarding entanglement growth and MIPTs in brickwork circuits with Noisy Intermediate-Scale Quan- tum (NISQ [26]) devices have also been performed [27– 29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' MIPTs come in two flavors—an entanglement MIPT and a purification MIPT—which are often conflated into the singular phenomenon of a MIPT, however we later arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content='05195v1 [quant-ph] 12 Jan 2023 2 Γm Γm Γegr Ψt → P (⃗r)ΨtP (⃗r) Tr(P (⃗r)Ψt) FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' Projective measurements sporadically interrupt the internal, unitary time evolution of a quantum system (here, 5 spins with all-to-all connectivity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' A competition between the measurement rate Γm and the entanglement growth rate Γegr determines the entanglement dynamics of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' discuss how these two phenomena are in fact distinct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' An entanglement MIPT refers to the transition from a quantum state with extensive entanglement (volume-law phase) to a quantum state with sub-extensive entangle- ment (area-law phase).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' Whereas a purification MIPT refers to the transition from a highly mixed quantum state (mixed phase) to an uncorrelated pure state (pure phase).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content='I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content='1 For discrete brickwork circuit models [9–17], the critical point marking a MIPT depends on the prob- ability that a local measurement will occur as well as the circuit depth prior to a measurement round [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' For physical systems evolving under a Hamiltonian [24], the measurement strength and the rate of entanglement growth in the closed system establishes a dynamical rate that competes against the local measurement rate and dictates which phase the system is in (as well as the cor- responding critical points).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' In this work, we numerically study entanglement and purification MIPTs in the all-to-all SYK model [38–40] with finite N, where N is the number of Majorana fermions (here, N ranges from 10 to 20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' We simulate monitored dynamics and track the entanglement or pu- rity of the resulting quantum trajectories through time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' We witness entanglement and purification MIPTs in the steady-state and observe a clear distinction between the two phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' II.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' ENTANGLEMENT GROWTH IN THE SYK MODEL The SYK model [38–40] is a strongly interacting model for many-body quantum systems without any quasipar- I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content='1 Another intriguing perspective on purification MIPTs comes from the theory of quantum error correction [30–37], whereby interprets the open quantum system as a quantum memory that is robust to decoherence due to measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' ticle excitations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' Low energy equilibrium states and dynamics of the system cannot be described in terms of quasiparticle excitations, as is the case for standard Fermi liquids, and even the ground state is an entangled quantum many-body state.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' Such systems are important from several different perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' From the point of view of condensed matter physics, such models provide a window into the fascinating world of strange metals and high temperature superconductors which are yet to be fully understood [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' A feature that underlies many interesting aspects of the SYK model (and other strongly interacting models without quasiparticles) is the fast scrambling of informa- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' From a physical point of view, fast scrambling can be understood as a faster-than-usual equilibration of the systemII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content='1 after a local perturbation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' This perspective is also important for understanding entanglement dynam- ics and effect of measurements on it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' Fast scramblers such as the SYK system quickly regenerate their exten- sive, steady-state entanglement after a short lived local perturbation (like a projective measurement) occurs on a few sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' Consider N all-to-all interacting Majorana fermions, where the each interaction term includes 4 sites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' The coupling constants are site dependent random variables with zero mean ⟨Jijkl⟩ = 0 and finite variance ⟨J 2 ijkl⟩ = 6J2/N 3, where J defines the strength of the interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' Let χi be the second-quantized Majorana field operator at the site i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/eNE4T4oBgHgl3EQfpw2r/content/2301.05195v1.pdf'} +page_content=' The SYK Hamiltonian is then HJ = � 1≤i 4000 nm∙μA/V2 and photo-spin-conductance > 2000 +(nm∙μA/V2 ℏ /2e) in the visible spectrum. The propagation and the spin-polarizations of +photocurrents can be switched via simply rotating the Néel vector. We unveil that the PT-symmetry, +mirror symmetries, and spin-orbital-couplings are the keys for the observed sizable and controllable +2D BPVEs. All the results provide insights into the BPVEs of 2D AFM, and suggest that the layered +MnPSe3 is an outstanding 2D platform for energy device and photo-spintronics. + + + + + +TOC GRAPHIC + +Anti-ferromagnetism enables efficient 2D solar cell in MnPSe3 atomic thin layer. + + + + +PT-MnPSe3 + +Bulk photovoltaic effects (BPVEs) convert the incident light into steady currents in +homogeneous crystals, sparking intense interests due to the potentials for energy harvesting, +rectifications, spintronics, spectroscopes, etc. 1-9 BPVEs have been thought to be dominated by the +profound shift mechanism, 10-12 in which the photocurrents are due to the continuous shifts of +valence and conduction electrons in the non-centrosymmetric lattice during the photo-pumping +processes. To date, the shift-type BPVEs have been realized in ferroelectrics, 3, 8, 10, 13 +piezoelectrics,14-17 and topological Weyl semimetals.18 On the other hand, it is also possible to +generate BPVEs via injection mechanism in which the net photocurrents are due to the unbalances +in group velocities amongst the photo-excited carriers.19-20 Recently, several studies have predicted +that the injection-type BPVEs can be observed in two-dimensional (2D) bilayer anti-ferromagnets +(AFM) CrI3 7 and MnBi2Te4,9, 21 which possess the parity-temporal (PT) symmetry. PT-BPVEs are +believed to be superior since the injection currents running in these systems are usually larger than +the shift currents by several magnitude orders. More importantly, the incorporation of magnetism in +BPVEs offers numerous modulation paths and opens a wealth of possibilities for opto-spintronic +applications. However, the 2D materials suitable for PT-BPVE are very few in records. For the +proposals of bilayer PT-AFM, the essential PT-symmetries stand on the long-range van der Waals +(vdW) interlayer couplings, 7, 9, 21-24 and the weak vdW strengths in these interactions limit the +magnitudes of photocurrents. Besides, the ubiquitous layer-slides, twists in vdW bilayers 25 might +break the PT-symmetries and harm the BPVEs. On the other hand, the poor magnetic and air +stabilities of CrI3 and MnBi2Te4 cannot fulfill the demanding of realistic applications perfectly. 21-24 +Hence, it is quite desired to discovery better platforms to realize PT-BPVEs. +MnPSe3 belongs to the family of transition metal thiophosphates (MPX3, with M=Mn, Fe, Co, +Ni; X=S, Se), which are layered magnetic semiconductors with band gaps suitable for visible light. +And they are easy to be exfoliated to 2D layers with high qualities due to the ultra-weak vdW +interlayer interactions and outstanding air stabilities. 26 So, they exhibit extraordinary performances +in optoelectronic responses and opto-chemistry. 27-32 However, there are notable paucity of studies +investigating the BPVEs in 2D MPX3, since MPX3 have centrosymmetric lattice and no shift- +currents are allowed. 33-35 Manganese thiophosphates are exceptional, the AFM hexagonal sublattice +expanded by Mn2+ ions break the inversion symmetry (P-symmetry) and the PT-polarization is thus + + + +hosted. 35-36 Furthermore, the anti-ferromagnetism of MnPSe3 is amenable to external modulations +via strains and magnetic fields. 37 Therefore, it is intriguing to see if the PT-AFM MnPSe3 can +exhibit modulable and large PT-BPVEs. +In this work, we predict the PT-BPVEs of monolayer MnPSe3 induced by the illuminations of +linearly polarized visible light. Based on the first-principle calculations, we show that the PT- +polarizations in MnPSe3 are stabilized by the intra-layer AFM order and the strong spin-orbital- +couplings (SOC). Surprisingly, the PT-polarizations can perfectly align the phases of local +photocurrents in (P2Se6)4- prisms, inducing large BPVEs with 2nd order photoconductance exceeding +4000 nm∙μA/V2 and photo-spin-conductance exceeding 2000 (nm∙μA/V2 ℏ /2e) in the visible +spectrum. We also unveil that the 2D BPVs and the Néel vectors are intimately intertwined through +the mirror symmetries, enabling abundant controlling routes for photocurrents and photo-spin- +currents. It is possible to regulate the magnitudes, switch the propagations, and reversing the spin +polarizations of photocurrents via rotating the Néel vectors. Hence, MnPSe3 is the ideal platform to +realize 2D PT-BPVEs, providing opportunities for high-efficient energy and controllable opto- +spintronic applications. +Figure 1(a) shows the lattice of MnPSe3 that consists of (P2Se6)4- prisms and two Mn- +sublattices. Our density functional theory calculations indicate that the Mn2+ ions possess local +magnetic moment of 5μB, and the nearest neighbored magnetic moments are anti-parallel, consist +with previous studies.36 The anti-ferromagnetic honeycomb framework of Mn-sublattices displayed +in Fig. 1(a) breaks the P-symmetry because the P-operation interchanges the two Mn-sublattices +with opposite magnetic moments. Once the P-operation is followed by time reversal (T) operation +which reverses all the magnetic moments, the system coincides with itself, that is, the PT-symmetry +is preserved in the monolayer MnPSe3. The lacking of P-symmetry indicates the MnPSe3 +monolayer is a polar crystal. This kind of polarization is apparently not related to the non- +centrosymmetric crystal geometry but the AFM emerged from the strong interactions between +electrons, and we call this as PT-polarization. + + + + +Figure 1. Lattice, magnetic, electronic, and photovoltaic structures of MnPSe3. (a) The top view of +monolayer MnPSe3 lattice and the photocurrents and photo-spin-currents induced by the +illuminations. The grey and green balls denote P and Se atoms. Blue and red balls denote the Mn +atoms with opposite magnetic moments. (b) The typical dual valley structure in PT-AFM. Thick +arrows denote the photo-induced hopping process and small arrows denote the group velocities of +photo-excited holes. (c) The mirror reflections in MnPSe3 monolayer. Dashed lines denote the +mirror planes. (d) The band structure of MnPSe3 with Néel vector orientation along x-, y-, and z- +directions. +It is important to note that the PT-polarization found in this study is distinguished with previous +reports on bilayer CrI3 7 and MnBi2Te4. 9, 21 In those systems, the PT-polarizations depend on the +stacking order of bilayers and the long-range interlayer AFM couplings across vdW gaps. On the +contrary, the PT-polarization in MnPSe3 is induced by the strong short-range intralayer AFM +exchange couplings. In addition, the intralayer crystal structure, which is based on the sturdy +covalence bonds, is also more stable than the interlayer structures, which are based on the long- +range vdW interactions. As a result, the monolayer MnPSe3 is expected to have more robust PT- +polarization, larger nonlinear opto-electronic couplings, and better stability. +Figure 1(b) shows the basic process of injection-type BPVs enabled by the PT-polarization. K + +(a) +(b) +hv +12 +hv +Mn +K +K' +(c) +(d) +n//x +n//y +n//z +2.00 +2.00 +2.00 +XKiXK! +1.75 +1.75 +.75 +(eV) +1.50. +0.58 +0.00 +0.25 +0.25 +-0.25 +-0.50 +KMK +0.50 +KMK +0.50 +KMK + +and K’ label the dual valleys with opposite momentum i.e., K’ = −K, and they are related to each +other by P- and T-operation. Since both P- and T-symmetries are broken, the degenerations between +K and K’ valleys are no longer to be enforced by these two symmetries. On the other hand, the +valley-polarizations are also ruled by the mirror symmetry since some mirror operations interchange +the dual valleys. Given the fact that the mirror symmetries are readily switchable via simply rotating +the Néel vectors, it is straight to see that the PT-AFM with suitable mirror symmetries possess +controllable valley-polarizations, exhibiting intriguing electronic structures for modulable +photoelectronic responses. +Figure 1(c) shows the two possible mirror operations in MnPSe3. The first one termed as My is +the reflection about the mirror plane My which is vertical to the basal plane and crosses the (P2Se6) +prisms. My interchanges the dual Mn-sublattices, and flips the magnetic moments with x/z- +orientations. Therefore, MnPSe3 with Néel vector along x/z-directions preserve the My-symmetry. +The second mirror operation termed as MxMz is a combination of double reflections about the one +mirror perpendicular and the other vertical to the atomic plane. The Mn-sublattices do not exchange +under MxMz, and the magnetic moments along y-directions are also preserved in MxMz. So, for the +MnPSe3 with Néel vector along y-direction, the MxMz-symmetry is preserved. More essentially, +since the MxMz-operation interchanges the dual valleys while My-operation does not, the valley- +polarizations in MnPSe3 are prohibited in MxMz-symmetric case but allowed in My-symmetric case. +Therefore, via simply rotating the magnetization orientations, we can readily obtain desired mirror- +symmetry and switch the valley-polarizations in MnPSe3. +Figure 1(d) shows the band structures of MnPSe3 predicted by relativistic DFT, with Néel +vectors along x-, y-, and z-directions. In all cases, the band gap emerged in the corners of Brillouin +zone (BZ), either K or K’, indicating the valley structures dominate the low-energy opto-electronic +responses. For the MnPSe3 with magnetic moments along z-axis, the asymmetries between K and +K’ valleys are obvious. The energy gaps at K and K’ are ΔK = 1.5196 eV and ΔK’ = 1.5838 eV, +corresponding to the valley-polarization energy of 64.2 meV, which is a large value and consistent +with previous studies.36 For the case with Néel vectors along x-axis, we have ΔK = 1.5632 eV and +ΔK’ = 1.5635 eV, so the valley-polarization energy shrinks to 0.3 meV. The reason for this significant +shrinking is that the valley-polarization is proportional to the efficiency of spin-orbit-coupling + + + +(SOC), and the system with magnetizations along x-axis exhibits negligible SOC for BZ corner +states. In 2D systems, the orbital moments of Bloch electrons around the BZ corners are dominated +by the z-component, the z-orientated spins thus display the strongest SOC and valley-polarizations. +For the y-magnetization, the valley polarization is forbidden by MxMy-symmetry and ΔK =ΔK’ +=1.5634 eV. +Besides, the symmetric aspects of band structure on the inner part of BZ also show clear +dependences on the magnetization orientation. For MnPSe3 with Néel vectors along x- and z- +directions, the asymmetries of valence bands about M point are shown by the red arrows marked in +Fig. 1(d). The extents of band asymmetries are similar in x- and z-magnetized cases, indicating that +the orbital moments around M point have comparable x- and z-components, so that the efficiencies +of SOC in these states are close to each other. +BPVE is the 2nd order opto-electronic responses, and the photocurrents jμC can be +phenomenologically expressed as: 𝑗𝐶 +𝜇 = 𝑅𝑒 ∑ +𝜎𝐶 +𝜇:𝛼𝛽(0;𝜔, −𝜔)𝐸𝛼(𝜔)𝐸𝛽(−𝜔) +𝛼𝛽 +, where μ, α, and +β can be x/y/z directions. ω denotes the frequency of photons. σCμ:αβ is the 3-ranked tensor of BPVE +photoconductance, Eα/β denotes the α/β component of electric fields of incident light. For the system +with P-symmetry, the P-operation will reverse the 𝑗𝐶 +𝜇 in l.h.s. but preserve the r.h.s., leading to the +vanishing of BPVEs. So, the anti-ferromagnetism which produces PT-polarizations and lifts the P- +symmetry in MnPSe3 is the key for the nonzero BPVEs. On the other hand, although σCμ:αβ always +breaks the T-symmetry due to the relaxation dynamics of photo-induced carriers which lacks time +reciprocities, the details of how the T-symmetry is broke decides the magnitude and direction of PT- +polarization, thus is also significantly relevant to PT-BPVEs.19 +In the following, we focus on the BPVEs generated by the light which are linearly polarized in +x-axis, and only the real part of σCx:xx and σCy:xx are relevant. Other directions of BPVE can be +obtained by the considerations on symmetry. Microscopically, the BPVE can be evaluated by the +nonlinear response theory, and the dominated contribution is expressed as: 7, 20, 38 +𝜎𝐶 +𝜇:𝛼𝛽(0; ω, −ω) = 2𝑒3 +𝑆ω2 ∑ +∑ +𝑓𝑙𝑛 +𝑣𝑘,𝑚𝑛 +𝜇 +𝑣𝑘,𝑛𝑙 +𝛼 +𝑣𝑘,𝑙𝑚 +𝛽 +(𝐸𝑘,𝑚𝑛 − 𝑖ℏ/𝜏)(𝐸𝑘,𝑙𝑚 − ℏΩ) +𝑙𝑚𝑛,Ω=±ω +𝑘∈𝐵𝑍 + (1) +here k labels the k-point in irreducible BZ and l, m, n label the band index, 𝑣𝑘,𝑙𝑚 +𝜇 + is the matrix + + + +elements of velocity operator, 𝐸𝑘,𝑚𝑙 = 𝐸𝑘,𝑚 − 𝐸𝑘,𝑙 denotes the difference in band energies, 𝑓𝑙𝑛 = +𝑓𝑙 − 𝑓𝑛 is the difference of occupations in lth and nth bands. ω is the magnitude of frequency of +incident light. τ is the relaxation time for intra-band process. In principle, the relaxation time τ might +depend on momentum, band indices, and frequencies of light, because of impurity scattering, +electron-phonons couplings, many-body interactions, etc. However, several previous studies have +showed that it is still reasonable to consider an average and constant relaxation time approximation +in the calculations of BPVEs.39-40 Hence, in this study we adopt the constant relaxation time +approximation and take the default value ℏ/𝜏 = 1 𝑚𝑒𝑉, i.e., τ≈0.6 ps by default. This setting is +rather conservative since the MnPSe3 is supposed to be a clean crystal due to its excellent chemical +stabilities. S is the area of MnPSe3 cell. Since the thickness of 2D monolayer is not well-defined, +we do not average the photoconductance over volume but area. So, the σC calculated in eq. 1 is +related to conventional definition of 2nd order photoconductances in 3D systems σC3D by σC=LσC3D, +in which L is the effective thickness of 2D monolayer. And the unit of σC in eq. 1 is nm⋅μA/V2. +Figure 2 shows the calculated nonlinear photoconductance of BPVE. For MnPSe3 with Néel +vector along z-axis [Fig. 2(a)], σCx:xx exhibits several peaks in the visible spectrum with photon +energy range from 1.6 eV to 3.6 eV. The first peak of σCx:xx occurs at 1.83 eV, slighter higher than +the energy gap of ~1.5 eV. The peak value is −187 (nm∙μA/V2), which is comparable to the highest +BPVE conductance previously reported in bilayer AFM systems. 7, 9 The strongest peak of σCx:xx is +at 2.98 eV, with magnitude 4152 (nm∙μA/V2), which is ~10-folds larger than the previous proposals. +On the other hand, σCy:xx vanishes at all photon energies, consistent with the My-symmetry since +σCy:xx is proportional to vy×vx×vx which is odd in My-reflection. Therefore, the photocurrents induced +by the linearly polarized light only propagate along the x-axis in this case. +Note that because of the injection mechanism of BPVEs in MnPSe3, the magnitude of +photoconductance is proportional to the value of relaxation time.7, 20 The explicit dependence of +BPVEs on relaxation time are shown in Fig. S1 in supporting information. Since the utilized +relaxation time constants of 0.6ps is conservative, the estimations on the BPVEs should be +conservative, too. + + + + +Figure 2. Photoconductance σCx:xx and σCy:xx for MnPSe3 with Néel vector along (a) z-direction, (b) +-z-direction, (c) x-direction, and (d) y-direction. The hexagon in the left-down part of each figure +denotes the magnetic lattice formed by Mn2+ ions, and the arrows on it denote the orientations of +local magnetic moments. The directions of Néel vectors are marked aside the hexagons. + +Then we reverse the Néel vector to −z-direction, and the σCx:xx displayed in Fig. 2(b) becomes +the opposite of the case discussed before, indicating that the propagation directions of photocurrents +are locked with the orientation of Néel vectors. This is in consistency with our previous discussions +on T-symmetry i.e., the photocurrent propagation is related to PT-polarization, which is further +controlled by the magnetizations. And this behavior suggests a promising route to read out the +nonvolatile information stored as Néel vectors in MnPSe3 via the BPVEs, which is essential for the +2D opto-spintronic memories. +Fig. 2(c) displays the photoconductance of MnPSe3 with Néel vector along x-axis. Once again, +due to the My-symmetry, σCy:xx is zero everywhere. The first peak of σCx:xx now occurs around 1.73 +eV with value −100 (nm∙μA/V2), and the highest peak of σCx:xx in Fig. 1(c) is 4436 (nm∙μA/V2) at +2.02 eV. Comparing to the ±z-cases discussed before, the photocurrents induced by low-energy +photons is smaller here. This can be explained by the valley structures show in Fig. 1(d). Since the +valley-polarizations in x-magnetized system are much smaller, the low-energy photoconductance, +which is dominated by the valley-polarization, should be weaker. Besides, the several high peaks in +Fig. 2(c) have magnitudes comparable with ±z-magnetized cases, revealing that the high-energy + +(a) +(b) +A +40N0 +4000 +i +3000 +000 +-u) +2000 +2000 +1000 +1000 +-1000 +Photoco +-2000 +-2000 +-3000 +n//z. +-3000 +n//-z +-4000 +000 +1.0 +1.5 +2.5 +3.0 +3.5 +1.0 +1.5 +2.0 +2.5 +3.0 +3.5 +(c) +Photonenergy (eV) +(d) +Photon energy (eV) +4000 +Photoconductance (nm:μA/V*) +000 +3000 +3000 +2000 +2000 +0001 +1000 +-1000 +-1000 +-2000 +-2000 +n//x +-3000 +n//y +-4000 +1000 +1.0 +1.5 +2.0 +2.5 +3.0 +3.5 +1.0 +1.5 +2.0 +2.5 +3.0 +3.5 +Photon encrgy (cV) +Photon energy (eV) + +photoconductance is free from the valley-related opto-electronic processes. +Fig. 2(d) displays the case with Néel vector along y-axis. σCx:xx becomes zero at all photon +energies, thus the photocurrents generated by linearly polarized light run in y-axis solely. This +perpendicular switching of photocurrents propagation is caused by the switching of mirror +symmetries from My to MxMz, which is brought about by the rotations of Néel vectors from x/z-axis +to y-axis. The σCx:xx is odd in My mirror operation, thus no photocurrents in x-axis are allowed. For +σCy:xx, it reaches the first peak at 1.97 eV with value 241 (nm∙μA/V2), and the highest peak value is +−3059 (nm∙μA/V2) occurred at photon energy of 2.98 eV. +In addition, the 2D BPVEs of MnPSe3 also generate pure spin-currents. We detect the spin- +resolved photocurrents with vector potentials projected to spin tunnels, and compute the +nonlinear photo-spin-conductance tensor σSzμ:αβ, which is relevant for spin-currents (See supporting +information for more details). The spin polarizations in photocurrents are dominate by the z- +component in most cases, we thus focused on the photo-spin-conductance with z-polarization, which +are displayed in Figure 3. + +Figure 3. Photo-spin-conductance σSzx:xx and σSzy:xx for MnPSe3 with Néel vector along (a) z- +direction, (b) x-direction, and (c) y-direction. + +Figure 3(a) shows the photo-spin-conductance in system with Néel vectors along z-axis. Firstly, +σSzx:xx vanishes at all energies. σSzy:xx acquires its first peak value 6 (nm∙μA/V2 ℏ/2e) around 1.99 +eV. The highest peak value is -40 (nm∙μA/V2 ℏ/2e) occurred at photon energy of 3.12 eV. When the +Néel vector rotate to x-axis, σSzx:xx keeps zero values, but the σSzy:xx is drastically enlarged [Fig. 3(b)]. +The first peak of σSzy:xx is -48 (nm∙μA/V2 ℏ/2e) at 1.61 eV. The strongest σSzy:xx peak in Fig. 3(b) is + +(a) +(b) +(c) +40 +2400 +24 +20 +30 +1800 +6 +20 +1200 +2 +10 +600 +-600 +4 +-20 +1200 +12 +-30 +n//z +n//x +0081 +16 +n//y +20 +2400 +24 +1.0 +1.5 +2.0 +2.5 +3.0 +3.5 +1.0 +1.5 +2.0 +2.5 +3.0 +3.5 +1.0 +1.5 +2.0 +2.5 +3.0 +3.5 +Photonenergy(eV) +Photon energy(eV) +Photon energy (eV) + +2237 (nm∙μA/V2 ℏ/2e) at 3.6 eV. For the MnPSe3 with Néel vector in y-axis, σSzx:xx presents finite +magnitudes while σSzy:xx vanishes [Fig. 3(c)]. And σSzx:xx get the first peak at 1.75 eV with value -2 +(nm∙μA/V2 ℏ/2e), and the largest σSzx:xx takes place at 3.09 eV with value 23 (nm∙μA/V2 ℏ/2e). +Hence, the photo-spin-currents are modulable via rotating the Néel vectors, which can be +explained by the switching of mirror symmetries. The photo-spin-conductance is related to the +conventional photoconductance by the equation σSz=sz×σC, and sz is odd about both My- and MxMz- +reflections. Therefore, the allowed propagation directions of spin currents (with sz-polarization) are +always orthogonal to the charge currents, i.e., the spin currents found here are pure without the net +movements of charges, which are desired for the low-consumption spintronics. Besides, it worths +noticing that the photo-spin-conductance for cases with Néel vectors along x-axis is stronger than +the other two cases by magnitude orders, indicating that the photon-to-spin conversions is switched +from shift-dominated mechanism to injection-dominated mechanism along with the rotations of +Néel vectors from y/z- to x-axis. This change in mechanism is further supported by the analysis of +the dependence of photo-spin-conductance on relaxation time (see Fig. S2 in supporting information +for more details). The injection-type spin-currents are intriguing and distinguished from the previous +reports,41-42 and the significantly large injection-spin-currents might open a new way for robust spin- +currents generations via illuminations. +To further investigate the structure of BPVs in MnPSe3, we plot the Brillouin zone (BZ) +distribution of photoconductance in Figure 4. The photon energy is 2.98 eV, corresponding to the +position of the strongest BPVE in Fig. 2. The most relevant states to the BPVE form several +butterfly-like regions in BZ. and their contributions and positions are controlled by the orientations +of Néel vectors, leading to the modulations on BPVE. Fig. 4(a) displays the BZ-distributions of +σCx:xx. The states in right part of BZ have positive crystal moments in x-direction and positively +contribute to the σCx:xx (blue colored), while the states in left part of BZ are negatively related to the +net σCx:xx (red colored). The topmost inset in Fig. 4(a) shows the case with Néel vectors along +z- +direction. The most relevant states are located at the right part of BZ. The contributions from +individual Bloch states reach as high as 4×106 (nm·μA/V2), three orders larger than the net value of +σCx:xx, indicating the net BPVE is the residual effect of many counteracting contributions. It is thus +hopeful to obtain ultra-large BPVE if one can optically excite the states with specific crystal + + + +momentums. When Néel vectors rotate to +x-direction [top right in Fig. 4(a)], the contributions from +left and right parts of BZ are both clear. For Néel vectors in +y-direction [bottom right in Fig. 4(a)], +the contribution regions move to the up part of BZ and become anti-symmetric to each other, in line +with the zero-value of σCx:xx in this case. The lowest inset in Fig. 4(a) shows the case with Néel +vectors in −z-direction. The contributions are dominated by the left part of BZ with negative values, +which is exactly the opposite of the case displayed in the topmost inset. Further rotating the Néel +vectors to −x- and −y-directions, we see the BZ-distributions of BPVE contributions are the opposite +of +x- and +y-cases. + +Figure 4. Photoconductances distributions on Brillouin zone that depend on the direction of Néel +vector of MnPSe3. (a) The BZ distributions of σCx:xx. (b) The BZ distributions of σCy:xx. The incident +light is linearly polarized in x-axis, with photon energy of 2.98 eV. The distributions placed at top, +top right, bottom right, bottom, bottom left, and up left correspond to the cases with Néel vectors +along +z, +x, +y, −z, −x, and −y directions. The hexagons are the irreducible Brillouin zone. For +better illustrations, τ is set to 0.1 ps here. + +Figure 4(b) displays the BZ-distributions of σCy:xx. They have the same positions as the +distributions of σCx:xx shown in Fig. 4(a), but the signs of contributions are different. The upper part +of BZ corresponds to the Bloch states with positive crystal moments in y-direction, and the +contributions in this region are blue, positively contributing to the net σCy:xx. The contributions of +lower part of BZ are in red color, exhibiting negative contributions to net σCy:xx. For cases with Néel +vectors along ±z- and ±x-directions, the contributions are anti-symmetric in the BZ, leading to the + +(a) +(b) +hw = 2.98eV +cx. (nm·A/V2) +hw =2.98eV +ox (nm-AV2) +Neel vecto +Neel vecto + +zero BPVEs. Only if the Néel vectors orient to ±y-directions, the contributions from upper and lower +parts of BZ are not anti-symmetric and nonzero BPVEs are permitted. All these results are in line +with former discussions on symmetries and agree with the integrated results displayed in Fig. 2. +To further understand the PT-BPVE in local coordinates and figure out how the PT- +polarizations interact with the dynamics of photo-electrons, we detect the real-space resolved +photoconductance with vector potentials projected to hopping tunnels (See supporting information +for more details), which are the spaces between atoms as shown in Fig. 5(a). Below, we focused on +the cases with Néel vectors along z-axis. + +Figure 5. Bulk photoconductance projected to real-space. (a) Atomic positions and possible hopping +tunnels in MnPSe3. The arrows denote several typical hopping tunnels in (P2Se6)4-. (b) σCx:xx in AFM +MnPSe3 projected to six types of tunnels. (c) σCx:xx in AFM MnPSe3 projected to six types of P-Se +tunnels. (d) σCx:xx in FM MnPSe3 projected to six types of P-Se tunnels. +We firstly classify the photoconductance σCx:xx into six types according to the hopping tunnels +including Mn-Mn, P-P, Se-Se, Mn-P, Mn-Se, and P-Se. The photocurrents are emitted by the +electron-hole combinations happened in either one of these tunnels. And the summation of all these +six types is exactly equal to the net BPVE displayed in Fig. 2(a). +Figure 5(b) shows the contributions from the six types. Comparing to the total σCx:xx shown in +Fig. 2(a), it is clear that the P-Se tunnels always dominate the BPVEs with highest value of 3795 +(nm·μA/V2), while the contributions of Se-Se tunnels are comparable but they are negative and the +strongest value is -2323 (nm·μA/V2). The Mn-Se tunnels are the third largest contributors, and its + +(a) +(b) +Se2 +Se; +Se2 +4000 +P +Mn-Mn +3000 +P-p +Ses +See +Se3 +Se-Se +2000 +Mn-P +1000 +Mn-Se +P-Se +Ses +Se. +Se4 +-1000 +Se +Se2 +Se +-3000 +n//z +-4000 +1.00 +1.25 +1.50 +1.75 +2.00 +2.25 +2.502.753.00 +(c) +(d) +Photon energy (eV) +1200 +250 +1000 +P-Se1 +200 +P-Se1 +800 +P-Se2 +150 +P-Se2 +600 +P-Se3 +P-Se3 +P-Se4 +100 +P-Se4 +400 +P-Se5 +P-Se5 +uu) +200 +P-Se6 +50 +P-Se6 +-200 +-50 +-400 +60 +6-100 +600 +-800 +-150 +n//z +-200 +m//z +0001- +1200 +250 +1.001.25 +1.50 +1.752.002.252.502.753.00 +1.00 +1.25 +1.50 +1.75 +2.00 +2.252.502.753.00 +Photon energy (eV) +Photon energy (eV) + +highest peak is 1772 (nm·μA/V2). Other tunnels contribute negligibly to the BPVEs. Therefore, the +BPVEs in MnPSe3 are mainly emitted by the hopping processes in the sublattice expanded by +(P2Se6)4- prisms. +Fig. 5(c) shows the σCx:xx further projected to the six types of P-Se tunnels, including tunnels +of P-Se1, P-Se2, P-Se3, P-Se4, P-Se5, P-Se6. The summation of all these six P-Se types is identical to +the contributions of P-Se tunnels displayed in Fig. 5(b) with grey lines. The real-space orientations +of tunnels of P-Se1 and P-Se2 are close to the x-axis [See Fig. 5(a)], and their contributions are nearly +coincided, showing the ideal phase alignment for the optoelectrical processes in these two tunnels. +And they constitute the most parts of photocurrents in the (P2Se6)4- prism sublattice with highest +peak values of ~1000 (nm·μA/V2). This ideal phase alignment is surprising since these two tunnels +are not symmetric counterparts in AFM MnPSe3. The contributions from the other four P-Se tunnels +are moderate, and their strongest peak value is 441 (nm·μA/V2). They coincide with each other due +to the My-mirror symmetry. +Fig. 5(d) shows the σCx:xx projected to the six P-Se tunnels [as the case in Fig. 5(c)] for the +MnPSe3 with parallel magnetic moments along z-axis, that is, the ferromagnetic (FM) case. +Although the P symmetry of FM MnPSe3 enforces the zero value for total BPVEs, the local +contributions are generally nonzero. The contributions from P-Se1 and P-Se2 tunnels are heavily +suppressed in this case, and the highest peak value is only 21 (nm·μA/V2), 100 times smaller than +the AFM case displayed in Fig. 5(c). On the other hand, the contributions of the other four P-Se +tunnels show peak values of 227 (nm·μA/V2), which is comparable to the AFM case, especially in +the low phonon energy range (<2 eV). Therefore, on the view of local photoelectrical responses, the +role of AFM order in Mn-sublattices is two-folds: aligning the phases of photocurrents, and +enhancing the photon-to-currents efficiencies in the direction of PT-polarization (x-direction in +present case). +In summary, we found the 2D monolayer MnPSe3 is promising to realize large and controllable +PT-BPVEs. The 2nd order photoconductance and photo-spin-conductance exceed 4000 (nm·μA/V2) +and 2000 (nm∙μA/V2 ℏ/2e) in the visible spectrum. Both the propagations and the spin-polarizations +of photocurrents are switchable via rotating the Néel vectors. These switching are enabled by the +mirror symmetries, which depend on the magnetization. The intralayer AFM orders of Mn2+ + + + +sublattice show essential roles in the 2D BPVEs, since they can stabilize the PT-polarizations and +lead to the phase alignments of photocurrents in the sublattice of (P2Se6)4-. Furthermore, we showed +that the PT-BPVEs in MnPSe3 are dominated by a small part of Bloch states in BZ, whose positions +and contributions are intimately controlled by the Néel vectors. All these results shed light into the +PT-BPVEs in 2D anti-ferromagnets, and indicate that the 2D monolayer MnPSe3 is an ideal platform +to achieve extraordinary PT-BPVEs, meriting future energy and spintronic applications. + +Computational Method. The geometry optimization and electronic structure of MnPSe3 in ground +state are calculated within Vienna atomic simulation pack (VASP),43 based on relativistic density +functional theory (DFT). Projected augmentation plane wave basis (PAW) is utilized and the plane +waves are cutoff at 400 eV. The exchange-correlation effects amongst electrons are captured via +generalized gradient approximation (GGA) with the functional of Perdew-Burke-Ernzerh (PBE) +form.44 A vacuum layer of 20 Å is set to isolate the layers in nonperiodic direction to eliminate the +unphysical interactions between neighboring slabs. Brillouin zone is sampled with a Γ-centered k- +mesh 10×10×1 using Monkhorst-Pack scheme.45 The geometry relaxation is carried out until the +maximum force is smaller than 0.001 eV/Å. Energy convergent criteria for the self-consistent +iterative calculations on the electronic structures is 10-6 eV/atom. +Since the GGA functional usually underestimates the strong interactions between d-electrons +of transition metal compounds (in our case, standard GGA leads to metal ground states of MnPSe3, +which is inconsistent with the experiments), we employed the GGA + Ueff method with Ueff = 3.0 +eV for d-electrons of Mn. This value of Ueff leads to the correct magnetic ground states and is in line +with former studies on the MnPS3.32 +For the calculations of BPVE based on eq. 1 and related expressions, we construct the effective +real-space tight-binding Hamiltonian via projecting the Bloch states obtained from relativistic DFT +into the Hilbert space expanded by Wannier orbitals using WANNIER90,46-47 then the k-space +Hamiltonians on general k-points are interpolated by solving the eigen-equations. The Wannier +orbital basis include the 3d and 4s orbitals for Mn ions, 3s and 3p orbitals for P ions, and 4s and 4p +orbitals for Se ions. It is found that the effective tight-binding Hamiltonian can reproduce the + + + +electronic states predicted by relativistic DFT and the band structures of the effective model and the +DFT coincide everywhere in the relevant energy window (see Figure S3 in Supporting information +for more details), revealing the efficiency of the basis transformation. The k-grid utilized for the +Brillouin zone integration in equation 1 is 800×800×1. A denser k-grid 1600×1600×1 is used to test +the convergence of k-mesh sampling and we find the difference < 5%. + + + + + +Notes +The authors declare no competing financial interest. + +ACKNOWLEDGMENT +This work was supported by Natural Science Foundation of Shandong (Grant No. ZR2022QA019), +National Natural Science Foundation of China (Grant Nos. 12074221, 52171181, 52002222, +51472150, 2021-869, 11904204). + +Supporting information available: Extracting out the expression of BPVEs from potentials; +Expressions of spin and real-space projected BPVEs. + +REFERENCES +(1) Kraut, W.; von Baltz, R. Anomalous Bulk Photovoltaic Effect in Ferroelectrics: A Quadratic +Response Theory. Physical Review B 1979, 19, 1548-1554. +(2) von Baltz, R.; Kraut, W. Theory of the Bulk Photovoltaic Effect in Pure Crystals. Physical Review +B 1981, 23, 5590-5596. +(3) Choi, T.; Lee, S.; Choi, Y. J.; Kiryukhin, V.; Cheong, S.-W. Switchable Ferroelectric Diode and +Photovoltaic Effect in Bifeo3. Science 2009, 324, 63-66. +(4) Yang, S. Y.; Seidel, J.; Byrnes, S. J.; Shafer, P.; Yang, C. H.; Rossell, M. D.; Yu, P.; Chu, Y. H.; Scott, +J. F.; Ager, J. W., 3rd, et al. Above-Bandgap Voltages from Ferroelectric Photovoltaic Devices. Nature +nanotechnology 2010, 5, 143-147. +(5) Daranciang, D.; Highland, M. J.; Wen, H.; Young, S. M.; Brandt, N. C.; Hwang, H. Y.; Vattilana, +M.; Nicoul, M.; Quirin, F.; Goodfellow, J., et al. Ultrafast Photovoltaic Response in Ferroelectric +Nanolayers. Phys Rev Lett 2012, 108, 087601. +(6) Spanier, J. E.; Fridkin, V. M.; Rappe, A. M.; Akbashev, A. R.; Polemi, A.; Qi, Y.; Gu, Z.; Young, S. +M.; Hawley, C. J.; Imbrenda, D. Power Conversion Efficiency Exceeding the Shockley–Queisser Limit +in a Ferroelectric Insulator. Nature Photonics 2016, 10, 611-616. +(7) Zhang, Y.; Holder, T.; Ishizuka, H.; de Juan, F.; Nagaosa, N.; Felser, C.; Yan, B. Switchable +Magnetic Bulk Photovoltaic Effect in the Two-Dimensional Magnet Cri3. Nature Communication 2019, +10, 3783. + + + +(8) Li, Y.; Fu, J.; Mao, X.; Chen, C.; Liu, H.; Gong, M.; Zeng, H. Enhanced Bulk Photovoltaic Effect +in Two-Dimensional Ferroelectric Cuinp2s6. Nature Communication 2021, 12, 5896. +(9) Xu, H.; Wang, H.; Zhou, J.; Li, J. Pure Spin Photocurrent in Non-Centrosymmetric Crystals: Bulk +Spin Photovoltaic Effect. Nature Communication 2021, 12, 4330. +(10) Paillard, C.; Bai, X.; Infante, I. C.; Guennou, M.; Geneste, G.; Alexe, M.; Kreisel, J.; Dkhil, B. +Photovoltaics with Ferroelectrics: Current Status and Beyond. Adv Mater 2016, 28, 5153-5168. +(11) Sipe, J. E.; Shkrebtii, A. I. Second-Order Optical Response in Semiconductors. Physical Review B +2000, 61, 5337. +(12) Fridkin, V. M. Bulk Photovoltaic Effect in Noncentrosymmetric Crystals. Crystallography Reports +2001, 46, 654-658. +(13) Lee, D.; Baek, S. H.; Kim, T. H.; Yoon, J. G.; Folkman, C. M.; Eom, C. B.; Noh, T. W. Polarity +Control of Carrier Injection at Ferroelectric/Metal Interfaces for Electrically Switchable Diode and +Photovoltaic Effects. Physical Review B 2011, 84. +(14) Yang, M.-M.; Kim Dong, J.; Alexe, M. Flexo-Photovoltaic Effect. Science 2018, 360, 904-907. +(15) Mu, X.; Pan, Y.; Zhou, J. Pure Bulk Orbital and Spin Photocurrent in Two-Dimensional +Ferroelectric Materials. npj Computational Materials 2021, 7. +(16) Xu, H.; Wang, H.; Zhou, J.; Guo, Y.; Kong, J.; Li, J. Colossal Switchable Photocurrents in +Topological Janus Transition Metal Dichalcogenides. npj Computational Materials 2021, 7. +(17) Guo, Y.; Zhou, J.; Xie, H.; Chen, Y.; Wang, Q. Screening Transition Metal-Based Polar Pentagonal +Monolayers with Large Piezoelectricity and Shift Current. npj Computational Materials 2022, 8. +(18) Wang, Q.; Zheng, J.; He, Y.; Cao, J.; Liu, X.; Wang, M.; Ma, J.; Lai, J.; Lu, H.; Jia, S., et al. Robust +Edge Photocurrent Response on Layered Type Ii Weyl Semimetal Wte2. Nature Communication 2019, +10, 5736. +(19) Holder, T.; Kaplan, D.; Yan, B. Consequences of Time-Reversal-Symmetry Breaking in the Light- +Matter Interaction: Berry Curvature, Quantum Metric, and Diabatic Motion. Physical Review Research +2020, 2. +(20) Watanabe, H.; Yanase, Y. Chiral Photocurrent in Parity-Violating Magnet and Enhanced Response +in Topological Antiferromagnet. Physical Review X 2021, 11. +(21) Wang, H.; Qian, X. Electrically and Magnetically Switchable Nonlinear Photocurrent in Рт- +Symmetric Magnetic Topological Quantum Materials. npj Computational Materials 2020, 6. +(22) Huang, B.; Clark, G.; Navarro-Moratalla, E.; Klein, D. R.; Cheng, R.; Seyler, K. L.; Zhong, D.; +Schmidgall, E.; McGuire, M. A.; Cobden, D. H., et al. Layer-Dependent Ferromagnetism in a Van Der +Waals Crystal Down to the Monolayer Limit. Nature 2017, 546, 270-273. +(23) Gong, Y.; Guo, J.; Li, J.; Zhu, K.; Liao, M.; Liu, X.; Zhang, Q.; Gu, L.; Tang, L.; Feng, X., et al. +Experimental Realization of an Intrinsic Magnetic Topological Insulator. Chinese Physics Letters 2019, +36. + + + +(24) Otrokov, M. M.; Klimovskikh, II; Bentmann, H.; Estyunin, D.; Zeugner, A.; Aliev, Z. S.; Gass, S.; +Wolter, A. U. B.; Koroleva, A. V.; Shikin, A. M., et al. Prediction and Observation of an +Antiferromagnetic Topological Insulator. Nature 2019, 576, 416-422. +(25) Cao, Y.; Fatemi, V.; Fang, S.; Watanabe, K.; Taniguchi, T.; Kaxiras, E.; Jarillo-Herrero, P. +Unconventional Superconductivity in Magic-Angle Graphene Superlattices. Nature 2018, 556, 43-50. +(26) Susner, M. A.; Chyasnavichyus, M.; McGuire, M. A.; Ganesh, P.; Maksymovych, P. Metal Thio- +and Selenophosphates as Multifunctional Van Der Waals Layered Materials. Adv Mater 2017, 29. +(27) Huang, H.; Shang, M.; Zou, Y.; Song, W.; Zhang, Y. Iron Phosphorus Trichalcogenide Ultrathin +Nanosheets: Enhanced Photoelectrochemical Activity under Visible-Light Irradiation. Nanoscale 2019, +11, 21188-21195. +(28) Lee, J.-U.; Lee, S.; Ryoo, J. H.; Kang, S.; Kim, T. Y.; Kim, P.; Park, C.-H.; Park, J.-G.; Cheong, H. +Ising-Type Magnetic Ordering in Atomically Thin Feps3. Nano Letters 2016, 16, 7433-7438. +(29) Ramos, M.; Carrascoso, F.; Frisenda, R.; Gant, P.; Mañas-Valero, S.; Esteras, D. L.; Baldoví, J. J.; +Coronado, E.; Castellanos-Gomez, A.; Calvo, M. R. Ultra-Broad Spectral Photo-Response in Feps3 Air- +Stable Devices. npj 2D Materials and Applications 2021, 5. +(30) Zhu, W.; Gan, W.; Muhammad, Z.; Wang, C.; Wu, C.; Liu, H.; Liu, D.; Zhang, K.; He, Q.; Jiang, +H., et al. Exfoliation of Ultrathin Feps3 Layers as a Promising Electrocatalyst for the Oxygen Evolution +Reaction. Chem Commun (Camb) 2018, 54, 4481-4484. +(31) Kumar, R.; Jenjeti, R. N.; Austeria, M. P.; Sampath, S. Bulk and Few-Layer Mnps3: A New +Candidate for Field Effect Transistors and Uv Photodetectors. Journal of Materials Chemistry C 2019, +7, 324-329. +(32) Long, G.; Henck, H.; Gibertini, M.; Dumcenco, D.; Wang, Z.; Taniguchi, T.; Watanabe, K.; Giannini, +E.; Morpurgo, A. F. Persistence of Magnetism in Atomically Thin Mnps3 Crystals. Nano Lett 2020, 20, +2452-2459. +(33) Wildes, A. R.; Simonet, V.; Ressouche, E.; McIntyre, G. J.; Avdeev, M.; Suard, E.; Kimber, S. A. J.; +Lançon, D.; Pepe, G.; Moubaraki, B., et al. Magnetic Structure of the Quasi-Two-Dimensional +Antiferromagnet Nips3. Physical Review B 2015, 92. +(34) Lançon, D.; Walker, H. C.; Ressouche, E.; Ouladdiaf, B.; Rule, K. C.; McIntyre, G. J.; Hicks, T. J.; +Rønnow, H. M.; Wildes, A. R. Magnetic Structure and Magnon Dynamics of the Quasi-Two-Dimensional +Antiferromagnet Feps3. Physical Review B 2016, 94. +(35) Kim, T. Y.; Park, C. H. Magnetic Anisotropy and Magnetic Ordering of Transition-Metal +Phosphorus Trisulfides. Nano Lett 2021, 21, 10114-10121. +(36) Li, X.; Cao, T.; Niu, Q.; Shi, J.; Feng, J. Coupling the Valley Degree of Freedom to +Antiferromagnetic Order. Proceedings of the National Academy of Sciences of the United States of +America 2013, 110, 3738-3742. +(37) Ni, Z.; Haglund, A. V.; Wang, H.; Xu, B.; Bernhard, C.; Mandrus, D. G.; Qian, X.; Mele, E. J.; Kane, +C. L.; Wu, L. Imaging the Neel Vector Switching in the Monolayer Antiferromagnet Mnpse3 with Strain- +Controlled Ising Order. Nature nanotechnology 2021, 16, 782-787. + + + +(38) Ibañez-Azpiroz, J.; Tsirkin, S. S.; Souza, I. Ab Initio Calculation of the Shift Photocurrent by +Wannier Interpolation. Physical Review B 2018, 97, 245143. +(39) Xu, H.; Wang, H.; Li, J. Nonlinear Nonreciprocal Photocurrents under Phonon Dressing. Physical +Review B 2022, 106. +(40) Dai, Z.; Schankler, A. M.; Gao, L.; Tan, L. Z.; Rappe, A. M. Phonon-Assisted Ballistic Current from +First-Principles Calculations. Phys Rev Lett 2021, 126, 177403. +(41) Fei, R.; Song, W.; Pusey-Nazzaro, L.; Yang, L. Pt-Symmetry-Enabled Spin Circular Photogalvanic +Effect in Antiferromagnetic Insulators. Physical Review Letters 2021, 127. +(42) Xiao, R.-C.; Shao, D.-F.; Li, Y.-H.; Jiang, H. Spin Photogalvanic Effect in Two-Dimensional +Collinear Antiferromagnets. npj Quantum Materials 2021, 6. +(43) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. +Physical Review B 1999, 59. +(44) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. +Rev. Lett. 1996, 77, 3865. +(45) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13, +5188-5192. +(46) Mostofi, A. A.; Yates, J. R.; Pizzi, G.; Lee, Y.-S.; Souza, I.; Vanderbilt, D.; Marzari, N. An Updated +Version of Wannier90: A Tool for Obtaining Maximally-Localised Wannier Functions. Computer Physics +Communications 2014, 185, 2309-2310. +(47) Pizzi, G.; Vitale, V.; Arita, R.; Blugel, S.; Freimuth, F.; Geranton, G.; Gibertini, M.; Gresch, D.; +Johnson, C.; Koretsune, T., et al. Wannier90 as a Community Code: New Features and Applications. +Journal of physics. Condensed matter : an Institute of Physics journal 2020, 32, 165902. + + diff --git a/f9E1T4oBgHgl3EQfMAPe/content/tmp_files/load_file.txt b/f9E1T4oBgHgl3EQfMAPe/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..2ebd9a35f6d5c32af6486dff5674e886720539d3 --- /dev/null +++ b/f9E1T4oBgHgl3EQfMAPe/content/tmp_files/load_file.txt @@ -0,0 +1,1104 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf,len=1103 +page_content='Switchable Giant Bulk Photocurrents and Photo-spin-currents in Monolayer PT- symmetric Anti-ferromagnet MnPSe3 Liang Liu, Weikang Liu, Bin Cheng, Bin Cui, Jifan Hu* School of Physics, State key laboratory for crystal materials, Shandong University, Jinan 250100, China.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' To who should be corresponded: hujf@sdu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='edu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='cn ABSTRACT Converting light into steady currents and spin-currents in two-dimensional (2D) platform is essential for future energy harvesting and spintronics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' We show that the giant and modulable bulk photovoltaic effects (BPVEs) can be achieved in air-stable 2D antiferromagnet (AFM) monolayer MnPSe3, with nonlinear photoconductance > 4000 nm∙μA/V2 and photo-spin-conductance > 2000 (nm∙μA/V2 ℏ /2e) in the visible spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The propagation and the spin-polarizations of photocurrents can be switched via simply rotating the Néel vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' We unveil that the PT-symmetry, mirror symmetries, and spin-orbital-couplings are the keys for the observed sizable and controllable 2D BPVEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' All the results provide insights into the BPVEs of 2D AFM, and suggest that the layered MnPSe3 is an outstanding 2D platform for energy device and photo-spintronics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' TOC GRAPHIC Anti-ferromagnetism enables efficient 2D solar cell in MnPSe3 atomic thin layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' PT MnPSe3 Bulk photovoltaic effects (BPVEs) convert the incident light into steady currents in homogeneous crystals, sparking intense interests due to the potentials for energy harvesting, rectifications, spintronics, spectroscopes, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 1-9 BPVEs have been thought to be dominated by the profound shift mechanism, 10-12 in which the photocurrents are due to the continuous shifts of valence and conduction electrons in the non-centrosymmetric lattice during the photo-pumping processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' To date, the shift-type BPVEs have been realized in ferroelectrics, 3, 8, 10, 13 piezoelectrics,14-17 and topological Weyl semimetals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='18 On the other hand, it is also possible to generate BPVEs via injection mechanism in which the net photocurrents are due to the unbalances in group velocities amongst the photo-excited carriers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='19-20 Recently, several studies have predicted that the injection-type BPVEs can be observed in two-dimensional (2D) bilayer anti-ferromagnets (AFM) CrI3 7 and MnBi2Te4,9, 21 which possess the parity-temporal (PT) symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' PT-BPVEs are believed to be superior since the injection currents running in these systems are usually larger than the shift currents by several magnitude orders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' More importantly, the incorporation of magnetism in BPVEs offers numerous modulation paths and opens a wealth of possibilities for opto-spintronic applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' However, the 2D materials suitable for PT-BPVE are very few in records.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' For the proposals of bilayer PT-AFM, the essential PT-symmetries stand on the long-range van der Waals (vdW) interlayer couplings, 7, 9, 21-24 and the weak vdW strengths in these interactions limit the magnitudes of photocurrents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Besides, the ubiquitous layer-slides, twists in vdW bilayers 25 might break the PT-symmetries and harm the BPVEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' On the other hand, the poor magnetic and air stabilities of CrI3 and MnBi2Te4 cannot fulfill the demanding of realistic applications perfectly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 21-24 Hence, it is quite desired to discovery better platforms to realize PT-BPVEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' MnPSe3 belongs to the family of transition metal thiophosphates (MPX3, with M=Mn, Fe, Co, Ni;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' X=S, Se), which are layered magnetic semiconductors with band gaps suitable for visible light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' And they are easy to be exfoliated to 2D layers with high qualities due to the ultra-weak vdW interlayer interactions and outstanding air stabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 26 So, they exhibit extraordinary performances in optoelectronic responses and opto-chemistry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 27-32 However, there are notable paucity of studies investigating the BPVEs in 2D MPX3, since MPX3 have centrosymmetric lattice and no shift- currents are allowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 33-35 Manganese thiophosphates are exceptional, the AFM hexagonal sublattice expanded by Mn2+ ions break the inversion symmetry (P-symmetry) and the PT-polarization is thus hosted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 35-36 Furthermore, the anti-ferromagnetism of MnPSe3 is amenable to external modulations via strains and magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 37 Therefore, it is intriguing to see if the PT-AFM MnPSe3 can exhibit modulable and large PT-BPVEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' In this work, we predict the PT-BPVEs of monolayer MnPSe3 induced by the illuminations of linearly polarized visible light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Based on the first-principle calculations, we show that the PT- polarizations in MnPSe3 are stabilized by the intra-layer AFM order and the strong spin-orbital- couplings (SOC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Surprisingly, the PT-polarizations can perfectly align the phases of local photocurrents in (P2Se6)4- prisms, inducing large BPVEs with 2nd order photoconductance exceeding 4000 nm∙μA/V2 and photo-spin-conductance exceeding 2000 (nm∙μA/V2 ℏ /2e) in the visible spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' We also unveil that the 2D BPVs and the Néel vectors are intimately intertwined through the mirror symmetries, enabling abundant controlling routes for photocurrents and photo-spin- currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' It is possible to regulate the magnitudes, switch the propagations, and reversing the spin polarizations of photocurrents via rotating the Néel vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Hence, MnPSe3 is the ideal platform to realize 2D PT-BPVEs, providing opportunities for high-efficient energy and controllable opto- spintronic applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Figure 1(a) shows the lattice of MnPSe3 that consists of (P2Se6)4- prisms and two Mn- sublattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Our density functional theory calculations indicate that the Mn2+ ions possess local magnetic moment of 5μB, and the nearest neighbored magnetic moments are anti-parallel, consist with previous studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='36 The anti-ferromagnetic honeycomb framework of Mn-sublattices displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 1(a) breaks the P-symmetry because the P-operation interchanges the two Mn-sublattices with opposite magnetic moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Once the P-operation is followed by time reversal (T) operation which reverses all the magnetic moments, the system coincides with itself, that is, the PT-symmetry is preserved in the monolayer MnPSe3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The lacking of P-symmetry indicates the MnPSe3 monolayer is a polar crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' This kind of polarization is apparently not related to the non- centrosymmetric crystal geometry but the AFM emerged from the strong interactions between electrons, and we call this as PT-polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Lattice, magnetic, electronic, and photovoltaic structures of MnPSe3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (a) The top view of monolayer MnPSe3 lattice and the photocurrents and photo-spin-currents induced by the illuminations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The grey and green balls denote P and Se atoms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Blue and red balls denote the Mn atoms with opposite magnetic moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (b) The typical dual valley structure in PT-AFM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Thick arrows denote the photo-induced hopping process and small arrows denote the group velocities of photo-excited holes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (c) The mirror reflections in MnPSe3 monolayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Dashed lines denote the mirror planes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (d) The band structure of MnPSe3 with Néel vector orientation along x-, y-, and z- directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' It is important to note that the PT-polarization found in this study is distinguished with previous reports on bilayer CrI3 7 and MnBi2Te4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 9, 21 In those systems, the PT-polarizations depend on the stacking order of bilayers and the long-range interlayer AFM couplings across vdW gaps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' On the contrary, the PT-polarization in MnPSe3 is induced by the strong short-range intralayer AFM exchange couplings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' In addition, the intralayer crystal structure, which is based on the sturdy covalence bonds, is also more stable than the interlayer structures, which are based on the long- range vdW interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' As a result, the monolayer MnPSe3 is expected to have more robust PT- polarization, larger nonlinear opto-electronic couplings, and better stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Figure 1(b) shows the basic process of injection-type BPVs enabled by the PT-polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=" K (a) (b) hv 12 hv Mn K K' (c) (d) n//x n//y n//z 2." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='00 XKiXK!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='75 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='75 (eV) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='58 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='50 KMK 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='50 KMK 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='50 KMK and K’ label the dual valleys with opposite momentum i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=', K’ = −K, and they are related to each other by P- and T-operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Since both P- and T-symmetries are broken, the degenerations between K and K’ valleys are no longer to be enforced by these two symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' On the other hand, the valley-polarizations are also ruled by the mirror symmetry since some mirror operations interchange the dual valleys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Given the fact that the mirror symmetries are readily switchable via simply rotating the Néel vectors, it is straight to see that the PT-AFM with suitable mirror symmetries possess controllable valley-polarizations, exhibiting intriguing electronic structures for modulable photoelectronic responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Figure 1(c) shows the two possible mirror operations in MnPSe3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The first one termed as My is the reflection about the mirror plane My which is vertical to the basal plane and crosses the (P2Se6) prisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' My interchanges the dual Mn-sublattices, and flips the magnetic moments with x/z- orientations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Therefore, MnPSe3 with Néel vector along x/z-directions preserve the My-symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The second mirror operation termed as MxMz is a combination of double reflections about the one mirror perpendicular and the other vertical to the atomic plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The Mn-sublattices do not exchange under MxMz, and the magnetic moments along y-directions are also preserved in MxMz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' So, for the MnPSe3 with Néel vector along y-direction, the MxMz-symmetry is preserved.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' More essentially, since the MxMz-operation interchanges the dual valleys while My-operation does not, the valley- polarizations in MnPSe3 are prohibited in MxMz-symmetric case but allowed in My-symmetric case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Therefore, via simply rotating the magnetization orientations, we can readily obtain desired mirror- symmetry and switch the valley-polarizations in MnPSe3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Figure 1(d) shows the band structures of MnPSe3 predicted by relativistic DFT, with Néel vectors along x-, y-, and z-directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' In all cases, the band gap emerged in the corners of Brillouin zone (BZ), either K or K’, indicating the valley structures dominate the low-energy opto-electronic responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' For the MnPSe3 with magnetic moments along z-axis, the asymmetries between K and K’ valleys are obvious.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The energy gaps at K and K’ are ΔK = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5196 eV and ΔK’ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5838 eV, corresponding to the valley-polarization energy of 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='2 meV, which is a large value and consistent with previous studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='36 For the case with Néel vectors along x-axis, we have ΔK = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5632 eV and ΔK’ = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5635 eV, so the valley-polarization energy shrinks to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='3 meV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The reason for this significant shrinking is that the valley-polarization is proportional to the efficiency of spin-orbit-coupling (SOC), and the system with magnetizations along x-axis exhibits negligible SOC for BZ corner states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' In 2D systems, the orbital moments of Bloch electrons around the BZ corners are dominated by the z-component, the z-orientated spins thus display the strongest SOC and valley-polarizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' For the y-magnetization, the valley polarization is forbidden by MxMy-symmetry and ΔK =ΔK’ =1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5634 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Besides, the symmetric aspects of band structure on the inner part of BZ also show clear dependences on the magnetization orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' For MnPSe3 with Néel vectors along x- and z- directions, the asymmetries of valence bands about M point are shown by the red arrows marked in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 1(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The extents of band asymmetries are similar in x- and z-magnetized cases, indicating that the orbital moments around M point have comparable x- and z-components, so that the efficiencies of SOC in these states are close to each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' BPVE is the 2nd order opto-electronic responses, and the photocurrents jμC can be phenomenologically expressed as: 𝑗𝐶 𝜇 = 𝑅𝑒 ∑ 𝜎𝐶 𝜇:𝛼𝛽(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='𝜔, −𝜔)𝐸𝛼(𝜔)𝐸𝛽(−𝜔) 𝛼𝛽 , where μ, α, and β can be x/y/z directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' ω denotes the frequency of photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' σCμ:αβ is the 3-ranked tensor of BPVE photoconductance, Eα/β denotes the α/β component of electric fields of incident light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' For the system with P-symmetry, the P-operation will reverse the 𝑗𝐶 𝜇 in l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' but preserve the r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='h.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=', leading to the vanishing of BPVEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' So, the anti-ferromagnetism which produces PT-polarizations and lifts the P- symmetry in MnPSe3 is the key for the nonzero BPVEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' On the other hand, although σCμ:αβ always breaks the T-symmetry due to the relaxation dynamics of photo-induced carriers which lacks time reciprocities, the details of how the T-symmetry is broke decides the magnitude and direction of PT- polarization, thus is also significantly relevant to PT-BPVEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='19 In the following, we focus on the BPVEs generated by the light which are linearly polarized in x-axis, and only the real part of σCx:xx and σCy:xx are relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Other directions of BPVE can be obtained by the considerations on symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Microscopically, the BPVE can be evaluated by the nonlinear response theory, and the dominated contribution is expressed as: 7, 20, 38 𝜎𝐶 𝜇:𝛼𝛽(0;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' ω, −ω) = 2𝑒3 𝑆ω2 ∑ ∑ 𝑓𝑙𝑛 𝑣𝑘,𝑚𝑛 𝜇 𝑣𝑘,𝑛𝑙 𝛼 𝑣𝑘,𝑙𝑚 𝛽 (𝐸𝑘,𝑚𝑛 − 𝑖ℏ/𝜏)(𝐸𝑘,𝑙𝑚 − ℏΩ) 𝑙𝑚𝑛,Ω=±ω 𝑘∈𝐵𝑍 (1) here k labels the k-point in irreducible BZ and l, m, n label the band index, 𝑣𝑘,𝑙𝑚 𝜇 is the matrix elements of velocity operator, 𝐸𝑘,𝑚𝑙 = 𝐸𝑘,𝑚 − 𝐸𝑘,𝑙 denotes the difference in band energies, 𝑓𝑙𝑛 = 𝑓𝑙 − 𝑓𝑛 is the difference of occupations in lth and nth bands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' ω is the magnitude of frequency of incident light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' τ is the relaxation time for intra-band process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' In principle, the relaxation time τ might depend on momentum, band indices, and frequencies of light, because of impurity scattering, electron-phonons couplings, many-body interactions, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' However, several previous studies have showed that it is still reasonable to consider an average and constant relaxation time approximation in the calculations of BPVEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='39-40 Hence, in this study we adopt the constant relaxation time approximation and take the default value ℏ/𝜏 = 1 𝑚𝑒𝑉, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=', τ≈0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='6 ps by default.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' This setting is rather conservative since the MnPSe3 is supposed to be a clean crystal due to its excellent chemical stabilities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' S is the area of MnPSe3 cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Since the thickness of 2D monolayer is not well-defined, we do not average the photoconductance over volume but area.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' So, the σC calculated in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 1 is related to conventional definition of 2nd order photoconductances in 3D systems σC3D by σC=LσC3D, in which L is the effective thickness of 2D monolayer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' And the unit of σC in eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 1 is nm⋅μA/V2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Figure 2 shows the calculated nonlinear photoconductance of BPVE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' For MnPSe3 with Néel vector along z-axis [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 2(a)], σCx:xx exhibits several peaks in the visible spectrum with photon energy range from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='6 eV to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='6 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The first peak of σCx:xx occurs at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='83 eV, slighter higher than the energy gap of ~1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The peak value is −187 (nm∙μA/V2), which is comparable to the highest BPVE conductance previously reported in bilayer AFM systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 7, 9 The strongest peak of σCx:xx is at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='98 eV, with magnitude 4152 (nm∙μA/V2), which is ~10-folds larger than the previous proposals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' On the other hand, σCy:xx vanishes at all photon energies, consistent with the My-symmetry since σCy:xx is proportional to vy×vx×vx which is odd in My-reflection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Therefore, the photocurrents induced by the linearly polarized light only propagate along the x-axis in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Note that because of the injection mechanism of BPVEs in MnPSe3, the magnitude of photoconductance is proportional to the value of relaxation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='7, 20 The explicit dependence of BPVEs on relaxation time are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' S1 in supporting information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Since the utilized relaxation time constants of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='6ps is conservative, the estimations on the BPVEs should be conservative, too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Photoconductance σCx:xx and σCy:xx for MnPSe3 with Néel vector along (a) z-direction, (b) -z-direction, (c) x-direction, and (d) y-direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The hexagon in the left-down part of each figure denotes the magnetic lattice formed by Mn2+ ions, and the arrows on it denote the orientations of local magnetic moments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The directions of Néel vectors are marked aside the hexagons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Then we reverse the Néel vector to −z-direction, and the σCx:xx displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 2(b) becomes the opposite of the case discussed before, indicating that the propagation directions of photocurrents are locked with the orientation of Néel vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' This is in consistency with our previous discussions on T-symmetry i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=', the photocurrent propagation is related to PT-polarization, which is further controlled by the magnetizations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' And this behavior suggests a promising route to read out the nonvolatile information stored as Néel vectors in MnPSe3 via the BPVEs, which is essential for the 2D opto-spintronic memories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 2(c) displays the photoconductance of MnPSe3 with Néel vector along x-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Once again, due to the My-symmetry, σCy:xx is zero everywhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The first peak of σCx:xx now occurs around 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='73 eV with value −100 (nm∙μA/V2), and the highest peak of σCx:xx in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 1(c) is 4436 (nm∙μA/V2) at 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='02 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Comparing to the ±z-cases discussed before, the photocurrents induced by low-energy photons is smaller here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' This can be explained by the valley structures show in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 1(d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Since the valley-polarizations in x-magnetized system are much smaller, the low-energy photoconductance, which is dominated by the valley-polarization, should be weaker.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Besides, the several high peaks in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 2(c) have magnitudes comparable with ±z-magnetized cases, revealing that the high-energy (a) (b) A 40N0 4000 i 3000 000 u) 2000 2000 1000 1000 1000 Photoco 2000 2000 3000 n//z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 3000 n// z 4000 000 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 (c) Photonenergy (eV) (d) Photon energy (eV) 4000 Photoconductance (nm:μA/V ) 000 3000 3000 2000 2000 0001 1000 1000 1000 2000 2000 n//x 3000 n//y 4000 1000 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 Photon encrgy (cV) Photon energy (eV) photoconductance is free from the valley-related opto-electronic processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 2(d) displays the case with Néel vector along y-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' σCx:xx becomes zero at all photon energies, thus the photocurrents generated by linearly polarized light run in y-axis solely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' This perpendicular switching of photocurrents propagation is caused by the switching of mirror symmetries from My to MxMz, which is brought about by the rotations of Néel vectors from x/z-axis to y-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The σCx:xx is odd in My mirror operation, thus no photocurrents in x-axis are allowed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' For σCy:xx, it reaches the first peak at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='97 eV with value 241 (nm∙μA/V2), and the highest peak value is −3059 (nm∙μA/V2) occurred at photon energy of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='98 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' In addition, the 2D BPVEs of MnPSe3 also generate pure spin-currents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' We detect the spin- resolved photocurrents with vector potentials projected to spin tunnels, and compute the nonlinear photo-spin-conductance tensor σSzμ:αβ, which is relevant for spin-currents (See supporting information for more details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The spin polarizations in photocurrents are dominate by the z- component in most cases, we thus focused on the photo-spin-conductance with z-polarization, which are displayed in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Photo-spin-conductance σSzx:xx and σSzy:xx for MnPSe3 with Néel vector along (a) z- direction, (b) x-direction, and (c) y-direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Figure 3(a) shows the photo-spin-conductance in system with Néel vectors along z-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Firstly, σSzx:xx vanishes at all energies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' σSzy:xx acquires its first peak value 6 (nm∙μA/V2 ℏ/2e) around 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='99 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The highest peak value is -40 (nm∙μA/V2 ℏ/2e) occurred at photon energy of 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='12 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' When the Néel vector rotate to x-axis, σSzx:xx keeps zero values, but the σSzy:xx is drastically enlarged [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 3(b)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The first peak of σSzy:xx is -48 (nm∙μA/V2 ℏ/2e) at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='61 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The strongest σSzy:xx peak in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 3(b) is (a) (b) (c) 40 2400 24 20 30 1800 6 20 1200 2 10 600 600 4 20 1200 12 30 n//z n//x 0081 16 n//y 20 2400 24 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='5 Photonenergy(eV) Photon energy(eV) Photon energy (eV) 2237 (nm∙μA/V2 ℏ/2e) at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='6 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' For the MnPSe3 with Néel vector in y-axis, σSzx:xx presents finite magnitudes while σSzy:xx vanishes [Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 3(c)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' And σSzx:xx get the first peak at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='75 eV with value -2 (nm∙μA/V2 ℏ/2e), and the largest σSzx:xx takes place at 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='09 eV with value 23 (nm∙μA/V2 ℏ/2e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Hence, the photo-spin-currents are modulable via rotating the Néel vectors, which can be explained by the switching of mirror symmetries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The photo-spin-conductance is related to the conventional photoconductance by the equation σSz=sz×σC, and sz is odd about both My- and MxMz- reflections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Therefore, the allowed propagation directions of spin currents (with sz-polarization) are always orthogonal to the charge currents, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=', the spin currents found here are pure without the net movements of charges, which are desired for the low-consumption spintronics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Besides, it worths noticing that the photo-spin-conductance for cases with Néel vectors along x-axis is stronger than the other two cases by magnitude orders, indicating that the photon-to-spin conversions is switched from shift-dominated mechanism to injection-dominated mechanism along with the rotations of Néel vectors from y/z- to x-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' This change in mechanism is further supported by the analysis of the dependence of photo-spin-conductance on relaxation time (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' S2 in supporting information for more details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The injection-type spin-currents are intriguing and distinguished from the previous reports,41-42 and the significantly large injection-spin-currents might open a new way for robust spin- currents generations via illuminations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' To further investigate the structure of BPVs in MnPSe3, we plot the Brillouin zone (BZ) distribution of photoconductance in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The photon energy is 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='98 eV, corresponding to the position of the strongest BPVE in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The most relevant states to the BPVE form several butterfly-like regions in BZ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' and their contributions and positions are controlled by the orientations of Néel vectors, leading to the modulations on BPVE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 4(a) displays the BZ-distributions of σCx:xx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The states in right part of BZ have positive crystal moments in x-direction and positively contribute to the σCx:xx (blue colored), while the states in left part of BZ are negatively related to the net σCx:xx (red colored).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The topmost inset in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 4(a) shows the case with Néel vectors along +z- direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The most relevant states are located at the right part of BZ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The contributions from individual Bloch states reach as high as 4×106 (nm·μA/V2), three orders larger than the net value of σCx:xx, indicating the net BPVE is the residual effect of many counteracting contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' It is thus hopeful to obtain ultra-large BPVE if one can optically excite the states with specific crystal momentums.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' When Néel vectors rotate to +x-direction [top right in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 4(a)], the contributions from left and right parts of BZ are both clear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' For Néel vectors in +y-direction [bottom right in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 4(a)], the contribution regions move to the up part of BZ and become anti-symmetric to each other, in line with the zero-value of σCx:xx in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The lowest inset in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 4(a) shows the case with Néel vectors in −z-direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The contributions are dominated by the left part of BZ with negative values, which is exactly the opposite of the case displayed in the topmost inset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Further rotating the Néel vectors to −x- and −y-directions, we see the BZ-distributions of BPVE contributions are the opposite of +x- and +y-cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Photoconductances distributions on Brillouin zone that depend on the direction of Néel vector of MnPSe3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (a) The BZ distributions of σCx:xx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (b) The BZ distributions of σCy:xx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The incident light is linearly polarized in x-axis, with photon energy of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='98 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The distributions placed at top, top right, bottom right, bottom, bottom left, and up left correspond to the cases with Néel vectors along +z, +x, +y, −z, −x, and −y directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The hexagons are the irreducible Brillouin zone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' For better illustrations, τ is set to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='1 ps here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Figure 4(b) displays the BZ-distributions of σCy:xx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' They have the same positions as the distributions of σCx:xx shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 4(a), but the signs of contributions are different.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The upper part of BZ corresponds to the Bloch states with positive crystal moments in y-direction, and the contributions in this region are blue, positively contributing to the net σCy:xx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The contributions of lower part of BZ are in red color, exhibiting negative contributions to net σCy:xx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' For cases with Néel vectors along ±z- and ±x-directions, the contributions are anti-symmetric in the BZ, leading to the (a) (b) hw = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='98eV cx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (nm A/V2) hw =2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='98eV ox (nm AV2) Neel vecto Neel vecto zero BPVEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Only if the Néel vectors orient to ±y-directions, the contributions from upper and lower parts of BZ are not anti-symmetric and nonzero BPVEs are permitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' All these results are in line with former discussions on symmetries and agree with the integrated results displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' To further understand the PT-BPVE in local coordinates and figure out how the PT- polarizations interact with the dynamics of photo-electrons, we detect the real-space resolved photoconductance with vector potentials projected to hopping tunnels (See supporting information for more details), which are the spaces between atoms as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 5(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Below, we focused on the cases with Néel vectors along z-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Bulk photoconductance projected to real-space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (a) Atomic positions and possible hopping tunnels in MnPSe3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The arrows denote several typical hopping tunnels in (P2Se6)4-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (b) σCx:xx in AFM MnPSe3 projected to six types of tunnels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (c) σCx:xx in AFM MnPSe3 projected to six types of P-Se tunnels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (d) σCx:xx in FM MnPSe3 projected to six types of P-Se tunnels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' We firstly classify the photoconductance σCx:xx into six types according to the hopping tunnels including Mn-Mn, P-P, Se-Se, Mn-P, Mn-Se, and P-Se.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The photocurrents are emitted by the electron-hole combinations happened in either one of these tunnels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' And the summation of all these six types is exactly equal to the net BPVE displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 2(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Figure 5(b) shows the contributions from the six types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Comparing to the total σCx:xx shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 2(a), it is clear that the P-Se tunnels always dominate the BPVEs with highest value of 3795 (nm·μA/V2), while the contributions of Se-Se tunnels are comparable but they are negative and the strongest value is -2323 (nm·μA/V2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The Mn-Se tunnels are the third largest contributors, and its (a) (b) Se2 Se;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Se2 4000 P Mn Mn 3000 P p Ses See Se3 Se Se 2000 Mn P 1000 Mn Se P Se Ses Se.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Se4 1000 Se Se2 Se 3000 n//z 4000 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='25 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='753.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='00 (c) (d) Photon energy (eV) 1200 250 1000 P Se1 200 P Se1 800 P Se2 150 P Se2 600 P Se3 P Se3 P Se4 100 P Se4 400 P Se5 P Se5 uu) 200 P Se6 50 P Se6 200 50 400 60 6 100 600 800 150 n//z 200 m//z 0001 1200 250 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='752.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='252.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='753.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='50 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='75 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='252.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='753.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='00 Photon energy (eV) Photon energy (eV) highest peak is 1772 (nm·μA/V2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Other tunnels contribute negligibly to the BPVEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Therefore, the BPVEs in MnPSe3 are mainly emitted by the hopping processes in the sublattice expanded by (P2Se6)4- prisms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 5(c) shows the σCx:xx further projected to the six types of P-Se tunnels, including tunnels of P-Se1, P-Se2, P-Se3, P-Se4, P-Se5, P-Se6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The summation of all these six P-Se types is identical to the contributions of P-Se tunnels displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 5(b) with grey lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The real-space orientations of tunnels of P-Se1 and P-Se2 are close to the x-axis [See Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 5(a)], and their contributions are nearly coincided, showing the ideal phase alignment for the optoelectrical processes in these two tunnels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' And they constitute the most parts of photocurrents in the (P2Se6)4- prism sublattice with highest peak values of ~1000 (nm·μA/V2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' This ideal phase alignment is surprising since these two tunnels are not symmetric counterparts in AFM MnPSe3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The contributions from the other four P-Se tunnels are moderate, and their strongest peak value is 441 (nm·μA/V2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' They coincide with each other due to the My-mirror symmetry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 5(d) shows the σCx:xx projected to the six P-Se tunnels [as the case in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 5(c)] for the MnPSe3 with parallel magnetic moments along z-axis, that is, the ferromagnetic (FM) case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Although the P symmetry of FM MnPSe3 enforces the zero value for total BPVEs, the local contributions are generally nonzero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The contributions from P-Se1 and P-Se2 tunnels are heavily suppressed in this case, and the highest peak value is only 21 (nm·μA/V2), 100 times smaller than the AFM case displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 5(c).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' On the other hand, the contributions of the other four P-Se tunnels show peak values of 227 (nm·μA/V2), which is comparable to the AFM case, especially in the low phonon energy range (<2 eV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Therefore, on the view of local photoelectrical responses, the role of AFM order in Mn-sublattices is two-folds: aligning the phases of photocurrents, and enhancing the photon-to-currents efficiencies in the direction of PT-polarization (x-direction in present case).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' In summary, we found the 2D monolayer MnPSe3 is promising to realize large and controllable PT-BPVEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The 2nd order photoconductance and photo-spin-conductance exceed 4000 (nm·μA/V2) and 2000 (nm∙μA/V2 ℏ/2e) in the visible spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Both the propagations and the spin-polarizations of photocurrents are switchable via rotating the Néel vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' These switching are enabled by the mirror symmetries, which depend on the magnetization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The intralayer AFM orders of Mn2+ sublattice show essential roles in the 2D BPVEs, since they can stabilize the PT-polarizations and lead to the phase alignments of photocurrents in the sublattice of (P2Se6)4-.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Furthermore, we showed that the PT-BPVEs in MnPSe3 are dominated by a small part of Bloch states in BZ, whose positions and contributions are intimately controlled by the Néel vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' All these results shed light into the PT-BPVEs in 2D anti-ferromagnets, and indicate that the 2D monolayer MnPSe3 is an ideal platform to achieve extraordinary PT-BPVEs, meriting future energy and spintronic applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Computational Method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The geometry optimization and electronic structure of MnPSe3 in ground state are calculated within Vienna atomic simulation pack (VASP),43 based on relativistic density functional theory (DFT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Projected augmentation plane wave basis (PAW) is utilized and the plane waves are cutoff at 400 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The exchange-correlation effects amongst electrons are captured via generalized gradient approximation (GGA) with the functional of Perdew-Burke-Ernzerh (PBE) form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='44 A vacuum layer of 20 Å is set to isolate the layers in nonperiodic direction to eliminate the unphysical interactions between neighboring slabs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Brillouin zone is sampled with a Γ-centered k- mesh 10×10×1 using Monkhorst-Pack scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='45 The geometry relaxation is carried out until the maximum force is smaller than 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='001 eV/Å.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Energy convergent criteria for the self-consistent iterative calculations on the electronic structures is 10-6 eV/atom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Since the GGA functional usually underestimates the strong interactions between d-electrons of transition metal compounds (in our case, standard GGA leads to metal ground states of MnPSe3, which is inconsistent with the experiments), we employed the GGA + Ueff method with Ueff = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='0 eV for d-electrons of Mn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' This value of Ueff leads to the correct magnetic ground states and is in line with former studies on the MnPS3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='32 For the calculations of BPVE based on eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 1 and related expressions, we construct the effective real-space tight-binding Hamiltonian via projecting the Bloch states obtained from relativistic DFT into the Hilbert space expanded by Wannier orbitals using WANNIER90,46-47 then the k-space Hamiltonians on general k-points are interpolated by solving the eigen-equations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The Wannier orbital basis include the 3d and 4s orbitals for Mn ions, 3s and 3p orbitals for P ions, and 4s and 4p orbitals for Se ions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' It is found that the effective tight-binding Hamiltonian can reproduce the electronic states predicted by relativistic DFT and the band structures of the effective model and the DFT coincide everywhere in the relevant energy window (see Figure S3 in Supporting information for more details), revealing the efficiency of the basis transformation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' The k-grid utilized for the Brillouin zone integration in equation 1 is 800×800×1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' A denser k-grid 1600×1600×1 is used to test the convergence of k-mesh sampling and we find the difference < 5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Notes The authors declare no competing financial interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' ACKNOWLEDGMENT This work was supported by Natural Science Foundation of Shandong (Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' ZR2022QA019), National Natural Science Foundation of China (Grant Nos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 12074221, 52171181, 52002222, 51472150, 2021-869, 11904204).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Supporting information available: Extracting out the expression of BPVEs from potentials;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Expressions of spin and real-space projected BPVEs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' REFERENCES (1) Kraut, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' von Baltz, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Anomalous Bulk Photovoltaic Effect in Ferroelectrics: A Quadratic Response Theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Physical Review B 1979, 19, 1548-1554.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (2) von Baltz, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Kraut, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Theory of the Bulk Photovoltaic Effect in Pure Crystals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Physical Review B 1981, 23, 5590-5596.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (3) Choi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Choi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Kiryukhin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Cheong, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Switchable Ferroelectric Diode and Photovoltaic Effect in Bifeo3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Science 2009, 324, 63-66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (4) Yang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Seidel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Byrnes, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Shafer, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Yang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Rossell, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Yu, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Chu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Scott, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Ager, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=', 3rd, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Above-Bandgap Voltages from Ferroelectric Photovoltaic Devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nature nanotechnology 2010, 5, 143-147.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (5) Daranciang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Highland, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Wen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Young, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Brandt, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Hwang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Vattilana, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nicoul, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Quirin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Goodfellow, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Ultrafast Photovoltaic Response in Ferroelectric Nanolayers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Phys Rev Lett 2012, 108, 087601.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (6) Spanier, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Fridkin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Rappe, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Akbashev, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Polemi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Qi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Gu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Young, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Hawley, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Imbrenda, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Power Conversion Efficiency Exceeding the Shockley–Queisser Limit in a Ferroelectric Insulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nature Photonics 2016, 10, 611-616.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (7) Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Holder, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Ishizuka, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' de Juan, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nagaosa, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Felser, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Yan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Switchable Magnetic Bulk Photovoltaic Effect in the Two-Dimensional Magnet Cri3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nature Communication 2019, 10, 3783.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (8) Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Fu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Mao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Chen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Gong, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Zeng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Enhanced Bulk Photovoltaic Effect in Two-Dimensional Ferroelectric Cuinp2s6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nature Communication 2021, 12, 5896.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (9) Xu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Pure Spin Photocurrent in Non-Centrosymmetric Crystals: Bulk Spin Photovoltaic Effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nature Communication 2021, 12, 4330.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (10) Paillard, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Bai, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Infante, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Guennou, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Geneste, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Alexe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Kreisel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Dkhil, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Photovoltaics with Ferroelectrics: Current Status and Beyond.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Adv Mater 2016, 28, 5153-5168.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (11) Sipe, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Shkrebtii, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Second-Order Optical Response in Semiconductors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Physical Review B 2000, 61, 5337.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (12) Fridkin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Bulk Photovoltaic Effect in Noncentrosymmetric Crystals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Crystallography Reports 2001, 46, 654-658.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (13) Lee, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Baek, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Kim, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Yoon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Folkman, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Eom, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Noh, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Polarity Control of Carrier Injection at Ferroelectric/Metal Interfaces for Electrically Switchable Diode and Photovoltaic Effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Physical Review B 2011, 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (14) Yang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Kim Dong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Alexe, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Flexo-Photovoltaic Effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Science 2018, 360, 904-907.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (15) Mu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Pan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Pure Bulk Orbital and Spin Photocurrent in Two-Dimensional Ferroelectric Materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' npj Computational Materials 2021, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (16) Xu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Guo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Kong, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Colossal Switchable Photocurrents in Topological Janus Transition Metal Dichalcogenides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' npj Computational Materials 2021, 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (17) Guo, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Zhou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Xie, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Wang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Screening Transition Metal-Based Polar Pentagonal Monolayers with Large Piezoelectricity and Shift Current.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' npj Computational Materials 2022, 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (18) Wang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Zheng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' He, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Cao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Wang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Ma, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Lai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Lu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Jia, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Robust Edge Photocurrent Response on Layered Type Ii Weyl Semimetal Wte2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nature Communication 2019, 10, 5736.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (19) Holder, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Kaplan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Yan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Consequences of Time-Reversal-Symmetry Breaking in the Light- Matter Interaction: Berry Curvature, Quantum Metric, and Diabatic Motion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Physical Review Research 2020, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (20) Watanabe, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Yanase, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Chiral Photocurrent in Parity-Violating Magnet and Enhanced Response in Topological Antiferromagnet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Physical Review X 2021, 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (21) Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Qian, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Electrically and Magnetically Switchable Nonlinear Photocurrent in Рт- Symmetric Magnetic Topological Quantum Materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' npj Computational Materials 2020, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (22) Huang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Clark, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Navarro-Moratalla, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Klein, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Cheng, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Seyler, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Zhong, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Schmidgall, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' McGuire, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Cobden, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Layer-Dependent Ferromagnetism in a Van Der Waals Crystal Down to the Monolayer Limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nature 2017, 546, 270-273.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (23) Gong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Guo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Zhu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Liao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Liu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Zhang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Gu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Tang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Feng, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Experimental Realization of an Intrinsic Magnetic Topological Insulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Chinese Physics Letters 2019, 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (24) Otrokov, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Klimovskikh, II;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Bentmann, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Estyunin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Zeugner, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Aliev, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Gass, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Wolter, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Koroleva, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Shikin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Prediction and Observation of an Antiferromagnetic Topological Insulator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nature 2019, 576, 416-422.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (25) Cao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Fatemi, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Fang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Watanabe, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Taniguchi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Kaxiras, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Jarillo-Herrero, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Unconventional Superconductivity in Magic-Angle Graphene Superlattices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nature 2018, 556, 43-50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (26) Susner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Chyasnavichyus, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' McGuire, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Ganesh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Maksymovych, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Metal Thio- and Selenophosphates as Multifunctional Van Der Waals Layered Materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Adv Mater 2017, 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (27) Huang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Shang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Zou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Song, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Iron Phosphorus Trichalcogenide Ultrathin Nanosheets: Enhanced Photoelectrochemical Activity under Visible-Light Irradiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nanoscale 2019, 11, 21188-21195.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (28) Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='-U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Ryoo, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Kang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Kim, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Kim, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Park, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Park, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Cheong, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Ising-Type Magnetic Ordering in Atomically Thin Feps3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nano Letters 2016, 16, 7433-7438.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (29) Ramos, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Carrascoso, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Frisenda, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Gant, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Mañas-Valero, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Esteras, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Baldoví, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Coronado, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Castellanos-Gomez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Calvo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Ultra-Broad Spectral Photo-Response in Feps3 Air- Stable Devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' npj 2D Materials and Applications 2021, 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (30) Zhu, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Gan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Muhammad, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Wu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Liu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Liu, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Zhang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' He, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Jiang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Exfoliation of Ultrathin Feps3 Layers as a Promising Electrocatalyst for the Oxygen Evolution Reaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Chem Commun (Camb) 2018, 54, 4481-4484.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (31) Kumar, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Jenjeti, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Austeria, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Sampath, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Bulk and Few-Layer Mnps3: A New Candidate for Field Effect Transistors and Uv Photodetectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Journal of Materials Chemistry C 2019, 7, 324-329.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (32) Long, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Henck, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Gibertini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Dumcenco, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Wang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Taniguchi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Watanabe, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Giannini, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Morpurgo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Persistence of Magnetism in Atomically Thin Mnps3 Crystals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nano Lett 2020, 20, 2452-2459.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (33) Wildes, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Simonet, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Ressouche, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' McIntyre, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Avdeev, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Suard, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Kimber, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Lançon, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Pepe, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Moubaraki, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Magnetic Structure of the Quasi-Two-Dimensional Antiferromagnet Nips3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Physical Review B 2015, 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (34) Lançon, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Walker, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Ressouche, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Ouladdiaf, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Rule, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' McIntyre, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Hicks, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Rønnow, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Wildes, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Magnetic Structure and Magnon Dynamics of the Quasi-Two-Dimensional Antiferromagnet Feps3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Physical Review B 2016, 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (35) Kim, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Park, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Magnetic Anisotropy and Magnetic Ordering of Transition-Metal Phosphorus Trisulfides.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nano Lett 2021, 21, 10114-10121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (36) Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Cao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Niu, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Shi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Feng, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Coupling the Valley Degree of Freedom to Antiferromagnetic Order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Proceedings of the National Academy of Sciences of the United States of America 2013, 110, 3738-3742.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (37) Ni, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Haglund, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Xu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Bernhard, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Mandrus, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Qian, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Mele, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Kane, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Wu, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Imaging the Neel Vector Switching in the Monolayer Antiferromagnet Mnpse3 with Strain- Controlled Ising Order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nature nanotechnology 2021, 16, 782-787.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (38) Ibañez-Azpiroz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Tsirkin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Souza, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Ab Initio Calculation of the Shift Photocurrent by Wannier Interpolation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Physical Review B 2018, 97, 245143.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (39) Xu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Nonlinear Nonreciprocal Photocurrents under Phonon Dressing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Physical Review B 2022, 106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (40) Dai, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Schankler, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Gao, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Tan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Rappe, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Phonon-Assisted Ballistic Current from First-Principles Calculations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Phys Rev Lett 2021, 126, 177403.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (41) Fei, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Song, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Pusey-Nazzaro, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Yang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Pt-Symmetry-Enabled Spin Circular Photogalvanic Effect in Antiferromagnetic Insulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Physical Review Letters 2021, 127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (42) Xiao, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Shao, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Li, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Jiang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Spin Photogalvanic Effect in Two-Dimensional Collinear Antiferromagnets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' npj Quantum Materials 2021, 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (43) Kresse, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Joubert, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Physical Review B 1999, 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (44) Perdew, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Burke, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Ernzerhof, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Generalized Gradient Approximation Made Simple.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' 1996, 77, 3865.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (45) Monkhorst, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Pack, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Special Points for Brillouin-Zone Integrations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' B 1976, 13, 5188-5192.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (46) Mostofi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Yates, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Pizzi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Lee, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content='-S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Souza, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Vanderbilt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Marzari, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' An Updated Version of Wannier90: A Tool for Obtaining Maximally-Localised Wannier Functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Computer Physics Communications 2014, 185, 2309-2310.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' (47) Pizzi, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Vitale, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Arita, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Blugel, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Freimuth, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Geranton, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Gibertini, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Gresch, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Johnson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=';' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Koretsune, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Wannier90 as a Community Code: New Features and Applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Journal of physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} +page_content=' Condensed matter : an Institute of Physics journal 2020, 32, 165902.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/f9E1T4oBgHgl3EQfMAPe/content/2301.02985v1.pdf'} diff --git a/h9AzT4oBgHgl3EQfMvvr/vector_store/index.faiss b/h9AzT4oBgHgl3EQfMvvr/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..c21fca599006fe1fc8f99e77a368650980203ee9 --- /dev/null +++ b/h9AzT4oBgHgl3EQfMvvr/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a5b5a14aa5f0b5c3122c78d0f7433f2ab9b03c73e084d562d1d1040899f6a8d5 +size 18808877 diff --git a/hNE3T4oBgHgl3EQf4AvA/content/2301.04769v1.pdf b/hNE3T4oBgHgl3EQf4AvA/content/2301.04769v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..840e2aa98dfb3819c8a0a77ad464340cf20ebf77 --- /dev/null +++ b/hNE3T4oBgHgl3EQf4AvA/content/2301.04769v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:68496ae56abcdb518a4056eded6e00712994d148273e85ed359bbacfbb51e6dc +size 3114896 diff --git a/jNE0T4oBgHgl3EQf7ALm/content/tmp_files/2301.02772v1.pdf.txt b/jNE0T4oBgHgl3EQf7ALm/content/tmp_files/2301.02772v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..e02f855898d1c0ab502606ff7deff55aa237b297 --- /dev/null +++ b/jNE0T4oBgHgl3EQf7ALm/content/tmp_files/2301.02772v1.pdf.txt @@ -0,0 +1,453 @@ +arXiv:2301.02772v1 [math.AC] 7 Jan 2023 +A note on a Cohen-type theorem for w-Artinian modules +Xiaolei Zhanga +a. School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, China +E-mail: zxlrghj@126.com +Abstract +In this note, we prove that a w-module M is w-Artinian if and only +if it is w-cofinitely generated and for every prime w-ideal p of R with +(0 :R M) ⊆ p, there exists a w-submodule Np of M such that (M/Np)w +is w-cofinitely generated and (M[p])w ⊆ Np ⊆ (0 :M p), where M[p] = +� +s∈R\p +s(0 :M p). Besides, we show that the w-operations are semi-star +operations rather than star operations in general. +Key Words: Cohen-type theorem; w-Artinian module; w-cofinitely +generated module; w-operation. +2020 Mathematics Subject Classification: 13E10, 13D30. +1. Introduction +Throughout this article, all rings are commutative rings with identity and all +modules are unitary. Let R be a ring, I an ideal of R and M an R-module. We +denote by (0 :R M) := {r ∈ R | rM = 0} and (0 :M I) := {m ∈ M | Im = 0}. The +well-known Cohen’s Theorem states that a ring R is a Noetherian ring if and only +if every prime ideal p of R is finitely generated (see [1, Theorem 2]). In 1994, Smith +[10] extended Cohen’s Theorem from rings to modules, that is, a finitely generated +R-module M is Noetherian if and only if the submodules pM of M are finitely +generated for every prime ideal p of R, if and only if M(p) is finitely generated +for each prime ideal p of R with (0 :R M) ⊆ p, where M(p) = {x ∈ M | sx ∈ +pM for some s ∈ R \ p}. In 2021, Parkash and Kour [8] generalized the Smith’s +result on Noetherian modules and obtained that a finitely generated R-module M is +Noetherian if and only if for every prime ideal p of R with (0 :R M) ⊆ p, there exists +a finitely generated submodule Np of M such that pM ⊆ Np ⊆ M(p). Recently, the +author et al. [13] gave a w-analogue of Parkash and Kour’s result which states that +a GV-torsion-free w-finite type R-module M is w-Noetherian if and only if for every +prime w-ideal p of R with (0 :R M) ⊆ p, there exists a w-finite type submodule Np +of M such that pM ⊆ Np ⊆ M(p). +1 + +Recall that an R-module M is said to be Artinian if it satisfies the minimal condi- +tion for submodules, or equivalently, the descending chain condition on submodules. +And M is said to be cofinitely generated (which is also called finitely embedded +in some other papers) if for any set {Mi|i ∈ Ω} of submodules of M satisfying +� +i∈Ω +Mi = 0, there exists a finite subset Ω0 ⊆ Ω such that � +i∈Ω0 +Mi = 0. A family +{Mi}i∈Λ of submodules of M is called an inverse system if for any finite number of +i1, i2, . . . , ik of an index set Λ, there is an element i ∈ Λ such that Mi ⊆ +k� +j=1 +Mij. By +[9, Proposition 3.19], M is cofinitely generated if and only if every inverse system of +nonzero submodules of M is bounded below by a nonzero submodule of M. +It is well known that a Noetherian module is exactly a module of which all sub- +modules are finitely generated. Dually, an R-module M is Artinian if and only if +every factor module of M is cofinitely generated (see [9, Theorem 3.21]). In 2006, +Nishitani [7] obtained a Cohen-type theorem for Artinian modules: a finitely em- +bedded module M is Artinian if and only if M/(0 :M p) is cofinitely generated for +every prime ideal p of R. Recently, the author et al. generalized the Nishitani’s +result and dualized the Parkash and Kour’s result as follows: +Theorem 1.1. [14, Theorem 2.1] A finitely embedded R-module M is Artinian if +and only if for every prime ideal p of R with (0 :R M) ⊆ p, there exists a submodule +Np of M such that M/Np is finitely embedded and M[p] ⊆ Np ⊆ (0 :M p), where +M[p] = +� +s∈R\p +s(0 :M p). +The main motivation of this note is to give a w-analogue of [14, Theorem 2.1]. We +recall some notions on w-operations. Let R be a commutative ring and J a finitely +generated ideal of R. Then J is called a GV-ideal if the natural homomorphism +R → HomR(J, R) is an isomorphism. The set of GV-ideals is denoted by GV(R). +Let M be an R-module. Define +torGV(M) := {x ∈ M|Jx = 0, for some J ∈ GV(R)}. +An R-module M is said to be GV-torsion (resp. GV-torsion-free) if torGV(M) = +M (resp. torGV(M) = 0). A GV-torsion-free module M is called a w-module if +Ext1 +R(R/J, M) = 0 for any J ∈ GV(R), and the w-envelope of M is given by +Mw := {x ∈ E(M)|Jx ⊆ M, for some J ∈ GV(R)}, +where E(M) is the injective envelope of M. Therefore, a GV-torsion-free module M +is a w-module if and only if Mw = M. The class of w-modules is closed under direct +limits and inverse limits (see [16, Theorem 7, Theorem 11]). Let 0 → M → N → +2 + +L → 0 be a short exact sequence. It is easy to verify that if N is a GV-torsion-free +R-module and M is a w-module, then L is a GV-torsion-free R-module. +Recall from [12, Definition 6.9.1] that a w-module M is said to be w-Artinian if +M satisfies the descending chain condition on w-submodules of M. Clearly every +Artinian module is w-Artinian, but the converse does not hold (see [12, Example +6.9.7]). By [12, Theorem 6.9.2] that a w-module M is w-Artinian if and only if it has +the minimal condition on w-submodules of M, if and only if for any set {Mi|i ∈ Ω} +of w-submodules of M, there is a finite subset Ω0 ⊆ Ω such that � +i∈Ω +Mi = � +i∈Ω0 +Mi. +To extend the notion of w-Artinian modules, Zhou, Kim and Hu [15, Definition +2.1] called a w-module M w-cofinitely generated if for any set {Mi|i ∈ Ω} of w- +submodules of M satisfying � +i∈Ω +Mi = 0, there exists a finite subset Ω0 ⊆ Ω such that +� +i∈Ω0 +Mi = 0. They showed that a w-module M is w-cofinitely generated if and only if +it is an essential extension of a w-Artinian module, if and only if every inverse system +of nonzero w-submodules of M is bounded below by a nonzero w-submodule of M +(see [15, Theorem 2.4, Proposition 2.11]). And finally, they obtained a Cohen-type +Theorem for w-Artinian modules, which can be seen as a w-analogue of Nishitani’s +result in [7]: +Theorem 1.2. [15, Theorem 4.10] Let R be a ring. A w-module M over R is w- +Artinian if and only if M is w-cofinitely generated and (M/(0 :M p))w is w-cofinitely +generated for every prime w-ideal p of R. +In this note, we gave a new Cohen-type Theorem for w-Artinian modules which +generalizes [15, Theorem 4.10] and [14, Theorem 2.1]. +Actually, we obtain the +following main result of this note. +Theorem 2.5 Let R be a ring and M a w-module. Then the following statements +are equivalent: +(1) M is w-Artinian; +(2) M is w-cofinitely generated and for every prime w-ideal p of R with (0 :R +M) ⊆ p, there exists a w-submodule Np of M such that (M/Np)w is w- +cofinitely generated and (M[p])w ⊆ Np ⊆ (0 :M p), where M[p] = +� +s∈R\p +s(0 :M +p). +We recall some notions on semi-star operations and star operations. Let R be a +ring, Q its total quotient ring and F(R) the set of all submodules of Q. Recall from +[2] that a set map ⋆ : F(R) → F(R) is said to be a semi-star operation provided +it satisfies the following properties for all A, B ∈ F(R) and all units u of Q: +(1) (Extension) A ⊆ A⋆; +3 + +(2) (Order-preservation) If A ⊆ B then A⋆ ⊆ B⋆; +(3) (Idempotence) A⋆ = (A⋆)⋆; +(4) (Divisibility) uA⋆ = (uA)⋆. +Furthermore, if for any a ∈ R and A ∈ F(R), +(5) (Principal) (aR)⋆ = aR and (aA)⋆ = aA, +then ⋆ is said to be a star operation (see [3, Chapter 32]). Trivially, w-operations +are star operations over integral domains. It is an interesting question whether w- +operations are star operations over any rings. In this note, we show that principal +ideals need not be a w-module even for Noetherian rings, and so w-operations are +generally semi-star operations rather than star operations (see Example 2.6). +2. Results +We begin with following easy result. +Lemma 2.1. Let R be a ring, I an ideal of R and M an w-module over R. Then +(0 :M I) is a w-submodule of M. +Proof. First assume I = Rr is a principal ideal of R. Suppose Jm ⊆ (0 :M r), where +J ∈ GV(R) and m ∈ M. Then Jmr = 0, and so mr = 0 since M is GV-torsion-free. +Hence m ∈ (0 :M r), and so (0 :M r) is a w-submodule of M by [12, Theorem 6.1.16]. +Now assume I is an arbitrary ideal of R. Then (0 :M I) = � +r∈I +(0 :M r). So (0 :M I) +is a w-submodule of M by [16, Theorem 11]. +□ +Recall some notations from [4, Chapter 18] on τw-cofinitely generated modules, +where the hereditary torsion theory τw is induced by the Gabriel topology F := {I|I +is an ideal of R with Iw = R}. Let M be an R-module and N an R-submodule of +M. Then N is said to be τw-pure in M if M/N is GV-torsion-free. An R-module M +is said to be τw-cofinitely generated if for any set {Mi|i ∈ Ω} of τw-pure submodules +of M satisfying � +i∈Ω +Mi = torGV(M), there exists a finite subset Ω0 of Ω such that +� +i∈Ω0 +Mi = torGV(M). +Lemma 2.2. [15, Lemma 2.9] The following statements hold. +(1) A submodule of a τw-cofinitely generated R-module is τw-cofinitely generated. +(2) If the sequence 0 → A → B → C → 0 is exact with A and C τw-cofinitely +generated, then B is τw-cofinitely generated. +Lemma 2.3. [15, Proposition 2.10] The following statements are equivalent for a +GV-torsion-free R-module M. +(1) Mw is w-cofinitely generated. +4 + +(2) Mw is τw-cofinitely generated. +(3) M is τw-cofinitely generated. +Corollary 2.4. Let 0 → A → B → C → 0 be a short exact sequence of GV-torsion- +free R-modules. Then the following statements hold. +(1) If Bw is w-cofinitely generated, so is Aw. +(2) If Aw and Cw are w-cofinitely generated, so is Bw. +Proof. They follow by Lemma 2.2 and Lemma 2.3. +□ +Let R be a ring, p be a prime ideal of R, and M an R-module. Following [14], set +M[p] = +� +s∈R\p +s(0 :M p). +Then M[p] is a submodule of M. We are ready to state and prove the main result +of this note. +Theorem 2.5. Let R be a ring and M a w-module. Then the following statements +are equivalent: +(1) M is w-Artinian; +(2) M is w-cofinitely generated and for every prime w-ideal p of R with (0 :R +M) ⊆ p, there exists a w-submodule Np of M such that (M/Np)w is w- +cofinitely generated and (M[p])w ⊆ Np ⊆ (0 :M p). +Proof. (1) ⇒ (2) Assume that the w-module M is a w-Artinian R-module. Let p be +a prime w-ideal with (0 :R M) ⊆ p. Set Np := (0 :M p). Then Np is a w-submodule +of M by Lemma 2.1. It follows by [15, Theorem 4.10] that (M/Np)w is w-cofinitely +generated with M[p] ⊆ Np ⊆ (0 :M p). +(2) ⇒ (1) On contrary, suppose that M is not w-Artinian. Then there exists +a w-submodule N′ of M such that (M/N′)w is not w-cofinitely generated by [15, +Theorem 4.7]. Consider the set +Γ := {N | N is a w-submodule of M and (M/N)w is not w-cofinitely generated}. +Then Γ is not empty since N′ ∈ Γ. Make a partial order on Γ by the opposite of +inclusion, that is, N1 ≥ N2 if and only if N1 ⊆ N2 in Γ. We will prove the following +three claims. +Claim 1: There exists a maximal element N ∈ Γ. Let {Ni | i ∈ Λ} be a total +ordered subset of Γ. Set N = � +i∈Λ +Ni. Then N is a w-module by [16, Theorem 11]. +We claim that (M/N)w is not w-cofinitely generated. Indeed, since {Ni | i ∈ Λ} is a +total ordered, we have {(Nj/N)w}j∈Λ is an inverse system of submodules of (M/N)w. +5 + +By [15, Proposition 2.11], there are two possibilities: either (Nj/N)w = 0 for some +j ∈ Λ, or (M/N)w is not w-cofinitely generated. In the former case, N = Nj and +so (M/N)w is not w-cofinitely generated. Hence both cases imply that (M/N)w is +not w-cofinitely generated, and so the totally ordered subset of Γ is bounded above +by N. Consequently, by Zorn’s Lemma, Γ has a maximal element, which is also +denoted by N. Set +p = (0 :R N). +Claim 2: p is a prime w-ideal of R. It follows by [12, Proposition 6.1.20] that +p is a w-ideal of R. Next we will show p is a prime ideal of R. Indeed, let a ̸∈ p, b ̸∈ p +be elements in R. Then (0 :N a) ⊊ N. Since (0 :N a) is a w-module by Lemma 2.1, +(M/(0 :N a))w is w-cofinitely generated by the maximality of N. So the submodule +((0 :M a)/(0 :N a))w is also w-cofinitely generated by Corollary 2.4(1). Consider the +exact sequence +0 → (0 :M a)/(0 :N a) → M/N → aM/aN → 0. +Since (M/N)w is not w-cofinitely generated and ((0 :M a)/(0 :N a))w is w-cofinitely +generated, aM/aN is not τw-cofinitely generated by Lemma 2.2. +Subclaim: (aM +(aN)w)/(aN)w is also not τw-cofinitely generated. We will +show it by contrary. For any {M′ +i/aN|i ∈ Ω} of τw-pure submodules of aM/aN with +� +i∈Ω +M′ +i/aN = torGV(aM/aN), where M′ +i ⊆ aM, then {M′ +i +(aN)w/(aN)w|i ∈ Ω} of +τw-pure submodules of (aM + (aN)w)/(aN)w satisfying � +i∈Ω +(M′ +i + (aN)w)/(aN)w = +torGV((aM +(aN)w)/(aN)w) = 0. Indeed, let x+(aN)w ∈ � +i∈Ω +(M′ +i +(aN)w)/(aN)w +with x ∈ +� +i∈Ω +(M′ +i + (aN)w). +Then there exists J ∈ GV(R) such that Jx ⊆ +(aN)w. And so x ∈ (aN)w. On contrary, suppose (aM + (aN)w)/(aN)w is τw- +cofinitely generated. Then there exists a finite subset Ω0 ⊆ Ω such that � +i∈Ω0 +(M′ +i + +(aN)w)/(aN)w = 0, that is, � +i∈Ω0 +M′ +i ⊆ (aN)w. We will show +� +i∈Ω0 +M′ +i/aN = torGV(aM/aN) +which contradicts that aM/aN is not τw-cofinitely generated. Indeed, since Ω0 is +finite, there exists J ∈ GV(R) such that J � +i∈Ω0 +M′ +i ⊆ aN. Hence +� +i∈Ω0 +M′ +i/aN = +torGV(aM/aN). +Now we are ready to prove that p is a prime ideal of R. By Lemma 2.3, we +have ((aM + (aN)w)/(aN)w)w is not w-cofinitely generated. Thus (M/(aN)w)w is +not w-cofinitely generated by Corollary 2.4(1). So (aN)w = N by the maximality +6 + +of N. Similarly, we have (bN)w = N. Hence, by [12, Theorem 6.2.2], (abN)w = +(a(bN)w)w = (aN)w = N ̸= 0 as M is w-cofinitely generated. So abN ̸= 0, and +hence ab ̸∈ p. +Claim 3: N ⊆ (M[p])w. Indeed, suppose that there is y ∈ N such that y ̸∈ +(M[p])w. Then for any J ∈ GV(R), Jy ̸⊆ M[p] = +� +s∈R\p +s(0 :M p). And so Jy ̸⊆ +(s(0 :M p))w for some s ∈ R\p, that is, y ̸∈ (s(0 :M p))w for some s ∈ R\p. It follows +that (sN)w ⊆ (s(0 :M p))w ⊊ N. And hence (M/(sN)w)w is w-cofinitely generated +by the maximality of N. Since s ̸∈ p, we have (0 :N s) ⊊ N. So (M/(0 :N s))w is +also w-cofinitely generated by the maximality of N. Consider the exact sequence +0 → (0 :M s)/(0 :N s) → M/N → sM/sN → 0. +Since (M/(sN)w)w is w-cofinitely generated, the submodule ((sM+(sN)w)/(sN)w)w +is also w-cofinitely generated by Corollary 2.4. By the proof of subclaim in that +of Claim 2, sM/sN is τw-cofinitely generated. Since (M/(0 :N s))w is w-cofinitely +generated, the submodule ((0 :M s)/(0 :N s))w is also w-cofinitely generated. Hence +(M/N)w is w-cofinitely generated, which is a contradiction. +Finally, we will show that M is w-Artinian. Suppose that the w-cofinitely gen- +erated R-module M is not w-Artinian. Then, by [15], there is a w-ideal I of R +such that (0 :M I) is w-Artinian and (M/(0 :M I))w is not w-cofinitely gener- +ated by [7, Lemma 7]. Furthermore there is a w-submodule N of (0 :M I) such +that (M/N)w is not w-cofinitely generated and p = (0 :R N) is a prime w-ideal +by Claim 1 and Claim 2. Since N ⊆ (0 :M I), we have (0 :M p) ⊆ (0 :M I). +Thus ((0 :M p)/N)w is w-Artinian, and hence is w-cofinitely generated. +Since +(0 :R M) ⊆ p, there is a w-submodule Np of M such that (M/Np)w is w-cofinitely +generated with N ⊆ (M[p])w ⊆ Np ⊆ (0 :M p) by assumption and Claim 3. Then +the submodule (Np/N)w of ((0 :M p)/N)w is w-cofinitely generated by Corollary +2.4.. Consider the following exact sequence +0 → Np/N → M/N → M/Np → 0. +Since (M/Np)w and (Np/N)w are w-cofinitely generated, (M/N)w is also w-cofinitely +generated, which is a contradiction. Therefore M is w-Artinian. +□ +Let R be a ring, r ∈ R and M a w-module over R. In the proof of Theorem 2.5, we +often consider R-modules of the form (rM)w rather than rM. Indeed, (rM)w ̸= rM, +that is, rM is not a w-module in general. In fact, the following example shows that +a principal ideal Rr need not be a w-module even for Noetherian rings R, and so +w-operations are semi-star operations rather than star operations in general (see +[2, 3] for details). +7 + +Example 2.6. Let D = Q[x1, x2, r, a, b, c, d] be a polynomial ring over the rational +numbers field Q with 7 variables. Set R = Q[x1, x2, r, a, b, c, d]/I, where +I = ⟨cr − ax1, cx2 − d − bx1, rd, ax2 − br, ca − rx1, r2 − a2, rx2 − ab⟩. +Let J = ⟨x1, x2⟩ be an ideal of R. One can verify that x1, x2 is an R-regular sequence +by Magama. So the depth of J is 2, and hence J is a GV-ideal of R by [12, Exercise +6.10]. By Koszul duality (see [6, Theorem 1.7]), we have +Ext1 +R(R/J, Rr) ∼= TorR +1 (R/J, Rr). +Moreover, the latter is isomorphic to (0 :R/(Rx1+(0:Rr)) x2). Indeed, since x1, x2 is an +R-regular sequence, we have the following quasi-isomorphism of complexes: +R/J ⊗L +R Rr +≃R/J ⊗L +R/Rx1 (R/Rx1 ⊗L +R Rr) +≃R/J ⊗L +R/Rx1 Rr/Rrx1 +≃R/J ⊗L +R/Rx1 R/(Rx1 + (0 :R r)) +≃[0 → R/Rx1 +·x2 +−→ R/Rx1 → 0] ⊗L +R/Rx1 R/(Rx1 + (0 :R r)). +Hence, +TorR +1 (R/J, Rr) ∼= Ker([R/(Rx1+(0 :R r)) +·x2 +−→ R/(Rx1+(0 :R r))]) = (0 :R/(Rx1+(0:Rr)) x2). +Claim that (0 :R/(Rx1+(0:Rr)) x2) ̸= 0. +In fact, c ̸∈ Rx1 + (0 :R r), but cx2 ∈ +Rx1 + (0 :R r). So c is a nonzero element in (0 :R/(Rx1+(0:Rr)) x2). Consequently, +Ext1 +R(R/J, Rr) ̸= 0. Hence the principal ideal Rr is not a w-ideal of R. Note that +we verify by the Magma calculation program that x1, x2 is an R-regular sequence, +c ̸∈ Rx1 + (0 :R r), and cx2 ∈ Rx1 + (0 :R r) in the final Appendix. +Obviously, we can deduce the following corollaries by Theorem 2.5. +Corollary 2.7. Let R be a ring. A w-module M over R is w-Artinian if and only +if M is w-cofinitely generated and (M/(0 :M p))w is w-cofinitely generated for every +prime w-ideal p of R with (0 :R M) ⊆ p. +Corollary 2.8. [15, Theorem 4.10] Let R be a ring. A w-module M over R is w- +Artinian if and only if M is w-cofinitely generated and (M/(0 :M p))w is w-cofinitely +generated for every prime w-ideal p of R. +Corollary 2.9. Let R be a ring. A w-module M over R is w-Artinian if and only +if M is w-cofinitely generated and (M/(M[p])w)w is w-cofinitely generated for every +prime w-ideal p of R with (0 :R M) ⊆ p, where M[p] = +� +s∈R\p +s(0 :M p). +8 + +Corollary 2.10. Let R be a ring. A w-module M over R is w-Artinian if and only +if M is w-cofinitely generated and (M/(M[p])w)w is w-cofinitely generated for every +prime w-ideal p of R, where M[p] = +� +s∈R\p +s(0 :M p). +Appendix: The Magma calculation program for Example 2.6. +P:=PolynomialRing(RationalField(),7); +I:=ideal; +J:=ideal+I; +K:=ideal+I; +L:=ideal+I; +T:=ideal+I; +IdealQuotient(I,K); +A1:=x1*r - a*c in I; +A2:=x2*r - a*b in I; +A3:= r^2 - a^2 in I; +A4:=x1*a - r*c in I; +A5:= x2*a - r*b in I; +A6:= x1*b - x2*c + d in I; +A7:= r*d in I; +A8:= a*d in I; +A1 and A2 and A3 and A4 and A5 and A6 and A7 and A8; +//verify x1,x2 is an R-regular sequence. +IdealQuotient(K,L); +B1:=x2*r - a*b in K; +B2:= r^2 - a^2 in K; +B3:= x2*a - r*b in K; +B4:= x2*c - d in K; +B5:= r*c in K; +B6:= a*c in K; +B7:= r*d in K; +B8:= a*d in K; +B9:=x1 in K; +B1 and B2 and B3 and B4 and B5 and B6 and B7 and B8 and B9; +S1:=IdealQuotient(I,K) eq I; +S2:=IdealQuotient(K,J) eq K; +S3:=c notin IdealQuotient(I,T)+K; //verify +c not in Rx1+(0:r). +S4:=x2*c in IdealQuotient(I,T)+K; //verify +cx2 in Rx1+(0:r). +9 + +S1 and S2 and S3 and S4; +Acknowledgement. +The first author was supported by the National Natural Science Foundation of China +(No. 12061001). +References +[1] I. S. Cohen, Commutative rings with restricted minimum condition, Duke Math. J. 17 (1950), +27-42. +[2] N. Epstein, Semistar operations and standard closure operations[J], Commun. Algebra,2015, +43:325-336. +[3] R. Gilmer, Multiplicative ideal theory, Pure and Applied Mathematics, No. 12, Marcel Dekker, +Inc., New York, 1972. +[4] J. S. Golan, Torsion Theories, Pitman Monographs and Surveys in Pure and Applied Mathe- +matics 29, Longman Scientific and Technical, Horlow, 1986. +[5] A. Hiremath, Cofinitely generated and cofinitely related modules, Acta Math. Acad. Sci. +Hungarica 39 (1982) 1-9. +[6] E. Matlis, The Koszul complex and duality, Comm. Algebra, 1, (1974), 87-144. +[7] I. Nishitani, A Cohen-type theorem for Artinian modules, Arch. Math. 87 (2006), 206-210. +[8] A. Parkash and S. Kour, On Cohen’s theorem for modules, Indian J. Pure Appl. Math. 52 +(2021), 869-871. +[9] D. W. Sharpe and P. Vamos, Injective Modules, Cambridge Univ. Press, Cambridge, 1972. +[10] P. F. Smith, Concerning a theorem of I. S. Cohen, XIth National Conference of Algebra +(Constanta, 1994), An. Stiint. Univ. Ovidius Constanta Ser. Mat. 2 (1994), 160-167. +[11] F. G. Wang and L. Qiao, The w-weak global dimension of commutative rings, Bull. Korean +Math. Soc. 52 (2015), no. 4, 1327-1338. +[12] F. G. Wang and H. Kim, Foundations of Commutative Rings and Their Modules, Springer, +Singapore, +[13] X. L. Zhang, H. Kim, and W. Qi, On two versions of Cohen’s theorem for modules, Kyungpook +Mathematical Journal, to appear. https://arxiv.org/abs/2205.15583 +[14] X. L. Zhang, H. Kim, and W. Qi, A note on a Cohen-type theorem for Artinian modules, +Beitr¨age zur Algebra und Geometrie, to appear. https://arxiv.org/abs/2205.15586 +[15] D. C. Zhou, H. Kim, and K. Hu, A Cohen-type theorem for w-Artinian modules, J. Algebra +Appl. 20 (2021), 2150106 (25 pages). +[16] D. C. Zhou and F. G. Wang, The direct and inverse limits of w-modules. Comm. Algebra +44(6) (2016), 2495-2500. +10 + diff --git a/jNE0T4oBgHgl3EQf7ALm/content/tmp_files/load_file.txt b/jNE0T4oBgHgl3EQf7ALm/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..e248e238a1606b5c8545bb483fbc37e28589d903 --- /dev/null +++ b/jNE0T4oBgHgl3EQf7ALm/content/tmp_files/load_file.txt @@ -0,0 +1,404 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf,len=403 +page_content='arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='02772v1 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='AC] 7 Jan 2023 A note on a Cohen-type theorem for w-Artinian modules Xiaolei Zhanga a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, China E-mail: zxlrghj@126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='com Abstract In this note, we prove that a w-module M is w-Artinian if and only if it is w-cofinitely generated and for every prime w-ideal p of R with (0 :R M) ⊆ p, there exists a w-submodule Np of M such that (M/Np)w is w-cofinitely generated and (M[p])w ⊆ Np ⊆ (0 :M p), where M[p] = � s∈R\\p s(0 :M p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Besides, we show that the w-operations are semi-star operations rather than star operations in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Key Words: Cohen-type theorem;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' w-Artinian module;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' w-cofinitely generated module;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' w-operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 2020 Mathematics Subject Classification: 13E10, 13D30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Introduction Throughout this article, all rings are commutative rings with identity and all modules are unitary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Let R be a ring, I an ideal of R and M an R-module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' We denote by (0 :R M) := {r ∈ R | rM = 0} and (0 :M I) := {m ∈ M | Im = 0}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' The well-known Cohen’s Theorem states that a ring R is a Noetherian ring if and only if every prime ideal p of R is finitely generated (see [1, Theorem 2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' In 1994, Smith [10] extended Cohen’s Theorem from rings to modules, that is, a finitely generated R-module M is Noetherian if and only if the submodules pM of M are finitely generated for every prime ideal p of R, if and only if M(p) is finitely generated for each prime ideal p of R with (0 :R M) ⊆ p, where M(p) = {x ∈ M | sx ∈ pM for some s ∈ R \\ p}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' In 2021, Parkash and Kour [8] generalized the Smith’s result on Noetherian modules and obtained that a finitely generated R-module M is Noetherian if and only if for every prime ideal p of R with (0 :R M) ⊆ p, there exists a finitely generated submodule Np of M such that pM ⊆ Np ⊆ M(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Recently, the author et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [13] gave a w-analogue of Parkash and Kour’s result which states that a GV-torsion-free w-finite type R-module M is w-Noetherian if and only if for every prime w-ideal p of R with (0 :R M) ⊆ p, there exists a w-finite type submodule Np of M such that pM ⊆ Np ⊆ M(p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 1 Recall that an R-module M is said to be Artinian if it satisfies the minimal condi- tion for submodules, or equivalently, the descending chain condition on submodules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' And M is said to be cofinitely generated (which is also called finitely embedded in some other papers) if for any set {Mi|i ∈ Ω} of submodules of M satisfying � i∈Ω Mi = 0, there exists a finite subset Ω0 ⊆ Ω such that � i∈Ω0 Mi = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' A family {Mi}i∈Λ of submodules of M is called an inverse system if for any finite number of i1, i2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' , ik of an index set Λ, there is an element i ∈ Λ such that Mi ⊆ k� j=1 Mij.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' By [9, Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='19], M is cofinitely generated if and only if every inverse system of nonzero submodules of M is bounded below by a nonzero submodule of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' It is well known that a Noetherian module is exactly a module of which all sub- modules are finitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Dually, an R-module M is Artinian if and only if every factor module of M is cofinitely generated (see [9, Theorem 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='21]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' In 2006, Nishitani [7] obtained a Cohen-type theorem for Artinian modules: a finitely em- bedded module M is Artinian if and only if M/(0 :M p) is cofinitely generated for every prime ideal p of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Recently, the author et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' generalized the Nishitani’s result and dualized the Parkash and Kour’s result as follows: Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [14, Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='1] A finitely embedded R-module M is Artinian if and only if for every prime ideal p of R with (0 :R M) ⊆ p, there exists a submodule Np of M such that M/Np is finitely embedded and M[p] ⊆ Np ⊆ (0 :M p), where M[p] = � s∈R\\p s(0 :M p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' The main motivation of this note is to give a w-analogue of [14, Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' We recall some notions on w-operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Let R be a commutative ring and J a finitely generated ideal of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then J is called a GV-ideal if the natural homomorphism R → HomR(J, R) is an isomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' The set of GV-ideals is denoted by GV(R).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Let M be an R-module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Define torGV(M) := {x ∈ M|Jx = 0, for some J ∈ GV(R)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' An R-module M is said to be GV-torsion (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' GV-torsion-free) if torGV(M) = M (resp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' torGV(M) = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' A GV-torsion-free module M is called a w-module if Ext1 R(R/J, M) = 0 for any J ∈ GV(R), and the w-envelope of M is given by Mw := {x ∈ E(M)|Jx ⊆ M, for some J ∈ GV(R)}, where E(M) is the injective envelope of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Therefore, a GV-torsion-free module M is a w-module if and only if Mw = M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' The class of w-modules is closed under direct limits and inverse limits (see [16, Theorem 7, Theorem 11]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Let 0 → M → N → 2 L → 0 be a short exact sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' It is easy to verify that if N is a GV-torsion-free R-module and M is a w-module, then L is a GV-torsion-free R-module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Recall from [12, Definition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='1] that a w-module M is said to be w-Artinian if M satisfies the descending chain condition on w-submodules of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Clearly every Artinian module is w-Artinian, but the converse does not hold (see [12, Example 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='7]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' By [12, Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='2] that a w-module M is w-Artinian if and only if it has the minimal condition on w-submodules of M, if and only if for any set {Mi|i ∈ Ω} of w-submodules of M, there is a finite subset Ω0 ⊆ Ω such that � i∈Ω Mi = � i∈Ω0 Mi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' To extend the notion of w-Artinian modules, Zhou, Kim and Hu [15, Definition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='1] called a w-module M w-cofinitely generated if for any set {Mi|i ∈ Ω} of w- submodules of M satisfying � i∈Ω Mi = 0, there exists a finite subset Ω0 ⊆ Ω such that � i∈Ω0 Mi = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' They showed that a w-module M is w-cofinitely generated if and only if it is an essential extension of a w-Artinian module, if and only if every inverse system of nonzero w-submodules of M is bounded below by a nonzero w-submodule of M (see [15, Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='4, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='11]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' And finally, they obtained a Cohen-type Theorem for w-Artinian modules, which can be seen as a w-analogue of Nishitani’s result in [7]: Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [15, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='10] Let R be a ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' A w-module M over R is w- Artinian if and only if M is w-cofinitely generated and (M/(0 :M p))w is w-cofinitely generated for every prime w-ideal p of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' In this note, we gave a new Cohen-type Theorem for w-Artinian modules which generalizes [15, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='10] and [14, Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Actually, we obtain the following main result of this note.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='5 Let R be a ring and M a w-module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then the following statements are equivalent: (1) M is w-Artinian;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' (2) M is w-cofinitely generated and for every prime w-ideal p of R with (0 :R M) ⊆ p, there exists a w-submodule Np of M such that (M/Np)w is w- cofinitely generated and (M[p])w ⊆ Np ⊆ (0 :M p), where M[p] = � s∈R\\p s(0 :M p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' We recall some notions on semi-star operations and star operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Let R be a ring, Q its total quotient ring and F(R) the set of all submodules of Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Recall from [2] that a set map ⋆ : F(R) → F(R) is said to be a semi-star operation provided it satisfies the following properties for all A, B ∈ F(R) and all units u of Q: (1) (Extension) A ⊆ A⋆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 3 (2) (Order-preservation) If A ⊆ B then A⋆ ⊆ B⋆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' (3) (Idempotence) A⋆ = (A⋆)⋆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' (4) (Divisibility) uA⋆ = (uA)⋆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Furthermore, if for any a ∈ R and A ∈ F(R), (5) (Principal) (aR)⋆ = aR and (aA)⋆ = aA, then ⋆ is said to be a star operation (see [3, Chapter 32]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Trivially, w-operations are star operations over integral domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' It is an interesting question whether w- operations are star operations over any rings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' In this note, we show that principal ideals need not be a w-module even for Noetherian rings, and so w-operations are generally semi-star operations rather than star operations (see Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Results We begin with following easy result.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Let R be a ring, I an ideal of R and M an w-module over R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then (0 :M I) is a w-submodule of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' First assume I = Rr is a principal ideal of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Suppose Jm ⊆ (0 :M r), where J ∈ GV(R) and m ∈ M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then Jmr = 0, and so mr = 0 since M is GV-torsion-free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Hence m ∈ (0 :M r), and so (0 :M r) is a w-submodule of M by [12, Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Now assume I is an arbitrary ideal of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then (0 :M I) = � r∈I (0 :M r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' So (0 :M I) is a w-submodule of M by [16, Theorem 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' □ Recall some notations from [4, Chapter 18] on τw-cofinitely generated modules, where the hereditary torsion theory τw is induced by the Gabriel topology F := {I|I is an ideal of R with Iw = R}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Let M be an R-module and N an R-submodule of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then N is said to be τw-pure in M if M/N is GV-torsion-free.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' An R-module M is said to be τw-cofinitely generated if for any set {Mi|i ∈ Ω} of τw-pure submodules of M satisfying � i∈Ω Mi = torGV(M), there exists a finite subset Ω0 of Ω such that � i∈Ω0 Mi = torGV(M).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [15, Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='9] The following statements hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' (1) A submodule of a τw-cofinitely generated R-module is τw-cofinitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' (2) If the sequence 0 → A → B → C → 0 is exact with A and C τw-cofinitely generated, then B is τw-cofinitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [15, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='10] The following statements are equivalent for a GV-torsion-free R-module M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' (1) Mw is w-cofinitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 4 (2) Mw is τw-cofinitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' (3) M is τw-cofinitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Let 0 → A → B → C → 0 be a short exact sequence of GV-torsion- free R-modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then the following statements hold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' (1) If Bw is w-cofinitely generated, so is Aw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' (2) If Aw and Cw are w-cofinitely generated, so is Bw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' They follow by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='2 and Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' □ Let R be a ring, p be a prime ideal of R, and M an R-module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Following [14], set M[p] = � s∈R\\p s(0 :M p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then M[p] is a submodule of M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' We are ready to state and prove the main result of this note.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Let R be a ring and M a w-module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then the following statements are equivalent: (1) M is w-Artinian;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' (2) M is w-cofinitely generated and for every prime w-ideal p of R with (0 :R M) ⊆ p, there exists a w-submodule Np of M such that (M/Np)w is w- cofinitely generated and (M[p])w ⊆ Np ⊆ (0 :M p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Proof.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' (1) ⇒ (2) Assume that the w-module M is a w-Artinian R-module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Let p be a prime w-ideal with (0 :R M) ⊆ p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Set Np := (0 :M p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then Np is a w-submodule of M by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' It follows by [15, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='10] that (M/Np)w is w-cofinitely generated with M[p] ⊆ Np ⊆ (0 :M p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' (2) ⇒ (1) On contrary, suppose that M is not w-Artinian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then there exists a w-submodule N′ of M such that (M/N′)w is not w-cofinitely generated by [15, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Consider the set Γ := {N | N is a w-submodule of M and (M/N)w is not w-cofinitely generated}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then Γ is not empty since N′ ∈ Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Make a partial order on Γ by the opposite of inclusion, that is, N1 ≥ N2 if and only if N1 ⊆ N2 in Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' We will prove the following three claims.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Claim 1: There exists a maximal element N ∈ Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Let {Ni | i ∈ Λ} be a total ordered subset of Γ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Set N = � i∈Λ Ni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then N is a w-module by [16, Theorem 11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' We claim that (M/N)w is not w-cofinitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Indeed, since {Ni | i ∈ Λ} is a total ordered, we have {(Nj/N)w}j∈Λ is an inverse system of submodules of (M/N)w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 5 By [15, Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='11], there are two possibilities: either (Nj/N)w = 0 for some j ∈ Λ, or (M/N)w is not w-cofinitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' In the former case, N = Nj and so (M/N)w is not w-cofinitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Hence both cases imply that (M/N)w is not w-cofinitely generated, and so the totally ordered subset of Γ is bounded above by N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Consequently, by Zorn’s Lemma, Γ has a maximal element, which is also denoted by N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Set p = (0 :R N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Claim 2: p is a prime w-ideal of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' It follows by [12, Proposition 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='20] that p is a w-ideal of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Next we will show p is a prime ideal of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Indeed, let a ̸∈ p, b ̸∈ p be elements in R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then (0 :N a) ⊊ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Since (0 :N a) is a w-module by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='1, (M/(0 :N a))w is w-cofinitely generated by the maximality of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' So the submodule ((0 :M a)/(0 :N a))w is also w-cofinitely generated by Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='4(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Consider the exact sequence 0 → (0 :M a)/(0 :N a) → M/N → aM/aN → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Since (M/N)w is not w-cofinitely generated and ((0 :M a)/(0 :N a))w is w-cofinitely generated, aM/aN is not τw-cofinitely generated by Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Subclaim: (aM +(aN)w)/(aN)w is also not τw-cofinitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' We will show it by contrary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' For any {M′ i/aN|i ∈ Ω} of τw-pure submodules of aM/aN with � i∈Ω M′ i/aN = torGV(aM/aN), where M′ i ⊆ aM, then {M′ i +(aN)w/(aN)w|i ∈ Ω} of τw-pure submodules of (aM + (aN)w)/(aN)w satisfying � i∈Ω (M′ i + (aN)w)/(aN)w = torGV((aM +(aN)w)/(aN)w) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Indeed, let x+(aN)w ∈ � i∈Ω (M′ i +(aN)w)/(aN)w with x ∈ � i∈Ω (M′ i + (aN)w).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then there exists J ∈ GV(R) such that Jx ⊆ (aN)w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' And so x ∈ (aN)w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' On contrary, suppose (aM + (aN)w)/(aN)w is τw- cofinitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then there exists a finite subset Ω0 ⊆ Ω such that � i∈Ω0 (M′ i + (aN)w)/(aN)w = 0, that is, � i∈Ω0 M′ i ⊆ (aN)w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' We will show � i∈Ω0 M′ i/aN = torGV(aM/aN) which contradicts that aM/aN is not τw-cofinitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Indeed, since Ω0 is finite, there exists J ∈ GV(R) such that J � i∈Ω0 M′ i ⊆ aN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Hence � i∈Ω0 M′ i/aN = torGV(aM/aN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Now we are ready to prove that p is a prime ideal of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' By Lemma 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='3, we have ((aM + (aN)w)/(aN)w)w is not w-cofinitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Thus (M/(aN)w)w is not w-cofinitely generated by Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='4(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' So (aN)w = N by the maximality 6 of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Similarly, we have (bN)w = N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Hence, by [12, Theorem 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='2], (abN)w = (a(bN)w)w = (aN)w = N ̸= 0 as M is w-cofinitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' So abN ̸= 0, and hence ab ̸∈ p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Claim 3: N ⊆ (M[p])w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Indeed, suppose that there is y ∈ N such that y ̸∈ (M[p])w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then for any J ∈ GV(R), Jy ̸⊆ M[p] = � s∈R\\p s(0 :M p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' And so Jy ̸⊆ (s(0 :M p))w for some s ∈ R\\p, that is, y ̸∈ (s(0 :M p))w for some s ∈ R\\p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' It follows that (sN)w ⊆ (s(0 :M p))w ⊊ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' And hence (M/(sN)w)w is w-cofinitely generated by the maximality of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Since s ̸∈ p, we have (0 :N s) ⊊ N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' So (M/(0 :N s))w is also w-cofinitely generated by the maximality of N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Consider the exact sequence 0 → (0 :M s)/(0 :N s) → M/N → sM/sN → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Since (M/(sN)w)w is w-cofinitely generated, the submodule ((sM+(sN)w)/(sN)w)w is also w-cofinitely generated by Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' By the proof of subclaim in that of Claim 2, sM/sN is τw-cofinitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Since (M/(0 :N s))w is w-cofinitely generated, the submodule ((0 :M s)/(0 :N s))w is also w-cofinitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Hence (M/N)w is w-cofinitely generated, which is a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Finally, we will show that M is w-Artinian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Suppose that the w-cofinitely gen- erated R-module M is not w-Artinian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then, by [15], there is a w-ideal I of R such that (0 :M I) is w-Artinian and (M/(0 :M I))w is not w-cofinitely gener- ated by [7, Lemma 7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Furthermore there is a w-submodule N of (0 :M I) such that (M/N)w is not w-cofinitely generated and p = (0 :R N) is a prime w-ideal by Claim 1 and Claim 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Since N ⊆ (0 :M I), we have (0 :M p) ⊆ (0 :M I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Thus ((0 :M p)/N)w is w-Artinian, and hence is w-cofinitely generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Since (0 :R M) ⊆ p, there is a w-submodule Np of M such that (M/Np)w is w-cofinitely generated with N ⊆ (M[p])w ⊆ Np ⊆ (0 :M p) by assumption and Claim 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Then the submodule (Np/N)w of ((0 :M p)/N)w is w-cofinitely generated by Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='. Consider the following exact sequence 0 → Np/N → M/N → M/Np → 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Since (M/Np)w and (Np/N)w are w-cofinitely generated, (M/N)w is also w-cofinitely generated, which is a contradiction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Therefore M is w-Artinian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' □ Let R be a ring, r ∈ R and M a w-module over R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' In the proof of Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='5, we often consider R-modules of the form (rM)w rather than rM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Indeed, (rM)w ̸= rM, that is, rM is not a w-module in general.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' In fact, the following example shows that a principal ideal Rr need not be a w-module even for Noetherian rings R, and so w-operations are semi-star operations rather than star operations in general (see [2, 3] for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 7 Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Let D = Q[x1, x2, r, a, b, c, d] be a polynomial ring over the rational numbers field Q with 7 variables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Set R = Q[x1, x2, r, a, b, c, d]/I, where I = ⟨cr − ax1, cx2 − d − bx1, rd, ax2 − br, ca − rx1, r2 − a2, rx2 − ab⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Let J = ⟨x1, x2⟩ be an ideal of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' One can verify that x1, x2 is an R-regular sequence by Magama.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' So the depth of J is 2, and hence J is a GV-ideal of R by [12, Exercise 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' By Koszul duality (see [6, Theorem 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='7]), we have Ext1 R(R/J, Rr) ∼= TorR 1 (R/J, Rr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Moreover, the latter is isomorphic to (0 :R/(Rx1+(0:Rr)) x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Indeed, since x1, x2 is an R-regular sequence, we have the following quasi-isomorphism of complexes: R/J ⊗L R Rr ≃R/J ⊗L R/Rx1 (R/Rx1 ⊗L R Rr) ≃R/J ⊗L R/Rx1 Rr/Rrx1 ≃R/J ⊗L R/Rx1 R/(Rx1 + (0 :R r)) ≃[0 → R/Rx1 x2 −→ R/Rx1 → 0] ⊗L R/Rx1 R/(Rx1 + (0 :R r)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Hence, TorR 1 (R/J, Rr) ∼= Ker([R/(Rx1+(0 :R r)) x2 −→ R/(Rx1+(0 :R r))]) = (0 :R/(Rx1+(0:Rr)) x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Claim that (0 :R/(Rx1+(0:Rr)) x2) ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' In fact, c ̸∈ Rx1 + (0 :R r), but cx2 ∈ Rx1 + (0 :R r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' So c is a nonzero element in (0 :R/(Rx1+(0:Rr)) x2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Consequently, Ext1 R(R/J, Rr) ̸= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Hence the principal ideal Rr is not a w-ideal of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Note that we verify by the Magma calculation program that x1, x2 is an R-regular sequence, c ̸∈ Rx1 + (0 :R r), and cx2 ∈ Rx1 + (0 :R r) in the final Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Obviously, we can deduce the following corollaries by Theorem 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Let R be a ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' A w-module M over R is w-Artinian if and only if M is w-cofinitely generated and (M/(0 :M p))w is w-cofinitely generated for every prime w-ideal p of R with (0 :R M) ⊆ p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [15, Theorem 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='10] Let R be a ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' A w-module M over R is w- Artinian if and only if M is w-cofinitely generated and (M/(0 :M p))w is w-cofinitely generated for every prime w-ideal p of R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Let R be a ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' A w-module M over R is w-Artinian if and only if M is w-cofinitely generated and (M/(M[p])w)w is w-cofinitely generated for every prime w-ideal p of R with (0 :R M) ⊆ p, where M[p] = � s∈R\\p s(0 :M p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 8 Corollary 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Let R be a ring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' A w-module M over R is w-Artinian if and only if M is w-cofinitely generated and (M/(M[p])w)w is w-cofinitely generated for every prime w-ideal p of R, where M[p] = � s∈R\\p s(0 :M p).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Appendix: The Magma calculation program for Example 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' P:=PolynomialRing(RationalField(),7);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' I:=ideal;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' J:=ideal+I;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' K:=ideal+I;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' L:=ideal+I;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' T:=ideal+I;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' IdealQuotient(I,K);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' A1:=x1*r - a*c in I;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' A2:=x2*r - a*b in I;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' A3:= r^2 - a^2 in I;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' A4:=x1*a - r*c in I;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' A5:= x2*a - r*b in I;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' A6:= x1*b - x2*c + d in I;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' A7:= r*d in I;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' A8:= a*d in I;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' A1 and A2 and A3 and A4 and A5 and A6 and A7 and A8;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' //verify x1,x2 is an R-regular sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' IdealQuotient(K,L);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' B1:=x2*r - a*b in K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' B2:= r^2 - a^2 in K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' B3:= x2*a - r*b in K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' B4:= x2*c - d in K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' B5:= r*c in K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' B6:= a*c in K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' B7:= r*d in K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' B8:= a*d in K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' B9:=x1 in K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' B1 and B2 and B3 and B4 and B5 and B6 and B7 and B8 and B9;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' S1:=IdealQuotient(I,K) eq I;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' S2:=IdealQuotient(K,J) eq K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' S3:=c notin IdealQuotient(I,T)+K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' //verify c not in Rx1+(0:r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' S4:=x2*c in IdealQuotient(I,T)+K;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' //verify cx2 in Rx1+(0:r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 9 S1 and S2 and S3 and S4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Acknowledgement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' The first author was supported by the National Natural Science Foundation of China (No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 12061001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' References [1] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Cohen, Commutative rings with restricted minimum condition, Duke Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 17 (1950), 27-42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [2] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Epstein, Semistar operations and standard closure operations[J], Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Algebra,2015, 43:325-336.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [3] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Gilmer, Multiplicative ideal theory, Pure and Applied Mathematics, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 12, Marcel Dekker, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=', New York, 1972.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [4] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Golan, Torsion Theories, Pitman Monographs and Surveys in Pure and Applied Mathe- matics 29, Longman Scientific and Technical, Horlow, 1986.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [5] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Hiremath, Cofinitely generated and cofinitely related modules, Acta Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Acad.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Hungarica 39 (1982) 1-9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [6] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Matlis, The Koszul complex and duality, Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Algebra, 1, (1974), 87-144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [7] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Nishitani, A Cohen-type theorem for Artinian modules, Arch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 87 (2006), 206-210.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [8] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Parkash and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Kour, On Cohen’s theorem for modules, Indian J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Pure Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 52 (2021), 869-871.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [9] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Sharpe and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Vamos, Injective Modules, Cambridge Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Press, Cambridge, 1972.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [10] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Smith, Concerning a theorem of I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Cohen, XIth National Conference of Algebra (Constanta, 1994), An.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Stiint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Univ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Ovidius Constanta Ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 2 (1994), 160-167.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [11] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Wang and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Qiao, The w-weak global dimension of commutative rings, Bull.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Korean Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 52 (2015), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 4, 1327-1338.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [12] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Wang and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Kim, Foundations of Commutative Rings and Their Modules, Springer, Singapore, [13] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Kim, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Qi, On two versions of Cohen’s theorem for modules, Kyungpook Mathematical Journal, to appear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='org/abs/2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='15583 [14] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Zhang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Kim, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Qi, A note on a Cohen-type theorem for Artinian modules, Beitr¨age zur Algebra und Geometrie, to appear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='org/abs/2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content='15586 [15] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Zhou, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Kim, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Hu, A Cohen-type theorem for w-Artinian modules, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Algebra Appl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 20 (2021), 2150106 (25 pages).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' [16] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Zhou and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Wang, The direct and inverse limits of w-modules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Comm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' Algebra 44(6) (2016), 2495-2500.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} +page_content=' 10' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE0T4oBgHgl3EQf7ALm/content/2301.02772v1.pdf'} diff --git a/jNE2T4oBgHgl3EQfIAbu/content/tmp_files/2301.03676v1.pdf.txt b/jNE2T4oBgHgl3EQfIAbu/content/tmp_files/2301.03676v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..40d5ec1da1dff3ab60bc554018959498bb8d3f7a --- /dev/null +++ b/jNE2T4oBgHgl3EQfIAbu/content/tmp_files/2301.03676v1.pdf.txt @@ -0,0 +1,410 @@ +Examples of homology 3-spheres whose +Chern-Simons function is not Morse-Bott +Hans U. Boden, Christopher Herald, and Paul Kirk +Abstract. We construct homology 3-spheres for which the (unperturbed) SU(2) +Chern-Simons function is not Morse-Bott. In one example, there is a degenerate isolated +critical point. In another, a path component of the critical set is not homeomorphic to +a manifold. The examples are +1 Dehn surgeries on connected sums of torus knots. +1. Introduction +The purpose of this article is to address a question raised by D. Ruberman1, namely, +whether there exist examples of homology 3-spheres M for which the SU(2) Chern-Simons +function +cM : B∗ → R/Z, +a circle-valued function on the space of gauge equivalence classes of irreducible SU(2) con- +nections, fails to be Morse-Bott. We construct an example of a homology 3-sphere whose +Chern-Simons function has a degenerate isolated critical point, as well as one for which +the critical set of the Chern-Simons function has a path component not homeomorphic +to a manifold. It is known that there are Seifert-fibered homology spheres for which the +SU(3) Chern-Simons function is not Morse-Bott [BHK05]. +As is well known, holonomy identifies the critical set of cM with the irreducible char- +acter variety (a real semi-algebraic set): +χ∗(M) = Hom(π1(M), SU(2)) ∖ {θ}/conjugation, +where θ denotes the trivial homomorphism. For any homomorphism ρ: π1(M) → SU(2) +(henceforth called a representation), the cohomology group H1(M; su(2)ad ρ) is called the +Zariski tangent space of χ(M) at ρ. Since M is a homology 3-sphere, the conjugacy class +[θ] of θ is isolated in the character variety; it follows that χ∗(M) is compact [AM90]. The +Hodge theorem identifies the kernel of the Hessian of cM at ρ with the Zariski tangent +space of χ(M) at ρ (e.g., see [Tau90]). The function cM is Morse if all its critical points +are non-degenerate; i.e., the Zariski tangent space is trivial at each critical point. It is +widely known that if M is a connected sum of nontrivial homology spheres, cM is not +2020 Mathematics Subject Classification. Primary 57K18, 57K31, 57R58; Secondary 81T13. +Key words and phrases. Chern-Simons function, flat moduli space. +HUB was supported by an NSERC Discovery Grant. CH was supported by a Simons Collaboration Grant +for Mathematicians. PK is thankful to MPIM in Bonn for support. +1Private communication. +1 +arXiv:2301.03676v1 [math.GT] 9 Jan 2023 + +2 +HANS U. BODEN, CHRISTOPHER HERALD, AND PAUL KIRK +Morse because π1 is a nontrivial free product; there are gluing parameters (also known +as bending parameters), related to conjugating a representation of one factor but not the +other. +The Chern-Simons function cM is called Morse-Bott if and only if every path com- +ponent of the critical set is a smooth manifold, and for each [ρ] ∈ χ∗(M) the dimension +of the Zariski tangent space of χ(M) at [ρ] equals the dimension of the path component +containing [ρ]. +Fintushel-Stern [FS90] showed that if M is a Seifert-fibered homology 3-sphere, then +cM is Morse-Bott. Given two homology spheres M1, M2 such that cMi is Morse-Bott for +i = 1, 2, the connected sum M1#M2 also has a Morse-Bott Chern-Simons function. In +fact, given path components C1 ⊂ χ∗(M1) and C2 ⊂ χ∗(M2), there are three associated +components in χ∗(M1#M2), diffeomorphic to C1×[θ2], [θ1]×C2, and C1×(SU(2)/{±1})× +C2 ⊂ χ∗(M1#M2). The latter is obtained by pairing each ρ1 representing an equivalence +class in C1 with all SU(2) conjugates of a ρ2 representing a class in C2. +Given relatively prime integers p, q, let Tp,q denote the (p, q) torus knot. Consider the +knot complements: +X = S3 ∖ nbd(T3,5), Y = S3 ∖ nbd(T2,7), and Z = S3 ∖ nbd (T−2,7#T−2,7) . +On a 2-torus T 2 with specified meridian µ and longitude λ, define h: T 2 → T 2 to be an +(orientation-reversing) homeomorphism inducing the map +(1) +h∗ : µ �→ µ, λ �→ −µ − λ +on the fundamental group. Equip the boundary ∂X with its natural oriented meridian- +longitude pair µX, λX, and similarly µY , λY for Y and µZ, λZ for Z. Define +Σ1 = X ∪h Y +and Σ2 = X ∪h Z. +It is immediate from the fact that X, Y, Z are all homology solid tori with H1 generated +by the meridians, and with the longitudes trivial in H1, that Σ1, Σ2 are homology spheres. +Theorem A. +(1) There exists an isolated point in χ∗(Σ1) with 2-dimensional Zariski tangent space. +(2) There exists a component of χ∗(Σ2) which is not homeomorphic to a manifold. +Corollary B. The critical set of cΣ1 contains an isolated point at which the Hessian +has a 2-dimensional kernel. The critical set of cΣ2 is not homeomorphic to a manifold. +Thus cΣ1 and cΣ1 are most decidedly not Morse-Bott. Taking connected sums of these +with themselves and with other homology 3-spheres provides many more complicated +examples. +We note that results of Kapovich and Millson [KM17] imply that arbitrarily bad sin- +gularities, including isolated points with nonzero Zariski tangent space and non-manifold +path components, occur in SU(2) character varieties of 3-manifolds. It is an open question +whether their universality results hold for homology 3-spheres (see, e.g., [KM17, Question +8.2]). + +3 +2. Character varieties of X and Y and their image in the character variety of +the separating torus +For any path-connected space A, let +χ(A) = Hom(π1(A), SU(2))/conjugation +denote its character variety. Its points are conjugacy classes, denoted [ρ: π1(A) → SU(2)], +or simply [ρ]. A representation ρ: π1(A) → SU(2) is called central, (non-central) abelian, +or irreducible, depending on whether the stabilizer of ρ under conjugation by SU(2) is +isomorphic to {±1}, U(1) or SU(2). +When T 2 is the 2-dimensional torus with a fixed set of generators µ, λ ∈ π1(T 2), χ(T 2) +is homeomorphic to a 2-sphere (usually called the pillowcase), and there is a branched +covering +(2) +R2 → χ(T 2), (x, y) �→ [µ �→ exi, λ �→ eyi] +which can be seen as the composite of the projection R2 → R2/(2πZ)2 and the orbit +map of the central involution induced by (x, y) �→ (−x, −y). Call a curve in χ(T 2) a line +segment if it is the image of a line segment in R2. Since the slope of a line is preserved +by both translations by (2πZ)2 and reflections through the origin, line segments in χ(T 2) +have well-defined slope. +For any knot K, χ(S3 ∖ nbd(K)) contains an arc of (conjugacy classes of) abelian +representations with central endpoints, mapping to the image of the x axis (i.e., with +slope zero) in χ(T 2). +We parameterize this arc with a path of representations µ �→ +eai, λ �→ 1, a ∈ [0, π], where µ, λ are a meridian, longitude pair. +Klassen [Kla91] explicitly identified the SU(2) character varieties of torus knot com- +plements. From his description of families of homomorphisms parameterizing the path +components of χ∗(S3 ∖ nbd(Tp,q)), one can readily restrict to a meridian/longitude which +generate π1(T 2) to identify the image of the restriction map +i∗ : χ +� +S3 ∖ nbd(Tp,q) +� +→ χ(T 2) +induced by the inclusion i: T 2 = ∂ (S3 ∖ nbd(Tp,q)) → S3 ∖ nbd(Tp,q). Along with the +abelian arc, χ(S3∖nbd(Tp,q)) consists a collection of arcs of conjugacy classes of irreducible +representations, mapping to χ(T 2) as line segments of slope −pq, with ends limiting +to certain points on the abelian arc. +The details in the case of T3,5 are summarized +in [HHK14]. For the purposes of this article, we require only the following part of this +calculation for T3,5, T2,7, and T−2,7. +Proposition 1 (Klassen [Kla91]). There is a path component of χ∗(S3 ∖ nbd(T3,5)) +which is an arc mapping onto a line segment in χ(T 2) of slope −15, r ∈ +� π +15, 11π +15 +� +�→ +(r, −15r), with ends limiting to the points a = π +15 and a = 11π +15 on the abelian arc. Similarly, +there is path component of χ∗(S3 ∖ nbd(T±2,7)) mapping onto a line segment in χ(T 2) of +slope ∓14, r ∈ +� π +14, 13π +14 +� +�→ (r, ∓14r), with ends limiting to the points a = π +14 and a = 13π +14 +on the abelian arc. +At each interior point on these irreducible arcs, the Zariski tangent space is 1- +dimensional. For the (abelian) endpoints of either irreducible arc, the Zariski tangent +space is 3-dimensional and the linearization of the restriction map to χ(T 2) has rank one, +with horizontal image. + +4 +HANS U. BODEN, CHRISTOPHER HERALD, AND PAUL KIRK +Figure 1 and Figure 2 illustrate neighborhoods of the left ends of the irreducible +arcs described in the theorem and (lifts to R2 of) their images under restriction to the +character variety of the boundary torus. In both cases, the neighborhoods embed into the +pillowcase. +··· +··· +[θ] +x +y +π +15 +−15 +Figure 1. Local picture of χ(X) = χ(S3 ∖nbd(T3,5)) near [θ] (on left) and +its image under i∗ +X : χ(X) → χ(∂X) (on right) +··· +··· +[θ] +x +y +π +14 +−14 +Figure 2. Local picture of χ(Y ) = χ(S3 ∖nbd(T2,7)) near [θ] (on left) and +its image under i∗ +Y : χ(Y ) → χ(∂Y ) (on right) +x +y +( π +14, − π +14) +π +15 +−1 +−15 +13 +Figure 3. The images i∗ +X (χ(X)) and h∗ ◦ i∗ +Y (χ(Y )) near [θ] in χ(∂X) +3. Proof of Theorem A +3.1. Proof of part (1). The homeomorphism h of Equation (1) induces a map +h∗ : χ(∂Y ) → χ(∂X) which lifts to the linear map +h∗ = +� +1 +0 +−1 +−1 +� +on R2, using (2). Figure 3 illustrates the line segments which make up the images under +the local embeddings i∗ +X and h∗ ◦ i∗ +Y of the portions of χ(X) and χ(Y ) in Figures 1 and 2. +Consider the fiber product +F := {([ρX], [ρY ]) | i∗ +X(ρX) = h∗ ◦ i∗ +Y (ρY )} ⊂ χ(X) × χ(Y ). + +5 +The restriction map χ(Σ1) → χ(X)×χ(Y ) has image F and fiber over ([ρX], [ρY ]) (known +as the space of gluing parameters) homeomorphic to the double coset space +(3) +StabρX \ Stabρ∂X / StabρY +(see, e.g., [HHK14]). +From the subsets of i∗ +X (χ(X)) , h∗(i∗ +Y (χ(Y ))) that we have identified and sketched +in Figure 3, it is clear that there are two isolated points of intersection. Specifically, +([θX], [θY ]) maps to the origin in χ(∂X) = R2/ ∼, and a pair ([ρX], [ρY ]) which maps to +( π +14, − π +14). Moreover, ρX has non-abelian image and ρY has abelian but non-central image. +For this second pair, Stabρ∂X = U(1) = StabρY , since the representations ρY and ρ∂X +are abelian non-central. Hence the pair ([ρX], [ρY ]) mapping to ( π +14, − π +14) corresponds to +an isolated point of (the real semi-algebraic set) χ(Σ1). +Consider the Mayer-Vietoris sequence (with local su(2) coefficients) +· · · +0 +−→ H1(Σ1) −→ H1(X) ⊕ H1(Y ) +i∗ +X−h∗◦i∗ +Y +−−−−−−→ H1(∂X) −→ · · · +We have: +• dim H1(X; su(2)adρX) = 1 because [ρX] is an interior point on the irreducible arc +of χ(X) identified in Proposition 1, +• dim H1(∂X; su(2)adρ∂X) = 2 since the restriction ρ∂X : π1(∂X) → SU(2) is +abelian and non-central, +• dim H1(Y ; su(2)adρY ) = 3 because ρY is the a = +π +14 abelian endpoint of the +irreducible arc of χ(Y ) identified in Proposition 1, and +• the image of the irreducible arc in χ∗(X) and the abelian arc in h∗(i∗ +Y (χ(Y ))) +have different slopes in χ(∂X), namely −15 and −1, respectively, which shows +i∗ +X − h∗ ◦ i∗ +Y is surjective. +Thus, the Mayer-Vietoris sequence implies that dim H1(Σ1; su(2)adρ) = 2, completing the +proof of the first assertion of Theorem A. +3.2. Proof of part (2). The proof of Part (2) of Theorem A follows a similar strategy +to that used to prove Part (1), but we replace Y by Z = S3 ∖ nbd(T−2,7#T−2,7). The +exterior Z of the composite knot T−2,7#T−2,7 may be viewed as the union of the two +exteriors +Z1 = Z2 = S3 ∖ nbd(T−2,7) +along an annulus representing a meridian. We begin by describing the relevant subset of +χ(Z) and its image i∗ +Z(χ(Z)) ⊂ χ(∂Z)). +The fundamental group π1(Z) is an amalgamated free product of π1(Z1) and π1(Z2), +where particular meridians on each of the two knot complements are identified. For any +representations ρi : π1(Zi) → SU(2), i = 1, 2, which agree on the identified meridians, +there is a representation of π1(Z) that restricts to ρi on π1(Zi). The longitude for the +composite knot is the product of the longitudes for Z1 and Z2 so, roughly speaking, the +longitudinal coordinates in the pillowcase pictures for Z1, Z2 add. +The fiber product/gluing parameter results above (this time with restrictions to the +annulus instead of to ∂X) demonstrate that abelian arcs and the irreducible arcs in χ(Zi), +i = 1, 2, described in Proposition 1 give rise to the following subsets of χ(Z): +(i) the abelian arc in χ(Z), + +6 +HANS U. BODEN, CHRISTOPHER HERALD, AND PAUL KIRK +(ii) two +half-abelian +arcs, +namely +an +abelian/irreducible +arc +and +an +irre- +ducible/abelian arc, consisting of representations of π1(Z) that are irreducible +on only one of π1(Zi), and +(iii) a cylinder of irreducible/irreducible representations with S1 gluing parameter. +All three components of χ(Z) described in (ii) and (iii) limit to the abelian points a = +π +14, 13π +14 on the abelian arc of χ(Z). Under i∗ +Z, the abelian arc maps to the (image in χ(∂Z) +of) the x axis; the two half abelian arcs in (ii) map to line segments of slope 14, and the +cylinder in (iii) maps onto a line segment of slope 28. This is summarized in Figure 4. +[θ] +x +y +π +14 +14 +28 +Figure 4. Local picture of χ(Z) = χ(S3 ∖ nbd(T−2,7#T−2,7)) near [θ] (on +left) and its image under i∗ +Z : χ(Z) → χ(∂Z) (on right) +Under the map h∗ : χ(∂Z) → χ(∂X), the origin is fixed (i.e., h∗([θ∂Z]) = [θ∂X]), the +abelian arc in χ(Z) maps to the line segment y = −x, the half abelian arcs described +above map onto line segments leaving the abelian arc with slope −15, and the image of +the cylinder maps onto a line segment of slope −29. This is summarized in Figure 5. +x +y +π +15 +−1 +−15 +−29 +Figure 5. The images i∗ +X (χ(X)) and h∗ ◦ i∗ +Z (χ(Z)) near [θ] in χ(∂X) +In Figure 5, we overlay the images of i∗ +X(χ(X)) and h∗(i∗ +Z(χ(Z))) in the same picture, +so that we can apply the same sort of fiber product/gluing parameter reasoning to Σ2 = +X ∪h Z. +We begin by noting that the abelian arc of χ(Z) meets the irreducible arc +in χ(X) drawn in Figure 1 at the point ( π +14, − π +14). This intersection corresponds to a +point [ρ0] ∈ χ(Σ2) restricting to an irreducible representation of π1(X) and an abelian +representation of π1(Z), so there is no gluing parameter. Nearby, however, the intersection +includes a line segment emanating down from this point with slope −15. The preimage +of that segment in χ(X) is the irreducible arc in Figure 1 and the preimage in χ(Z) is +the left ends of the two half-abelian arcs on in Figure 4. +Taking gluing parameters into account, [ρ0] has a neighborhood in χ(Σ2) which is a +cone on two disjoint circles, so the path component containing [ρ0] is not a manifold. This +proves the second assertion of Theorem A. +□ + +7 +4. Further discussion and other examples +We note the following fact about the homology 3-spheres Σ1, Σ2. +Proposition 2. The homology 3-sphere Σ1 is diffeomorphic to +1 Dehn surgery on +T3,5#T2,7, and Σ2 is diffeomorphic to +1 Dehn surgery on T3,5#T−2,7#T−2,7. They are +both graph manifolds. +More lengthy calculations using similar techniques allow the analysis of the full charac- +ter varieties of Σ1 and Σ2, as well as more complicated constructions involving additional +torus knot complements. We highlight a few related results without proof for the inter- +ested reader. +Proposition 3. The irreducible character variety χ∗(Σ1) consists of 22 isolated points +with trivial Zariski tangent space, six isolated points with 2-dimensional Zariski tangent +space like the one we described in detail, and a collection of Morse-Bott circle components. +While we have focused in this paper on the unperturbed Chern-Simons function, the +effect of a small (carefully selected) holonomy perturbations on χ(Σ1) is also reasonably +straightforward to understand. A simple holonomy perturbation in a neighborhood of ∂X +can be selected so that i∗ +X(χ(X)) undergoes a vertical Hamiltonian flow supported away +from the central endpoints on the abelian arc, so that each of the six singular isolated +points resolves into a Morse critical point and the Morse-Bott circle components remain +(see, for example, [HK18]). Under a further perturbation using a curve that cuts through +∂X to break the symmetry giving rise to the gluing parameters, the Chern-Simons function +can be made into a Morse function; the Morse-Bott circles can be seen to each contribute +two isolated critical points (contributing zero points, counted algebraically, to the Casson +invariant). +For clarity, the figures only show the neighborhood of the left endpoints of the ir- +reducible arcs described in Proposition 1, but the irreducible arc parameterizations in +that proposition show that the T±2,7 arcs extend further to the right than the irreducible +T3,5 arc. The following proposition is easily proved by tracking the images of the entire +half-abelian arcs (see the last two paragraphs of Section 3.2). +Proposition 4. The path component of χ∗(Σ2) containing the singular point [ρ0] is +homeomorphic to a wedge of two 2-spheres. +Proposition 5. If one replaces Z with S3 ∖ nbd(3T−2,7#T2,7) in the construction of +Σ2, then the corresponding point at ( π +14, − π +14) has a neighborhood that is a cone on the +disjoint union of two circles and a 3-torus. +Finally, we note that the homology spheres Σ1, Σ2 can also be decomposed into Hee- +gaard decompositions, giving rise to different fiber product descriptions of the singularities +in Theorem A. In this case, the character varieties of the handlebodies are smooth man- +ifolds and the local singular structure in the fiber product for this decomposition is a +consequence of these handlebody character varieties intersecting nontransversely in the +smooth locus of the character variety of the surface. +References +[AM90] +Selman Akbulut and John D. McCarthy, Casson’s invariant for oriented homology 3-spheres, +Mathematical Notes, vol. 36, Princeton University Press, Princeton, NJ, 1990, An exposition. +MR 1030042 + +8 +HANS U. BODEN, CHRISTOPHER HERALD, AND PAUL KIRK +[BHK05] Hans U. Boden, Christopher M. Herald, and Paul A. Kirk, The integer valued SU(3) Casson +invariant for Brieskorn spheres, J. Differential Geom. 71 (2005), no. 1, 23–83. MR 2191768 +[FS90] +Ronald Fintushel and Ronald J. Stern, Instanton homology of Seifert fibred homology three +spheres, Proc. London Math. Soc. (3) 61 (1990), no. 1, 109–137. MR 1051101 +[HHK14] Matthew Hedden, Christopher M. Herald, and Paul Kirk, The pillowcase and perturbations of +traceless representations of knot groups, Geom. Topol. 18 (2014), no. 1, 211–287. MR 3158776 +[HK18] +Christopher M. Herald and Paul Kirk, Holonomy perturbations and regularity for traceless +SU(2) character varieties of tangles, Quantum Topol. 9 (2018), no. 2, 349–418. MR 3812815 +[Kla91] +Eric Paul Klassen, Representations of knot groups in SU(2), Trans. Amer. Math. Soc. 326 +(1991), no. 2, 795–828. MR 1008696 +[KM17] +Michael Kapovich and John J. Millson, On representation varieties of 3-manifold groups, Geom. +Topol. 21 (2017), no. 4, 1931–1968. MR 3654101 +[Tau90] +Clifford Henry Taubes, Casson’s invariant and gauge theory, J. Differential Geom. 31 (1990), +no. 2, 547–599. MR 1037415 +Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada +Email address: boden@mcmaster.ca +Department of Mathematics and Statistics, University of Nevada, Reno, NV 89557 +Email address: herald@unr.edu +Department of Mathematics, Indiana University, Bloomington, IN 47405 +Email address: pkirk@indiana.edu + diff --git a/jNE2T4oBgHgl3EQfIAbu/content/tmp_files/load_file.txt b/jNE2T4oBgHgl3EQfIAbu/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..5016eebc8148ddd2f2b705607dc8c2339c77d6ce --- /dev/null +++ b/jNE2T4oBgHgl3EQfIAbu/content/tmp_files/load_file.txt @@ -0,0 +1,205 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf,len=204 +page_content='Examples of homology 3-spheres whose Chern-Simons function is not Morse-Bott Hans U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Boden, Christopher Herald, and Paul Kirk Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' We construct homology 3-spheres for which the (unperturbed) SU(2) Chern-Simons function is not Morse-Bott.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' In one example, there is a degenerate isolated critical point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' In another, a path component of the critical set is not homeomorphic to a manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The examples are +1 Dehn surgeries on connected sums of torus knots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Introduction The purpose of this article is to address a question raised by D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Ruberman1, namely, whether there exist examples of homology 3-spheres M for which the SU(2) Chern-Simons function cM : B∗ → R/Z, a circle-valued function on the space of gauge equivalence classes of irreducible SU(2) con- nections, fails to be Morse-Bott.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' We construct an example of a homology 3-sphere whose Chern-Simons function has a degenerate isolated critical point, as well as one for which the critical set of the Chern-Simons function has a path component not homeomorphic to a manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' It is known that there are Seifert-fibered homology spheres for which the SU(3) Chern-Simons function is not Morse-Bott [BHK05].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' As is well known, holonomy identifies the critical set of cM with the irreducible char- acter variety (a real semi-algebraic set): χ∗(M) = Hom(π1(M), SU(2)) ∖ {θ}/conjugation, where θ denotes the trivial homomorphism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' For any homomorphism ρ: π1(M) → SU(2) (henceforth called a representation), the cohomology group H1(M;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' su(2)ad ρ) is called the Zariski tangent space of χ(M) at ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Since M is a homology 3-sphere, the conjugacy class [θ] of θ is isolated in the character variety;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' it follows that χ∗(M) is compact [AM90].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The Hodge theorem identifies the kernel of the Hessian of cM at ρ with the Zariski tangent space of χ(M) at ρ (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=', see [Tau90]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The function cM is Morse if all its critical points are non-degenerate;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=', the Zariski tangent space is trivial at each critical point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' It is widely known that if M is a connected sum of nontrivial homology spheres, cM is not 2020 Mathematics Subject Classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Primary 57K18, 57K31, 57R58;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Secondary 81T13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Key words and phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Chern-Simons function, flat moduli space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' HUB was supported by an NSERC Discovery Grant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' CH was supported by a Simons Collaboration Grant for Mathematicians.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' PK is thankful to MPIM in Bonn for support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 1Private communication.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content='03676v1 [math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content='GT] 9 Jan 2023 2 HANS U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' BODEN, CHRISTOPHER HERALD, AND PAUL KIRK Morse because π1 is a nontrivial free product;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' there are gluing parameters (also known as bending parameters), related to conjugating a representation of one factor but not the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The Chern-Simons function cM is called Morse-Bott if and only if every path com- ponent of the critical set is a smooth manifold, and for each [ρ] ∈ χ∗(M) the dimension of the Zariski tangent space of χ(M) at [ρ] equals the dimension of the path component containing [ρ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Fintushel-Stern [FS90] showed that if M is a Seifert-fibered homology 3-sphere, then cM is Morse-Bott.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Given two homology spheres M1, M2 such that cMi is Morse-Bott for i = 1, 2, the connected sum M1#M2 also has a Morse-Bott Chern-Simons function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' In fact, given path components C1 ⊂ χ∗(M1) and C2 ⊂ χ∗(M2), there are three associated components in χ∗(M1#M2), diffeomorphic to C1×[θ2], [θ1]×C2, and C1×(SU(2)/{±1})× C2 ⊂ χ∗(M1#M2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The latter is obtained by pairing each ρ1 representing an equivalence class in C1 with all SU(2) conjugates of a ρ2 representing a class in C2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Given relatively prime integers p, q, let Tp,q denote the (p, q) torus knot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Consider the knot complements: X = S3 ∖ nbd(T3,5), Y = S3 ∖ nbd(T2,7), and Z = S3 ∖ nbd (T−2,7#T−2,7) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' On a 2-torus T 2 with specified meridian µ and longitude λ, define h: T 2 → T 2 to be an (orientation-reversing) homeomorphism inducing the map (1) h∗ : µ �→ µ, λ �→ −µ − λ on the fundamental group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Equip the boundary ∂X with its natural oriented meridian- longitude pair µX, λX, and similarly µY , λY for Y and µZ, λZ for Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Define Σ1 = X ∪h Y and Σ2 = X ∪h Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' It is immediate from the fact that X, Y, Z are all homology solid tori with H1 generated by the meridians, and with the longitudes trivial in H1, that Σ1, Σ2 are homology spheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' (1) There exists an isolated point in χ∗(Σ1) with 2-dimensional Zariski tangent space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' (2) There exists a component of χ∗(Σ2) which is not homeomorphic to a manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Corollary B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The critical set of cΣ1 contains an isolated point at which the Hessian has a 2-dimensional kernel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The critical set of cΣ2 is not homeomorphic to a manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Thus cΣ1 and cΣ1 are most decidedly not Morse-Bott.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Taking connected sums of these with themselves and with other homology 3-spheres provides many more complicated examples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' We note that results of Kapovich and Millson [KM17] imply that arbitrarily bad sin- gularities, including isolated points with nonzero Zariski tangent space and non-manifold path components, occur in SU(2) character varieties of 3-manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' It is an open question whether their universality results hold for homology 3-spheres (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=', [KM17, Question 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content='2]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 3 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Character varieties of X and Y and their image in the character variety of the separating torus For any path-connected space A, let χ(A) = Hom(π1(A), SU(2))/conjugation denote its character variety.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Its points are conjugacy classes, denoted [ρ: π1(A) → SU(2)], or simply [ρ].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' A representation ρ: π1(A) → SU(2) is called central, (non-central) abelian, or irreducible, depending on whether the stabilizer of ρ under conjugation by SU(2) is isomorphic to {±1}, U(1) or SU(2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' When T 2 is the 2-dimensional torus with a fixed set of generators µ, λ ∈ π1(T 2), χ(T 2) is homeomorphic to a 2-sphere (usually called the pillowcase), and there is a branched covering (2) R2 → χ(T 2), (x, y) �→ [µ �→ exi, λ �→ eyi] which can be seen as the composite of the projection R2 → R2/(2πZ)2 and the orbit map of the central involution induced by (x, y) �→ (−x, −y).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Call a curve in χ(T 2) a line segment if it is the image of a line segment in R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Since the slope of a line is preserved by both translations by (2πZ)2 and reflections through the origin, line segments in χ(T 2) have well-defined slope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' For any knot K, χ(S3 ∖ nbd(K)) contains an arc of (conjugacy classes of) abelian representations with central endpoints, mapping to the image of the x axis (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=', with slope zero) in χ(T 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' We parameterize this arc with a path of representations µ �→ eai, λ �→ 1, a ∈ [0, π], where µ, λ are a meridian, longitude pair.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Klassen [Kla91] explicitly identified the SU(2) character varieties of torus knot com- plements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' From his description of families of homomorphisms parameterizing the path components of χ∗(S3 ∖ nbd(Tp,q)), one can readily restrict to a meridian/longitude which generate π1(T 2) to identify the image of the restriction map i∗ : χ � S3 ∖ nbd(Tp,q) � → χ(T 2) induced by the inclusion i: T 2 = ∂ (S3 ∖ nbd(Tp,q)) → S3 ∖ nbd(Tp,q).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Along with the abelian arc, χ(S3∖nbd(Tp,q)) consists a collection of arcs of conjugacy classes of irreducible representations, mapping to χ(T 2) as line segments of slope −pq, with ends limiting to certain points on the abelian arc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The details in the case of T3,5 are summarized in [HHK14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' For the purposes of this article, we require only the following part of this calculation for T3,5, T2,7, and T−2,7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Proposition 1 (Klassen [Kla91]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' There is a path component of χ∗(S3 ∖ nbd(T3,5)) which is an arc mapping onto a line segment in χ(T 2) of slope −15, r ∈ � π 15, 11π 15 � �→ (r, −15r), with ends limiting to the points a = π 15 and a = 11π 15 on the abelian arc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Similarly, there is path component of χ∗(S3 ∖ nbd(T±2,7)) mapping onto a line segment in χ(T 2) of slope ∓14, r ∈ � π 14, 13π 14 � �→ (r, ∓14r), with ends limiting to the points a = π 14 and a = 13π 14 on the abelian arc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' At each interior point on these irreducible arcs, the Zariski tangent space is 1- dimensional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' For the (abelian) endpoints of either irreducible arc, the Zariski tangent space is 3-dimensional and the linearization of the restriction map to χ(T 2) has rank one, with horizontal image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 4 HANS U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' BODEN, CHRISTOPHER HERALD, AND PAUL KIRK Figure 1 and Figure 2 illustrate neighborhoods of the left ends of the irreducible arcs described in the theorem and (lifts to R2 of) their images under restriction to the character variety of the boundary torus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' In both cases, the neighborhoods embed into the pillowcase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' ··· ··· [θ] x y π 15 −15 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Local picture of χ(X) = χ(S3 ∖nbd(T3,5)) near [θ] (on left) and its image under i∗ X : χ(X) → χ(∂X) (on right) ··· ··· [θ] x y π 14 −14 Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Local picture of χ(Y ) = χ(S3 ∖nbd(T2,7)) near [θ] (on left) and its image under i∗ Y : χ(Y ) → χ(∂Y ) (on right) x y ( π 14, − π 14) π 15 −1 −15 13 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The images i∗ X (χ(X)) and h∗ ◦ i∗ Y (χ(Y )) near [θ] in χ(∂X) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Proof of Theorem A 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Proof of part (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The homeomorphism h of Equation (1) induces a map h∗ : χ(∂Y ) → χ(∂X) which lifts to the linear map h∗ = � 1 0 −1 −1 � on R2, using (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Figure 3 illustrates the line segments which make up the images under the local embeddings i∗ X and h∗ ◦ i∗ Y of the portions of χ(X) and χ(Y ) in Figures 1 and 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Consider the fiber product F := {([ρX], [ρY ]) | i∗ X(ρX) = h∗ ◦ i∗ Y (ρY )} ⊂ χ(X) × χ(Y ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 5 The restriction map χ(Σ1) → χ(X)×χ(Y ) has image F and fiber over ([ρX], [ρY ]) (known as the space of gluing parameters) homeomorphic to the double coset space (3) StabρX \\ Stabρ∂X / StabρY (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=', [HHK14]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' From the subsets of i∗ X (χ(X)) , h∗(i∗ Y (χ(Y ))) that we have identified and sketched in Figure 3, it is clear that there are two isolated points of intersection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Specifically, ([θX], [θY ]) maps to the origin in χ(∂X) = R2/ ∼, and a pair ([ρX], [ρY ]) which maps to ( π 14, − π 14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Moreover, ρX has non-abelian image and ρY has abelian but non-central image.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' For this second pair, Stabρ∂X = U(1) = StabρY , since the representations ρY and ρ∂X are abelian non-central.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Hence the pair ([ρX], [ρY ]) mapping to ( π 14, − π 14) corresponds to an isolated point of (the real semi-algebraic set) χ(Σ1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Consider the Mayer-Vietoris sequence (with local su(2) coefficients) · · 0 −→ H1(Σ1) −→ H1(X) ⊕ H1(Y ) i∗ X−h∗◦i∗ Y −−−−−−→ H1(∂X) −→ · · · We have: dim H1(X;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' su(2)adρX) = 1 because [ρX] is an interior point on the irreducible arc of χ(X) identified in Proposition 1, dim H1(∂X;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' su(2)adρ∂X) = 2 since the restriction ρ∂X : π1(∂X) → SU(2) is abelian and non-central, dim H1(Y ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' su(2)adρY ) = 3 because ρY is the a = π 14 abelian endpoint of the irreducible arc of χ(Y ) identified in Proposition 1, and the image of the irreducible arc in χ∗(X) and the abelian arc in h∗(i∗ Y (χ(Y ))) have different slopes in χ(∂X), namely −15 and −1, respectively, which shows i∗ X − h∗ ◦ i∗ Y is surjective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Thus, the Mayer-Vietoris sequence implies that dim H1(Σ1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' su(2)adρ) = 2, completing the proof of the first assertion of Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Proof of part (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The proof of Part (2) of Theorem A follows a similar strategy to that used to prove Part (1), but we replace Y by Z = S3 ∖ nbd(T−2,7#T−2,7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The exterior Z of the composite knot T−2,7#T−2,7 may be viewed as the union of the two exteriors Z1 = Z2 = S3 ∖ nbd(T−2,7) along an annulus representing a meridian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' We begin by describing the relevant subset of χ(Z) and its image i∗ Z(χ(Z)) ⊂ χ(∂Z)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The fundamental group π1(Z) is an amalgamated free product of π1(Z1) and π1(Z2), where particular meridians on each of the two knot complements are identified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' For any representations ρi : π1(Zi) → SU(2), i = 1, 2, which agree on the identified meridians, there is a representation of π1(Z) that restricts to ρi on π1(Zi).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The longitude for the composite knot is the product of the longitudes for Z1 and Z2 so, roughly speaking, the longitudinal coordinates in the pillowcase pictures for Z1, Z2 add.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The fiber product/gluing parameter results above (this time with restrictions to the annulus instead of to ∂X) demonstrate that abelian arcs and the irreducible arcs in χ(Zi), i = 1, 2, described in Proposition 1 give rise to the following subsets of χ(Z): (i) the abelian arc in χ(Z), 6 HANS U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' BODEN, CHRISTOPHER HERALD, AND PAUL KIRK (ii) two half-abelian arcs, namely an abelian/irreducible arc and an irre- ducible/abelian arc, consisting of representations of π1(Z) that are irreducible on only one of π1(Zi), and (iii) a cylinder of irreducible/irreducible representations with S1 gluing parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' All three components of χ(Z) described in (ii) and (iii) limit to the abelian points a = π 14, 13π 14 on the abelian arc of χ(Z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Under i∗ Z, the abelian arc maps to the (image in χ(∂Z) of) the x axis;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' the two half abelian arcs in (ii) map to line segments of slope 14, and the cylinder in (iii) maps onto a line segment of slope 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' This is summarized in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' [θ] x y π 14 14 28 Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Local picture of χ(Z) = χ(S3 ∖ nbd(T−2,7#T−2,7)) near [θ] (on left) and its image under i∗ Z : χ(Z) → χ(∂Z) (on right) Under the map h∗ : χ(∂Z) → χ(∂X), the origin is fixed (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=', h∗([θ∂Z]) = [θ∂X]), the abelian arc in χ(Z) maps to the line segment y = −x, the half abelian arcs described above map onto line segments leaving the abelian arc with slope −15, and the image of the cylinder maps onto a line segment of slope −29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' This is summarized in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' x y π 15 −1 −15 −29 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The images i∗ X (χ(X)) and h∗ ◦ i∗ Z (χ(Z)) near [θ] in χ(∂X) In Figure 5, we overlay the images of i∗ X(χ(X)) and h∗(i∗ Z(χ(Z))) in the same picture, so that we can apply the same sort of fiber product/gluing parameter reasoning to Σ2 = X ∪h Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' We begin by noting that the abelian arc of χ(Z) meets the irreducible arc in χ(X) drawn in Figure 1 at the point ( π 14, − π 14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' This intersection corresponds to a point [ρ0] ∈ χ(Σ2) restricting to an irreducible representation of π1(X) and an abelian representation of π1(Z), so there is no gluing parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Nearby, however, the intersection includes a line segment emanating down from this point with slope −15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The preimage of that segment in χ(X) is the irreducible arc in Figure 1 and the preimage in χ(Z) is the left ends of the two half-abelian arcs on in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Taking gluing parameters into account, [ρ0] has a neighborhood in χ(Σ2) which is a cone on two disjoint circles, so the path component containing [ρ0] is not a manifold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' This proves the second assertion of Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' □ 7 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Further discussion and other examples We note the following fact about the homology 3-spheres Σ1, Σ2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Proposition 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The homology 3-sphere Σ1 is diffeomorphic to +1 Dehn surgery on T3,5#T2,7, and Σ2 is diffeomorphic to +1 Dehn surgery on T3,5#T−2,7#T−2,7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' They are both graph manifolds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' More lengthy calculations using similar techniques allow the analysis of the full charac- ter varieties of Σ1 and Σ2, as well as more complicated constructions involving additional torus knot complements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' We highlight a few related results without proof for the inter- ested reader.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Proposition 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The irreducible character variety χ∗(Σ1) consists of 22 isolated points with trivial Zariski tangent space, six isolated points with 2-dimensional Zariski tangent space like the one we described in detail, and a collection of Morse-Bott circle components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' While we have focused in this paper on the unperturbed Chern-Simons function, the effect of a small (carefully selected) holonomy perturbations on χ(Σ1) is also reasonably straightforward to understand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' A simple holonomy perturbation in a neighborhood of ∂X can be selected so that i∗ X(χ(X)) undergoes a vertical Hamiltonian flow supported away from the central endpoints on the abelian arc, so that each of the six singular isolated points resolves into a Morse critical point and the Morse-Bott circle components remain (see, for example, [HK18]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Under a further perturbation using a curve that cuts through ∂X to break the symmetry giving rise to the gluing parameters, the Chern-Simons function can be made into a Morse function;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' the Morse-Bott circles can be seen to each contribute two isolated critical points (contributing zero points, counted algebraically, to the Casson invariant).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' For clarity, the figures only show the neighborhood of the left endpoints of the ir- reducible arcs described in Proposition 1, but the irreducible arc parameterizations in that proposition show that the T±2,7 arcs extend further to the right than the irreducible T3,5 arc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The following proposition is easily proved by tracking the images of the entire half-abelian arcs (see the last two paragraphs of Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Proposition 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' The path component of χ∗(Σ2) containing the singular point [ρ0] is homeomorphic to a wedge of two 2-spheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Proposition 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' If one replaces Z with S3 ∖ nbd(3T−2,7#T2,7) in the construction of Σ2, then the corresponding point at ( π 14, − π 14) has a neighborhood that is a cone on the disjoint union of two circles and a 3-torus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Finally, we note that the homology spheres Σ1, Σ2 can also be decomposed into Hee- gaard decompositions, giving rise to different fiber product descriptions of the singularities in Theorem A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' In this case, the character varieties of the handlebodies are smooth man- ifolds and the local singular structure in the fiber product for this decomposition is a consequence of these handlebody character varieties intersecting nontransversely in the smooth locus of the character variety of the surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' References [AM90] Selman Akbulut and John D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' McCarthy, Casson’s invariant for oriented homology 3-spheres, Mathematical Notes, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 36, Princeton University Press, Princeton, NJ, 1990, An exposition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' MR 1030042 8 HANS U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' BODEN, CHRISTOPHER HERALD, AND PAUL KIRK [BHK05] Hans U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Boden, Christopher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Herald, and Paul A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Kirk, The integer valued SU(3) Casson invariant for Brieskorn spheres, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Differential Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 71 (2005), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 1, 23–83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' MR 2191768 [FS90] Ronald Fintushel and Ronald J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Stern, Instanton homology of Seifert fibred homology three spheres, Proc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' London Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' (3) 61 (1990), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 1, 109–137.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' MR 1051101 [HHK14] Matthew Hedden, Christopher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Herald, and Paul Kirk, The pillowcase and perturbations of traceless representations of knot groups, Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Topol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 18 (2014), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 1, 211–287.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' MR 3158776 [HK18] Christopher M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Herald and Paul Kirk, Holonomy perturbations and regularity for traceless SU(2) character varieties of tangles, Quantum Topol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 9 (2018), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 2, 349–418.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' MR 3812815 [Kla91] Eric Paul Klassen, Representations of knot groups in SU(2), Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Amer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Soc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 326 (1991), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 2, 795–828.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' MR 1008696 [KM17] Michael Kapovich and John J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Millson, On representation varieties of 3-manifold groups, Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Topol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 21 (2017), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 4, 1931–1968.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' MR 3654101 [Tau90] Clifford Henry Taubes, Casson’s invariant and gauge theory, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' Differential Geom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 31 (1990), no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' 2, 547–599.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content=' MR 1037415 Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada Email address: boden@mcmaster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content='ca Department of Mathematics and Statistics, University of Nevada, Reno, NV 89557 Email address: herald@unr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content='edu Department of Mathematics, Indiana University, Bloomington, IN 47405 Email address: pkirk@indiana.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} +page_content='edu' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/jNE2T4oBgHgl3EQfIAbu/content/2301.03676v1.pdf'} diff --git a/jdE1T4oBgHgl3EQfNQNY/vector_store/index.faiss b/jdE1T4oBgHgl3EQfNQNY/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..da76ebbdada70080c3188b42f27410d7d6f1444f --- /dev/null +++ b/jdE1T4oBgHgl3EQfNQNY/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:961373ef3a03fea79c662a3dfd2ffb33f06904e05b9ef7145dcf1a19b7aaaa6a +size 5570605 diff --git a/kb_27/content/tmp_files/kb_27.pdf.txt b/kb_27/content/tmp_files/kb_27.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..78aaa183d25fe30879e2b6e9df02ed8ea45f0520 --- /dev/null +++ b/kb_27/content/tmp_files/kb_27.pdf.txt @@ -0,0 +1,1769 @@ +RESEARCH +Open Access +A metagenomics roadmap to the +uncultured genome diversity in hypersaline +soda lake sediments +Charlotte D. Vavourakis1 +, Adrian-Stefan Andrei2†, Maliheh Mehrshad2†, Rohit Ghai2, Dimitry Y. Sorokin3,4 +and Gerard Muyzer1* +Abstract +Background: Hypersaline soda lakes are characterized by extreme high soluble carbonate alkalinity. Despite the +high pH and salt content, highly diverse microbial communities are known to be present in soda lake brines but +the microbiome of soda lake sediments received much less attention of microbiologists. Here, we performed metagenomic +sequencing on soda lake sediments to give the first extensive overview of the taxonomic diversity found in these complex, +extreme environments and to gain novel physiological insights into the most abundant, uncultured prokaryote lineages. +Results: We sequenced five metagenomes obtained from four surface sediments of Siberian soda lakes with a pH 10 and +a salt content between 70 and 400 g L−1. The recovered 16S rRNA gene sequences were mostly from Bacteria, even in +the salt-saturated lakes. Most OTUs were assigned to uncultured families. We reconstructed 871 metagenome-assembled +genomes (MAGs) spanning more than 45 phyla and discovered the first extremophilic members of the Candidate Phyla +Radiation (CPR). Five new species of CPR were among the most dominant community members. Novel dominant +lineages were found within previously well-characterized functional groups involved in carbon, sulfur, and nitrogen +cycling. Moreover, key enzymes of the Wood-Ljungdahl pathway were encoded within at least four bacterial phyla +never previously associated with this ancient anaerobic pathway for carbon fixation and dissimilation, including the +Actinobacteria. +Conclusions: Our first sequencing effort of hypersaline soda lake sediment metagenomes led to two important +advances. First, we showed the existence and obtained the first genomes of haloalkaliphilic members of the CPR +and several hundred other novel prokaryote lineages. The soda lake CPR is a functionally diverse group, but the most +abundant organisms in this study are likely fermenters with a possible role in primary carbon degradation. Second, +we found evidence for the presence of the Wood-Ljungdahl pathway in many more taxonomic groups than those +encompassing known homo-acetogens, sulfate-reducers, and methanogens. Since only few environmental metagenomics +studies have targeted sediment microbial communities and never to this extent, we expect that our findings are relevant +not only for the understanding of haloalkaline environments but can also be used to set targets for future studies on marine +and freshwater sediments. +Keywords: Soda lake sediments, Metagenomics, Haloalkaliphilic extremophiles, Candidate Phyla Radiation, Wood-Ljungdahl +pathway +* Correspondence: G.Muijzer@uva.nl +†Adrian-Stefan Andrei and Maliheh Mehrshad contributed equally to this +work. +1Microbial Systems Ecology, Department of Freshwater and Marine Ecology, +Institute for Biodiversity and Ecosystem Dynamics, Faculty of Science, +University of Amsterdam, Postbus 94248, 1090, GE, Amsterdam, the +Netherlands +Full list of author information is available at the end of the article +© The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 +International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and +reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to +the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver +(http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. +Vavourakis et al. Microbiome (2018) 6:168 +https://doi.org/10.1186/s40168-018-0548-7 + +MicrobiomeBackground +Soda lakes are evaporative, athallasic salt lakes with low cal- +cium and magnesium concentrations and a high-alkaline +pH up to 11 buffered by dissolved (bi-) carbonate ions [1]. +They are constrained to arid regions across the globe, +mainly the tropical East African Rift Valley [2], the Libyan +Desert [3], the deserts in California and Nevada [4], and the +dry steppe belt of Central Asia that spans to southern Si- +beria, north-eastern Mongolia, and Inner Mongolia in +China [1]. On top of the extreme salinity and alkaline pH, +the Eurasian soda lakes experience extreme seasonal +temperature differences, causing highly unstable water re- +gimes and fluctuating salinities [5]. Yet, soda lakes harbor +diverse communities of haloalkaliphilic microbes, mostly +prokaryotes that are well adapted to survive and grow in +these extreme environments and consist of similar func- +tional groups in soda lakes around the world [1, 2, 6]. The +relative abundance of different groups is typically governed +by the salinity of the brine [1, 7, 8], and microbial-mediated +nutrient +cycles +become +partially +hampered +only +at +salt-saturating conditions [1]. +So far, all characterized prokaryotic lineages cultured +from soda lakes comprise over 70 different species within +more than 30 genera [1, 6, 9, 10]. From these, only a lim- +ited number of genomes have been sequenced today, +mostly from chemolithoautotrophic sulfur-oxidizing bac- +teria belonging to the genus Thioalkalivibrio (class Gam- +maproteobacteria) [1, 11, 12]. It is well established that +metagenomics enables the recovery of genomes and the +identification of novel genetic diversity where culturing ef- +forts fail [13, 14]. In recent years, next-generation sequen- +cing has recovered a massive number of genomes from +previously unknown groups of prokaryotes [15, 16], +including a strikingly large and diverse group called +“Candidate Phyla Radiation” (CPR), only distantly related +to other cultured bacterial lineages [17]. Previously, we +conducted a metagenomics study on soda lakes and re- +constructed novel genomes from uncultured Bacteroidetes +and “Candidatus Nanohaloarchaeaota” living in hypersa- +line Siberian soda brines [7]. Here, we turned our atten- +tion to the far more complex prokaryotic communities +living in the sediments of the hypersaline soda lakes from +the same region. We give a broad overview of all the +taxonomic groups sequenced and focus on the metabolic +diversity found in the reconstructed genomes of the most +abundant, uncultured organisms. +Results +Overall prokaryote community structure +The salinities from the studied soda lakes ranged from +moderately hypersaline (between 70 and 110 g L−1) to +salt-saturated (400 g L−1 salt). The soluble carbonate al- +kalinity was in the molar range, and the pH in all lakes +was around ten (see Additional file 1: Table S1). To give +an overview of the overall prokaryotic community com- +position in each of the samples, we looked at the taxo- +nomic classification of 16S rRNA genes recovered both +by amplicon sequencing and direct metagenomics se- +quencing (Fig. 1, see also Additional file 2: Figure S1; +Additional file 3). The prokaryotic communities of all +five sediment samples were highly diverse and consisted +mostly of uncultured taxonomic groups. Bacteria were +more abundant than Archaea, regardless of the salinity +of the overlaying brine [7] (Fig. 1). Euryarchaeota were +the second and third largest group in the sediments of +the two salt-saturated lakes comprising ~ 10 and ~ 20% +of the 16S rRNA genes in the metagenomes. Most +Euryarchaeota-related OTUs detected by amplicon se- +quencing belonged either to the uncultured Thermoplas- +mata group KTK 4A (SILVA classification) or the genera +Halohasta and Halorubrum (class Halobacteria). In ac- +cordance with cultivation-dependent studies [6], most +OTUs assigned to methanogens were from the class +Methanomicrobia, +especially +the +lithotrophic +genus +Methanocalculus (up to ~ 3%) and the methylotrophic +genus Methanosalsum (Additional file 3). +The varying ratio of the three dominant bacterial groups, +Firmicutes, Bacteroidetes (including the newly proposed +phyla +Rhodothermaeota +and +Balneolaeota +[18]), +and +Gammaproteobacteria, showed no clear trend in relation to +the salinity in the lakes, but when Firmicutes were domin- +ant, Bacteroidetes were less abundant and vice versa. Most +Firmicutes belonged to the order Clostridales. Uncultured +members from the family Syntrophomonadaceae had a +relative abundance of more than 5% in all five metagen- +omes and comprised in two lakes even ~ 11–20% of the +recovered amplicon sequences. The second most abundant +Firmicutes order was Halanaerobiales, particularly the +genus Halanaerobium (family Halanaerobiaceae) and un- +cultured members of the Halobacteroidaceae. The majority +of Bacteroidetes-related OTUs could not be assigned down +to the genus level. The uncultured ML635J-40 aquatic +group (order Bacteroidales) comprised at least 5% of all five +prokaryotic communities. This group has been previously +found to be abundant in Mono Lake [4] (a soda lake) and +in an anoxic bioreactor degrading cyanobacterial biomass +under haloalkaline conditions [19]. Two other highly abun- +dant (up to ~ 8%) uncultured groups from the class Balneo- +lia (proposed new phylum Balneolaeota [18]) were also +detected in other soda lakes before [3, 4]. Within the Gam- +maproteobacteria, the genus Thioalkalivibrio was abundant +(~ 3% of the total community), but also uncultured +members of HOC36 were prevailing at moderate salinities. +Members of the Deltaproteobacteria, Alphaproteobacteria, +and Chloroflexi comprised up to ~ 10% of the detected 16S +rRNA gene in some of the metagenomes. The GIF9 family +of the class Dehalococcoidia was among the top three most +abundant OTUs in two lakes. The extremely salt-tolerant +Vavourakis et al. Microbiome (2018) 6:168 +Page 2 of 18 + +and alkaliphilic genera Desulfonatronobacter (order Desulfo- +bacterales) and Desulfonatronospira (order Desulfovibrio- +nales) +were +the +dominant +Deltaproteobacteria. +Highly +abundant OTUs, within the Actinobacteria belonged to the +class Nitriliruptoria and within the Alphaproteobacteria to +the family Rhodobacteraceae and the genus Roseibaca. The +important nitrifying genus Nitrobacter (Alphaproteobacteria) +was present in only one of the lakes with moderate salinity +(Additional file 3). +Some bacterial top-level taxa appeared less dominant +(< 5%) from the 16S rRNA genes recovered from the +metagenomes but were represented mainly by a single +highly abundant OTU in the amplicon sequences, in- +cluding the haloalkaliphilic genus Truepera within the +phylum Deinococcus-Thermus, the genus Spirochaeata +within the phylum Spirochaetes, the family BSN166 +within the phylum Ignavibacteriae, the BD2–11 terres- +trial group within the Gemmatimonadetes, and the +WCHB1–41 +order +within +the +Verrucomicrobia. +All +OTUs +within +the +Thermotogae +and +Lentisphaerae +belonged to uncultured genera from the family Kosmoto- +gaceae and Oligosphaeraceae, respectively. All Tenericu- +tes-related OTUs belonged to the class Mollicutes, and +especially the order NB1-n was dominant. In contrast, +the phylum Planctomycetes was relatively diverse, with +at least 11 different genus-level OTUs spread over four +class-level groups. +High-throughput genome recovery +We obtained 717 medium-quality (≥ 50% complete, +< 10% contamination) and 154 near-complete (≥ 90% +complete, < 5% contamination) metagenome-assembled +genomes (MAGs) across three major prokaryote groups: +Archaea, Bacteria, and CPR (see Additional file 4 and +Additional file 2: Figure S2). Figures 2 and 3 show the +top-level phylogeny of all MAGs based on 16 ribosomal +proteins. The reference database used contains a repre- +sentative for each major prokaryote lineage [17]. We +a +b +Fig. 1 Abundant prokaryotic groups in five hypersaline soda lake sediments. a Relative abundance of the top-level taxa (those with ≥ 1% abundance +in at least one dataset) based on 16S rRNA reads in unassembled metagenomic datasets. b Relative abundance of the 16S rRNA OTUs (those with sum +of abundance in all datasets ≥ 3%) recovered by amplicon sequencing assigned where possible down to the genus-level. Three of the assessed soda +lakes have a moderate salinity (70–110 g L−1), two are salt-saturated (400 g L− 1) +Vavourakis et al. Microbiome (2018) 6:168 +Page 3 of 18 + +colored the different phyla from which we obtained a +MAG +in +alternate +blue +and +orange +colors, +and +highlighted the MAGs obtained here in a darker shade. +Many MAGs belonged to uncultured groups commonly +detected in soda lake 16S rRNA gene surveys, over 100 +MAGs still belonged to candidate prokaryote phyla and +divisions that to our knowledge were never detected be- +fore in soda lakes, including CPR. Although only few +MAGs had near-complete 16S rRNA genes, in most +cases we were able to link available taxonomic gene an- +notations and ribosomal protein phylogeny to the SILVA +taxonomy of the OTUs assigned to the amplicon se- +quences, while cross-checking the abundance profiles of +both MAGs (Additional file 5) and OTUs. +The soda lake CPR recovered from the metagenomes was +restricted to a few distinct phyla within the Parcubacteria +group, mostly affiliating with “Candidatus Nealsonbacteria” +and “Ca. Zambryskibacteria” [15] (Fig. 2). The first group of +MAGs encompassed four different branches in our riboso- +mal protein tree, suggesting a high-phylogenetic diversity, +with 33 putative new species sampled here (ANI and con- +DNA matrices given in Additional file 6). The “Ca. Zambrys- +kibacteria-”related MAGs consisted of at least five new +species. Few MAGs were recovered from CPR groups also +detected by amplicon sequencing (see Additional file 2: +Figure S1), namely the “Ca. Dojkabacteria” (former WS6), +“Ca. Saccharibacteria” (former TM7), CPR2, and “Ca. +Katanobacteria” (former WWE3). +Fig. 2 Maximum-likelihood phylogeny of the CPR and archaeal MAGs based on 16 ribosomal proteins. The archaeal tree is unrooted. The CPR tree is rooted +to the Wirthbacteria. Alternate orange and blue colors show phyla/classes from which we obtained MAGs (labeled as “Phyla present”). Reconstructed MAGs of +this study are highlighted by darker shades (labeled as “MAG present”). Phyla/classes for which there was no representative in the reconstructed MAGs of this +study are shown as gray cartoons (labeled as “Phyla not present”), and the numerical labels are represented at the bottom. Colored circles at the nodes show +confidence percentage of the bootstraps analysis (100×) +Vavourakis et al. Microbiome (2018) 6:168 +Page 4 of 18 + +Most archaeal MAGs belonged to the phylum Euryarch- +aeota and the abundant classes Halobacteria, Methanomi- +crobia, and Thermoplasmata (related to OTU KTK 4A) +within. In addition, three Thermoplasmata-related MAGs +that encoded for the key enzyme for methanogenesis +(methyl-coenzyme M reductase, mcr) affiliated with refer- +ence genomes from Methanomassilicoccales, the seventh +order of methanogens have been recovered [20, 21]. +Another MCR-encoding MAG was closely related to the +latest +discovered +group +of +poly-extremophilic, +methyl-reducing methanogens from hypersaline lakes +from the class Methanonatronarchaeia [9] (related to +OTU ST-12K10A). We recovered also one MAG from the +class Methanobacteria and a high-quality MAG from the +WCHA1–57 +group +(“Candidatus +Methanofastidiosa” +[22]) in the candidate division WSA2 (Arc I). Several +MAGs were recovered from the DPANN archaeal +groups “Ca. Diapherotrites,” “Ca. Aenigmarchaeota,” +(see Additional file 2: Figure S3) and “Ca. Woesearch- +aeota” (former Deep Sea Hydrothermal Vent Group 6, +DHVEG-6). Although we did not reconstruct any +reasonable-sized MAGs from the TACK superphylum, +we found several 16S rRNA genes on the assembled +contigs that affiliated to the Thaumarchaeota (see +Additional file 1: Table S2). +Nearly every known bacterial phylum had an extremo- +philic lineage sampled from our hypersaline soda lake +sediments (Fig. 3). In most cases, the soda lake lineages +clearly formed separate branches appearing as sister +groups to known reference lineages. The highest genome +recovery was from the same top-level taxonomic groups +that were also abundant in our 16S rRNA gene analysis. +From the Verrucomicrobia, most MAGs belonged to the +order WCHB1-41 (16S rRNA gene identity 92–100%). +However, in our ribosomal protein tree, they branched +within the phylum Lentisphaerae. Sixteen Tenericutes +MAGs from at least 12 different species (Additional file 6) +were closely related to the NB1-n group of Mollicutes. +Based on the recovered genome size and encoded meta- +bolic potential, these organisms are free-living anaerobic +fermenters of simple sugars, similar to what has recently +been +proposed +for +“Candidatus +Izimaplasma” +[23]. +Fig. 3 Maximum-likelihood phylogeny of the bacterial MAGs (CPR excluded) based on 16 ribosomal proteins. Alternate orange and blue colors show phyla/ +classes from which we obtained MAGs (labeled as “Phyla present”). Reconstructed MAGs of this study are highlighted by darker shades (labeled as “MAG +present”). Phyla/classes for which there was no representative in the reconstructed MAGs of this study are shown as gray cartoons (labeled as “Phyla not +present”), and the numerical labels are represented at the bottom. Colored circles at the nodes show confidence percentage of the bootstraps analysis (100×) +Vavourakis et al. Microbiome (2018) 6:168 +Page 5 of 18 + +Several MAGs belonged to the candidate phyla “Ca. +Omnitrophica,” “Ca. Atribacteria,” and “Ca. Acetother- +mia” (former OP1), which were moderately abundant +also in some sediment (see Additional file 2: Figure S1). +For the latter phylum, we suspect that four MAGs were +more closely related to ca. div. WS1 and “Ca. Lindow- +bacteria” for which only few reference genomes are +currently available in NCBI (see Additional file 2: +Figure S4). Due to a high-sequencing coverage, we also +managed to reconstruct several MAGs from rare Bacteria +(< 100 amplicon sequences detected, see Additional file 2: +Figure S1), including the phyla “Ca. Hydrogenedentes,” +“Ca. Cloacimonetes,” ca. div. BRC1, Elusimicrobia, Caldi- +serica, and “Ca. Latescibacteria.” The MAGs from the +latter phylum were more closely related to the recently +proposed phylum “Ca. Handelsmanbacteria” [15]. Two +additional MAGs with 16S rRNA gene fragments with +94–95% identity to the class MD2898-B26 (Nitrospinae) +were more likely members of ca. div. KSB3 (proposed +“Ca. Moduliflexus” [24], see Additional file 2: Figure S5). +Draft genomes of haloalkaliphilic CPR +Strikingly, members of the CPR related to “Ca. Nealson- +bacteria” and “Ca. Vogelbacteria” were among the top +5% of abundant organisms in the surface sediments of +the soda lakes, especially those with moderate salinity +(Fig. 4). Like most members of the CPR, the MAGs of +the four most abundant “Ca. Nealsonbacteria” seem to +be anaerobic fermenters [25]. They lacked a complete +TCA cycle and most complexes from the oxidative elec- +tron transfer chain, except for the subunit F of a +NADH-quinone oxidoreductase (complex I, nuoF, nuoG, +nuoA) and coxB genes (complex II). All CPR MAGs had +a near-complete glycolysis pathway (Embden-Meyerhof- +Parnas) encoded, but pentose phosphate pathways were +severely truncated. The commonly encoded F- and +V-type ATPase can establish a membrane potential for +symporter-antiporters by utilizing the ATP formed by +substrate-level phosphorylation during fermentation. All +CPR have V-type ATPases that can translocate Na+ in +addition to H+ (see Additional file 2: Figure S6), while +only two members of the “Ca. Falkowbacteria” had puta- +tive Na+-coupled F-type ATPases (see Additional file 2: +Figure S7). The coupling of ATP hydrolysis to sodium +translocation is advantageous to maintain pH homeosta- +sis in alkaline environments. Interestingly, with only two +exceptions [26, 27], all CPR genomes recovered from +other environments with neutral pH were reported to +encode only F-type ATPases [28–32]. One low-abundant +MAG affiliated to “Ca. Peregrinibacteria” contained both +the +large +subunit +of +a +RuBisCO +(type +II/III, +see +Additional file 2: Figure S8) and a putative phosphoribu- +lokinase (PRK, K00855) encoded in the same contig. +This is remarkable because PRK homologs were not +previously identified among CPR, and RuBisCo form II/ +III was inferred to function in a nucleoside salvage path- +way [33]. One “Ca. Saccharibacteria” MAG encoded for +a putative channelrhodopsin (see Additional file 2: +Figure S9). This is the first rhodopsin found among the +CPR and suggests that this enigmatic group of organ- +isms may have acquired evolutionary adaptations to a +life in sunlit surface environments. +A previous study showed that most CPR has coccoid +cell morphotypes with a monoderm cell envelope resem- +bling those from Gram-positives and Archaea but with a +distinct S-layer [34]. Thick peptidoglycans coated with +acidic surface polymers such as teichoic acids help pro- +tect the cells of Gram-positives against reactive hydroxyl +ions in highly alkaline environments [35] (Fig. 5a). All +soda lake CPR had indeed the capability for peptidogly- +can biosynthesis, but we found proteins typical for +Gram-negatives for the biosynthesis of lipopolysaccha- +rides (see Additional file 1: Table S3), homologous to the +inner membrane proteins of type II secretion systems +and +to +several +proteins +associated +to +the +outer +membrane and peptidoglycan, including OmpA. +It remains to be determined whether the soda lake +CPR also lacks an outer membrane and perhaps anchor +lipopolysaccharides, S-layer proteins, and lipoproteins to +the inner cell membrane or peptidoglycan. We also +found gene encoding cardiolipin and squalene synthases. +Increased levels of cardiolipin and the presence of squa- +lene make the cytoplasmic membrane less leaky for +protons [36]. In addition, cation/proton exchangers are +known to play a crucial role for pH homeostasis in alka- +liphilic prokaryotes as they help acidify the cytoplasm +during the extrusion of cations [35]. Putative Na+/H+ +exchangers of the Nha-type and multi-subunit Mnh-type +were found only within a few soda lake CPR. Secondary +active transport of K+ might be mediated in most soda +lake CPR by KefB (COG0475)/kch Kef-type, glutathione- +dependent K+ transport systems, with or without H+ +antiport (67,68). +Various soda lake CPR had an acidic proteome, with +pI curves resembling those found in extremely halophilic +Bacteria. Intracellular proteins enriched in acidic amino +acids might be an adaptation to a “salt-in” strategy, i.e., +maintaining high intracellular potassium (K+) concentra- +tions to keep osmotic balance [7, 37] (Fig. 5b; see +Additional file 2: Figure S10). Such a strategy is energet- +ically favorable over de novo synthesis or import of +osmolytes such as ectoine and glycine betaine. We did +not find genes for the synthesis of organic osmolytes and +homologs of ABC-type transporters for primary active +uptake of proline/glycine betaine which were encoded +only in one MAG (Fig. 5a). For the “Ca. Nealsonbac- +teria” and “Ca. Vogelbacteria,” the salt-in strategy might +be a unique feature for the soda lake species explaining +Vavourakis et al. Microbiome (2018) 6:168 +Page 6 of 18 + +their high abundance in the hypersaline soda lake sedi- +ments, as we did not found an acidic proteome pre- +dicted from genomes obtained from other non-saline +environments (See Additional file 2: Figure S11). The +uptake of K+ ions remains enigmatic for most soda lake +CPR. Low-affinity Trk-type K+ uptake transporters (gen- +erally with symport of H+) (67,68) were encoded only by +a limited number of MAGs. We found three MAGs +Fig. 4 Relative abundance and metabolic potential of the dominant species. Abundance values, expressed as reads per kilobase of MAG per gigabase +of mapped reads (RPKG), were averaged for the top ten abundant MAGs from each dataset that were (likely) the same species (Additional file 5, +Additional file 6). Population genomes were ranked by their “salinity preference scores”: those recruiting relatively more from moderate salinity datasets +(cold colors) are drawn to the top, from high salinity datasets (warm colors) to the bottom. The metabolic potential derived from functional marker +genes (Additional file 7) is depicted by the colored symbols. CBB = Calvin-Benson-Bassham cycle, DNRA = dissimilatory nitrite reduction to ammonia, +fix. = fixation, red. = reduction, ox. = oxidation, dis. = disproportionation +Vavourakis et al. Microbiome (2018) 6:168 +Page 7 of 18 + +a +b +Fig. 5 (See legend on next page.) +Vavourakis et al. Microbiome (2018) 6:168 +Page 8 of 18 + +encoding for Kdp-type sensor kinases (kdpD) but no +corresponding genes for the response regulator (kdpE) +or for Kdp-ATPases that function as the inducible, high- +affinity K+ transporters in other Bacteria (67,68). Finally, +mechanosensitive ion channels (mscS, mscL) and ABC- +type multidrug transport systems (AcrAB, ccmA, EmrA, +MdlB, NorM) and sodium efflux permeases (NatB) were +encoded in almost every MAG. The first might rapidly +restore the turgor pressure under fluctuating salinity +conditions by releasing cytoplasmic ions [38]. +Novel abundant groups involved in sulfur, nitrogen, and +carbon cycles +A new species of Thioalkalivibrio (family Ectothiorhodospir- +aceae) was by far the most abundant in the sediments of +the two salt-saturated lakes (Fig. 4). In the sediment of +Bitter-1, also a purple sulfur bacterium from the same fam- +ily was highly abundant. It was closely related to Halorho- +dospira, a genus also frequently cultured from hypersaline +soda lakes [1]. None of the abundant Ectothiorhodospira- +ceae spp. had already a species-representative genome +sequenced (Additional file 6). The potential of the Thioalk- +alivibrio spp. for chemolithotrophic sulfur oxidation was +evident (Additional file 7; see Additional file 8: Information +S1). Interestingly, the encoded nitrogen metabolisms were +quite versatile. While Thioalkalivibrio sp. 1 had the poten- +tial for nitrate reduction to nitrite, Thioalkalivibrio sp. 2 +might perform dissimilatory nitrite reduction to ammonia +(DNRA; see Additional file 2: Figure S12). +Two +deltaproteobacterial +lineages +of +dissimilatory +sulfate-reducing bacteria (SRB) were highly abundant in +the soda lake sediment of Bitter-1. One MAG from the +family Desulfobacteraceae (order Desulfobacterales) is +the first genome from the genus Desulfonatronobacter. It +encodes the genes for complete sulfate reduction to sul- +fide using various electron donors, as well as for the +complete oxidation of volatile fatty acids and alcohols, a +unique +feature +for +the +genus +Desulfonatronobacter +among haloalkaliphilic SRB [10] (see Additional file 8: +Information S2). Fumarate and nitrite (DNRA, NrfAH) +could be used as alternative electron acceptors. The sec- +ond dominant lineage was a new species from the genus +Desulfonatronospira (family Desulfohalobiaceae, order +Desulfovibrionales). Like other members of this genus, it +had the potential to reduce or disproportionate partially +reduced sulfur compounds. In addition, it could also use +nitrite as an alternative electron acceptor (NrfAH) [6]. +A novel lineage of gammaproteobacterial SOB was +highly abundant in the sediments of the moderately hy- +persaline Cock Soda Lake. It appeared as a sister group of +the family Xanthomonadaceae in the ribosomal protein +tree. This heterotrophic organism could conserve energy +through aerobic respiration. It might detoxify sulfide by +oxidizing it to elemental sulfur (sqr) with subsequent re- +duction or disproportionation of the polysulfides (psrA) +chemically formed from the sulfur. It also encoded the po- +tential for DNRA (nrfA and napC). Genes likely involved +in sulfide detoxification (sqr and psrA) were found also in +several other abundant MAGs of heterotrophs, including +one new abundant species from the family of Nitrilirup- +toraceae (class Nitriliruptoria, phylum Actinobacteria). +We found a wide variety of carbohydrate-active enzymes +in these MAGs, such as cellulases (GH1 family) in +addition to genes for glycolysis and TCA cycle and a +chlorophyll/bacteriochlorophyll a/b synthase (bchG gene). +The latter was also found in other Actinobacteria from the +genus Rubrobacter [39]. No evidence was found for +nitrile-degrading potential. +A second novel, uncultured lineage of Gammaproteo- +bacteria that was highly abundant at moderate salinities +branched in our ribosomal protein tree as a sister group +to the family Halothiobacillaceae. The MAGs encoded +for a versatile metabolism typical for purple non-sulfur +bacteria. The MAGs contained puf genes, bch genes, +genes for carotenoid biosynthesis (not shown), and a +Calvin cycle for photoautotrophic growth. Alternatively, +energy may be conserved through aerobic respiration, +while acetate and proprionate could be taken up via an +acetate permease (actP) and further used for acetyl-CoA +biosynthesis and carbon assimilation. Since the sqr gene +was present, but no dsr or sox genes, the organism +might oxidize sulfide only to elemental sulfur. One bin +contained also nifDKH genes suggesting putative diazo- +trophy, as well as a coenzyme F420 hydrogenase suggest- +ing photoproduction of hydrogen [40]. +The abundant Euryarchaeota organism showed a clear +preference for higher salinities. We obtained one highly +abundant MAG from the class Thermoplasmata that +encoded a full-length 16S rRNA gene only distantly re- +lated (91,2% identity, e value 0) to that of a member of +the KTK 4A group found in a hypersaline endoevaporitic +microbial mat [8]. The abundant soda lake organism is +likely a new genus and species. All KTK 4A-related +MAGs found here encoded for similar heterotrophic, +fermentative +metabolisms, +with +the +potential +for +(See figure on previous page.) +Fig. 5 Potential mechanisms for regulating the intracellular pH and cytoplasmic ion content in different CPR phyla. a Membrane transporters, +channels, and lipids. Peptidoglycan is depicted in gray and S-layer proteins in cyan. b Predicted isoelectric points (bin width 0.2) for the coding +sequences of MAGs. A representative proteome is depicted for each phylum for which several members had a pronounced acidic peak (see also +Additional file 2: Figure S11) +Vavourakis et al. Microbiome (2018) 6:168 +Page 9 of 18 + +anaerobic formate and CO oxidation. The KTK 4A +might be also primary degraders since they encoded pu- +tative cellulases (CAZY-families GH1, GH5) and chiti- +nases (GH18). Interestingly, half of the MAGs encoded a +putative +chlorophyll/bacteriochlorophyll +a/b +synthase +(bchG), which is highly unusual for Archaea. Although +little can be inferred from the presence of only one +marker gene, a functional bchG was previously also +found in Crenarchaeota [41]. The remaining two highly +abundant Euryarchaeota-related MAGs belonged to a +new species of Halorubrum (Additional file 6). +Key genes of the Wood-Ljungdahl pathway found in +novel phylogenetic groups +More than 50 MAGs were related to the family Syntro- +phomonadaceae (class Clostridia, phylum Firmicutes) +based on ribosomal protein phylogeny. All 16S rRNA +gene sequences found in the MAGS had 86–95% iden- +tity to sequences obtained from uncultured organisms +related to the genus Dethiobacter. While an isolated +strain of Dethiobacter alkaliphilus is a facultative auto- +troph +that +respires +thiosulfate, +elemental +sulfur +or +polysulfides with hydrogen as an electron donor [42] or +disproportionates +sulfur +[43], +other +haloalkaliphilic +members +of +the +Syntrophomonadaceae +are +reverse +acetogens, oxidizing acetate in syntrophy with a hydro- +genotrophic partner [44]. Two populations (different +species, Additional file 6) were especially abundant in +Cock Soda Lake (Fig. 4). They encoded for a full +CODH/ACS complex, the key enzyme for the reductive +acetyl-CoA or Wood-Ljungdahl pathway (WL) and a +complete +Eastern +branch +for +CO2 +conversion +to +5-methyl-tetrahydrofolate (Additional file 9) [45, 46]. +Acetogens use the WL to reduce CO2 to acetyl-CoA, +which can be fixed into the cell or used to conserve en- +ergy via acetogenesis. Syntrophic acetate oxidizers, some +sulfate reducing bacteria and aceticlastic methanogens +run the WL in reverse. Syntrophomonadaceae sp. 2 +encoded for a putative thiosulfate/polysulfide reductase +as well as a phosphotransacetylase (pta) and an acetate +kinase (ack) for the ATP-dependent conversion of acet- +ate to acetyl-CoA. Although alternative pathways for the +latter interconversion can exist, this second species has +the complete potential for (reversed) acetogenesis. +Highly remarkable was the presence of a bacterial-type +CODH/ACS +complex +and +a +near-complete +eastern +branch of the WL in a highly abundant species in Cock +Soda Lake from the family Coriobacteriaceae (phylum +Actinobacteria). This prompted us to scan all 871 MAGs +for the presence of acsB encoding for the beta-subunit +of the oxido-reductase module of CODH/ACS. We con- +firmed an encoded +(near)-complete +WL in several +additional organisms belonging to phylogenetic groups +not +previously +associated +with +this +pathway +[46] +(Additional file 9). We removed the Coriobacteriaceae +acsB genes from the final dataset to construct a phylo- +genetic tree since they were < 500 aa (Fig. 6) but found +seven MAGs from the OPB41 class within the Actino- +bacteria (16S rRNA gene fragment identity 94–96%). +The eastern branch of WL can function independently +in folate-dependent C1 metabolism [45], but the pres- +ence of the Western-branch in a phylum that comprises +mostly aerobic isolates is very surprising. The WL in +combination with the potential for acetate to acetyl-CoA +interconversion (pta/ack) and a glycolysis pathway were +also present in the soda lake MAGs from the phyla “Ca. +Handelsmanbacteria,” “Ca. Atribacteria” (latter branched +within the “Ca. Acetothermia”), and the class LD1-PA32 +(Chlamydiae), suggesting all these uncultured organisms +might be heterotrophic acetogens. However, it should be +noted that a PFOR typically connecting glycolysis to the +WL was only encoded in the LD1-PA32 MAGs. More- +over, from the genetic make-up alone, it cannot be +excluded that acetate is activated, and the WL run in +reverse for syntrophic acetate oxidation. Finally, the +novel acsB genes from soda lake Halanaerobiaceae, +Natranaerobiaceae, and Halobacteroidaceae (Firmicutes) +and from Brocadiaceae and Planctomycetaceae (Plancto- +mycetes) disrupt the previously proposed dichotomy +between Terrabacteria and Gracilicutes bacterial groups +unifying 16S rRNA and acsB gene phylogenies [46] and +suggest a far more complex evolutionary history of the +WL pathway than previously anticipated. +Discussion +Extensive +classical +microbiology +efforts +have +been +already undertaken to explore the unique extremophilic +microbial communities inhabiting soda lakes. These un- +covered the presence of most of the functional groups +participating in carbon, nitrogen, sulfur, and minor +element cycling at haloalkaline conditions. The main re- +sults of this work are summarized in several recent re- +views [1, 6, 47, 48]. Since most microbes, including +those living in soda lakes, still evade all cultivation ef- +forts, a very effective way to discover new microbes and +assess their physiology based on their genetic repertoire +is either through single cell genomics or by directly se- +quenced environmental DNA. This exploratory metage- +nomics +study +performed +on +soda +lake +sediments +effectively overcame the existing cultivation bottleneck. +First, we expanded the known diversity of CPR consider- +ably with the first genomes of poly-extremophiles sam- +pled from soda lake sediments. Although the presence of +16S rRNA genes from CPR in marine sediments and hy- +persaline microbial mats was previously shown [34], +until now, CPR MAGs were mainly obtained from deep, +subsurface environments [15, 26, 29, 32, 49–52], and hu- +man microbiota [30]. Despite being highly abundant +Vavourakis et al. Microbiome (2018) 6:168 +Page 10 of 18 + +100 % +90-100 % +70-90 % +50-70 % +some MAGs +all MAGs +Bootstraps +Genes present +Glycolysis (EMP) +PFOR +WL-Eastern branch +H4MPT +TH4 +WL-Western branch +CODH/ACS +Acetogenesis/ +acetate activation +(pta/ack) +0.4 +PVC group (Chlamydiae LD1-PA32) +Syntrophorhabdus aromaticivorans +PVC group bacterium CSSed11_184 +Aerophobetes bacterium SCGC_AAA255-F10 +Ca. Acetothermia +Ca. Handelsmanbacteria +Planctomycetaceae +Anaerolineae +Firmicutes +Brocadiaceae +Planctomycetes +Methanomassiliicoccales +Halobacteroidaceae +Natranaerobiaceae +Methanomicrobiales +Desulfonatronospira +Firmicutes +Dehalococcoidia +Armatimonadetes bacterium CSP1-3 +Deltaproteobacteria +Thermodesulfobacteria +Desulfobulbaceae +Halanaerobiaceae +Nitrospirae +Actinobacteria (OPB41) +Fig. 6 Maximum likelihood phylogeny of the bacterial-type acetyl-coA synthases (acsB) found in the MAGs. Only sequences ≥ 500 aa +were included. Lineages for which we discovered the Wood-Ljungdahl (WL) in this study are highlighted in orange, and the presence +of genes in the respective MAGs related to WL, glycolysis, pyruvate, and acetate conversion is indicated by the colored symbols (see +also Additional file 9: Dataset S6). Additional lineages found in this study are marked in blue. The three was rooted according to [46]. +Circles at the nodes show confidence percentage of the bootstraps analysis (100×). EMP = Embden-Meyerhof-Parnas, PFOR = pyruvate:ferredoxin +oxidoreductase complex, pta = phosphotransacetylase gene, ack = acetate kinase gene, H4MPT = tetrahydromethanopterin-linked pathway, TH4 = +tetrahydrofolate pathway, CODH/ACS = carbon monoxide dehydrogenase/acetyl-CoA synthase. PVC group bacterium CSSed11_184 is likely a member +of the WCHB1-41 class within the Verrucomicrobia +Vavourakis et al. Microbiome (2018) 6:168 +Page 11 of 18 + +here, CPR went unnoticed in previous amplicon sequen- +cing studies. This might be due to the fact that many +CPR representatives have random inserts of various +length in their 16S rRNA genes or due to primer mis- +matches [29, 34]. This illustrates also that direct metage- +nomics should not only be preferred over amplicon +sequencing to infer functional potential, but the former +is far more effective for the discovery of novel organ- +isms. Second, we obtained many more genomes from +“traditional” bacterial phyla such as the Planctomycetes +and Chloroflexi, as well as candidate phyla, for which no +soda lake isolates, hence no genomes were previously +obtained. Third, even within the sulfur cycle, the most +active and frequently studied element cycle in soda lakes +[1], we found considerable metabolic novelty. Finally, we +found the Wood-Ljungdahl pathway in several novel +phyla, not closely related to any known acetogens, +methanogens, or sulfate-reducing bacteria [46]. The lat- +ter shows that our sequencing recovery effort has also +significantly contributed to the discovery of metabolic +novelty within various prokaryote phylogenetic groups. +Salinity is often considered to be the major factor +shaping prokaryote community composition in diverse +habitats [53, 54]. Extreme halophilic Euryarchaeota +seem to be always the dominant group in salt-saturated +hypersaline brines, both those with neutral or alkaline +pH [1, 7, 37]. Here, we found that although these +haloarchaea are still relatively more abundant in the sed- +iments exposed to brines with salt-saturating conditions, +the clear majority of microbes in all investigated hyper- +saline soda lake sediments are Bacteria. It could be +hypothesized that the sediment is a hide-out for the +extreme alkalinity and salinity governing the water +column, and that sediment stratification, especially in +the anoxic part, offers plenty of opportunities for niche +diversification. On the other hand, it should no longer +be a surprise that soda lakes are such productive and +biodiverse +systems. +First, +it +has +been +previously +elaborated that soda lake organisms are exposed to +approximately half the osmotic pressure in sodium +carbonate-dominated +brines +compared +to +sodium +chloride-dominated brines with the same Na+ molarity +[47]. Second, nitrogen limitation in the community can +be overcome when many members contribute to the +fixation of atmospheric N2, and various forms of organic +nitrogen are efficiently recycled. The soda lakes exam- +ined in this study were also eutrophic, and sulfur com- +pounds were abundant. Sulfide is also far less toxic at +high pH as it mostly occurs in the form of bisulfide +(HS−). Besides the evident high metabolic and taxo- +nomic diversity of dissimilatory sulfur-cycling bacteria, a +diverse heterotrophic community can be sustained com- +prising both generalist and very specialized carbon de- +graders. Less eutrophic soda lakes might not suffer from +carbon +limitation +either, +due +to +a +presence +of +high-bicarbonate concentrations. These effectively elim- +inate the inorganic carbon limitation for primary pro- +ducers who are highly active in soda lakes, especially +Cyanobacteria [55, 56]. Third, light that penetrates the +surface of the sediment seems to stimulate oxygenic and +anoxygenic phototrophic growth. Moreover, various het- +erotrophs, such as the rhodopsin-containing haloarchaea +and Bacteroidetes, have the option to tap into this un- +limited energy source for example to help sustain the +costly maintenance of osmotic balance. Unexpectedly, +we even found the first rhodopsin encoded by a member +of the CPR. Fourth, tight syntrophic relations, as pro- +posed for CPR members and Syntrophomonadaceae +spp., might be the solution to successful growth in an +energetically challenging environment. +Since our metagenomes are snapshots in time and space, +the failure to reconstruct specific MAGs gives no conclu- +sive evidence for the absence of certain microbial-mediated +element transformation in hypersaline soda lake sediments. +Additionally, technical limitations of the assembly and bin- +ning of highly micro-diverse genome populations might +hamper genome recovery [57]. More importantly, the +abundance of a specific microbe is not necessarily corre- +lated to the importance of its performance in an ecosystem. +Many metabolic capacities are redundant, and often key +transformations are reserved for a few rare organisms that +might proliferate for a short time-span when specific condi- +tions allow for it. For example, although no MAGs were re- +covered from chemolithoautotrophic nitrifiers [58], we did +detect a Nitrobacter-related OTU by amplicon sequencing +and assembled 16S rRNA genes from Thaumarchaeota, +suggesting bacterial and archaeal nitrifiers are present in +the surface sediments of soda lakes at very low abundance. +Finally, the method of DNA isolation might impact the +community composition apparent in the final metagenome +sequenced. Environmental samples contain complex mix- +tures of different organisms, and it is impossible to find a +protocol where the DNA from every single organism is ex- +tracted as efficiently without compromising the final quality +of the extracted DNA. However, since we find all the im- +portant taxonomic and functional groups known from pre- +vious cultivation-dependent studies back in either our +amplicon sequencing datasets or our directly sequenced +metagenomes, we are confident that the community com- +position and the MAGs presented here are representative +for the microbiomes of the soda lake sediments in the +Kulunda Steppe. +Conclusion +Years of intensive microbiological research on soda lakes +seem to have paid off, since many of the described gen- +era we could detect here have a cultured representative +from soda lakes. However, as many of the abundant +Vavourakis et al. Microbiome (2018) 6:168 +Page 12 of 18 + +lineages and groups found in soda lake sediments are +still uncultured, metagenomics proved to be a helpful +tool to gain primary insights in the potential physiology +and ecology of these poly-extremophilic prokaryotes. +We reconstructed the first genomes for many of such +organisms and proposed new functional roles for the +most abundant ones. Future studies should provide +more in depth analyses of these genomes, especially +from the less abundant organisms that might perform +key ecological processes, such as methanogens and nitri- +fiers. In addition, they should focus on gaining physio- +logical culture-based evidence or proof for in situ +activity for the abundant organisms described here. The +key metabolic insights provided by this metagenomics +study can lead to the design of new cultivation strategies. +In general, sediment communities are far more complex +than those found in the corresponding water column +[53, 59] and are therefore often considered too complex +for efficient metagenomic analysis. Many of the novel +lineages found here may therefore have related neutro- +philic lineages in marine and freshwater sediments that +await discovery. We demonstrate here that, by providing +sufficient sequencing depth, the “state of the art metage- +nomics toolbox” can effectively be used on sediments as +well. +Methods +Site description and sample collection +The top 10 cm sediments from four hypersaline, eutrophic +soda lakes located in the Kulunda Steppe (south-western +Siberia, Altai, Russia) were sampled in July of 2010 and +2011. General features and exact location of the sampled +soda lakes are summarized in Additional file 1: Table S1; a +map of the area was published previously [5]. Cock Soda +Lake (a stand-alone lake, sampled both in 2010 and 2011) +and Tanatar-3 (Tanatar system) were moderately hypersa- +line (~ 100 g L−1) with sandy sediment, while Tanatar-1 +and Bitter-1 (Bitter system) were salt-saturated (400 g L−1) +with sulfide-rich sapropel sediments underlined by rock +trona deposits [7, 60]. Especially, Bitter-1 harbors a very +active microbial community, probably due to its high- +organic and -mineral content. Surface sediments were col- +lected by a plastic corer into sterile glass containers and +transported to the laboratory in a cooler. +DNA isolation, 16S rRNA amplicon, and metagenomic +sequencing +The colloidal fraction of each sediment sample (~ 10% +of 50 g) was separated from the course sandy fraction by +several short (30–60 s) low-speed (1–2,000 rpm in +50 mL Falcon tubes) centrifugation steps and washed +with 1–2 M NaCl solution. The pelleted colloidal sedi- +ment fraction was first subjected to 3 cycles of freezing +in liquid nitrogen/thawing, then re-suspended in 0.1 M +Tris (pH 8)/10 mM EDTA, and then subjected to harsh +bead beating treatment. Next, the samples were incu- +bated with lysozyme (15 mg/mL) for 2 h at 37 °C +followed by a SDS (10% w/v) and proteinase K (10 μg/ +mL) treatment for 30 min. at 45 °C. High molecular +weight DNA was isolated using phenol/chloroform ex- +traction, quality-checked, and sequenced as described +previously [7]. Direct high-throughput sequencing of the +DNA was performed on an Illumina HiSeq 2000 plat- +form to generate 150 b paired-end reads. Amplification +of the V4-V6 region of prokaryote 16S rRNA genes +using barcoded 926F-1392R primers, amplicon purifica- +tion, quantification, and Roche (454)-sequencing was +performed together in a batch with brine samples from +the same sampling campaigns. Barcodes and adapter se- +quences were removed from de-multiplexed amplicon +sequence reads and analyzed with the automated NGS +analysis pipeline of the SILVA rRNA gene database pro- +ject [61] (SILVAngs 1.3, database release version 128) +using default parameters. The OTUs (97% identity) +assigned down to the genus level were only considered +when they had a relative abundance ≥ 0.1% in at least +one of the five datasets. +Processing metagenomics reads, assembly, binning, and +post-binning +Metagenomic raw reads were quality trimmed using +Sickle [62] (version 1.33), and only reads ≥ 21 b were +retained. The prokaryotic community structure at taxo- +nomic top levels was extrapolated from ten million ran- +domly sampled singletons from each dataset. Candidate +16S rRNA fragments > 90 b were identified [63] and +compared against the SILVA SSU database 128 (blastn, +min. length 90, min. identity 80%, e value 1e-5). To ver- +ify that the microbial community composition was in- +deed +mostly +prokaryotic, +we +did +a +more +general +screening of the metagenomics reads that identified also +candidate 18S rRNA fragments > 90 b (see Additional +file 1: Tables S4-S5). The complete trimmed read sets +were assembled into contigs ≥ 1 kb with MEGAHIT [64] +(v1.0.3–6-gc3983f9) using paired-end mode, k min = 21, +k max = 131, k step = 10. Genes were predicted using +Prodigal [65] (v.2.6.2) and RNAs with rna_hmm3 [66] +and tRNAscan-SE [67]. Assembled 16S rRNA sequences +were compared to a manually curated version from the +SILVA SSU database (e value ≥ 1e-5). Predicted protein +sequences +were +annotated +against +KEGG +with +GhostKOALA (genus_prokaryotes + family_eukaryotes ++ viruses) [68]. Marker genes for central metabolic +pathways and key environmental element transforma- +tions were identified based on K number assignments +[15, 69–71]. +Contigs ≥ 2.5 kb were binned with METABAT [72] +(superspecific mode) based on differential coverage +Vavourakis et al. Microbiome (2018) 6:168 +Page 13 of 18 + +values obtained by mapping all five trimmed readsets to +all five contig sets with Bowtie2 [73]. The bins were sub- +jected to post-binning (an overview of the workflow is +given in Additional file 2: Figure S13). Bins were +assessed with lineage-specific single copy genes using +CheckM [74] and further processed with the metage- +nomics workflow in Anvi’o [75] (v2.3.2). Since Candidate +Phyla Radiant (CPR) is not included in the CheckM ref- +erence trees and are likely to have low-genome com- +pleteness, we used an existing training file of 797 CPR +genomes to identify putative CPR bins [76]. Bins with +CheckM-completeness ≥ 50% (884 out of 1778) and an +additional four CPR bins were further processed. Coding +sequences +were +annotated +for +taxonomy +against +NCBI-nr (July, 2017) with USEARCH [77] (5.2.32) to +verify that most hits in each bin were to prokaryotic ref- +erences. Phage or viral contigs were manually removed. +Genome +contamination (redundancy) +was estimated +based on marker sets of universal single copy genes +identified for Bacteria [30] and Archaea [78] as imple- +mented in Anvi’o. Genome coverage was obtained by +mapping trimmed reads with BBMap [79] v36.x (kfilter +31, subfilter 15, maxindel 80). Bins with ≥ 5% redun- +dancy were further refined with Anvi’o using circle phy- +lograms +(guide +trees +tnf-cov: +euclidian +ward) +and +scanned again for CPR. Post-binning resulted in a total +of 2499 metagenome-assembled genomes (MAGs), of +which 871 were either medium-quality genome drafts +(CheckM estimated completeness ≥ 50% and contamin- +ation ≤ 10% [80], Additional file 4) or lower quality draft +genomes from CPR. +Phylogeny of the MAGs was assessed based on 16 +single-copy ribosomal proteins and representative refer- +ence genomes of major prokaryote lineages across the +tree of life [17]. Individual ribosomal proteins in our +MAGs were identified by K number assignments. Only +ribosomal proteins ≥ 80 aa were considered. Initial +maximum-likelihood (ML) trees were constructed to de- +termine which organisms belonged to the Archaea, Bac- +teria, or CPR with FastTree 2 [81] (WAG + CAT). Final +separate trees for the three distant evolutionary groups +were constructed in the same manner. Each ribosomal +protein set was aligned separately with MAFFT [82] +(v7.055b, − auto) and concatenated only if a MAG +encoded at least 8 out of 16 proteins. For all trees, a +100× posterior bootstraps +analysis +was +performed. +Phylogenetic trees were visualized together with gen- +ome statistics and abundance information using iTOL +[83]. We cross-checked the taxonomic assignments +based on the phylogeny of the ribosomal protein cas- +sette +with +the +top +hit +contig annotations +against +NCBI-nr and with the reference lineage obtained with +CheckM. Lastly, we manually corrected the MAGs for +misplaced 16S rRNA genes. The final trees presented +in the manuscript were redrawn using FigTree v1.4.3 +[84]. +Detailed genome analyses +CPR +MAGs +were +re-annotated +more +thoroughly: +genes were predicted with Prokka [85], and functional +predictions were performed by running InterProScan +5 locally on the supplied COG, CDD, TIGRFAMs, +HAMAP, Pfam, and SMART databases [86]. BLAST +Koala was used for KEGG pathway predictions [68]. +To find putative carbohydrate-active enzymes in all +final MAGs, we used the web-resource dbCAN [87] +to annotate all predicted proteins ≥ 80 aa against +CAZy [88]. +To identify the top ten abundant MAGs from each re- +spective dataset, ten million randomly sampled single- +tons were mapped onto each MAG with a cut-off of 95% +identity in minimum of 50 bases. Coverage values were +additionally normalized for genome size and expressed +as reads per kilobase of sequence per gigabase of +mapped reads (RPKG) [89]. A positive score (from 871 +to 1) was assigned to each MAG according to the rank- +ing of the summed RPKG of MAGs in the high-salinity +datasets (B1Sed10 and T1Sed) and a negative score ac- +cording to the ranking of the summed RPKGs in the +moderate salinity datasets (CSSed10, CSSed11, T3Se +d10). Both scores were summed to get a “salinity prefer- +ence score” with MAGs recruiting preferably from high +salinity datasets on the positive end, moderate salinity +datasets in the negative end, and those without prefer- +ence in the middle. +We determined species delineation for the most +abundant MAGs and their closest reference genomes +(NCBI-nr) by Average Nucleotide Identity (ANI) and +conserved DNA-matrices, as follows [90]: ANI ≥ 95%, +conDNA ≥ 69% = same species, ANI ≥ 95%, condDNA +< 69% = might be same species, ANI < 95%, condDNA +< 69% = different species. Single gene trees based on +maximum +likelihood +were +constructed +with +un- +trimmed alignments (MAFFT, L-INS-i model) and +FastTree 2 (WAG + CAT, increased accuracy, -spr4 +-mlacc 2 -slownni) using 100× bootstraps. References +were pulled from eggNOG (v4.5.1) [91] and supple- +mented +with +sequences +from +NCBI-nr +or +refined +according to [7, 33, 46, 92–94]. The curated MAGs +were +scanned +for +the +presence +of +rhodopsin +sequences with the hmmsearch software [95] and a +profile +hidden +Markov +model +(HMM) +of +the +bacteriorhodopsin-like protein family (Pfam accession +number +PF01036). +The +identified +sequences +with +significant similarity were aligned together with a +curated database composed of a collection of type-1 +rhodopsins, using MAFFT (L-INS-i accuracy model) +[82]. This protein alignment was further utilized to +Vavourakis et al. Microbiome (2018) 6:168 +Page 14 of 18 + +construct a maximum likelihood tree with 100× boot- +strap with FastTree 2 [81]. All other genes were +identified using the KEGG annotation. +Additional files +Additional file 1: Table S1. General features of the four sampled soda +lakes at time of sampling. Table S2. SILVA classification of the 16S rRNA +gene sequences found in all ≥1 kb contigs of five soda sediment +metagenomic datasets. Table S3. Enzymes involved in lipopolysaccharide +biosynthesis found among different members of the CPR. Table S4. +Sub-kingdom classification of candidate SSU rRNA gene fragments +found in subsamples of 10 million random forward reads from the +five soda sediment metagenomes. Table S5. Top-level taxonomic +classification of the 18S rRNA gene fragments found in subsamples +of 10 million random forward reads from the five soda sediment +metagenomes. Table S6. Description of the metagenomic datasets, +NCBI Sequence Read Archive (SRA) accession numbers and general +statistics of the assembled contigs. (PDF 740 kb) +Additional file 2: Figure S1. Taxonomic fingerprints determined by 16S +rRNA gene amplicon sequencing. Figure S2. Genome statistics of the +871 MAGs. Figure S3. Phylogeny of MAGs belonging to “Candidatus +Aenigmarchaeota” and “Ca. Nanohaloarchaeota”. Figure S4. Phylogeny of +MAGs related to “Candidatus Acetothermia”, candidate division WS1 and +“Candidatus Lindowbacteria”. Figure S5. Phylogeny of MAGs related to +candidate division KSB3 and “Candidatus Schekmanbacteria”. Figure S6. +Multiple sequence alignment of the V-type ATPase subunits K. Figure S7. +Multiple sequence alignment of the F-type ATPase subunits c. Figure S8. +Maximum likelihood tree of the large subunits of RuBisCo and RubisCo- +like proteins. Figure S9. Maximum likelihood tree of the putative +rhodopsins. Figure S10. Predicted isoelectric points (pI) profiles of all +MAGs from CPR members. Figure S11. Predicted isoelectric points +profiles for members of the “Ca. Nealsonbacteria” and “Ca. Vogelbacteria”. +Figure S12. Multiple sequence alignment of the dissimilatory +cytochrome c nitrite reductases (nrfA/TvNiR, K03385). Figure S13. +Overview of the post-binning workflow used for genome recovery. +(PDF 6548 kb) +Additional file 3: Dataset S1. Relative abundance of the OTUs assigned +to the genus-level within the Archaea, Bacteria and organelles from +Eukaryota detected by 16S rRNA gene amplicon sequencing. The OTUs +with less than 0.1% abundance accross all five datasets are not shown. +The names of highly abundant genera (≥1% in at least one of the data- +sets) are shown in bold. (XLSX 24 kb) +Additional file 4: Dataset S2. Organism names, statistics and general +description incl. Completeness and contamination estimates, phylogeny +and DDBJ/EMBL/Genbank accession numbers of the metagenome +assembled genomes (MAGs) described in this paper. All submitted +versions described in this paper are version XXXX01000000. Size = +recovered genome size, Completeness (Compl1), contamination (Cont), +strain heterogenity (Str het) and Taxon CheckM were inferred from +lineage-specific marker sets and a reference tree build with CheckM [74]. +Additional completeness (compl2) and redundancy (red) estimates were +inferred based on the presence of universal single copy genes for Bacteria +and Archaea [75]. Decision and confidence intervals from the Candidate +Phyla Radiation (CPR) scan [75] are given, as well as the taxonomy of the +besthit in SILVA when 16S rRNA genes were present. Phylum/class 16 +ribosomal proteins is the taxonomy derived from our ribosomal protein +trees (see main text: Figs. 2 and 3). OTU gives the inferred link of a +population genome with our 16S rRNA gene amplicon dataset +(Additional file 3). (XLSX 253 kb) +Additional file 5: Dataset S3. Estimated abundance and derived +salinity preference from each MAG in each metagenomic dataset +expressed as Reads per Kilobase of MAG per Gigabase of mapped reads +(RPKG) and “salinity preference score” (see Methods section), basis for +Fig. 4. (XLSX 143 kb) +Additional file 6: Dataset S4. Average Nucleotide Identity (ANI) and +conserved DNA (condna) matrices to determine species delineation +between the most abundant MAGs shown in Fig. 4, closely related +(less abundant) MAGs and NCBI reference genomes. Decision matrix +shows: 1 = same species, − 1 = might be same species, 0 = different +species (see Methods section). (XLSX 1161 kb) +Additional file 7: Dataset S5. Sheet 1 Presence and absence of marker +genes and putative carbohydrate-active enzymes in the MAGs to infer putative +roles in C, N and S element cycles based on K-number assignments and CAZy +annotations. Sheet 2 Summary basis for Fig. 4. (XLSX 41 kb) +Additional file 8: Information S1. More detailed description of the +main metabolisms encoded by Thioalkalivibrio-related MAGs. +Information S2 More detailed description of the main metabolisms +encoded by Deltaproteobacterial-related MAGs. (PDF 219 kb) +Additional file 9: Dataset 6. Sheet 1 shows the MAGs positive for the +marker gene acsB (K14138) encoding an acetyl-CoA synthase (ACS). The +basis for Fig. 6, namely presence and absence of key genes involved in +the Wood-Ljungdahly pathway, acetogenesis, methanogenesis, glycolysis +and pyruvate to CO2 conversion is shown for each MAG. Sheet 2 shows +the MAGs positive for the marker gene cdhC (K00193) encoding for the +beta subunit of an acetyl-CoA decarboxylase synthase complex. While +acsB and cdhC correspond roughly to the Bacterial-type and Archaeal- +type (methanogens) enzymes with the same function, we found few +discrepancies between marker gene and genome phylogeny within the +Methanomassiliicoccaceae and Chloroflexi. (XLSX 52 kb) +Acknowledgments +We thank Dr. Nikolai Chernych for his technical assistance during the +isolation and purification of metagenomics DNA. We also thank the +Department of Energy Joint Genome Institute for sequencing the +metagenomes. +Funding +CDV and GM were supported by the ERC Advanced Grant PARASOL (no. 322551). +A-SA and RG were supported by the research grant 17-04828S from the Grant +Agency of the Czech Republic. MM was supported by the Czech Academy of +Sciences (Postdoc program PPPLZ application number L200961651). DYS was +supported by the SIAM/Gravitation Program (Dutch Ministry of Education and +Science, grant 24002002) and by the Russian Science Foundation (grant 16–14- +00121). Sequencing was performed by the U.S. Department of Energy Joint +Genome Institute, a DOE Office of Science User Facility, as part of the Community +Sequencing Program (contract no. DE-AC02- 05CH11231). +Availability of data and materials +The raw sequence reads of the five metagenomes have been deposited to +the NCBI Sequence Read Archive (see Additional file 1: Table S6 for accession +numbers and read and contig statistics). The final 871 MAGs described in this +paper have been deposited as Whole Genome Shotgun projects at DDBJ/ +EMBL/GenBank, and accession numbers are listed in Additional file 4 +(BioProject ID PRJNA434545). All versions described in this paper are version +XXXX01000000. The cleaned and dereplicated amplicon sequence datasets +are available in FigShare (https://figshare.com/s/7684627445e3621aba24). +Maximum likelihood trees based on the concatenated alignment of 16 +ribosomal proteins, basis for Figs. 2 and 3, in newick format (.tre file) and +complementary datasets (used to plot completeness, contamination, +genome recovery size, G + C mol% and RPKG in iTOL), as well as K number +assignments for the predicted proteins of all MAGs (KEGG-orthologues, +Ghost Koala) and the fully annotated CPR MAGs supporting the conclusions +of this article are also available in FigShare (https://figshare.com/s/ +7684627445e3621aba24). +Authors’ contributions +GM and DYS initiated this study and were responsible for the fieldwork, +sample preparation, and sequencing effort. CDV conceptualized the research +goals under supervision of DYS and GM, and performed the bioinformatics +analysis under close guidance of A-SA and RG. CDV is the primary author of +this manuscript. MM, RG, and CDV prepared the main figures. All authors +read and approved the final manuscript. +Ethics approval and consent to participate +Not applicable. +Vavourakis et al. Microbiome (2018) 6:168 +Page 15 of 18 + +Consent for publication +Not applicable. +Competing interests +The authors declare that they have no competing interests. +Publisher’s Note +Springer Nature remains neutral with regard to jurisdictional claims in +published maps and institutional affiliations. +Author details +1Microbial Systems Ecology, Department of Freshwater and Marine Ecology, +Institute for Biodiversity and Ecosystem Dynamics, Faculty of Science, +University of Amsterdam, Postbus 94248, 1090, GE, Amsterdam, the +Netherlands. 2Department of Aquatic Microbial Ecology, Institute of +Hydrobiology, Biology Centre CAS, Na Sadkach 7, 370 05 Ceske Budejovice, +Czech Republic. 3Winogradsky Institute of Microbiology, Research Centre of +Biotechnology, Russian Academy of Sciences, 60 let Oktyabrya pr-t, 7, bld. 2, +Moscow, Russian Federation117312. 4Environmental Biotechnology, +Department of Biotechnology, Delft University of Technology, Van der +Maasweg 9, 2629, HZ, Delft, the Netherlands. +Received: 23 June 2018 Accepted: 3 September 2018 +References +1. +Sorokin DY, Berben T, Melton ED, Overmars L, Vavourakis CD, Muyzer G. +Microbial diversity and biogeochemical cycling in soda lakes. Extremophiles. +2014;18:791–809. +2. +Oduor SO, Kotut K. Soda lakes of the East African Rift System: the past, the +present and the future. In: Schagerl M, editor. Soda lakes of East Africa. +Berlin: Springer; 2016. p. 365–74. +3. +Mesbah NM, Abou-El-Ela SH, Wiegel J. Novel and unexpected prokaryotic +diversity in water and sediments of the alkaline, hypersaline lakes of the +Wadi An Natrun, Egypt. Microb Ecol. 2007;54:598–617. +4. +Humayoun SB, Bano N, James T, Hollibaugh JT. Depth distribution of +microbial diversity in Mono Lake, a meromictic soda lake in California. Appl +Environ Microbiol. 2003;69:1030–42. +5. +Foti MJ, Sorokin DY, Zacharova EE, Pimenov NV, Kuenen JG, Muyzer G. +Bacterial diversity and activity along a salinity gradient in soda lakes of the +Kulunda Steppe (Altai, Russia). Extremophiles. 2008;12:133–45. +6. +Sorokin DY. Anaerobic haloalkaliphiles. eLS. 2017; https://doi.org/10.1002/ +9780470015902.a0027654. +7. +Vavourakis CD, Ghai R, Rodriguez-Valera F, Sorokin DY, Tringe SG, +Hugenholtz P, et al. Metagenomic insights into the uncultured diversity and +physiology of microbes in four hypersaline soda lake brines. Front Microbiol. +2016;7:211. +8. +Sørensen KB, Canfield DE, Oren A. Salinity responses of benthic microbial +communities in a solar saltern (Eilat, Israel). Appl Environ Microbiol. 2004;70: +1608–16. +9. +Sorokin DY, Makarova KS, Abbas B, Ferrer M, Golyshin PN, Galinski EA, et al. +Discovery of extremely halophilic, methyl-reducing euryarchaea provides +insights into the evolutionary origin of methanogenesis. Nat Microbiol. +2017;2:17081. +10. +Sorokin DY, Chernyh NA, Poroshina MN. Desulfonatronobacter acetoxydans +sp. nov.,: a first acetate-oxidizing, extremely salt-tolerant alkaliphilic SRB from +a hypersaline soda lake. Extremophiles. 2015;19:899–907. +11. +Ahn A-C, Meier-Kolthoff JP, Overmars L, Richter M, Woyke T, Sorokin DY, +et al. Genomic diversity within the haloalkaliphilic genus Thioalkalivibrio. +PLoS One. 2017;12:e0173517. +12. +Sorokin DY, Kuenen JG. Haloalkaliphilic sulfur-oxidizing bacteria in soda +lakes. FEMS Microbiol Rev. 2005;29:685–702. +13. +Albertsen M, Hugenholtz P, Skarshewski A, Nielsen KL, Tyson GW, Nielsen +PH. Genome sequences of rare, uncultured bacteria obtained by differential +coverage binning of multiple metagenomes. Nat Biotechnol. 2013;31:533–8. +14. +Qin J, Li R, Raes J, Arumugam M, Burgdorf KS, Manichanh C, et al. A human +gut microbial gene catalogue established by metagenomic sequencing. +Nature. 2010;464:59–65. +15. +Anantharaman K, Brown CT, Hug LA, Sharon I, Castelle CJ, Probst AJ, et al. +Thousands of microbial genomes shed light on interconnected +biogeochemical processes in an aquifer system. Nat Commun. 2016;7:13219. +16. +Parks DH, Rinke C, Chuvochina M, Chaumeil P-A, Woodcroft BJ, Evans PN, +et al. Recovery of nearly 8,000 metagenome-assembled genomes +substantially expands the tree of life. Nat Microbiol. 2017;2:1533–42. +17. +Hug LA, Baker BJ, Anantharaman K, Brown CT, Probst AJ, Castelle CJ, et al. A +new view of the tree of life. Nat Microbiol. 2016;1:16048. +18. +Hahnke RL, Meier-Kolthoff JP, García-López M, Mukherjee S, Huntemann M, +Ivanova NN, et al. Genome-based taxonomic classification of Bacteroidetes. +Front Microbiol. 2016;7:2003. +19. +Nolla-Ardevol V, Strous M, Tegetmeyer HE. Anaerobic digestion of the +microalga Spirulina at extreme alkaline conditions: biogas production, +metagenome and metatranscriptome. Front Microbiol. 2015;6:597. +20. +Borrel G, Parisot N, Harris HM, Peyretaillade E, Gaci N, Tottey W, et al. +Comparative genomics highlights the unique biology of +Methanomassiliicoccales, a Thermoplasmatales-related seventh order +of methanogenic archaea that encodes pyrrolysine. BMC Genomics. +2014;15:679. +21. +Sorokin DY, Abbas B, Geleijnse M, Pimenov NV, Sukhacheva MV, van +Loosdrecht MCM. Methanogenesis at extremely haloalkaline conditions in the +soda lakes of Kulunda Steppe (Altai, Russia). FEMS Microbiol Ecol. 2015;91:4. +22. +Nobu MK, Narihiro T, Kuroda K, Mei R, Liu WT. Chasing the elusive +Euryarchaeota class WSA2: genomes reveal a uniquely fastidious methyl- +reducing methanogen. ISME J. 2016;10:2478–87. +23. +Skennerton CT, Haroon MF, Briegel A, Shi J, Jensen GJ, Tyson GW, et al. +Phylogenomic analysis of Candidatus “Izimaplasma” species: free-living +representatives from a Tenericutes clade found in methane seeps. ISME J. +2016;10:2679–92. +24. +Sekiguchi Y, Ohashi A, Parks DH, Yamauchi T, Tyson GW, Hugenholtz P. First +genomic insights into members of a candidate bacterial phylum +responsible for wastewater bulking. PeerJ. 2015;3:e740. +25. +Wrighton KC, Thomas BC, Sharon I, Miller CS, Castelle CJ, VerBerkmoes NC, +et al. Fermentation, hydrogen, and sulfur metabolism in multiple +uncultivated bacterial phyla. Science. 2012;337:1661–5. +26. +León-Zayas R, Peoples L, Biddle JF, Podell S, Novotny M, Cameron J, et al. +The metabolic potential of the single cell genomes obtained from the +Challenger Deep, Mariana Trench within the candidate superphylum +Parcubacteria (OD1). Environ Microbiol. 2017;19:2769–84. +27. +Castelle CJ, Brown CT, Thomas BC, Williams KH, Banfield JF. Unusual +respiratory capacity and nitrogen metabolism in a Parcubacterium (OD1) of +the Candidate Phyla Radiation. Sci Rep. 2017;7:40101. +28. +Anantharaman K, Brown CT, Burstein D, Castelle CJ, Probst AJ, Thomas BC, +et al. Analysis of five complete genome sequences for members of the class +Peribacteria in the recently recognized Peregrinibacteria bacterial phylum. +PeerJ. 2016;4:e1607. +29. +Brown CT, Hug LA, Thomas BC, Sharon I, Castelle CJ, Singh A, et al. Unusual +biology across a group comprising more than 15% of domain Bacteria. +Nature. 2015;523:208–11. +30. +Campbell JH, O ‘donoghue P, Campbell AG, Schwientek P, Sczyrba A, +Woyke T, et al. UGA is an additional glycine codon in uncultured SR1 +bacteria from the human microbiota. 2013; doi:https://doi.org/10.1073/pnas. +1303090110. +31. +Hanke A, Hamann E, Sharma R, Geelhoed JS, Hargesheimer T, Kraft B, et al. +Recoding of the stop codon UGA to glycine by a BD1-5/SN-2 bacterium +and niche partitioning between Alpha- and Gammaproteobacteria in a tidal +sediment microbial community naturally selected in a laboratory chemostat. +Front Microbiol. 2014;5:231. +32. +Kantor RS, Wrighton KC, Handley KM, Sharon I, Hug LA, Castelle CJ, et al. +Small genomes and sparse metabolisms of sediment-associated bacteria +from four candidate phyla. MBio. 2013;4:1–11. +33. +Wrighton KC, Castelle CJ, Varaljay VA, Satagopan S, Brown CT, Wilkins MJ, +et al. RubisCO of a nucleoside pathway known from Archaea is found in +diverse uncultivated phyla in bacteria. ISME J. 2016;10:2702–14. +34. +Luef B, Frischkorn KR, Wrighton KC, Holman HYN, Birarda G, Thomas BC, +et al. Diverse uncultivated ultra-small bacterial cells in groundwater. Nat +Commun. 2015;6:1–8. +35. +Krulwich TA, Sachs G, Padan E. Molecular aspects of bacterial pH sensing +and homeostasis. Nat Rev Microbiol. 2011;9:330–43. +36. +Hauß T, Dante S, Dencher NA, Haines TH. Squalane is in the midplane of +the lipid bilayer: implications for its function as a proton permeability +barrier. Biochim Biophys Acta Bioenerg. 2002;1556:149–54. +37. +Oren A. Life at high salt concentrations, intracellular KCl concentrations, and +acidic proteomes. Front Microbiol. 2013;4:315. +Vavourakis et al. Microbiome (2018) 6:168 +Page 16 of 18 + +Published online: 19 September 201838. +Levina N. Protection of Escherichia coli cells against extreme turgor by +activation of MscS and MscL mechanosensitive channels: identification of +genes required for MscS activity. EMBO J. 1999;18:1730–7. +39. +Gupta RS, Khadka B. Evidence for the presence of key chlorophyll- +biosynthesis-related proteins in the genus Rubrobacter (phylum +Actinobacteria) and its implications for the evolution and origin of +photosynthesis. Photosynth Res. 2016;127:201–18. +40. +Basak N, Das D. The prospect of purple non-sulfur (PNS) photosynthetic +bacteria for hydrogen production:the present state of the art. World J +Microbiol Biotechnol. 2007;23:31–42. +41. +Meng J, Wang F, Wang F, Zheng Y, Peng X, Zhou H, et al. An uncultivated +crenarchaeota contains functional bacteriochlorophyll a synthase. ISME J. +2009;3:106–16. +42. +Sorokin DY, Tourova TP, Mußmann M, Muyzer G. Dethiobacter alkaliphilus +gen. nov. sp. nov., and Desulfurivibrio alkaliphilus gen. nov. sp. nov.: two novel +representatives of reductive sulfur cycle from soda lakes. Extremophiles. +2008;12:431–9. +43. +Poser A, Lohmayer R, Vogt C. Extremophiles KK-, 2013 U. Disproportionation +of elemental sulfur by haloalkaliphilic bacteria from soda lakes. +Extremophiles. 2013;17:1003–12. +44. +Sorokin DY, Abbas B, Tourova TP, Bumazhkin BK, Kolganova TV, Muyzer G. +Sulfate-dependent acetate oxidation under extremely natron-alkaline +conditions by syntrophic associations from hypersaline soda lakes. +Microbiology. 2014;160(Pt_4):723–32. +45. +Ragsdale SW. Enzymology of the Wood-Ljungdahl pathway of acetogenesis. +Ann N Y Acad Sci. 2008;1125:129–36. +46. +Adam PS, Borrel G, Gribaldo S. Evolutionary history of carbon monoxide +dehydrogenase/acetyl-CoA synthase, one of the oldest enzymatic +complexes. Proc Natl Acad Sci. 2018;115:E1166–73. +47. +Sorokin DY, Banciu HL, Muyzer G. Functional microbiology of soda lakes. +Curr Opin Microbiol. 2015;25:88–96. +48. +Grant WD, Jones BE. Bacteria, Archaea and viruses of soda lakes. In: Schagerl +M, editor. Soda lakes of East Africa. Berlin: Springer; 2016. p. 97–147. +49. +Bruno A, Sandionigi A, Rizzi E, Bernasconi M, Vicario S, Galimberti A, et al. +Exploring the under-investigated “microbial dark matter” of drinking water +treatment plants. Sci Rep. 2017;7:1–7. +50. +Danczak RE, Johnston MD, Kenah C, Slattery M, Wrighton KC, Wilkins MJ. +Members of the Candidate Phyla Radiation are functionally differentiated by +carbon- and nitrogen-cycling capabilities. Microbiome. 2017;5:112. +51. +Hu P, Tom L, Singh A, Thomas BC, Baker BJ, Piceno YM, et al. Genome- +resolved metagenomic analysis reveals roles for candidate phyla and other +microbial community members in biogeochemical transformations in oil +reservoirs. MBio. 2016;7:e01669–15. +52. +Probst AJ, Castelle CJ, Singh A, Brown CT, Anantharaman K, Sharon I, et al. +Genomic resolution of a cold subsurface aquifer community provides +metabolic insights for novel microbes adapted to high CO2 concentrations. +Environ Microbiol. 2017;19:459–74. +53. +Lozupone CA, Knight R. Global patterns in bacterial diversity. Proc Natl Acad +Sci. 2007;104:11436–40. +54. +Thompson LR, Sanders JG, McDonald D, Amir A, Ladau J, Locey KJ, et al. A +communal catalogue reveals Earth’s multiscale microbial diversity. Nature. +2017;551:457. +55. +Samylina OS, Sapozhnikov FV, Gainanova OY, Ryabova AV, Nikitin MA, +Sorokin DY. Algo-bacterial communities of the Kulunda steppe (Altai region, +Russia) Soda Lakes. Microbiology. 2014;83:849–60. +56. +Krienitz L, Schagerl M. Tiny and tough: microphytes of east African soda lakes. In: +Schagerl M, editor. Soda lakes of East Africa. Berlin: Springer; 2016. p. 149–77. +57. +Nelson WC, Maezato Y, Wu Y-W, Romine MF, Lindemann SR. Identification +and resolution of microdiversity through metagenomic sequencing of +parallel consortia. Appl Environ Microbiol. 2015;82:255–67. +58. +Hansel C. Small but mighty: how minor components drive major +biogeochemical cycles. Environ Microbiol Rep. 2017;9:8–10. +59. +Zinger L, Amaral-Zettler LA, Fuhrman JA, Horner-Devine MC, Huse SM, +Welch DBM, et al. Global patterns of bacterial beta-diversity in seafloor and +seawater ecosystems. PLoS One. 2011;6:e24570. +60. +Isachenko BL. Chloride sulfate and soda lakes of Kulunda steppe and its +biogenic processes. In: Selected works, vol. 2. Leningrad: Academy of +Sciences USSR; 1951. p. 143–62. +61. +Quast C, Pruesse E, Yilmaz P, Gerken J, Schweer T, Yarza P, et al. The SILVA +ribosomal RNA gene database project: improved data processing and web- +based tools. Nucleic Acids Res. 2012;41:D590–6. +62. +Joshi NA, Fass JN. Sickle: a sliding-window, adaptive, quality-based trimming +tool for FastQ files (Version 1.33). 2011. +63. +Ghai R, Pašić L, Fernández AB, Martin-Cuadrado A-B, Mizuno CM, McMahon +KD, et al. New abundant microbial groups in aquatic hypersaline +environments. Sci Rep. 2011;1:135. +64. +Li D, Liu CM, Luo R, Sadakane K, Lam TW. MEGAHIT: An ultra-fast single- +node solution for large and complex metagenomics assembly via succinct +de Bruijn graph. Bioinformatics. 2015;31:1674–6. +65. +Hyatt D, Chen G-L, LoCascio PF, Land ML, Larimer FW, Hauser LJ. Prodigal: +prokaryotic gene recognition and translation initiation site identification. +BMC Bioinformatics. 2010;11:119. +66. +Huang Y, Li W, Finn PW, Perkins DL. Ribosomal RNA identification in +metagenomic and metatranscriptomic datasets. In: De Bruijn FJ, +editor. Handbook of Molecular Microbial Ecology I. Hoboken: Wiley; +2011. p. 387–91. +67. +Lowe TM, Eddy SR. tRNAscan-SE: a program for improved detection of +transfer RNA genes in genomic sequence. Nucleic Acids Res. 1997;25: +955–64. +68. +Kanehisa M, Sato Y, Morishima K. BlastKOALA and GhostKOALA: KEGG tools +for functional characterization of genome and metagenome sequences. J +Mol Biol. 2016;428:726–31. +69. +Lauro FM, Demaere MZ, Yau S, Brown MV, Ng C, Wilkins D, et al. An +integrative study of a meromictic lake ecosystem in Antarctica. ISME J. 2010; +5:879–95. +70. +Hernsdorf AW, Amano Y, Miyakawa K, Ise K, Suzuki Y, Anantharaman K, et al. +Potential for microbial H2 and metal transformations associated with novel +bacteria and archaea in deep terrestrial subsurface sediments. Nat Publ Gr. +2017;11:1915–29. +71. +Llorens-Marès T, Yooseph S, Goll J, Hoffman J, Vila-Costa M, Borrego CM, +et al. Connecting biodiversity and potential functional role in modern +euxinic environments by microbial metagenomics. ISME J. 2015;9:1648–61. +72. +Kang DD, Froula J, Egan R, Wang Z. MetaBAT, an efficient tool for accurately +reconstructing single genomes from complex microbial communities. PeerJ. +2015;3:e1165. +73. +Langmead B, Salzberg SL. Fast gapped-read alignment with bowtie 2. Nat +Methods. 2012;9:357–9. +74. +Parks DH, Imelfort M, Skennerton CT, Hugenholtz P, Tyson GW. CheckM: +assessing the quality of microbial genomes recovered from isolates, single +cells, and metagenomes. Genome Res. 2015;25:1043–55. +75. +Eren AM, Esen ÖC, Quince C, Vineis JH, Morrison HG, Sogin ML, et al. Anvi’o: +an advanced analysis and visualization platform for ‘omics data. PeerJ. 2015; +3:e1319. +76. +Eren AM, Delmot TO. Predicting CPR genomes in metagenomic bins. http:// +merenlab.org/2016/04/17/predicting-CPR-Genomes/. +77. +Edgar RC. Search and clustering orders of magnitude faster than BLAST. +Bioinformatics. 2010;26:2460–1. +78. +Rinke C, Schwientek P, Sczyrba A, Ivanova NN, Anderson IJ, Cheng JF, et al. +Insights into the phylogeny and coding potential of microbial dark matter. +Nature. 2013;499:431–7. +79. +Bushnell B. BBMap short read aligner. 2016. +80. +Bowers RM, Kyrpides NC, Stepanauskas R, Harmon-Smith M, Doud D, Reddy +TBK, et al. Minimum information about a single amplified genome (MISAG) +and a metagenome-assembled genome (MIMAG) of bacteria and archaea. +Nat Biotechnol. 2017;35:725–31. +81. +Price MN, Dehal PS, Arkin AP. FastTree 2--approximately maximum- +likelihood trees for large alignments. PLoS One. 2010;5:e9490. +82. +Katoh K, Standley DM. MAFFT multiple sequence alignment software +version 7: improvements in performance and usability. Mol Biol Evol. 2013; +30:772–80. +83. +Letunic I, Bork P. Interactive tree of life (iTOL) v3: an online tool for the +display and annotation of phylogenetic and other trees. Nucleic Acids Res. +2016;44:W242–5. +84. +FigTree. http://tree.bio.ed.ac.uk/software/figtree/. +85. +Seemann T. Prokka: rapid prokaryotic genome annotation. Bioinformatics. +2014;30:2068–9. +86. +Jones P, Binns D, Chang H-Y, Fraser M, Li W, McAnulla C, et al. InterProScan +5: genome-scale protein function classification. Bioinformatics. 2014;30: +1236–40. +87. +Yin Y, Mao X, Yang J, Chen X, Mao F, Xu Y. dbCAN: a web resource for +automated carbohydrate-active enzyme annotation. Nucleic Acids Res. 2012; +40:W445–51. +Vavourakis et al. Microbiome (2018) 6:168 +Page 17 of 18 + +88. +Cantarel BL, Coutinho PM, Rancurel C, Bernard T, Lombard V, Henrissat B. +The Carbohydrate-Active EnZymes database (CAZy): an expert resource for +glycogenomics. Nucleic Acids Res. 2009;37:D233–8. +89. +Nayfach S, Pollard KS. Average genome size estimation improves +comparative metagenomics and sheds light on the functional ecology of +the human microbiome. Genome Biol. 2015;16:1–18. +90. +Goris J, Konstantinidis KT, Klappenbach JA, Coenye T, Vandamme P, Tiedje +JM. DNA-DNA hybridization values and their relationship to whole-genome +sequence similarities. Int J Syst Evol Microbiol. 2007;57:81–91. +91. +Huerta-Cepas J, Szklarczyk D, Forslund K, Cook H, Heller D, Walter MC, et al. +eggNOG 4.5: a hierarchical orthology framework with improved functional +annotations for eukaryotic, prokaryotic and viral sequences. Nucleic Acids +Res. 2016;44:D286–93. +92. +Tikhonova TV, Slutsky A, Antipov AN, Boyko KM, Polyakov KM, Sorokin DY, +et al. Molecular and catalytic properties of a novel cytochrome c nitrite +reductase from nitrate-reducing haloalkaliphilic sulfur-oxidizing bacterium +Thioalkalivibrio nitratireducens. Biochim Biophys Acta - Proteins Proteomics. +2006;1764:715–23. +93. +Tikhonova T, Tikhonov A, Trofimov A, Polyakov K, Boyko K, Cherkashin E, +et al. Comparative structural and functional analysis of two octaheme nitrite +reductases from closely related Thioalkalivibrio species. FEBS J. 2012;279: +4052–61. +94. +Tabita FR, Hanson TE, Li H, Satagopan S, Singh J, Chan S. Function, structure, +and evolution of the RuBisCO-like proteins and their RuBisCO homologs. +Microbiol Mol Biol Rev. 2007;71:576–99. +95. +Eddy SR. Accelerated profile HMM searches. PLoS Comput Biol. 2011;7: +e1002195. +Vavourakis et al. Microbiome (2018) 6:168 +Page 18 of 18 + diff --git a/kb_27/content/tmp_files/load_file.txt b/kb_27/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..efb2d9c9cff30de2cf17c9600e46f177a91b9b86 --- /dev/null +++ b/kb_27/content/tmp_files/load_file.txt @@ -0,0 +1,1142 @@ +filepath=D:\projects\langchain-ChatGLM-master\knowledge_base\kb_27\content\kb_27.pdf,len=1141 +page_content='RESEARCH Open Access A metagenomics roadmap to the uncultured genome diversity in hypersaline soda lake sediments Charlotte D.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Vavourakis1 , Adrian-Stefan Andrei2†, Maliheh Mehrshad2†, Rohit Ghai2, Dimitry Y.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sorokin3,4 and Gerard Muyzer1* Abstract Background: Hypersaline soda lakes are characterized by extreme high soluble carbonate alkalinity.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Despite the high pH and salt content, highly diverse microbial communities are known to be present in soda lake brines but the microbiome of soda lake sediments received much less attention of microbiologists.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Here, we performed metagenomic sequencing on soda lake sediments to give the first extensive overview of the taxonomic diversity found in these complex, extreme environments and to gain novel physiological insights into the most abundant, uncultured prokaryote lineages.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Results: We sequenced five metagenomes obtained from four surface sediments of Siberian soda lakes with a pH 10 and a salt content between 70 and 400 g L−1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The recovered 16S rRNA gene sequences were mostly from Bacteria, even in the salt-saturated lakes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Most OTUs were assigned to uncultured families.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' We reconstructed 871 metagenome-assembled genomes (MAGs) spanning more than 45 phyla and discovered the first extremophilic members of the Candidate Phyla Radiation (CPR).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Five new species of CPR were among the most dominant community members.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Novel dominant lineages were found within previously well-characterized functional groups involved in carbon, sulfur, and nitrogen cycling.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Moreover, key enzymes of the Wood-Ljungdahl pathway were encoded within at least four bacterial phyla never previously associated with this ancient anaerobic pathway for carbon fixation and dissimilation, including the Actinobacteria.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Conclusions: Our first sequencing effort of hypersaline soda lake sediment metagenomes led to two important advances.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' First, we showed the existence and obtained the first genomes of haloalkaliphilic members of the CPR and several hundred other novel prokaryote lineages.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The soda lake CPR is a functionally diverse group, but the most abundant organisms in this study are likely fermenters with a possible role in primary carbon degradation.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Second, we found evidence for the presence of the Wood-Ljungdahl pathway in many more taxonomic groups than those encompassing known homo-acetogens, sulfate-reducers, and methanogens.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Since only few environmental metagenomics studies have targeted sediment microbial communities and never to this extent, we expect that our findings are relevant not only for the understanding of haloalkaline environments but can also be used to set targets for future studies on marine and freshwater sediments.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Keywords: Soda lake sediments, Metagenomics, Haloalkaliphilic extremophiles, Candidate Phyla Radiation, Wood-Ljungdahl pathway * Correspondence: G.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='Muijzer@uva.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='nl †Adrian-Stefan Andrei and Maliheh Mehrshad contributed equally to this work.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 1Microbial Systems Ecology, Department of Freshwater and Marine Ecology, Institute for Biodiversity and Ecosystem Dynamics, Faculty of Science, University of Amsterdam, Postbus 94248, 1090, GE, Amsterdam, the Netherlands Full list of author information is available at the end of the article © The Author(s).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='0 International License (http://creativecommons.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='org/licenses/by/4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The Creative Commons Public Domain Dedication waiver (http://creativecommons.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='org/publicdomain/zero/1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='0/) applies to the data made available in this article, unless otherwise stated.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 https://doi.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='org/10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='1186/s40168-018-0548-7 MicrobiomeBackground Soda lakes are evaporative, athallasic salt lakes with low cal- cium and magnesium concentrations and a high-alkaline pH up to 11 buffered by dissolved (bi-) carbonate ions [1].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' They are constrained to arid regions across the globe, mainly the tropical East African Rift Valley [2], the Libyan Desert [3], the deserts in California and Nevada [4], and the dry steppe belt of Central Asia that spans to southern Si- beria, north-eastern Mongolia, and Inner Mongolia in China [1].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' On top of the extreme salinity and alkaline pH, the Eurasian soda lakes experience extreme seasonal temperature differences, causing highly unstable water re- gimes and fluctuating salinities [5].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Yet, soda lakes harbor diverse communities of haloalkaliphilic microbes, mostly prokaryotes that are well adapted to survive and grow in these extreme environments and consist of similar func- tional groups in soda lakes around the world [1, 2, 6].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The relative abundance of different groups is typically governed by the salinity of the brine [1, 7, 8], and microbial-mediated nutrient cycles become partially hampered only at salt-saturating conditions [1].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' So far, all characterized prokaryotic lineages cultured from soda lakes comprise over 70 different species within more than 30 genera [1, 6, 9, 10].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' From these, only a lim- ited number of genomes have been sequenced today, mostly from chemolithoautotrophic sulfur-oxidizing bac- teria belonging to the genus Thioalkalivibrio (class Gam- maproteobacteria) [1, 11, 12].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' It is well established that metagenomics enables the recovery of genomes and the identification of novel genetic diversity where culturing ef- forts fail [13, 14].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' In recent years, next-generation sequen- cing has recovered a massive number of genomes from previously unknown groups of prokaryotes [15, 16], including a strikingly large and diverse group called “Candidate Phyla Radiation” (CPR), only distantly related to other cultured bacterial lineages [17].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Previously, we conducted a metagenomics study on soda lakes and re- constructed novel genomes from uncultured Bacteroidetes and “Candidatus Nanohaloarchaeaota” living in hypersa- line Siberian soda brines [7].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Here, we turned our atten- tion to the far more complex prokaryotic communities living in the sediments of the hypersaline soda lakes from the same region.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' We give a broad overview of all the taxonomic groups sequenced and focus on the metabolic diversity found in the reconstructed genomes of the most abundant, uncultured organisms.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Results Overall prokaryote community structure The salinities from the studied soda lakes ranged from moderately hypersaline (between 70 and 110 g L−1) to salt-saturated (400 g L−1 salt).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The soluble carbonate al- kalinity was in the molar range, and the pH in all lakes was around ten (see Additional file 1: Table S1).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' To give an overview of the overall prokaryotic community com- position in each of the samples, we looked at the taxo- nomic classification of 16S rRNA genes recovered both by amplicon sequencing and direct metagenomics se- quencing (Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 1, see also Additional file 2: Figure S1;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Additional file 3).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The prokaryotic communities of all five sediment samples were highly diverse and consisted mostly of uncultured taxonomic groups.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Bacteria were more abundant than Archaea, regardless of the salinity of the overlaying brine [7] (Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 1).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Euryarchaeota were the second and third largest group in the sediments of the two salt-saturated lakes comprising ~ 10 and ~ 20% of the 16S rRNA genes in the metagenomes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Most Euryarchaeota-related OTUs detected by amplicon se- quencing belonged either to the uncultured Thermoplas- mata group KTK 4A (SILVA classification) or the genera Halohasta and Halorubrum (class Halobacteria).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' In ac- cordance with cultivation-dependent studies [6], most OTUs assigned to methanogens were from the class Methanomicrobia, especially the lithotrophic genus Methanocalculus (up to ~ 3%) and the methylotrophic genus Methanosalsum (Additional file 3).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The varying ratio of the three dominant bacterial groups, Firmicutes, Bacteroidetes (including the newly proposed phyla Rhodothermaeota and Balneolaeota [18]), and Gammaproteobacteria, showed no clear trend in relation to the salinity in the lakes, but when Firmicutes were domin- ant, Bacteroidetes were less abundant and vice versa.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Most Firmicutes belonged to the order Clostridales.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Uncultured members from the family Syntrophomonadaceae had a relative abundance of more than 5% in all five metagen- omes and comprised in two lakes even ~ 11–20% of the recovered amplicon sequences.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The second most abundant Firmicutes order was Halanaerobiales, particularly the genus Halanaerobium (family Halanaerobiaceae) and un- cultured members of the Halobacteroidaceae.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The majority of Bacteroidetes-related OTUs could not be assigned down to the genus level.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The uncultured ML635J-40 aquatic group (order Bacteroidales) comprised at least 5% of all five prokaryotic communities.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' This group has been previously found to be abundant in Mono Lake [4] (a soda lake) and in an anoxic bioreactor degrading cyanobacterial biomass under haloalkaline conditions [19].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Two other highly abun- dant (up to ~ 8%) uncultured groups from the class Balneo- lia (proposed new phylum Balneolaeota [18]) were also detected in other soda lakes before [3, 4].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Within the Gam- maproteobacteria, the genus Thioalkalivibrio was abundant (~ 3% of the total community), but also uncultured members of HOC36 were prevailing at moderate salinities.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Members of the Deltaproteobacteria, Alphaproteobacteria, and Chloroflexi comprised up to ~ 10% of the detected 16S rRNA gene in some of the metagenomes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The GIF9 family of the class Dehalococcoidia was among the top three most abundant OTUs in two lakes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The extremely salt-tolerant Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 2 of 18 and alkaliphilic genera Desulfonatronobacter (order Desulfo- bacterales) and Desulfonatronospira (order Desulfovibrio- nales) were the dominant Deltaproteobacteria.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Highly abundant OTUs, within the Actinobacteria belonged to the class Nitriliruptoria and within the Alphaproteobacteria to the family Rhodobacteraceae and the genus Roseibaca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The important nitrifying genus Nitrobacter (Alphaproteobacteria) was present in only one of the lakes with moderate salinity (Additional file 3).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Some bacterial top-level taxa appeared less dominant (< 5%) from the 16S rRNA genes recovered from the metagenomes but were represented mainly by a single highly abundant OTU in the amplicon sequences, in- cluding the haloalkaliphilic genus Truepera within the phylum Deinococcus-Thermus, the genus Spirochaeata within the phylum Spirochaetes, the family BSN166 within the phylum Ignavibacteriae, the BD2–11 terres- trial group within the Gemmatimonadetes, and the WCHB1–41 order within the Verrucomicrobia.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' All OTUs within the Thermotogae and Lentisphaerae belonged to uncultured genera from the family Kosmoto- gaceae and Oligosphaeraceae, respectively.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' All Tenericu- tes-related OTUs belonged to the class Mollicutes, and especially the order NB1-n was dominant.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' In contrast, the phylum Planctomycetes was relatively diverse, with at least 11 different genus-level OTUs spread over four class-level groups.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' High-throughput genome recovery We obtained 717 medium-quality (≥ 50% complete, < 10% contamination) and 154 near-complete (≥ 90% complete, < 5% contamination) metagenome-assembled genomes (MAGs) across three major prokaryote groups: Archaea, Bacteria, and CPR (see Additional file 4 and Additional file 2: Figure S2).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Figures 2 and 3 show the top-level phylogeny of all MAGs based on 16 ribosomal proteins.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The reference database used contains a repre- sentative for each major prokaryote lineage [17].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' We a b Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 1 Abundant prokaryotic groups in five hypersaline soda lake sediments.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' a Relative abundance of the top-level taxa (those with ≥ 1% abundance in at least one dataset) based on 16S rRNA reads in unassembled metagenomic datasets.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' b Relative abundance of the 16S rRNA OTUs (those with sum of abundance in all datasets ≥ 3%) recovered by amplicon sequencing assigned where possible down to the genus-level.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Three of the assessed soda lakes have a moderate salinity (70–110 g L−1), two are salt-saturated (400 g L− 1) Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 3 of 18 colored the different phyla from which we obtained a MAG in alternate blue and orange colors, and highlighted the MAGs obtained here in a darker shade.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Many MAGs belonged to uncultured groups commonly detected in soda lake 16S rRNA gene surveys, over 100 MAGs still belonged to candidate prokaryote phyla and divisions that to our knowledge were never detected be- fore in soda lakes, including CPR.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Although only few MAGs had near-complete 16S rRNA genes, in most cases we were able to link available taxonomic gene an- notations and ribosomal protein phylogeny to the SILVA taxonomy of the OTUs assigned to the amplicon se- quences, while cross-checking the abundance profiles of both MAGs (Additional file 5) and OTUs.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The soda lake CPR recovered from the metagenomes was restricted to a few distinct phyla within the Parcubacteria group, mostly affiliating with “Candidatus Nealsonbacteria” and “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Zambryskibacteria” [15] (Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The first group of MAGs encompassed four different branches in our riboso- mal protein tree, suggesting a high-phylogenetic diversity, with 33 putative new species sampled here (ANI and con- DNA matrices given in Additional file 6).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Zambrys- kibacteria-”related MAGs consisted of at least five new species.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Few MAGs were recovered from CPR groups also detected by amplicon sequencing (see Additional file 2: Figure S1), namely the “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Dojkabacteria” (former WS6), “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Saccharibacteria” (former TM7), CPR2, and “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Katanobacteria” (former WWE3).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2 Maximum-likelihood phylogeny of the CPR and archaeal MAGs based on 16 ribosomal proteins.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The archaeal tree is unrooted.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The CPR tree is rooted to the Wirthbacteria.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Alternate orange and blue colors show phyla/classes from which we obtained MAGs (labeled as “Phyla present”).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Reconstructed MAGs of this study are highlighted by darker shades (labeled as “MAG present”).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Phyla/classes for which there was no representative in the reconstructed MAGs of this study are shown as gray cartoons (labeled as “Phyla not present”), and the numerical labels are represented at the bottom.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Colored circles at the nodes show confidence percentage of the bootstraps analysis (100×) Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 4 of 18 Most archaeal MAGs belonged to the phylum Euryarch- aeota and the abundant classes Halobacteria, Methanomi- crobia, and Thermoplasmata (related to OTU KTK 4A) within.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' In addition, three Thermoplasmata-related MAGs that encoded for the key enzyme for methanogenesis (methyl-coenzyme M reductase, mcr) affiliated with refer- ence genomes from Methanomassilicoccales, the seventh order of methanogens have been recovered [20, 21].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Another MCR-encoding MAG was closely related to the latest discovered group of poly-extremophilic, methyl-reducing methanogens from hypersaline lakes from the class Methanonatronarchaeia [9] (related to OTU ST-12K10A).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' We recovered also one MAG from the class Methanobacteria and a high-quality MAG from the WCHA1–57 group (“Candidatus Methanofastidiosa” [22]) in the candidate division WSA2 (Arc I).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Several MAGs were recovered from the DPANN archaeal groups “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Diapherotrites,” “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Aenigmarchaeota,” (see Additional file 2: Figure S3) and “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Woesearch- aeota” (former Deep Sea Hydrothermal Vent Group 6, DHVEG-6).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Although we did not reconstruct any reasonable-sized MAGs from the TACK superphylum, we found several 16S rRNA genes on the assembled contigs that affiliated to the Thaumarchaeota (see Additional file 1: Table S2).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nearly every known bacterial phylum had an extremo- philic lineage sampled from our hypersaline soda lake sediments (Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 3).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' In most cases, the soda lake lineages clearly formed separate branches appearing as sister groups to known reference lineages.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The highest genome recovery was from the same top-level taxonomic groups that were also abundant in our 16S rRNA gene analysis.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' From the Verrucomicrobia, most MAGs belonged to the order WCHB1-41 (16S rRNA gene identity 92–100%).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' However, in our ribosomal protein tree, they branched within the phylum Lentisphaerae.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sixteen Tenericutes MAGs from at least 12 different species (Additional file 6) were closely related to the NB1-n group of Mollicutes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Based on the recovered genome size and encoded meta- bolic potential, these organisms are free-living anaerobic fermenters of simple sugars, similar to what has recently been proposed for “Candidatus Izimaplasma” [23].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 3 Maximum-likelihood phylogeny of the bacterial MAGs (CPR excluded) based on 16 ribosomal proteins.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Alternate orange and blue colors show phyla/ classes from which we obtained MAGs (labeled as “Phyla present”).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Reconstructed MAGs of this study are highlighted by darker shades (labeled as “MAG present”).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Phyla/classes for which there was no representative in the reconstructed MAGs of this study are shown as gray cartoons (labeled as “Phyla not present”), and the numerical labels are represented at the bottom.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Colored circles at the nodes show confidence percentage of the bootstraps analysis (100×) Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 5 of 18 Several MAGs belonged to the candidate phyla “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Omnitrophica,” “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Atribacteria,” and “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Acetother- mia” (former OP1), which were moderately abundant also in some sediment (see Additional file 2: Figure S1).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' For the latter phylum, we suspect that four MAGs were more closely related to ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' div.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' WS1 and “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Lindow- bacteria” for which only few reference genomes are currently available in NCBI (see Additional file 2: Figure S4).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Due to a high-sequencing coverage, we also managed to reconstruct several MAGs from rare Bacteria (< 100 amplicon sequences detected, see Additional file 2: Figure S1), including the phyla “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Hydrogenedentes,” “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Cloacimonetes,” ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' div.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' BRC1, Elusimicrobia, Caldi- serica, and “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Latescibacteria.” The MAGs from the latter phylum were more closely related to the recently proposed phylum “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Handelsmanbacteria” [15].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Two additional MAGs with 16S rRNA gene fragments with 94–95% identity to the class MD2898-B26 (Nitrospinae) were more likely members of ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' div.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' KSB3 (proposed “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Moduliflexus” [24], see Additional file 2: Figure S5).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Draft genomes of haloalkaliphilic CPR Strikingly, members of the CPR related to “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nealson- bacteria” and “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Vogelbacteria” were among the top 5% of abundant organisms in the surface sediments of the soda lakes, especially those with moderate salinity (Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 4).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Like most members of the CPR, the MAGs of the four most abundant “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nealsonbacteria” seem to be anaerobic fermenters [25].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' They lacked a complete TCA cycle and most complexes from the oxidative elec- tron transfer chain, except for the subunit F of a NADH-quinone oxidoreductase (complex I, nuoF, nuoG, nuoA) and coxB genes (complex II).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' All CPR MAGs had a near-complete glycolysis pathway (Embden-Meyerhof- Parnas) encoded, but pentose phosphate pathways were severely truncated.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The commonly encoded F- and V-type ATPase can establish a membrane potential for symporter-antiporters by utilizing the ATP formed by substrate-level phosphorylation during fermentation.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' All CPR have V-type ATPases that can translocate Na+ in addition to H+ (see Additional file 2: Figure S6), while only two members of the “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Falkowbacteria” had puta- tive Na+-coupled F-type ATPases (see Additional file 2: Figure S7).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The coupling of ATP hydrolysis to sodium translocation is advantageous to maintain pH homeosta- sis in alkaline environments.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Interestingly, with only two exceptions [26, 27], all CPR genomes recovered from other environments with neutral pH were reported to encode only F-type ATPases [28–32].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' One low-abundant MAG affiliated to “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Peregrinibacteria” contained both the large subunit of a RuBisCO (type II/III, see Additional file 2: Figure S8) and a putative phosphoribu- lokinase (PRK, K00855) encoded in the same contig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' This is remarkable because PRK homologs were not previously identified among CPR, and RuBisCo form II/ III was inferred to function in a nucleoside salvage path- way [33].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' One “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Saccharibacteria” MAG encoded for a putative channelrhodopsin (see Additional file 2: Figure S9).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' This is the first rhodopsin found among the CPR and suggests that this enigmatic group of organ- isms may have acquired evolutionary adaptations to a life in sunlit surface environments.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' A previous study showed that most CPR has coccoid cell morphotypes with a monoderm cell envelope resem- bling those from Gram-positives and Archaea but with a distinct S-layer [34].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Thick peptidoglycans coated with acidic surface polymers such as teichoic acids help pro- tect the cells of Gram-positives against reactive hydroxyl ions in highly alkaline environments [35] (Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 5a).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' All soda lake CPR had indeed the capability for peptidogly- can biosynthesis, but we found proteins typical for Gram-negatives for the biosynthesis of lipopolysaccha- rides (see Additional file 1: Table S3), homologous to the inner membrane proteins of type II secretion systems and to several proteins associated to the outer membrane and peptidoglycan, including OmpA.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' It remains to be determined whether the soda lake CPR also lacks an outer membrane and perhaps anchor lipopolysaccharides, S-layer proteins, and lipoproteins to the inner cell membrane or peptidoglycan.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' We also found gene encoding cardiolipin and squalene synthases.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Increased levels of cardiolipin and the presence of squa- lene make the cytoplasmic membrane less leaky for protons [36].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' In addition, cation/proton exchangers are known to play a crucial role for pH homeostasis in alka- liphilic prokaryotes as they help acidify the cytoplasm during the extrusion of cations [35].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Putative Na+/H+ exchangers of the Nha-type and multi-subunit Mnh-type were found only within a few soda lake CPR.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Secondary active transport of K+ might be mediated in most soda lake CPR by KefB (COG0475)/kch Kef-type, glutathione- dependent K+ transport systems, with or without H+ antiport (67,68).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Various soda lake CPR had an acidic proteome, with pI curves resembling those found in extremely halophilic Bacteria.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Intracellular proteins enriched in acidic amino acids might be an adaptation to a “salt-in” strategy, i.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='e.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=', maintaining high intracellular potassium (K+) concentra- tions to keep osmotic balance [7, 37] (Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 5b;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' see Additional file 2: Figure S10).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Such a strategy is energet- ically favorable over de novo synthesis or import of osmolytes such as ectoine and glycine betaine.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' We did not find genes for the synthesis of organic osmolytes and homologs of ABC-type transporters for primary active uptake of proline/glycine betaine which were encoded only in one MAG (Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 5a).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' For the “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nealsonbac- teria” and “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Vogelbacteria,” the salt-in strategy might be a unique feature for the soda lake species explaining Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 6 of 18 their high abundance in the hypersaline soda lake sedi- ments, as we did not found an acidic proteome pre- dicted from genomes obtained from other non-saline environments (See Additional file 2: Figure S11).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The uptake of K+ ions remains enigmatic for most soda lake CPR.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Low-affinity Trk-type K+ uptake transporters (gen- erally with symport of H+) (67,68) were encoded only by a limited number of MAGs.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' We found three MAGs Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 4 Relative abundance and metabolic potential of the dominant species.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Abundance values, expressed as reads per kilobase of MAG per gigabase of mapped reads (RPKG), were averaged for the top ten abundant MAGs from each dataset that were (likely) the same species (Additional file 5, Additional file 6).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Population genomes were ranked by their “salinity preference scores”: those recruiting relatively more from moderate salinity datasets (cold colors) are drawn to the top, from high salinity datasets (warm colors) to the bottom.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The metabolic potential derived from functional marker genes (Additional file 7) is depicted by the colored symbols.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' CBB = Calvin-Benson-Bassham cycle, DNRA = dissimilatory nitrite reduction to ammonia, fix.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' = fixation, red.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' = reduction, ox.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' = oxidation, dis.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' = disproportionation Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 7 of 18 a b Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 5 (See legend on next page.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=') Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 8 of 18 encoding for Kdp-type sensor kinases (kdpD) but no corresponding genes for the response regulator (kdpE) or for Kdp-ATPases that function as the inducible, high- affinity K+ transporters in other Bacteria (67,68).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Finally, mechanosensitive ion channels (mscS, mscL) and ABC- type multidrug transport systems (AcrAB, ccmA, EmrA, MdlB, NorM) and sodium efflux permeases (NatB) were encoded in almost every MAG.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The first might rapidly restore the turgor pressure under fluctuating salinity conditions by releasing cytoplasmic ions [38].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Novel abundant groups involved in sulfur, nitrogen, and carbon cycles A new species of Thioalkalivibrio (family Ectothiorhodospir- aceae) was by far the most abundant in the sediments of the two salt-saturated lakes (Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 4).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' In the sediment of Bitter-1, also a purple sulfur bacterium from the same fam- ily was highly abundant.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' It was closely related to Halorho- dospira, a genus also frequently cultured from hypersaline soda lakes [1].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' None of the abundant Ectothiorhodospira- ceae spp.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' had already a species-representative genome sequenced (Additional file 6).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The potential of the Thioalk- alivibrio spp.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' for chemolithotrophic sulfur oxidation was evident (Additional file 7;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' see Additional file 8: Information S1).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Interestingly, the encoded nitrogen metabolisms were quite versatile.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' While Thioalkalivibrio sp.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 1 had the poten- tial for nitrate reduction to nitrite, Thioalkalivibrio sp.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2 might perform dissimilatory nitrite reduction to ammonia (DNRA;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' see Additional file 2: Figure S12).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Two deltaproteobacterial lineages of dissimilatory sulfate-reducing bacteria (SRB) were highly abundant in the soda lake sediment of Bitter-1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' One MAG from the family Desulfobacteraceae (order Desulfobacterales) is the first genome from the genus Desulfonatronobacter.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' It encodes the genes for complete sulfate reduction to sul- fide using various electron donors, as well as for the complete oxidation of volatile fatty acids and alcohols, a unique feature for the genus Desulfonatronobacter among haloalkaliphilic SRB [10] (see Additional file 8: Information S2).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Fumarate and nitrite (DNRA, NrfAH) could be used as alternative electron acceptors.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The sec- ond dominant lineage was a new species from the genus Desulfonatronospira (family Desulfohalobiaceae, order Desulfovibrionales).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Like other members of this genus, it had the potential to reduce or disproportionate partially reduced sulfur compounds.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' In addition, it could also use nitrite as an alternative electron acceptor (NrfAH) [6].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' A novel lineage of gammaproteobacterial SOB was highly abundant in the sediments of the moderately hy- persaline Cock Soda Lake.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' It appeared as a sister group of the family Xanthomonadaceae in the ribosomal protein tree.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' This heterotrophic organism could conserve energy through aerobic respiration.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' It might detoxify sulfide by oxidizing it to elemental sulfur (sqr) with subsequent re- duction or disproportionation of the polysulfides (psrA) chemically formed from the sulfur.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' It also encoded the po- tential for DNRA (nrfA and napC).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Genes likely involved in sulfide detoxification (sqr and psrA) were found also in several other abundant MAGs of heterotrophs, including one new abundant species from the family of Nitrilirup- toraceae (class Nitriliruptoria, phylum Actinobacteria).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' We found a wide variety of carbohydrate-active enzymes in these MAGs, such as cellulases (GH1 family) in addition to genes for glycolysis and TCA cycle and a chlorophyll/bacteriochlorophyll a/b synthase (bchG gene).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The latter was also found in other Actinobacteria from the genus Rubrobacter [39].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' No evidence was found for nitrile-degrading potential.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' A second novel, uncultured lineage of Gammaproteo- bacteria that was highly abundant at moderate salinities branched in our ribosomal protein tree as a sister group to the family Halothiobacillaceae.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The MAGs encoded for a versatile metabolism typical for purple non-sulfur bacteria.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The MAGs contained puf genes, bch genes, genes for carotenoid biosynthesis (not shown), and a Calvin cycle for photoautotrophic growth.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Alternatively, energy may be conserved through aerobic respiration, while acetate and proprionate could be taken up via an acetate permease (actP) and further used for acetyl-CoA biosynthesis and carbon assimilation.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Since the sqr gene was present, but no dsr or sox genes, the organism might oxidize sulfide only to elemental sulfur.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' One bin contained also nifDKH genes suggesting putative diazo- trophy, as well as a coenzyme F420 hydrogenase suggest- ing photoproduction of hydrogen [40].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The abundant Euryarchaeota organism showed a clear preference for higher salinities.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' We obtained one highly abundant MAG from the class Thermoplasmata that encoded a full-length 16S rRNA gene only distantly re- lated (91,2% identity, e value 0) to that of a member of the KTK 4A group found in a hypersaline endoevaporitic microbial mat [8].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The abundant soda lake organism is likely a new genus and species.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' All KTK 4A-related MAGs found here encoded for similar heterotrophic, fermentative metabolisms, with the potential for (See figure on previous page.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=') Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 5 Potential mechanisms for regulating the intracellular pH and cytoplasmic ion content in different CPR phyla.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' a Membrane transporters, channels, and lipids.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Peptidoglycan is depicted in gray and S-layer proteins in cyan.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' b Predicted isoelectric points (bin width 0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='2) for the coding sequences of MAGs.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' A representative proteome is depicted for each phylum for which several members had a pronounced acidic peak (see also Additional file 2: Figure S11) Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 9 of 18 anaerobic formate and CO oxidation.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The KTK 4A might be also primary degraders since they encoded pu- tative cellulases (CAZY-families GH1, GH5) and chiti- nases (GH18).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Interestingly, half of the MAGs encoded a putative chlorophyll/bacteriochlorophyll a/b synthase (bchG), which is highly unusual for Archaea.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Although little can be inferred from the presence of only one marker gene, a functional bchG was previously also found in Crenarchaeota [41].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The remaining two highly abundant Euryarchaeota-related MAGs belonged to a new species of Halorubrum (Additional file 6).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Key genes of the Wood-Ljungdahl pathway found in novel phylogenetic groups More than 50 MAGs were related to the family Syntro- phomonadaceae (class Clostridia, phylum Firmicutes) based on ribosomal protein phylogeny.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' All 16S rRNA gene sequences found in the MAGS had 86–95% iden- tity to sequences obtained from uncultured organisms related to the genus Dethiobacter.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' While an isolated strain of Dethiobacter alkaliphilus is a facultative auto- troph that respires thiosulfate, elemental sulfur or polysulfides with hydrogen as an electron donor [42] or disproportionates sulfur [43], other haloalkaliphilic members of the Syntrophomonadaceae are reverse acetogens, oxidizing acetate in syntrophy with a hydro- genotrophic partner [44].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Two populations (different species, Additional file 6) were especially abundant in Cock Soda Lake (Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 4).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' They encoded for a full CODH/ACS complex, the key enzyme for the reductive acetyl-CoA or Wood-Ljungdahl pathway (WL) and a complete Eastern branch for CO2 conversion to 5-methyl-tetrahydrofolate (Additional file 9) [45, 46].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Acetogens use the WL to reduce CO2 to acetyl-CoA, which can be fixed into the cell or used to conserve en- ergy via acetogenesis.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Syntrophic acetate oxidizers, some sulfate reducing bacteria and aceticlastic methanogens run the WL in reverse.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Syntrophomonadaceae sp.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2 encoded for a putative thiosulfate/polysulfide reductase as well as a phosphotransacetylase (pta) and an acetate kinase (ack) for the ATP-dependent conversion of acet- ate to acetyl-CoA.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Although alternative pathways for the latter interconversion can exist, this second species has the complete potential for (reversed) acetogenesis.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Highly remarkable was the presence of a bacterial-type CODH/ACS complex and a near-complete eastern branch of the WL in a highly abundant species in Cock Soda Lake from the family Coriobacteriaceae (phylum Actinobacteria).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' This prompted us to scan all 871 MAGs for the presence of acsB encoding for the beta-subunit of the oxido-reductase module of CODH/ACS.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' We con- firmed an encoded (near)-complete WL in several additional organisms belonging to phylogenetic groups not previously associated with this pathway [46] (Additional file 9).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' We removed the Coriobacteriaceae acsB genes from the final dataset to construct a phylo- genetic tree since they were < 500 aa (Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 6) but found seven MAGs from the OPB41 class within the Actino- bacteria (16S rRNA gene fragment identity 94–96%).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The eastern branch of WL can function independently in folate-dependent C1 metabolism [45], but the pres- ence of the Western-branch in a phylum that comprises mostly aerobic isolates is very surprising.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The WL in combination with the potential for acetate to acetyl-CoA interconversion (pta/ack) and a glycolysis pathway were also present in the soda lake MAGs from the phyla “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Handelsmanbacteria,” “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Atribacteria” (latter branched within the “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Acetothermia”), and the class LD1-PA32 (Chlamydiae), suggesting all these uncultured organisms might be heterotrophic acetogens.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' However, it should be noted that a PFOR typically connecting glycolysis to the WL was only encoded in the LD1-PA32 MAGs.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' More- over, from the genetic make-up alone, it cannot be excluded that acetate is activated, and the WL run in reverse for syntrophic acetate oxidation.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Finally, the novel acsB genes from soda lake Halanaerobiaceae, Natranaerobiaceae, and Halobacteroidaceae (Firmicutes) and from Brocadiaceae and Planctomycetaceae (Plancto- mycetes) disrupt the previously proposed dichotomy between Terrabacteria and Gracilicutes bacterial groups unifying 16S rRNA and acsB gene phylogenies [46] and suggest a far more complex evolutionary history of the WL pathway than previously anticipated.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Discussion Extensive classical microbiology efforts have been already undertaken to explore the unique extremophilic microbial communities inhabiting soda lakes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' These un- covered the presence of most of the functional groups participating in carbon, nitrogen, sulfur, and minor element cycling at haloalkaline conditions.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The main re- sults of this work are summarized in several recent re- views [1, 6, 47, 48].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Since most microbes, including those living in soda lakes, still evade all cultivation ef- forts, a very effective way to discover new microbes and assess their physiology based on their genetic repertoire is either through single cell genomics or by directly se- quenced environmental DNA.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' This exploratory metage- nomics study performed on soda lake sediments effectively overcame the existing cultivation bottleneck.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' First, we expanded the known diversity of CPR consider- ably with the first genomes of poly-extremophiles sam- pled from soda lake sediments.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Although the presence of 16S rRNA genes from CPR in marine sediments and hy- persaline microbial mats was previously shown [34], until now, CPR MAGs were mainly obtained from deep, subsurface environments [15, 26, 29, 32, 49–52], and hu- man microbiota [30].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Despite being highly abundant Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 10 of 18 100 % 90-100 % 70-90 % 50-70 % some MAGs all MAGs Bootstraps Genes present Glycolysis (EMP) PFOR WL-Eastern branch H4MPT TH4 WL-Western branch CODH/ACS Acetogenesis/ acetate activation (pta/ack) 0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='4 PVC group (Chlamydiae LD1-PA32) Syntrophorhabdus aromaticivorans PVC group bacterium CSSed11_184 Aerophobetes bacterium SCGC_AAA255-F10 Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Acetothermia Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Handelsmanbacteria Planctomycetaceae Anaerolineae Firmicutes Brocadiaceae Planctomycetes Methanomassiliicoccales Halobacteroidaceae Natranaerobiaceae Methanomicrobiales Desulfonatronospira Firmicutes Dehalococcoidia Armatimonadetes bacterium CSP1-3 Deltaproteobacteria Thermodesulfobacteria Desulfobulbaceae Halanaerobiaceae Nitrospirae Actinobacteria (OPB41) Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 6 Maximum likelihood phylogeny of the bacterial-type acetyl-coA synthases (acsB) found in the MAGs.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Only sequences ≥ 500 aa were included.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Lineages for which we discovered the Wood-Ljungdahl (WL) in this study are highlighted in orange, and the presence of genes in the respective MAGs related to WL, glycolysis, pyruvate, and acetate conversion is indicated by the colored symbols (see also Additional file 9: Dataset S6).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Additional lineages found in this study are marked in blue.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The three was rooted according to [46].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Circles at the nodes show confidence percentage of the bootstraps analysis (100×).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' EMP = Embden-Meyerhof-Parnas, PFOR = pyruvate:ferredoxin oxidoreductase complex, pta = phosphotransacetylase gene, ack = acetate kinase gene, H4MPT = tetrahydromethanopterin-linked pathway, TH4 = tetrahydrofolate pathway, CODH/ACS = carbon monoxide dehydrogenase/acetyl-CoA synthase.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' PVC group bacterium CSSed11_184 is likely a member of the WCHB1-41 class within the Verrucomicrobia Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 11 of 18 here, CPR went unnoticed in previous amplicon sequen- cing studies.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' This might be due to the fact that many CPR representatives have random inserts of various length in their 16S rRNA genes or due to primer mis- matches [29, 34].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' This illustrates also that direct metage- nomics should not only be preferred over amplicon sequencing to infer functional potential, but the former is far more effective for the discovery of novel organ- isms.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Second, we obtained many more genomes from “traditional” bacterial phyla such as the Planctomycetes and Chloroflexi, as well as candidate phyla, for which no soda lake isolates, hence no genomes were previously obtained.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Third, even within the sulfur cycle, the most active and frequently studied element cycle in soda lakes [1], we found considerable metabolic novelty.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Finally, we found the Wood-Ljungdahl pathway in several novel phyla, not closely related to any known acetogens, methanogens, or sulfate-reducing bacteria [46].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The lat- ter shows that our sequencing recovery effort has also significantly contributed to the discovery of metabolic novelty within various prokaryote phylogenetic groups.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Salinity is often considered to be the major factor shaping prokaryote community composition in diverse habitats [53, 54].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Extreme halophilic Euryarchaeota seem to be always the dominant group in salt-saturated hypersaline brines, both those with neutral or alkaline pH [1, 7, 37].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Here, we found that although these haloarchaea are still relatively more abundant in the sed- iments exposed to brines with salt-saturating conditions, the clear majority of microbes in all investigated hyper- saline soda lake sediments are Bacteria.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' It could be hypothesized that the sediment is a hide-out for the extreme alkalinity and salinity governing the water column, and that sediment stratification, especially in the anoxic part, offers plenty of opportunities for niche diversification.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' On the other hand, it should no longer be a surprise that soda lakes are such productive and biodiverse systems.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' First, it has been previously elaborated that soda lake organisms are exposed to approximately half the osmotic pressure in sodium carbonate-dominated brines compared to sodium chloride-dominated brines with the same Na+ molarity [47].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Second, nitrogen limitation in the community can be overcome when many members contribute to the fixation of atmospheric N2, and various forms of organic nitrogen are efficiently recycled.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The soda lakes exam- ined in this study were also eutrophic, and sulfur com- pounds were abundant.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sulfide is also far less toxic at high pH as it mostly occurs in the form of bisulfide (HS−).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Besides the evident high metabolic and taxo- nomic diversity of dissimilatory sulfur-cycling bacteria, a diverse heterotrophic community can be sustained com- prising both generalist and very specialized carbon de- graders.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Less eutrophic soda lakes might not suffer from carbon limitation either, due to a presence of high-bicarbonate concentrations.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' These effectively elim- inate the inorganic carbon limitation for primary pro- ducers who are highly active in soda lakes, especially Cyanobacteria [55, 56].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Third, light that penetrates the surface of the sediment seems to stimulate oxygenic and anoxygenic phototrophic growth.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Moreover, various het- erotrophs, such as the rhodopsin-containing haloarchaea and Bacteroidetes, have the option to tap into this un- limited energy source for example to help sustain the costly maintenance of osmotic balance.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Unexpectedly, we even found the first rhodopsin encoded by a member of the CPR.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Fourth, tight syntrophic relations, as pro- posed for CPR members and Syntrophomonadaceae spp.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=', might be the solution to successful growth in an energetically challenging environment.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Since our metagenomes are snapshots in time and space, the failure to reconstruct specific MAGs gives no conclu- sive evidence for the absence of certain microbial-mediated element transformation in hypersaline soda lake sediments.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Additionally, technical limitations of the assembly and bin- ning of highly micro-diverse genome populations might hamper genome recovery [57].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' More importantly, the abundance of a specific microbe is not necessarily corre- lated to the importance of its performance in an ecosystem.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Many metabolic capacities are redundant, and often key transformations are reserved for a few rare organisms that might proliferate for a short time-span when specific condi- tions allow for it.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' For example, although no MAGs were re- covered from chemolithoautotrophic nitrifiers [58], we did detect a Nitrobacter-related OTU by amplicon sequencing and assembled 16S rRNA genes from Thaumarchaeota, suggesting bacterial and archaeal nitrifiers are present in the surface sediments of soda lakes at very low abundance.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Finally, the method of DNA isolation might impact the community composition apparent in the final metagenome sequenced.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Environmental samples contain complex mix- tures of different organisms, and it is impossible to find a protocol where the DNA from every single organism is ex- tracted as efficiently without compromising the final quality of the extracted DNA.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' However, since we find all the im- portant taxonomic and functional groups known from pre- vious cultivation-dependent studies back in either our amplicon sequencing datasets or our directly sequenced metagenomes, we are confident that the community com- position and the MAGs presented here are representative for the microbiomes of the soda lake sediments in the Kulunda Steppe.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Conclusion Years of intensive microbiological research on soda lakes seem to have paid off, since many of the described gen- era we could detect here have a cultured representative from soda lakes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' However, as many of the abundant Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 12 of 18 lineages and groups found in soda lake sediments are still uncultured, metagenomics proved to be a helpful tool to gain primary insights in the potential physiology and ecology of these poly-extremophilic prokaryotes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' We reconstructed the first genomes for many of such organisms and proposed new functional roles for the most abundant ones.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Future studies should provide more in depth analyses of these genomes, especially from the less abundant organisms that might perform key ecological processes, such as methanogens and nitri- fiers.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' In addition, they should focus on gaining physio- logical culture-based evidence or proof for in situ activity for the abundant organisms described here.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The key metabolic insights provided by this metagenomics study can lead to the design of new cultivation strategies.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' In general, sediment communities are far more complex than those found in the corresponding water column [53, 59] and are therefore often considered too complex for efficient metagenomic analysis.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Many of the novel lineages found here may therefore have related neutro- philic lineages in marine and freshwater sediments that await discovery.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' We demonstrate here that, by providing sufficient sequencing depth, the “state of the art metage- nomics toolbox” can effectively be used on sediments as well.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Methods Site description and sample collection The top 10 cm sediments from four hypersaline, eutrophic soda lakes located in the Kulunda Steppe (south-western Siberia, Altai, Russia) were sampled in July of 2010 and 2011.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' General features and exact location of the sampled soda lakes are summarized in Additional file 1: Table S1;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' a map of the area was published previously [5].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Cock Soda Lake (a stand-alone lake, sampled both in 2010 and 2011) and Tanatar-3 (Tanatar system) were moderately hypersa- line (~ 100 g L−1) with sandy sediment, while Tanatar-1 and Bitter-1 (Bitter system) were salt-saturated (400 g L−1) with sulfide-rich sapropel sediments underlined by rock trona deposits [7, 60].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Especially, Bitter-1 harbors a very active microbial community, probably due to its high- organic and -mineral content.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Surface sediments were col- lected by a plastic corer into sterile glass containers and transported to the laboratory in a cooler.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' DNA isolation, 16S rRNA amplicon, and metagenomic sequencing The colloidal fraction of each sediment sample (~ 10% of 50 g) was separated from the course sandy fraction by several short (30–60 s) low-speed (1–2,000 rpm in 50 mL Falcon tubes) centrifugation steps and washed with 1–2 M NaCl solution.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The pelleted colloidal sedi- ment fraction was first subjected to 3 cycles of freezing in liquid nitrogen/thawing, then re-suspended in 0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='1 M Tris (pH 8)/10 mM EDTA, and then subjected to harsh bead beating treatment.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Next, the samples were incu- bated with lysozyme (15 mg/mL) for 2 h at 37 °C followed by a SDS (10% w/v) and proteinase K (10 μg/ mL) treatment for 30 min.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' at 45 °C.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' High molecular weight DNA was isolated using phenol/chloroform ex- traction, quality-checked, and sequenced as described previously [7].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Direct high-throughput sequencing of the DNA was performed on an Illumina HiSeq 2000 plat- form to generate 150 b paired-end reads.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Amplification of the V4-V6 region of prokaryote 16S rRNA genes using barcoded 926F-1392R primers, amplicon purifica- tion, quantification, and Roche (454)-sequencing was performed together in a batch with brine samples from the same sampling campaigns.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Barcodes and adapter se- quences were removed from de-multiplexed amplicon sequence reads and analyzed with the automated NGS analysis pipeline of the SILVA rRNA gene database pro- ject [61] (SILVAngs 1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='3, database release version 128) using default parameters.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The OTUs (97% identity) assigned down to the genus level were only considered when they had a relative abundance ≥ 0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='1% in at least one of the five datasets.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Processing metagenomics reads, assembly, binning, and post-binning Metagenomic raw reads were quality trimmed using Sickle [62] (version 1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='33), and only reads ≥ 21 b were retained.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The prokaryotic community structure at taxo- nomic top levels was extrapolated from ten million ran- domly sampled singletons from each dataset.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Candidate 16S rRNA fragments > 90 b were identified [63] and compared against the SILVA SSU database 128 (blastn, min.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' length 90, min.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' identity 80%, e value 1e-5).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' To ver- ify that the microbial community composition was in- deed mostly prokaryotic, we did a more general screening of the metagenomics reads that identified also candidate 18S rRNA fragments > 90 b (see Additional file 1: Tables S4-S5).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The complete trimmed read sets were assembled into contigs ≥ 1 kb with MEGAHIT [64] (v1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='3–6-gc3983f9) using paired-end mode, k min = 21, k max = 131, k step = 10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Genes were predicted using Prodigal [65] (v.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='2) and RNAs with rna_hmm3 [66] and tRNAscan-SE [67].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Assembled 16S rRNA sequences were compared to a manually curated version from the SILVA SSU database (e value ≥ 1e-5).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Predicted protein sequences were annotated against KEGG with GhostKOALA (genus_prokaryotes + family_eukaryotes + viruses) [68].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Marker genes for central metabolic pathways and key environmental element transforma- tions were identified based on K number assignments [15, 69–71].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Contigs ≥ 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='5 kb were binned with METABAT [72] (superspecific mode) based on differential coverage Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 13 of 18 values obtained by mapping all five trimmed readsets to all five contig sets with Bowtie2 [73].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The bins were sub- jected to post-binning (an overview of the workflow is given in Additional file 2: Figure S13).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Bins were assessed with lineage-specific single copy genes using CheckM [74] and further processed with the metage- nomics workflow in Anvi’o [75] (v2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='2).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Since Candidate Phyla Radiant (CPR) is not included in the CheckM ref- erence trees and are likely to have low-genome com- pleteness, we used an existing training file of 797 CPR genomes to identify putative CPR bins [76].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Bins with CheckM-completeness ≥ 50% (884 out of 1778) and an additional four CPR bins were further processed.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Coding sequences were annotated for taxonomy against NCBI-nr (July, 2017) with USEARCH [77] (5.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='32) to verify that most hits in each bin were to prokaryotic ref- erences.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Phage or viral contigs were manually removed.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Genome contamination (redundancy) was estimated based on marker sets of universal single copy genes identified for Bacteria [30] and Archaea [78] as imple- mented in Anvi’o.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Genome coverage was obtained by mapping trimmed reads with BBMap [79] v36.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='x (kfilter 31, subfilter 15, maxindel 80).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Bins with ≥ 5% redun- dancy were further refined with Anvi’o using circle phy- lograms (guide trees tnf-cov: euclidian ward) and scanned again for CPR.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Post-binning resulted in a total of 2499 metagenome-assembled genomes (MAGs), of which 871 were either medium-quality genome drafts (CheckM estimated completeness ≥ 50% and contamin- ation ≤ 10% [80], Additional file 4) or lower quality draft genomes from CPR.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Phylogeny of the MAGs was assessed based on 16 single-copy ribosomal proteins and representative refer- ence genomes of major prokaryote lineages across the tree of life [17].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Individual ribosomal proteins in our MAGs were identified by K number assignments.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Only ribosomal proteins ≥ 80 aa were considered.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Initial maximum-likelihood (ML) trees were constructed to de- termine which organisms belonged to the Archaea, Bac- teria, or CPR with FastTree 2 [81] (WAG + CAT).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Final separate trees for the three distant evolutionary groups were constructed in the same manner.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Each ribosomal protein set was aligned separately with MAFFT [82] (v7.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='055b, − auto) and concatenated only if a MAG encoded at least 8 out of 16 proteins.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' For all trees, a 100× posterior bootstraps analysis was performed.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Phylogenetic trees were visualized together with gen- ome statistics and abundance information using iTOL [83].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' We cross-checked the taxonomic assignments based on the phylogeny of the ribosomal protein cas- sette with the top hit contig annotations against NCBI-nr and with the reference lineage obtained with CheckM.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Lastly, we manually corrected the MAGs for misplaced 16S rRNA genes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The final trees presented in the manuscript were redrawn using FigTree v1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='3 [84].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Detailed genome analyses CPR MAGs were re-annotated more thoroughly: genes were predicted with Prokka [85], and functional predictions were performed by running InterProScan 5 locally on the supplied COG, CDD, TIGRFAMs, HAMAP, Pfam, and SMART databases [86].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' BLAST Koala was used for KEGG pathway predictions [68].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' To find putative carbohydrate-active enzymes in all final MAGs, we used the web-resource dbCAN [87] to annotate all predicted proteins ≥ 80 aa against CAZy [88].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' To identify the top ten abundant MAGs from each re- spective dataset, ten million randomly sampled single- tons were mapped onto each MAG with a cut-off of 95% identity in minimum of 50 bases.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Coverage values were additionally normalized for genome size and expressed as reads per kilobase of sequence per gigabase of mapped reads (RPKG) [89].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' A positive score (from 871 to 1) was assigned to each MAG according to the rank- ing of the summed RPKG of MAGs in the high-salinity datasets (B1Sed10 and T1Sed) and a negative score ac- cording to the ranking of the summed RPKGs in the moderate salinity datasets (CSSed10, CSSed11, T3Se d10).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Both scores were summed to get a “salinity prefer- ence score” with MAGs recruiting preferably from high salinity datasets on the positive end, moderate salinity datasets in the negative end, and those without prefer- ence in the middle.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' We determined species delineation for the most abundant MAGs and their closest reference genomes (NCBI-nr) by Average Nucleotide Identity (ANI) and conserved DNA-matrices, as follows [90]: ANI ≥ 95%, conDNA ≥ 69% = same species, ANI ≥ 95%, condDNA < 69% = might be same species, ANI < 95%, condDNA < 69% = different species.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Single gene trees based on maximum likelihood were constructed with un- trimmed alignments (MAFFT, L-INS-i model) and FastTree 2 (WAG + CAT, increased accuracy, -spr4 -mlacc 2 -slownni) using 100× bootstraps.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' References were pulled from eggNOG (v4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='5.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='1) [91] and supple- mented with sequences from NCBI-nr or refined according to [7, 33, 46, 92–94].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The curated MAGs were scanned for the presence of rhodopsin sequences with the hmmsearch software [95] and a profile hidden Markov model (HMM) of the bacteriorhodopsin-like protein family (Pfam accession number PF01036).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The identified sequences with significant similarity were aligned together with a curated database composed of a collection of type-1 rhodopsins, using MAFFT (L-INS-i accuracy model) [82].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' This protein alignment was further utilized to Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 14 of 18 construct a maximum likelihood tree with 100× boot- strap with FastTree 2 [81].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' All other genes were identified using the KEGG annotation.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Additional files Additional file 1: Table S1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' General features of the four sampled soda lakes at time of sampling.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Table S2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' SILVA classification of the 16S rRNA gene sequences found in all ≥1 kb contigs of five soda sediment metagenomic datasets.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Table S3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Enzymes involved in lipopolysaccharide biosynthesis found among different members of the CPR.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Table S4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sub-kingdom classification of candidate SSU rRNA gene fragments found in subsamples of 10 million random forward reads from the five soda sediment metagenomes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Table S5.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Top-level taxonomic classification of the 18S rRNA gene fragments found in subsamples of 10 million random forward reads from the five soda sediment metagenomes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Table S6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Description of the metagenomic datasets, NCBI Sequence Read Archive (SRA) accession numbers and general statistics of the assembled contigs.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' (PDF 740 kb) Additional file 2: Figure S1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Taxonomic fingerprints determined by 16S rRNA gene amplicon sequencing.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Figure S2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Genome statistics of the 871 MAGs.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Figure S3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Phylogeny of MAGs belonging to “Candidatus Aenigmarchaeota” and “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nanohaloarchaeota”.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Figure S4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Phylogeny of MAGs related to “Candidatus Acetothermia”, candidate division WS1 and “Candidatus Lindowbacteria”.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Figure S5.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Phylogeny of MAGs related to candidate division KSB3 and “Candidatus Schekmanbacteria”.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Figure S6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Multiple sequence alignment of the V-type ATPase subunits K.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Figure S7.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Multiple sequence alignment of the F-type ATPase subunits c.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Figure S8.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Maximum likelihood tree of the large subunits of RuBisCo and RubisCo- like proteins.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Figure S9.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Maximum likelihood tree of the putative rhodopsins.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Figure S10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Predicted isoelectric points (pI) profiles of all MAGs from CPR members.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Figure S11.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Predicted isoelectric points profiles for members of the “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nealsonbacteria” and “Ca.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Vogelbacteria”.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Figure S12.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Multiple sequence alignment of the dissimilatory cytochrome c nitrite reductases (nrfA/TvNiR, K03385).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Figure S13.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Overview of the post-binning workflow used for genome recovery.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' (PDF 6548 kb) Additional file 3: Dataset S1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Relative abundance of the OTUs assigned to the genus-level within the Archaea, Bacteria and organelles from Eukaryota detected by 16S rRNA gene amplicon sequencing.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The OTUs with less than 0.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='1% abundance accross all five datasets are not shown.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The names of highly abundant genera (≥1% in at least one of the data- sets) are shown in bold.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' (XLSX 24 kb) Additional file 4: Dataset S2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Organism names, statistics and general description incl.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Completeness and contamination estimates, phylogeny and DDBJ/EMBL/Genbank accession numbers of the metagenome assembled genomes (MAGs) described in this paper.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' All submitted versions described in this paper are version XXXX01000000.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Size = recovered genome size, Completeness (Compl1), contamination (Cont), strain heterogenity (Str het) and Taxon CheckM were inferred from lineage-specific marker sets and a reference tree build with CheckM [74].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Additional completeness (compl2) and redundancy (red) estimates were inferred based on the presence of universal single copy genes for Bacteria and Archaea [75].' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Decision and confidence intervals from the Candidate Phyla Radiation (CPR) scan [75] are given, as well as the taxonomy of the besthit in SILVA when 16S rRNA genes were present.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Phylum/class 16 ribosomal proteins is the taxonomy derived from our ribosomal protein trees (see main text: Figs.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2 and 3).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' OTU gives the inferred link of a population genome with our 16S rRNA gene amplicon dataset (Additional file 3).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' (XLSX 253 kb) Additional file 5: Dataset S3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Estimated abundance and derived salinity preference from each MAG in each metagenomic dataset expressed as Reads per Kilobase of MAG per Gigabase of mapped reads (RPKG) and “salinity preference score” (see Methods section), basis for Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' (XLSX 143 kb) Additional file 6: Dataset S4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Average Nucleotide Identity (ANI) and conserved DNA (condna) matrices to determine species delineation between the most abundant MAGs shown in Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 4, closely related (less abundant) MAGs and NCBI reference genomes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Decision matrix shows: 1 = same species, − 1 = might be same species, 0 = different species (see Methods section).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' (XLSX 1161 kb) Additional file 7: Dataset S5.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sheet 1 Presence and absence of marker genes and putative carbohydrate-active enzymes in the MAGs to infer putative roles in C, N and S element cycles based on K-number assignments and CAZy annotations.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sheet 2 Summary basis for Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' (XLSX 41 kb) Additional file 8: Information S1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' More detailed description of the main metabolisms encoded by Thioalkalivibrio-related MAGs.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Information S2 More detailed description of the main metabolisms encoded by Deltaproteobacterial-related MAGs.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' (PDF 219 kb) Additional file 9: Dataset 6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sheet 1 shows the MAGs positive for the marker gene acsB (K14138) encoding an acetyl-CoA synthase (ACS).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The basis for Fig.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 6, namely presence and absence of key genes involved in the Wood-Ljungdahly pathway, acetogenesis, methanogenesis, glycolysis and pyruvate to CO2 conversion is shown for each MAG.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sheet 2 shows the MAGs positive for the marker gene cdhC (K00193) encoding for the beta subunit of an acetyl-CoA decarboxylase synthase complex.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' While acsB and cdhC correspond roughly to the Bacterial-type and Archaeal- type (methanogens) enzymes with the same function, we found few discrepancies between marker gene and genome phylogeny within the Methanomassiliicoccaceae and Chloroflexi.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' (XLSX 52 kb) Acknowledgments We thank Dr.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nikolai Chernych for his technical assistance during the isolation and purification of metagenomics DNA.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' We also thank the Department of Energy Joint Genome Institute for sequencing the metagenomes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Funding CDV and GM were supported by the ERC Advanced Grant PARASOL (no.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 322551).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' A-SA and RG were supported by the research grant 17-04828S from the Grant Agency of the Czech Republic.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' MM was supported by the Czech Academy of Sciences (Postdoc program PPPLZ application number L200961651).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' DYS was supported by the SIAM/Gravitation Program (Dutch Ministry of Education and Science, grant 24002002) and by the Russian Science Foundation (grant 16–14- 00121).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sequencing was performed by the U.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='S.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Department of Energy Joint Genome Institute, a DOE Office of Science User Facility, as part of the Community Sequencing Program (contract no.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' DE-AC02- 05CH11231).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Availability of data and materials The raw sequence reads of the five metagenomes have been deposited to the NCBI Sequence Read Archive (see Additional file 1: Table S6 for accession numbers and read and contig statistics).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The final 871 MAGs described in this paper have been deposited as Whole Genome Shotgun projects at DDBJ/ EMBL/GenBank, and accession numbers are listed in Additional file 4 (BioProject ID PRJNA434545).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' All versions described in this paper are version XXXX01000000.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The cleaned and dereplicated amplicon sequence datasets are available in FigShare (https://figshare.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='com/s/7684627445e3621aba24).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Maximum likelihood trees based on the concatenated alignment of 16 ribosomal proteins, basis for Figs.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2 and 3, in newick format (.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='tre file) and complementary datasets (used to plot completeness, contamination, genome recovery size, G + C mol% and RPKG in iTOL), as well as K number assignments for the predicted proteins of all MAGs (KEGG-orthologues, Ghost Koala) and the fully annotated CPR MAGs supporting the conclusions of this article are also available in FigShare (https://figshare.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='com/s/ 7684627445e3621aba24).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Authors’ contributions GM and DYS initiated this study and were responsible for the fieldwork, sample preparation, and sequencing effort.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' CDV conceptualized the research goals under supervision of DYS and GM, and performed the bioinformatics analysis under close guidance of A-SA and RG.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' CDV is the primary author of this manuscript.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' MM, RG, and CDV prepared the main figures.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' All authors read and approved the final manuscript.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Ethics approval and consent to participate Not applicable.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 15 of 18 Consent for publication Not applicable.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Competing interests The authors declare that they have no competing interests.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Author details 1Microbial Systems Ecology, Department of Freshwater and Marine Ecology, Institute for Biodiversity and Ecosystem Dynamics, Faculty of Science, University of Amsterdam, Postbus 94248, 1090, GE, Amsterdam, the Netherlands.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2Department of Aquatic Microbial Ecology, Institute of Hydrobiology, Biology Centre CAS, Na Sadkach 7, 370 05 Ceske Budejovice, Czech Republic.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 3Winogradsky Institute of Microbiology, Research Centre of Biotechnology, Russian Academy of Sciences, 60 let Oktyabrya pr-t, 7, bld.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2, Moscow, Russian Federation117312.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 4Environmental Biotechnology, Department of Biotechnology, Delft University of Technology, Van der Maasweg 9, 2629, HZ, Delft, the Netherlands.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Received: 23 June 2018 Accepted: 3 September 2018 References 1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sorokin DY, Berben T, Melton ED, Overmars L, Vavourakis CD, Muyzer G.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbial diversity and biogeochemical cycling in soda lakes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Extremophiles.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2014;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='18:791–809.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Oduor SO, Kotut K.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Soda lakes of the East African Rift System: the past, the present and the future.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' In: Schagerl M, editor.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Soda lakes of East Africa.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Berlin: Springer;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' p.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 365–74.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 3.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Mesbah NM, Abou-El-Ela SH, Wiegel J.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Novel and unexpected prokaryotic diversity in water and sediments of the alkaline, hypersaline lakes of the Wadi An Natrun, Egypt.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microb Ecol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2007;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='54:598–617.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Humayoun SB, Bano N, James T, Hollibaugh JT.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Depth distribution of microbial diversity in Mono Lake, a meromictic soda lake in California.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Appl Environ Microbiol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2003;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='69:1030–42.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 5.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Foti MJ, Sorokin DY, Zacharova EE, Pimenov NV, Kuenen JG, Muyzer G.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Bacterial diversity and activity along a salinity gradient in soda lakes of the Kulunda Steppe (Altai, Russia).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Extremophiles.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2008;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='12:133–45.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sorokin DY.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Anaerobic haloalkaliphiles.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' eLS.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2017;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' https://doi.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='org/10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='1002/ 9780470015902.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='a0027654.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 7.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Vavourakis CD, Ghai R, Rodriguez-Valera F, Sorokin DY, Tringe SG, Hugenholtz P, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Metagenomic insights into the uncultured diversity and physiology of microbes in four hypersaline soda lake brines.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Front Microbiol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='7:211.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 8.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sørensen KB, Canfield DE, Oren A.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Salinity responses of benthic microbial communities in a solar saltern (Eilat, Israel).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Appl Environ Microbiol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2004;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='70: 1608–16.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 9.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sorokin DY, Makarova KS, Abbas B, Ferrer M, Golyshin PN, Galinski EA, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Discovery of extremely halophilic, methyl-reducing euryarchaea provides insights into the evolutionary origin of methanogenesis.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nat Microbiol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2017;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='2:17081.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sorokin DY, Chernyh NA, Poroshina MN.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Desulfonatronobacter acetoxydans sp.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' nov.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=',: a first acetate-oxidizing, extremely salt-tolerant alkaliphilic SRB from a hypersaline soda lake.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Extremophiles.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2015;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='19:899–907.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 11.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Ahn A-C, Meier-Kolthoff JP, Overmars L, Richter M, Woyke T, Sorokin DY, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Genomic diversity within the haloalkaliphilic genus Thioalkalivibrio.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' PLoS One.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2017;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='12:e0173517.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 12.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sorokin DY, Kuenen JG.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Haloalkaliphilic sulfur-oxidizing bacteria in soda lakes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' FEMS Microbiol Rev.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2005;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='29:685–702.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 13.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Albertsen M, Hugenholtz P, Skarshewski A, Nielsen KL, Tyson GW, Nielsen PH.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Genome sequences of rare, uncultured bacteria obtained by differential coverage binning of multiple metagenomes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nat Biotechnol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2013;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='31:533–8.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 14.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Qin J, Li R, Raes J, Arumugam M, Burgdorf KS, Manichanh C, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' A human gut microbial gene catalogue established by metagenomic sequencing.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nature.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2010;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='464:59–65.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 15.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Anantharaman K, Brown CT, Hug LA, Sharon I, Castelle CJ, Probst AJ, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Thousands of microbial genomes shed light on interconnected biogeochemical processes in an aquifer system.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nat Commun.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='7:13219.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 16.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Parks DH, Rinke C, Chuvochina M, Chaumeil P-A, Woodcroft BJ, Evans PN, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Recovery of nearly 8,000 metagenome-assembled genomes substantially expands the tree of life.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nat Microbiol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2017;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='2:1533–42.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 17.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Hug LA, Baker BJ, Anantharaman K, Brown CT, Probst AJ, Castelle CJ, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' A new view of the tree of life.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nat Microbiol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='1:16048.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 18.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Hahnke RL, Meier-Kolthoff JP, García-López M, Mukherjee S, Huntemann M, Ivanova NN, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Genome-based taxonomic classification of Bacteroidetes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Front Microbiol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='7:2003.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 19.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nolla-Ardevol V, Strous M, Tegetmeyer HE.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Anaerobic digestion of the microalga Spirulina at extreme alkaline conditions: biogas production, metagenome and metatranscriptome.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Front Microbiol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2015;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='6:597.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 20.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Borrel G, Parisot N, Harris HM, Peyretaillade E, Gaci N, Tottey W, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Comparative genomics highlights the unique biology of Methanomassiliicoccales, a Thermoplasmatales-related seventh order of methanogenic archaea that encodes pyrrolysine.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' BMC Genomics.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2014;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='15:679.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 21.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sorokin DY, Abbas B, Geleijnse M, Pimenov NV, Sukhacheva MV, van Loosdrecht MCM.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Methanogenesis at extremely haloalkaline conditions in the soda lakes of Kulunda Steppe (Altai, Russia).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' FEMS Microbiol Ecol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2015;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='91:4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 22.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nobu MK, Narihiro T, Kuroda K, Mei R, Liu WT.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Chasing the elusive Euryarchaeota class WSA2: genomes reveal a uniquely fastidious methyl- reducing methanogen.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' ISME J.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='10:2478–87.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 23.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Skennerton CT, Haroon MF, Briegel A, Shi J, Jensen GJ, Tyson GW, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Phylogenomic analysis of Candidatus “Izimaplasma” species: free-living representatives from a Tenericutes clade found in methane seeps.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' ISME J.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='10:2679–92.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 24.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sekiguchi Y, Ohashi A, Parks DH, Yamauchi T, Tyson GW, Hugenholtz P.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' First genomic insights into members of a candidate bacterial phylum responsible for wastewater bulking.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' PeerJ.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2015;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='3:e740.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 25.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Wrighton KC, Thomas BC, Sharon I, Miller CS, Castelle CJ, VerBerkmoes NC, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Fermentation, hydrogen, and sulfur metabolism in multiple uncultivated bacterial phyla.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Science.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2012;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='337:1661–5.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 26.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' León-Zayas R, Peoples L, Biddle JF, Podell S, Novotny M, Cameron J, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The metabolic potential of the single cell genomes obtained from the Challenger Deep, Mariana Trench within the candidate superphylum Parcubacteria (OD1).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Environ Microbiol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2017;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='19:2769–84.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 27.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Castelle CJ, Brown CT, Thomas BC, Williams KH, Banfield JF.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Unusual respiratory capacity and nitrogen metabolism in a Parcubacterium (OD1) of the Candidate Phyla Radiation.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sci Rep.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2017;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='7:40101.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 28.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Anantharaman K, Brown CT, Burstein D, Castelle CJ, Probst AJ, Thomas BC, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Analysis of five complete genome sequences for members of the class Peribacteria in the recently recognized Peregrinibacteria bacterial phylum.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' PeerJ.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='4:e1607.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 29.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Brown CT, Hug LA, Thomas BC, Sharon I, Castelle CJ, Singh A, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Unusual biology across a group comprising more than 15% of domain Bacteria.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nature.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2015;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='523:208–11.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 30.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Campbell JH, O ‘donoghue P, Campbell AG, Schwientek P, Sczyrba A, Woyke T, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' UGA is an additional glycine codon in uncultured SR1 bacteria from the human microbiota.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2013;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' doi:https://doi.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='org/10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='1073/pnas.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 1303090110.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 31.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Hanke A, Hamann E, Sharma R, Geelhoed JS, Hargesheimer T, Kraft B, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Recoding of the stop codon UGA to glycine by a BD1-5/SN-2 bacterium and niche partitioning between Alpha- and Gammaproteobacteria in a tidal sediment microbial community naturally selected in a laboratory chemostat.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Front Microbiol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2014;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='5:231.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 32.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Kantor RS, Wrighton KC, Handley KM, Sharon I, Hug LA, Castelle CJ, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Small genomes and sparse metabolisms of sediment-associated bacteria from four candidate phyla.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' MBio.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2013;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='4:1–11.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 33.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Wrighton KC, Castelle CJ, Varaljay VA, Satagopan S, Brown CT, Wilkins MJ, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' RubisCO of a nucleoside pathway known from Archaea is found in diverse uncultivated phyla in bacteria.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' ISME J.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='10:2702–14.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 34.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Luef B, Frischkorn KR, Wrighton KC, Holman HYN, Birarda G, Thomas BC, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Diverse uncultivated ultra-small bacterial cells in groundwater.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nat Commun.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2015;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='6:1–8.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 35.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Krulwich TA, Sachs G, Padan E.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Molecular aspects of bacterial pH sensing and homeostasis.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nat Rev Microbiol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2011;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='9:330–43.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 36.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Hauß T, Dante S, Dencher NA, Haines TH.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Squalane is in the midplane of the lipid bilayer: implications for its function as a proton permeability barrier.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Biochim Biophys Acta Bioenerg.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2002;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='1556:149–54.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 37.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Oren A.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Life at high salt concentrations, intracellular KCl concentrations, and acidic proteomes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Front Microbiol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2013;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='4:315.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 16 of 18 Published online: 19 September 201838.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Levina N.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Protection of Escherichia coli cells against extreme turgor by activation of MscS and MscL mechanosensitive channels: identification of genes required for MscS activity.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' EMBO J.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 1999;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='18:1730–7.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 39.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Gupta RS, Khadka B.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Evidence for the presence of key chlorophyll- biosynthesis-related proteins in the genus Rubrobacter (phylum Actinobacteria) and its implications for the evolution and origin of photosynthesis.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Photosynth Res.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='127:201–18.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 40.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Basak N, Das D.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The prospect of purple non-sulfur (PNS) photosynthetic bacteria for hydrogen production:the present state of the art.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' World J Microbiol Biotechnol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2007;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='23:31–42.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 41.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Meng J, Wang F, Wang F, Zheng Y, Peng X, Zhou H, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' An uncultivated crenarchaeota contains functional bacteriochlorophyll a synthase.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' ISME J.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2009;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='3:106–16.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 42.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sorokin DY, Tourova TP, Mußmann M, Muyzer G.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Dethiobacter alkaliphilus gen.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' nov.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' sp.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' nov.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=', and Desulfurivibrio alkaliphilus gen.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' nov.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' sp.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' nov.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=': two novel representatives of reductive sulfur cycle from soda lakes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Extremophiles.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2008;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='12:431–9.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 43.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Poser A, Lohmayer R, Vogt C.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Extremophiles KK-, 2013 U.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Disproportionation of elemental sulfur by haloalkaliphilic bacteria from soda lakes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Extremophiles.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2013;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='17:1003–12.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 44.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sorokin DY, Abbas B, Tourova TP, Bumazhkin BK, Kolganova TV, Muyzer G.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sulfate-dependent acetate oxidation under extremely natron-alkaline conditions by syntrophic associations from hypersaline soda lakes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiology.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2014;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='160(Pt_4):723–32.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 45.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Ragsdale SW.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Enzymology of the Wood-Ljungdahl pathway of acetogenesis.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Ann N Y Acad Sci.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2008;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='1125:129–36.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 46.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Adam PS, Borrel G, Gribaldo S.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Evolutionary history of carbon monoxide dehydrogenase/acetyl-CoA synthase, one of the oldest enzymatic complexes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Proc Natl Acad Sci.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2018;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='115:E1166–73.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 47.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sorokin DY, Banciu HL, Muyzer G.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Functional microbiology of soda lakes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Curr Opin Microbiol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2015;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='25:88–96.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 48.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Grant WD, Jones BE.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Bacteria, Archaea and viruses of soda lakes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' In: Schagerl M, editor.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Soda lakes of East Africa.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Berlin: Springer;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' p.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 97–147.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 49.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Bruno A, Sandionigi A, Rizzi E, Bernasconi M, Vicario S, Galimberti A, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Exploring the under-investigated “microbial dark matter” of drinking water treatment plants.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sci Rep.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2017;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='7:1–7.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 50.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Danczak RE, Johnston MD, Kenah C, Slattery M, Wrighton KC, Wilkins MJ.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Members of the Candidate Phyla Radiation are functionally differentiated by carbon- and nitrogen-cycling capabilities.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2017;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='5:112.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 51.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Hu P, Tom L, Singh A, Thomas BC, Baker BJ, Piceno YM, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Genome- resolved metagenomic analysis reveals roles for candidate phyla and other microbial community members in biogeochemical transformations in oil reservoirs.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' MBio.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='7:e01669–15.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 52.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Probst AJ, Castelle CJ, Singh A, Brown CT, Anantharaman K, Sharon I, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Genomic resolution of a cold subsurface aquifer community provides metabolic insights for novel microbes adapted to high CO2 concentrations.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Environ Microbiol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2017;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='19:459–74.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 53.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Lozupone CA, Knight R.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Global patterns in bacterial diversity.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Proc Natl Acad Sci.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2007;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='104:11436–40.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 54.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Thompson LR, Sanders JG, McDonald D, Amir A, Ladau J, Locey KJ, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' A communal catalogue reveals Earth’s multiscale microbial diversity.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nature.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2017;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='551:457.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 55.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Samylina OS, Sapozhnikov FV, Gainanova OY, Ryabova AV, Nikitin MA, Sorokin DY.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Algo-bacterial communities of the Kulunda steppe (Altai region, Russia) Soda Lakes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiology.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2014;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='83:849–60.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 56.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Krienitz L, Schagerl M.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Tiny and tough: microphytes of east African soda lakes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' In: Schagerl M, editor.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Soda lakes of East Africa.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Berlin: Springer;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' p.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 149–77.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 57.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nelson WC, Maezato Y, Wu Y-W, Romine MF, Lindemann SR.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Identification and resolution of microdiversity through metagenomic sequencing of parallel consortia.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Appl Environ Microbiol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2015;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='82:255–67.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 58.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Hansel C.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Small but mighty: how minor components drive major biogeochemical cycles.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Environ Microbiol Rep.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2017;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='9:8–10.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 59.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Zinger L, Amaral-Zettler LA, Fuhrman JA, Horner-Devine MC, Huse SM, Welch DBM, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Global patterns of bacterial beta-diversity in seafloor and seawater ecosystems.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' PLoS One.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2011;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='6:e24570.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 60.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Isachenko BL.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Chloride sulfate and soda lakes of Kulunda steppe and its biogenic processes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' In: Selected works, vol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Leningrad: Academy of Sciences USSR;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 1951.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' p.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 143–62.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 61.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Quast C, Pruesse E, Yilmaz P, Gerken J, Schweer T, Yarza P, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The SILVA ribosomal RNA gene database project: improved data processing and web- based tools.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nucleic Acids Res.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2012;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='41:D590–6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 62.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Joshi NA, Fass JN.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sickle: a sliding-window, adaptive, quality-based trimming tool for FastQ files (Version 1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='33).' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2011.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 63.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Ghai R, Pašić L, Fernández AB, Martin-Cuadrado A-B, Mizuno CM, McMahon KD, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' New abundant microbial groups in aquatic hypersaline environments.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Sci Rep.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2011;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='1:135.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 64.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Li D, Liu CM, Luo R, Sadakane K, Lam TW.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' MEGAHIT: An ultra-fast single- node solution for large and complex metagenomics assembly via succinct de Bruijn graph.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Bioinformatics.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2015;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='31:1674–6.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 65.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Hyatt D, Chen G-L, LoCascio PF, Land ML, Larimer FW, Hauser LJ.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Prodigal: prokaryotic gene recognition and translation initiation site identification.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' BMC Bioinformatics.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2010;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='11:119.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 66.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Huang Y, Li W, Finn PW, Perkins DL.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Ribosomal RNA identification in metagenomic and metatranscriptomic datasets.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' In: De Bruijn FJ, editor.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Handbook of Molecular Microbial Ecology I.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Hoboken: Wiley;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2011.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' p.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 387–91.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 67.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Lowe TM, Eddy SR.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' tRNAscan-SE: a program for improved detection of transfer RNA genes in genomic sequence.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nucleic Acids Res.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 1997;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='25: 955–64.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 68.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Kanehisa M, Sato Y, Morishima K.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' BlastKOALA and GhostKOALA: KEGG tools for functional characterization of genome and metagenome sequences.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' J Mol Biol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='428:726–31.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 69.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Lauro FM, Demaere MZ, Yau S, Brown MV, Ng C, Wilkins D, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' An integrative study of a meromictic lake ecosystem in Antarctica.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' ISME J.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2010;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 5:879–95.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 70.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Hernsdorf AW, Amano Y, Miyakawa K, Ise K, Suzuki Y, Anantharaman K, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Potential for microbial H2 and metal transformations associated with novel bacteria and archaea in deep terrestrial subsurface sediments.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nat Publ Gr.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2017;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='11:1915–29.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 71.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Llorens-Marès T, Yooseph S, Goll J, Hoffman J, Vila-Costa M, Borrego CM, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Connecting biodiversity and potential functional role in modern euxinic environments by microbial metagenomics.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' ISME J.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2015;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='9:1648–61.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 72.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Kang DD, Froula J, Egan R, Wang Z.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' MetaBAT, an efficient tool for accurately reconstructing single genomes from complex microbial communities.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' PeerJ.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2015;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='3:e1165.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 73.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Langmead B, Salzberg SL.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Fast gapped-read alignment with bowtie 2.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nat Methods.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2012;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='9:357–9.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 74.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Parks DH, Imelfort M, Skennerton CT, Hugenholtz P, Tyson GW.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' CheckM: assessing the quality of microbial genomes recovered from isolates, single cells, and metagenomes.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Genome Res.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2015;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='25:1043–55.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 75.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Eren AM, Esen ÖC, Quince C, Vineis JH, Morrison HG, Sogin ML, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Anvi’o: an advanced analysis and visualization platform for ‘omics data.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' PeerJ.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2015;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 3:e1319.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 76.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Eren AM, Delmot TO.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Predicting CPR genomes in metagenomic bins.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' http:// merenlab.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='org/2016/04/17/predicting-CPR-Genomes/.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 77.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Edgar RC.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Search and clustering orders of magnitude faster than BLAST.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Bioinformatics.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2010;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='26:2460–1.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 78.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Rinke C, Schwientek P, Sczyrba A, Ivanova NN, Anderson IJ, Cheng JF, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Insights into the phylogeny and coding potential of microbial dark matter.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nature.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2013;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='499:431–7.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 79.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Bushnell B.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' BBMap short read aligner.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 80.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Bowers RM, Kyrpides NC, Stepanauskas R, Harmon-Smith M, Doud D, Reddy TBK, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Minimum information about a single amplified genome (MISAG) and a metagenome-assembled genome (MIMAG) of bacteria and archaea.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nat Biotechnol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2017;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='35:725–31.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 81.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Price MN, Dehal PS, Arkin AP.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' FastTree 2--approximately maximum- likelihood trees for large alignments.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' PLoS One.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2010;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='5:e9490.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 82.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Katoh K, Standley DM.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' MAFFT multiple sequence alignment software version 7: improvements in performance and usability.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Mol Biol Evol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2013;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 30:772–80.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 83.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Letunic I, Bork P.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Interactive tree of life (iTOL) v3: an online tool for the display and annotation of phylogenetic and other trees.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nucleic Acids Res.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='44:W242–5.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 84.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' FigTree.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' http://tree.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='bio.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='ed.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='ac.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='uk/software/figtree/.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 85.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Seemann T.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Prokka: rapid prokaryotic genome annotation.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Bioinformatics.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2014;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='30:2068–9.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 86.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Jones P, Binns D, Chang H-Y, Fraser M, Li W, McAnulla C, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' InterProScan 5: genome-scale protein function classification.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Bioinformatics.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2014;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='30: 1236–40.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 87.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Yin Y, Mao X, Yang J, Chen X, Mao F, Xu Y.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' dbCAN: a web resource for automated carbohydrate-active enzyme annotation.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nucleic Acids Res.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2012;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 40:W445–51.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 17 of 18 88.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Cantarel BL, Coutinho PM, Rancurel C, Bernard T, Lombard V, Henrissat B.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' The Carbohydrate-Active EnZymes database (CAZy): an expert resource for glycogenomics.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nucleic Acids Res.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2009;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='37:D233–8.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 89.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nayfach S, Pollard KS.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Average genome size estimation improves comparative metagenomics and sheds light on the functional ecology of the human microbiome.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Genome Biol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2015;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='16:1–18.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 90.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Goris J, Konstantinidis KT, Klappenbach JA, Coenye T, Vandamme P, Tiedje JM.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' DNA-DNA hybridization values and their relationship to whole-genome sequence similarities.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Int J Syst Evol Microbiol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2007;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='57:81–91.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 91.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Huerta-Cepas J, Szklarczyk D, Forslund K, Cook H, Heller D, Walter MC, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' eggNOG 4.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='5: a hierarchical orthology framework with improved functional annotations for eukaryotic, prokaryotic and viral sequences.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Nucleic Acids Res.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2016;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='44:D286–93.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 92.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Tikhonova TV, Slutsky A, Antipov AN, Boyko KM, Polyakov KM, Sorokin DY, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Molecular and catalytic properties of a novel cytochrome c nitrite reductase from nitrate-reducing haloalkaliphilic sulfur-oxidizing bacterium Thioalkalivibrio nitratireducens.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Biochim Biophys Acta - Proteins Proteomics.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2006;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='1764:715–23.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 93.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Tikhonova T, Tikhonov A, Trofimov A, Polyakov K, Boyko K, Cherkashin E, et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Comparative structural and functional analysis of two octaheme nitrite reductases from closely related Thioalkalivibrio species.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' FEBS J.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2012;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='279: 4052–61.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 94.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Tabita FR, Hanson TE, Li H, Satagopan S, Singh J, Chan S.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Function, structure, and evolution of the RuBisCO-like proteins and their RuBisCO homologs.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiol Mol Biol Rev.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2007;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='71:576–99.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 95.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Eddy SR.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Accelerated profile HMM searches.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' PLoS Comput Biol.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' 2011;' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content='7: e1002195.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Vavourakis et al.' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} +page_content=' Microbiome (2018) 6:168 Page 18 of 18' metadata={'source': 'D:\\projects\\langchain-ChatGLM-master\\knowledge_base\\kb_27\\content\\kb_27.pdf'} diff --git a/ktAyT4oBgHgl3EQfyPnx/content/2301.00682v1.pdf b/ktAyT4oBgHgl3EQfyPnx/content/2301.00682v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7e13f11cda9126a2e6e538d4072a65d682031525 --- /dev/null +++ b/ktAyT4oBgHgl3EQfyPnx/content/2301.00682v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:68337bf6178f96f92ffa3f1b19e3f7456b186bb22b0deefea5639382dac8a5ed +size 272668 diff --git a/ktAyT4oBgHgl3EQfyPnx/vector_store/index.faiss b/ktAyT4oBgHgl3EQfyPnx/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..7b2007df53ea01ead6ac707c6eb3ae7d1ded8b43 --- /dev/null +++ b/ktAyT4oBgHgl3EQfyPnx/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2b4e170293ee94cca7674fd1063b4f6bf4fbaa4aba88091bb9f8848703eec9c6 +size 1572909 diff --git a/ktAyT4oBgHgl3EQfyPnx/vector_store/index.pkl b/ktAyT4oBgHgl3EQfyPnx/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..fd8fe828dd5d687ac979ec7d392bb24698e65f0a --- /dev/null +++ b/ktAyT4oBgHgl3EQfyPnx/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:99e4ba58befaf56514f04e357732af42acf3e50fa983572465a39bb485930088 +size 55599 diff --git a/ldE3T4oBgHgl3EQfiAoP/vector_store/index.faiss b/ldE3T4oBgHgl3EQfiAoP/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..9f04ce4948f987d534a31e7e71801d25f309a78f --- /dev/null +++ b/ldE3T4oBgHgl3EQfiAoP/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0a12de71633a8120d59a2c54bb2339b11e3220e8cf57434f05f9d6e9d82b9e68 +size 3932205 diff --git a/m9E0T4oBgHgl3EQfpwHn/content/tmp_files/2301.02545v1.pdf.txt b/m9E0T4oBgHgl3EQfpwHn/content/tmp_files/2301.02545v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..b55165d005445a85ee0ee19271da8a17b4473bb9 --- /dev/null +++ b/m9E0T4oBgHgl3EQfpwHn/content/tmp_files/2301.02545v1.pdf.txt @@ -0,0 +1,1714 @@ +arXiv:2301.02545v1 [math.AG] 6 Jan 2023 +A SURVEY ON TORIC DEGENERATIONS OF PROJECTIVE VARIETIES +LARA BOSSINGER +Abstract. In this survey we summarize the constructions of toric degenerations obtained from +valuations and Gröbner theory and describe in which sense they are equivalent. +We show how +adapted bases can be used to generalize the classical Newton polytope to what we call a B-Newton +polytope. The B-Newton polytope determines the Newton–Okounkov polytopes of all Khovanskii- +finite valuations sharing the adapted standard monomial basis B. +1. Introduction +Toric varieties are popular objects in algebraic geometry due to a dictionary between their geomet- +ric properties (e.g. dimension, degree) and properties of associated combinatorial objects (e.g. fans, +polytopes). This dictionary can be extended from toric varieties to varieties admitting a toric degen- +eration. A toric degeneration is a (flat) family of varieties that share many properties with each other +(e.g. dimension, degree, Hilbert-polynomial). This family contains the variety we are interested in, a +toric variety, so properties of our variety can be read from the combinatorics of the toric variety. +The study of toric degenerations has various applications in pure and applied mathematics, e.g. +in probability, statistics, and mathematical biology. Tailored to the variety of interest, it is a great +challenge to decide which toric degeneration has the desired properties. The task is therefore to study +and compare possible constructions. +Besides its applications in classical algebraic geometry, toric degenerations have proven to be useful +in several other subjects such as +• Symplectic geometry [NNU12, HK14, FLP18, HP18, HK15, Kav19], +• Newton–Okounkov bodies [LM09, KK12, KL17], +• Representation theory [GL96, Cal02, AB05, KM05, HJL+09, FFL11, Kav15, FFL17], +• Mirror symmetry [Giv97, BCFKvS00, Bat04, GS11, FOOO11, ACGK12, Nis15], +• Cluster algebras [GHKK18, BFF+18, RW19, BFMN20], +• Numerical and computational algebraic geometry [CM97, BLMM17, BSW20] +• Algebraic statistics [KMS15, Ber17] +The above list and the included citations are far from being complete as the subject is broad and new +applications are discovered on a regular basis. I apologize if I have missed your favorite paper using +toric degenerations and I would be happy to receive emails with hints to more exiting applications. +The aim of this survey is to describe two main constructions of toric degenerations and how they +are related. In particular, we focus on the constructions from valuations which go back to Anderson +[And13] and those from Gröbner theory or the tropicalization of an ideal. In practice the bridges +connecting one construction to another are particularly useful as each approach has its own benefits +and shortcomings. +To be more precise consider a projective variety X. A toric degeneration of X is a flat morphism +φ : X → A1 that trivializes away from the fibre over 0 ∈ A1 +X \ φ−1(0) +∼ +� +φ +�▼ +▼ +▼ +▼ +▼ +▼ +▼ +▼ +▼ +▼ +X × A1 \ {0} +�♣♣♣♣♣♣♣♣♣♣♣ +A1 \ {0} +We will work with T -equivariant toric degenerations, that is we assume that the action on the central +fibre is an extension of the torus action on X. +1 + +Outline: We summarize the background on valuations in §2.1 and on Gröbner theory and tropical- +ization of ideals in §2.2. In §3 we explain the equivalence of the constructions of toric degenerations +from valuations and from the tropicalization of an ideal [KM19, Bos21b]. In §3.3 we consider more +general algebraic toric degenerations and under which circumstances they can be obtained as the toric +degenerations from a valuation [KMM17]. In §4 we explain the importance of adapted bases for toric +degenerations. In particular, in §4.1 we show how adapted bases give rise to B-Newton polytopes +that project to all Newton–Okounkov polytopes of valuations that share an adapted basis. In §4.2 we +recall the definition of wall-crossing formulas for Newton–Okounkov polytopes [EH20]. We review this +notion from a more geometric point of view in the context of flat families incorporating various toric +degenerations in §5, [BMNC21]. In §6 we elaborate on the example of the Grassmannian Gr3(C6). +Acknowledgements: I would like to thank the editors of the proceeding for the opportunity to con- +tribute with a survey on my favorite topic. The ideas of §4.1 arose in the context of Newton–Okounkov +bodies for cluster varieties in collaboration with Man-Wai Cheung, Timothy Magee and Alfredo Nájera +Chávez. I am grateful for all the inspiring discussions over the course of our collaboration. +2. Preliminaries +In this section we introduce the main tools used in this article to construct toric degenerations. In +particular we review background on valuations and Newton–Okounkov bodies as well as background +on initial ideals, Gröbner theory and the tropicalization of an ideal. We use the maximum convention +throughout the paper which might imply slight differences in the definitions (mostly just a sign) in +comparison to the original articles cited. +2.1. Valuations. Let k be an algebraically closed field of characteristic zero. Throughout the paper +we denote by A a positively (multi-)graded algebra and domain, that is A = � +w∈Zm +≥0 Aw. Let +Γ be an abelian group that is totally ordered by <. By a (Krull) valuation on A we mean a map +ν : A \ {0} → Γ that satisfies for all a, b ∈ A and c ∈ k +ν(ab) = ν(a) + ν(b), +ν(a + b) ≤ max{ν(a), ν(b)}, +ν(ca) = ν(a). +If ν only satisfies ν(ab) ≤ ν(a) + ν(b) it is called a quasivaluation. +Notice that the image of a +valuation ν carries the structure of an additive semigroup. It is therefore called the value semigroup +of ν and we denote it by S(A, ν). The rank of ν is defined as the rank of the group completion of its +semigroup inside Γ, ν is said to have full rank if its rank coincides with the Krull dimension of A. +Every valuation induces a filtration on A with filtered pieces for γ ∈ Γ defined by +Fν,γ := {a ∈ A : ν(a) ≥ γ} +(resp. Fν,>γ := {a ∈ A : ν(a) > γ}) . +The associated graded algebra is grν(A) := � +γ∈Γ Fν,γ/Fν,>γ. There is a natural quotient map +of vector spaces from A to grν(A) given by sending f ∈ A to Fν,ν(f)/Fν,>ν(f), denote its image by +ˆf ∈ grν(A). Note that ν(fg) = ν(f) + ν(g) implies that � +fg = ˆfˆg. If the quotients Fν,γ/Fν,>γ are at +most one-dimensional, then we say ν has one-dimensional leaves. This property is desirable as it +gives an identification +grν(A) → k[S(A, ν)], +given by +ˆfγ �→ ν(fγ), +where ˆfγ ∈ Fν,γ/Fν,>γ is a generator and fγ ∈ A lies in the preimage of ˆfγ under the quotient +map ˆ : A → grν(A). It is a consequence of Abhyankar’s inequality that full-rank valuations have +one-dimensional leaves. +An important definition is the notion of a Khovanskii basis for a valuation ν: that is a subset B +of A whose image in grν(A) is an algebra generating set. It is not hard to see that if B is a Khovanskii +basis for ν then the set {ν(b) : b ∈ B} generates the value semigroup [KM19, Lemma 2.10]. +A valuation is called homogeneous if it respects the grading on A, more precisely if f ∈ A has +homogeneous presentation � +i fi then ν(f) = max{ν(fi)}. +A valuation is fully homogeneous if +ν(f) = (deg(f), ν′(f)), that is S(A, ν) ⊂ Zm +≥0 × Γ′. Any homogeneous valuation is obtained from a +fully homogeneous one by composing with an isomorphism of semigroups [IW20, Remark 2.6]. So when +studying homogeneous valuation we may without loss of generality assume they are fully homogeneous. +2 + +Given a fully homogeneous valuation ν : A \ {0} → Zm +≥0 × Γ′ we define its Newton–Okounkov +cone +(1) +C(A, ν) := cone(S(A, ν)) = cone(ν(f) : f ∈ A), +where the closure (in the Euclidean topology) is taken inside (Zm +≥0 × Γ′) ⊗Z R. Let Γ′ +R = Γ′ ⊗Z R. The +Newton–Okounkov body of ν is then defined as the intersection +(2) +∆(A, ν) := C(A, ν) ∩ {(1, . . . , 1)} × Γ′ +R, +where (1, . . . , 1) denotes the element whose entries are all one in Zm +≥0. The definition was introduced +independently by Lazarsfeld–Mustata [LM09] and Kaveh–Khovanskii [KK12] who based their work on +a construction of Okounkov [Oko98]. Newton–Okounkov bodies far generalize Newton polytopes of +polynomials and carry a lot of information about the algebra A or the (weighted)projective variety +X = Proj(A)1. +Theorem 2.1 (Corollary 3.2 [KK12]). Let X = Proj(A) and ν : A \ {0} → Zd be a full-rank +homogeneous valuation. +Then the dimension q of ∆(A, ν) coincides with the dimension of X and +moreover, the q-dimensional integral volume of ∆(A, ν) multiplied by q!/ind(S(A, ν)) is the degree of +X, where ind(S(A, ν)) refers to the index of the sublattice spanned by S(A, ν) inside Zd. +In general the Newton–Okounkov body of a valuation need not be bounded nor polyhedral, but +they are convex. Computing them is in general challenging, but much simplified when the valuation +posses a finite Khovanskii basis as we will see in what follows. +2.1.1. Khovanskii-finite valuations. A Khovanskii-finite valuation is a homogeneous (Krull) valua- +tion of full rank whose value semigroup is finitely generated. In particular, Khovanskii-finite valuations +have finite Khovanskii bases. The concept was introduced and studied in great detail by Ilten and +Wrobel in [IW20]. +The existence of Khovanskii bases has computational advantages. Given a Khovanskii basis {b1, . . . , bn} +for ν we may represent grν(A) as a quotient of a polynomial ring S := k[x1, . . . , xn]. Define +πν : k[x1, . . . , xn] → grν(A) +by +xi �→ bi. +Then Iν := ker(πν) gives S/Iν ∼= grν(A). +We say the value semigroup S(A, ν) ⊂ (Γ, <) is minimum well-ordered if every subset of S(A, ν) +has a unique minimal element with respect to <. In this case by [KM19, Proposition 2.13] the following +version of the subduction algorithm terminates in finite time. +Algorithm 2.2. Let A be positively graded algebra and domain, ν : A \ {0} → (Γ, <) full-rank homo- +geneous Khovanskii-finite valuation with minimum well-ordered S(A, ν) with {b1, . . . , bn} a Khovanskii +basis. +Input: f ∈ A \ {0}; +Output: a polynomial expression of f in terms of {b1, . . . , bn}. +(1) As ¯b1, . . . ,¯bn generate grν(A) we may find a polynomial expression for ¯f in terms of ¯b1, . . . ,¯bn: +¯f = p(¯b1, . . . ,¯bn), here p ∈ π−1 +ν ( ¯f). +(2) We distinguish two cases +a. If f = p(b1, . . . , bn) then output p; +b. If ν(f − p(b1, . . . , bn)) < ν(f) replace f by f − p(b1, . . . , bn) and go back to Step 1. +In particular, every Khovanskii basis is a generating set for the algebra. +1Recall, that the projective spectrum of the Zm +≥0-graded polynomial ring whose generators have degrees diei, +{e1, . . . , em} being the standard basis of Zm, is the weighted projective space P(d1, . . . , dm). +In particular, if A is +multigraded, Proj(A) can be seen as a subvariety of a weighted projective space. For details we refer to [Dol82]. +3 + +2.2. Initial ideals and tropicalization. Our second tool box for toric degenerations comes from +Gröbner theory. For more detailed information we refer to [HH11, CLO15, Eis13, Stu96]. +For m ∈ Zn +≥0 we write xm := xm1 +1 +· · · xmn +n +∈ k[x1, . . . , xn]. A total order on the set of monomials in +S := k[x1, . . . , xn] is a term order if it satisfies: +(i) 1 < xm ∀m ∈ Zn +≥0 \ {0} +and +(ii) xa < xb ⇒ xa+c < xb+c ∀a, b, c ∈ Zn +≥0. +The leading term of an element f = � caxa ∈ S with respect to a term order < is in<(f) = +cbxb := max<{caxa : ca ̸= 0}, where cb is called the leading coefficient and xb is called the leading +monomial. For an ideal in I ⊂ S we define its initial ideal with respect to < as +in<(I) := (in<(f) : f ∈ I). +The initial ideal is finitely generated and a generating set G of I that satisfies (in<(g) : g ∈ G) = in<(I) +is called a Gröbner basis of I with respect to <. Every ideal possesses only a finite number of +distinct initial ideals [Stu96, Theorem 1.2]. It has been shown by Mora and Robbiano that the initial +ideals can be organized in a polyhedral fan [MR88]. To see how, we need the notion of initial ideals +with respect to weight vectors: fix w ∈ Rn, we call it a weight vector and define the initial form of +an element f = � caxa with respect to w as +inw(f) = +� +b: w·b=max{w·a:ca̸=0} +cbxb. +Notice that depending on w and f the initial form inw(f) is not necessarily just one term. Similarly, +we define the initial ideal of I with respect to w as inw(I) := (inw(f) : f ∈ I). For any weight +vector w we may define the homogenization of I in k[x1, . . . , xn, t]: for a single element f = � caxa +we set +f h;w := +� +caxatmax{w·b:cb̸=0}−w·a. +Similarly, for the ideal I we define Ih;w := (f h;w : f ∈ I). The homogenization of I is a family of +deformations of I and the quotient algebra Ah;w := k[x1, . . . , xn, t]/Ih;w is a free k[t]-module [Eis13, +§15.8]. Let Aw := S/ inw(I). The degeneration of Spec(A) to Spec(Aw) defined by Spec(Ah;w) is called +a Gröbner degeneration. +Given the ideal I any term order can be represented by a weight vector in w ∈ Zn +>0 (see, e.g. +[HH11, Lemma 3.1.1]), that is inw(I) = in<(I). Conversely, a weight vector w belongs to the Gröbner +region GR(I) if there exists a term order < such that in<(inw(I)) = in<(I). The Gröbner region +carries a fan structure, called the Gröbner fan GF(I) that was discovered by Mora and Robbiano in +[MR88]. Two weight vectors v, w ∈ Rn lie in the relative interior of a cone C, denoted by v, w ∈ C◦, +if and only if inv(I) = inw(I). The maximal dimensional cones in GF(I) correspond to monomial +initial ideals associated with term orders on S. These are particularly useful as they induce vector +space bases for the quotient algebra A = S/I: we call a monomial xa that is not contained in in<(I) +a standard monomial. The set B< := {¯xa ∈ A : xa ̸∈ in<(I)} is a vector space basis of A called a +standard monomial basis. In fact, if w ∈ C for some maximal cone C ∈ GF(I) associated to <, +then B< is a basis for the free k[t]-module Ah;w, see e.g. [Eis13, Proof of Theorem 15.17]. +The Gröbner fan has an interesting subfan that will lead us back to valuations on A: we define the +tropicalization of I: +Trop(I) := {w ∈ GR(I) : inw(I) does not contain monomials}. +The dimension of Trop(I) coincides with the Krulldimension of A [EKL06]. We may in fact reduce our +attention to homogeneous ideals according to [BJS+07, Lemma 4]. For homogeneous ideals we have +GR(I) = Rn by [Stu96, Proposition 1.12]. In this case the tropicalization is a pure fan whose dimension +coincides with the Krull-dimension of A. Moreover, Trop(I) and GF(I) have a linear subspace LI, +called the lineality space which consists of elements w ∈ Rn such that inw(I) = I. More precisely +we have the following straight forward Lemma: +Lemma 2.3. Let I be a (multi-)homogeneous ideal inside S with respect to a Zm +≥0-grading given by +deg(xij ) = ei where S = k[xij : 1 ≤ i ≤ m, 1 ≤ j ≤ ki] for some ki that satisfy k1 + · · · + km = n and +{ei : 1 ≤ i ≤ m} is the standard basis of Zm. Then for 1 ≤ i ≤ m we have +(3) +ℓi := (0, . . . , 0, 1, . . ., 1, 0 . . . , 0) ∈ LI +4 + +w1 +w2 +w3 = 0 +×LI = +�� 1 +1 +1 +�� +(y2z) +(x3) +(z3) +(y2z + z3) +(z3 − x3) +(y2z − x3) +Figure 1. The Gröbner fan of I = (y2z − x3 + z3) ⊂ C[x, y, z] modulo LI, its one- +skeleton is Trop(I), and all initial ideals. +where the 1’s appear in the positions i1, . . . , iki. +Among the maximal cones of Trop(I) we may look for prime cones whose associated initial ideal +is binomial and prime. Hence, their vanishing sets define toric varieties. In particular, any Gröbner +degeneration associated to a weight vector in the interior of a maximal prime cone is in fact a toric +degeneration. +Example 2.4. Consider I = (y2z − x3 + z3) ⊂ C[x, y, z]. +The lineality space LI is one dimen- +sional generated by (1, 1, 1)T . +We draw the Gröbner fan GF(I) modulo LI inside the hyperplane +{(w1, w2, w3)T ∈ R3 : w3 = 0} in Figure 1. The one skeleton whose maximal cones correspond to the +rays in the above picture is the tropicalization of I. +2.2.1. Initial ideals with respect to weighting matrices. Before moving on to the next section we need +a bit more background on a slight generalization of initial ideals: a higher dimensional analogue of +Gröbner theory (see e.g. [FR16]). +Recall that S = k[x1, . . . , xn] and consider as before f = � caxa ∈ S. We call a matrix M ∈ Qd×n +a weighting matrix and together with a linear order ≺ on Zd we define the initial form of f with +respect to M as +inM(f) := inM,≺(f) := +� +b: Mb=max≺{Ma:ca̸=0} +cbxb. +As before we define the initial ideal of an ideal I ⊂ S with respect to M (and ≺) as inM;≺(I) := +(inM(f) : f ∈ I). To simplify notation we will drop the linear order from the index and simply assume +that we have fixed it once and for all. The Gröbner region also has a higher dimensional analogue: the +dth Gröbner region is denoted GRd(I) and defined as the set of all weighting matrices M ∈ Qd×n +such that there exists a term order < on S with in<(I) = in<(inM(I)). Given < let Cd +< ⊂ GRd(I) be +the set of all M satisfying the previous relation. We may also define equivalence classes of weighting +matrices by setting CM := {M ′ ∈ GRd(I) : inM(I) = inM′(I)}. +In the higher dimensional case +several features of Gröbner theory still hold, among these the existence of standard monomial bases. +For example, GRd(I) always contains the positive orthant Qd×n +≥0 +and if I is homogeneous we have +GRd(I) = Qd×n (see [KM19, Lemma 8.7] but be aware that the authors are using the minimum +convention which introduces a sign). +We may use weighting matrices to define quasivaluations as follows. Consider the quotient map +π : S → S/I =: A and denote by ¯f the coset of f in the quotient. +For f = � caxa ∈ S set +˜νM(f) := max≺{Ma : ca ̸= 0}. This defines a valuation ˜νM : S \ {0} → Zd. By [KM19, Lemma 3.2] +there exists a quasivaluation νM : A \ {0} → (Zd, ≺) given for ¯f ∈ A by +νM( ¯f) = min +≺ {˜νM(f) : f ∈ ¯f} +5 + +called the quasivaluation with weighting matrix M. +Its associated graded algebra, denoted +grM(A), satisfies grM(A) ∼= S/ inM(I). In particular, this isomorphism gives us standard monomial +bases for grM(A): let < be a term order with M ∈ Cd +<. Then B< is a vector space basis for grM(A). +Moreover, we may use B< to compute the values of νM: for ¯f ∈ A let ¯f = � +¯xb∈B< cb¯xn be its +expression in B<. Then +νM(π(f)) = max +≺ {Mb : cb ̸= 0}. +We explore standard monomial bases and their influence on valuations further in §4. +3. Valuations, tropicalization and toric degenerations +In this section we merge the concepts of Khovanskii-finite valuations and the tropicalization of an +ideal. This section is based on results in [KM19] and [Bos21b]. +3.1. Valuations from tropicalization. The main aim of Kaveh and Manon in [KM19] is to establish +a connection between the toric degenerations from prime cones in a tropicalization to toric degener- +ations obtained from Newton–Okounkov polytopes. It relies on the quasivaluations with weighting +matrices introduced above. +As before, let I ⊂ S be a homogeneous ideal. Suppose there exists a maximal prime cone τ ∈ Trop(I) +and choose a basis r1, . . . , rd ∈ Qn for the real vector space spanned by τ. The quotient τ/LI is a +strongly convex cone (see e.g. [BMNC21, Lemma 2.13]) so we may take a maximal linearly independent +set of cosets of primitive ray generators of τ/LI. Together with a basis of the lineality space this will +be our choice for r := {r1, . . . , rd}. In particular, we set ri = ℓi for 1 ≤ i ≤ m, see Lemma 2.3. Define +Mr := (rij)1≤i≤d,1≤j≤n +where rij is the jth entry in ri, so the ri are the rows of Mr. +Proposition 3.1 (Proposition 4.2 and 4.6 in [KM19]). If τ is a maximal prime cone in Trop(I) then +quasivaluation with weighting matrix Mr is in fact a full rank valuation with one-dimensional leaves. +Its value semigroup is generated by the images of ¯x1, . . . , ¯xn and it only depends on τ, not on our +choice of r. +Given the Proposition we adopt our notation and set Mτ := Mr and ντ := νMτ . We obtain the +following corollary about the associated Newton–Okounkov polytopes: +Corollary 3.2 (Corollary 4.7 in [KM19]). The Newton–Okounkov body of the valuation ντ is a convex +polytope whose vertices are ντ(¯x1), . . . , ντ(¯xn), which are exactly the columns of Mτ. Moreover, up to +linear isomorphism ∆(A, ντ) only depends on τ. +S(A, ντ) +1 +2 +1 +2 +3 +4 +5 +6 +× +× +× +× +◦ +× +◦ +× +× +× +◦ +× +Notice that for I homogeneous with respect to the standard grading and r1 = +(1, . . . , 1) as above the Corollary implies that (up to linear isomorphism) we have +∆(A, ν) ⊂ {1} × Rd−1. +Example 3.3. Consider I = (y2z − x3 + z3) ⊂ C[x, y, z] from Example 2.4 above. The +initial ideal (y2z−x3) corresponding to the ray (2, 3, 0)T in Figure 1 is a maximal prime +cone τ in Trop(I). The associated ray matrix is Mτ = ( 1 1 1 +2 3 0 ). Let A = C[x, y, z]/I, +then the valuation ντ : A \ {0} → Z≥0 × Z satisfies ντ(¯x) = (1, 2), ντ(¯y) = (1, 3) and +ντ(¯z) = (1, 0). In particular, the value semigroup of ντ is generated by these three +elements and depicted on the right. +Here × denotes the lattice points in S(A, ντ) and ◦ denotes lattice points not con- +tained in S(A, ντ). The shaded region is the Newton–Okounkov cone C(A, ντ) and the +line segment connecting (1, 0)T and (1, 3)T is the Newton–Okounkov polytope ∆(A, ντ). +Note that S(A, ντ) is not saturated: for example, (2, 2)T is in S(A, ντ), but (1, 1)T is +not. +6 + +3.2. Tropicalization from valuations. Fix a Khovanskii-finite valuation ν : A \ {0} → Zd on a +positively graded algebra and domain A. We may assume without loss of generality that dimKrull(A) = +d (if this was not the case we may apply [BG09, Proposition 2.17(e)] as the image of ν is in fact a +monoid whose only unit is 0). Moreover, we may assume that the underlying total order on Zd is the +lexicographic order (if this was not the case we may follow Mora and Robbiano [MR88] and represent +the order by a d × s matrix M such that our order coincides with the lexicographic order on MZd). +Choose a finite generating set a1, . . . , an for the value semigroup ν(A\{0}) and let Mν be d×n matrix +whose columns are a1, . . . , an. Notice that +rank(Mν) = dim(im(Mν) = dim(spanZ(a1, . . . , an)) = dim(cone(a1, . . . , an)) = rank(ν). +In particular, Mν is of full rank. +Lemma 3.4. Given the generators a1, . . . , an of the value semigroup S(A, ν) choose b1, . . . , bn ∈ A +with ν(bi) = ai. Then the set {b1, . . . , bn} is a Khovanskii basis. +Proof. As k[S(A, ν)] ∼= grv(A) the elements a1, . . . , an form a set of algebra generators for grv(A). +□ +Notice further that for dimension reasons the Khovsankii basis {b1, . . . , bn} is a generating set for +A as ν is full-rank. Hence, we may use it to obtain a presentation of A. Define +π : S := k[x1, . . . , xn] → A, +by +xi �→ bi. +Notice that b1, . . . , bn not necessarily are of degree one in A. To have a graded presentation of A +we endow the polynomial ring with a (not necessarily standard) grading given by deg(xi) := deg(bi). +Then I := ker(π) is a homogeneous ideal and S/I ∼= A. Our valuation ν is intimately related with the +tropicalization of the ideal I. +Theorem 3.5 ([Bos21b]). Let ν : A \ {0} → Zd be a full rank valuation with finitely generated value +semigroup and let S/I ∼= A be the presentation induced by a Khovanskii basis b1, . . . , bn. +Then there exists a maximal prime cone τ ∈ Trop(I) such that ν = ντ and +k[S(A, ν)] ∼= grν(A) ∼= S/ inτ(I). +Proof. Notice that M := Mν the weighting matrix of ν is of full rank d ≤ n as ν is of full rank. Then +by [Bos21b, Theorem 1] the initial ideal inM(I) is prime as the value semigroup S(A, ν) is generated +by ν(b1), . . . , ν(bn). Here we use the total order on Zd given by ν. We may restrict our attention to +the case of usual initial ideals as by [Bos21b, Lemma 3] there exists a weight vector w ∈ Zn such that +inw(I) = inM(I). It is left to show that +(1) w ∈ Trop(J); +(2) k[S(A, ν)] ∼= S/ inτ(J), where w ∈ τ ◦. +The first item follows from [Bos21b, Corollary 3]. For the second consider the quasivaluation νM. By +Proposition 2.1 νM is a valuation and by [Bos21b, Proposition 1] it satisfies ν = νM. Further, by +[Bos21b, Equation 3.3] we have +S/ inw(I) ∼= grν(A) ∼= k[S(A, ν)], +which finishes the proof. +□ +One nice feature of this connection is that it may be used to characterize when a toric degeneration +is a Gröbner degeneration. We explore this direction further in the following subsection. +Theorem 3.5 depends on a choice of Khovanskii basis, so naturally one may ask how strong this +dependence is. If we change the Khovanskii basis, the presentation of A changes and so does the +tropicalization. +Proposition 3.6. Assume B := {b1, . . . , bn} and B′ := {b′ +1, . . . , b′ +n} are two Khovsankii bases of (A, ν). +Let I and I′ be the ideals presenting A and let τ and τ′ be the cones in the corresponding tropicalizations +from Theorem 3.5. Then there exists an ideal ˜I ⊂ k[y1, . . . , ym] for some m ≥ n presenting A and +projections p : Rm → Rn and p′ : Rm → Rn such that for a maximal prime cone ˜τ ∈ Trop(˜I) we have +p(˜τ) = τ and p′(˜τ) = τ ′. +7 + +Proof. We have two presentations of A: +π : S → A, π(xi) = bi +and +π′ : S → A, π′(xi) = b′ +i +given by ker(π) = I and ker(π′) = I′. To see how the two tropicalizations Trop(I) and Trop(I′) are +related we proceed recursively and introduce another presentations of A given by B∪B′. For simplicity +assume bi = b′ +i for all i < n. Consider ˜π : k[x1, . . . , xn+1] → A given by xi �→ bi, xn+1 �→ b′ +n and let +˜I := ker(˜π). +Let p : k[x1, . . . , xn+1] → k[x1, . . . , xn] and p′ : k[x1, . . . , xn−1, xn+1] be the natural +projections. By construction we have I ⊂ p(˜I) and I′ ⊂ p′(˜I). Let ˜τ ∈ Trop(˜I) be the maximal prime +cone given by Theorem 3.5. Then the corresponding projections p and p′ from Rn+1 → Rn have the +desired properties. +□ +Proposition 3.6 invites us to change our point of view: suppose we have two Khovanskii-finite +valuations ν and ν′ on A with two different Khovanskii bases B and B′. We may use the proof of +Proposition 3.6 to construct a tropicalization that contains simultaneously prime cones corresponding +to ν and ν′. This idea is closely related to a procedure in [BLMM17] for constructing new prime cones +by changing the presentation of A ([BLMM17, Procedure 1]). It was shown in [IW20] that for non +Khovanskii-finite valuations the above mentioned procedure does not terminate. We further elaborate +on these ideas in the example of the Grassmannian Gr3(C6) in §6. +3.3. Which toric degenerations are Gröbner? Theorem 3.5 shows that toric degenerations in- +duced by Khovanskii-finite valuations equivalently arise as Gröbner degenerations from the tropical- +ization of an adequate ideal. Naturally we may extend the question and ask which toric degenerations +are Gröbner degenerations. +Recall the definition of a toric degeneration from §1. Assume X is a projective variety and we have +X = Proj(A). Given ν : A \ {0} → Zd a Khovanskii-finite valuation, grν(A) is a Zd-graded toric +algebra. Anderson showed how to construct a toric degenerations of X given ν and we briefly recall +his construction [And13]. In order to associate a (Noetherian) Rees algebra to ν that deforms A to +grν(A) we apply a standard trick [Bay82, Proposition 1.8] to change from the Zd-grading on grν(A) +to a Z-grading: +Lemma 3.7. Let F be a finite subset of Zd. Then there exists an order preserving projection +e : Zd → Z≥0 such that for all m, n ∈ F we have m < n (in Zd) implies e(m) < e(n) (in Z). +In our setting the set F is induced by a Gröbner basis. Consider a presentation of A = S/I given +by a Khovanskii-basis for ν and let τ ∈ Trop(I) be the maximal prime cone corresponding to ν. Then +choose a maximal cone C ∈ GF(I) who contains τ as a face and fix a Gröbner basis g1, . . . , gs for I +with respect to the monomial initial ideal inC(I). We may assume without loss of generality that ν is +the valuation associated to the matrix M whose rows are representatives of the rays of τ. If this is not +the case by Corollary 3.2 there is a linear isomorphism that maps S(A, ν) to S(A, νM). The valuation +νM has the advantage that it compatible with ˜νM : S \ {0} → Zd defined as above by +˜νM(f) = max +≺ +� +Ma : f = +� +caxa, ca ̸= 0 +� +where ≺ is the total order on Zd. For every element of the Gröbner basis g we have an expression +g = +� +a: Ma=νM (g) +caxa + +� +b: Mb≺νM (g) +cbxb, +where in particular Ma ≻ Mb. The elements Ma, Mb for all g in the Gröbner basis constitute the +finite set F of Lemma 3.7 that determines the order preserving projection e : Zd → Z. It induces a +Z-filtration of A with filtered pieces +Fν,i := {f ∈ A : e(ν(f)) ≥ i}. +The associated graded algebra coincides with grν(A) by construction. We define the Rees algebra +of ν as +Rν,A := +� +i≥0 +tiFν,i ⊂ A[t]. +8 + +Proposition 3.8 (Proposition 5.1 in [And13]). The Rees algebra Rν,A is a flat k[t]-algebra with +Rν,A/(t) ∼= grν(A) and Rν,A[t−1] ∼= A[t, t−1] as k[t]-modules. +Moreover, the isomorphisms on the above proposition hold for the graded algebras (remember that +ν is homogeneous). In particular, φ : Proj(Rν,A) → A1 is a toric degeneration of X with special fibre +φ−1(0) = X0 = Proj(grν(A)). While X0 is normal if and only if S(A, ν) is saturated, Anderson shows +that its normalization is the projective toric variety associated with the Newton–Okounkov polytope +∆(A, ν). +Given the example of a toric degeneration induced by a valuation we may formulate an algebraic +definition of toric degeneration. +We summarize the definiton and its relation to valuations in the +following result of Kaveh, Manon and Murata: +Theorem 3.9 (Theorem 1.11 in [KMM17]). Let A be a positively graded domain and let R be a finitely +generated positively graded k[t]-module and domain with the following properties: +• R[t−1] ∼= A[t, t−1] as k[t]-modules and graded algebras; +• the algebra R/(t) is a graded semigroup algebra k[S] where S ⊂ Z≥0 × Zd; +• the standard k∗-action on k[t] extends to an action on R respecting its grading, moreover this +k[t]-action acts through (k∗)d on the semigroup algebra k[S]. +Then there is a full-rank valuation ν : A \ {0} → Z≥0 × Zd such that S = S(A, ν). +We call a toric degeneration of Proj(A) induced by an algebra R as in Theorem 3.9 an algebraic +toric degeneration. We obtain the following Corollary by combining Theorem 3.9 and Theorem 3.5: +Corollary 3.10. Every algebraic toric degeneration is induced by a valuation and can be realized as +a Gröbner degeneration associated with a maximal prime cone in the tropicalization of an apropriate +ideal. +4. Adapted bases and wall-crossing formulas +Suppose A = � +j≥0 Aj is a graded algebra, for example the section ring of a line bundle, and it is +equipped with a vector space basis B. We assume that the basis is graded, i.e. basis elements are +homogeneous and a homogeneous element f of degree i is a linear combination of basis elements of +degree i. Recall that given a valuation ν : A \ {0} → Γ the basis B is adapted to ν if for every γ ∈ Γ +the set B ∩ Fν,γ is a vector space basis of the filtered piece Fν,γ ⊂ A. Reversely we say that ν is +adapted to B. In particular, if ν has one-dimensional leaves we have a bijection of sets +B +↔ +S(A, ν). +In this section we explore the consequences. Assume the basis is parametrized by lattice points, +so we have an assignment of b �→ m(b) ∈ Zn for all b ∈ B. In fact we may find an adapted basis with +a parametrization by lattice points for every Khovanskii-finite valuation. Consider ν : A \ {0} → Zd +with Khovanskii basis b1, . . . , bn and let S/I ∼= A and τ ∈ Trop(I) be the presentation of A and the +maximal prime cone in Trop(I) as in Theorem 3.5. By definition Trop(I) is a subfan of the Gröbner +fan GF(I) and τ is a face of at least one maximal cone in GF(I). Maximal cones in GF(I) are in +correspondence with monomial initial ideals of I as defined above. For a maximal cone C we denote +by inC(I) ⊂ S the corresponding monomial ideal. In particular, the set +BC := {xm : xm ̸∈ inC(I)} +is a vector space basis for all quotients Aw := S/ inw(I) with w ∈ C called a standard monomial +basis. Notice that for w = 0 the quotient Aw = A and for w ∈ τ ◦ we have Aw ∼= grν(A). Hence, BC +is an adapted basis for ν. The assignment +xm �→ m ∈ Zn +is a parametrization by lattice points. Recall that every monomial ideal has a unique set of monomial +generators (see e.g. [HH11, Proposition 1.1.6]). Let xg1, . . . , xgt be this generating set. Then xm ∈ +inC(I) if and only if there exists i such that xgi divides xm. This translates to m ̸∈ �t +i=1 gt + Zn +≥0 for +9 + +elements of the standard monomial basis, where + denotes the Minkowski sum. So we have bijections +of sets +S(A, ν) +↔ +BC +↔ +Zn +≥0 \ +t� +i=1 +gi + Zn +≥0 +Hence, we obtain the following corollary: +Corollary 4.1. Every Khovanskii-finite valuation has an adapted basis parametrized by lattice points. +Example 4.2. Consider as above I = (y2z − x3 + z3) ⊂ C[x, y, z] and the maximal prime cone +τ ∈ Trop(I) spanned by the ray (2, 3, 0)T modulo LI. Inside GF(I) the cone τ is adjacent to two +maximal cones: one of them has associated initial monomial ideal (x3) (see Figure 1). Let C be this +maximal cone. Then BC = {xaybzc : a < 3} is the set of all monomials in C[x, y, z] that are not +divisible by x3, hence they are not in inC(I). +4.1. Polytopes from adapted bases. Fix a Khovanskii-finite valuation ν : A \ {0} → Zd and an +associated adapted standard monomial basis B := BC with the parametrization given above. For an +element f ∈ A let f = � +xm∈B cmxm be its linear extension in B. Let M be the matrix whose rows +r1, . . . , rm are representatives of primitive ray generators of C. In particular, let r1, . . . , rs be the +generators of the lineality space. Define suppB(f) := {m ∈ Zn : cm ̸= 0} ⊂ Zn and the B-Newton +polytope of f by +NewB(f) := conv (Ma : a ∈ suppB(f)) ⊂ Rm. +Notice that NewB(f) depends on our choice of ray generators for C. We will slightly abuse notation +and not include M in the index. We think of the NewB(f) as placeholder for a valuation adapted to +B and we define a placeholder for the Newton–Okounkov body of ν: +∆B(A) := conv + +� +j≥1 +�1 +j NewB(f) : f ∈ Aj +� + ⊂ Rm. +Recall that the Newton–Okounkov body of a valuation ν : A \ {0} → Zd is defined as +∆(A, ν) := conv + +� +j≥1 +�ν(f) +j +: f ∈ Aj +� + . +If ν is fully homogeneous, i.e. of form ν : A \ {0} → Zm +≥0 × Γ′ given by ν(f) = (deg(f), ν(f)) then the +above definition coincides with the one in Equation (2). Any valuation constructed from a maximal +prime cone τ in the tropicalization of an ideal as in §3.1 is by construction fully homogeneous. Recall +that the first m rows of Mτ are the elements ℓi from Lemma 2.3. Let Mℓ be the submatrix with rows +ℓ1, . . . , ℓm. Denote by pr : Zm +≥0 × Γ′ → Zm +≥0 the projection. Then for any element f ∈ A we have +pr(νM(f)) = Mℓb = deg(f) +where b is such that Mτb = max<{Mτa : f = � caxa, ca ̸= 0}. Moreover, in this context the bijection +between the basis B = BC and the valuation νMτ is given explicitly by +B → S(A, νM), +xa �→ Mτa +Theorem 4.3. Let C ∈ GF(I) be a maximal cone that contains the maximal prime cones τ1, . . . , τq ∈ +Trop(I) as d-dimensional face with associated Khovanskii-finite valuations νi : A \ {0} → Zd. Assume +additionally that inC(I) does not contain any variables. Then there exist projections pi : Rn → Rd for +1 ≤ i ≤ q such that +pi(∆B(A)) = ∆(A, νi). +Proof. Let M be the matrix whose rows r1, . . . , rnC are either generators of the lineality space LI +or representatives of primitive ray generators for C/LI. +Notice that nC ≥ n as C is a maximal +cone with equality if and only if C/LI is simplicial. For every cone τi choose a collection of rows +r1, . . . , rs, ri1, . . . , rid−s (where r1, . . . , rs are the generators of the lineality space), that correspond to +rays spanning the same real vector space as τi: +⟨r1, . . . , rs, ri1, . . . , rid−s⟩R = ⟨τi⟩R. +10 + +Denote the matrix whose rows are r1, . . . , rs, ri1, . . . , rid−s by Mi and define pi : RnC → Rd as the +projection onto the coordinates 1, . . . , s, i1, . . . , id−s. Recall that ∆(A, νi) without loss of generality +by Corollary 3.2 is the convex hull of the columns of the matrix Mi. We verify pi(∆B(A)) = ∆(A, νi) +pointwise by tracing the elements of B through both constructions. As B is in bijection with S(A, νi) +the claim follows. Consider xa ∈ B, then NewB(xa) = Ma. In ∆B(A) the element xa corresponds to +the point +1 +a1+···+an Ma and +pi +� +1 +a1 + · · · + an +Ma +� += +1 +a1 + · · · + an +Mia = +1 +a1 + · · · + an +νi(xa) ∈ ∆(A, νi), +so pi(∆B(A)) ⊂ ∆(A, νi). +To show equality it suffices to verify that the vertices of ∆(A, νi) are +contained in pi(∆B(A)). By the additional assumption that inC(I) does not contain any variables we +know that x1, . . . , xn ∈ B. The computation above applied to a variable xj = xa yields: +pi +� +1 +a1 + · · · + an +Ma +� += Miej = Mij, +where Mij is the jth column of Mi and a vertex of ∆(A, νi) by Corolary 3.2. +□ +Example 4.4. We continue with the Example 4.2. For the maximal cone C we choose the ray matrix: +MC = + + +1 +1 +1 +2 +3 +0 +1 +0 +1 + + . +Notice that (1, 0, 1) mod LI = (0, −1, 0) mod LI which corresponds to the teal ray in Figure 1. Let +B = BC and A = C[x, y, z]/I. Then +∆B(A) = conv +� +1 +a + b + c +� a+b+c +2a+3b +a+c +� +: a + b + c ≥ 1, a < 3 +a, b, c ∈ Z≥0 +� += conv +�� 1 +2 +1 +� +, +� 1 +3 +0 +� +, +� 1 +0 +1 +�� +. +Let p1 be the projection away from the third coordinate in R3, then +p1(∆B(A)) = conv +��1 +3 +� +, +�1 +0 +�� += ∆(A, ντ). +Where τ ∈ Trop(I) is the maximal prime cone spanned by (2, 3, 0)T +mod LI as in Example 3.3. +4.2. Wall-crossing formulas. The Newton–Okounkov polytopes associated to the faces τ1, . . . , τq +of C are related by piecewise-linear maps called wall-crossing formulas that were introduced by +Escobar and Harada in [EH20]. We briefly review their construction. +Assume that τ1 and τ2 are two adjacent faces of the maximal cone C ∈ GF(I), so that τ := τ1 ∩τ2 is +a facet of both. Then we may choose the ray matrices M1 and M2 such that they agree in all rows but +the last one. Let M1,2 be the matrix with the d−1 rows that M1 and M2 have in common. In particular, +we have two full-rank homogeneous valuations ν1 := ντ1, ν2 := ντ2 : A \ {0} → Zm +≥0 × Zd−m and one +homogeneous valuation ν1,2 : A\{0} → Zm +≥0×Zd−m−1 of almost full rank, that is rank d−1. We denote +by p[d−m−1] : Rd−m → Rd−m−1 the projection onto the first d − m − 1 coordinates. By construction +(and Corollary 3.2) we have the following relation between the associated Newton–Okounkov polytopes +∆(A, ν1) +p[d−m−1] +�▼ +▼ +▼ +▼ +▼ +▼ +▼ +▼ +▼ +▼ +∆(A, ν2) +p[d−m−1] +�qqqqqqqqqq +∆(A, ν1,2) +In particular there exist piecewise linear maps ϕi : ∆(A, ν1,2) → R and ψi : ∆(A, ν1,2) → R for +i ∈ {1, 2} such that +(4) +∆(A, νi) = +� +(1, v, z) ∈ {1} × Rd−m−1 × R : +(1, v) ∈ ∆(A, ν1,2) +ϕi(1, v) ≤ z ≤ ψi(1, v) +� +, +where 1 = (1, . . . , 1) ∈ Rm. By [EH20, Theorem 3.4] there exists a constant κ > 0 such that for all +(1, v) ∈ ∆(A, ν1,2): +κ(ψ1(1, v) − ϕ1(1, v)) = ψ2(1, v) − ϕ2(1, v) +11 + +We define the piecewise linear wall-crossing maps +S12 : Rd → Rd given by (1, v, z) �→ (1, v, κ(z − ϕ1(1, v)) + ϕ2(1, v)) +F12 : Rd → Rd given by (1, v, z) �→ (1, v, κ(ϕ1(1, v) − z) + ψ2(1, v)). +(5) +The map S12 is called the shift and the map F12 is called the flip. +Theorem 4.5 (Theorem 2.7 in [EH20]). Let I be a (multi-)homogeneous ideal in S and C a maximal +cone in GF(I) such that there exist two maximal prime cones τ1, τ2 ⊂ C ∩ Trop(I) that share a +common facet τ = τ1 ∩ τ2. Let ν1, ν2 and ν1,2 be the associated homogeneous valuations. Then for +Φ12 ∈ {F12, S12} the associated Newton–Okounkov polytopes are related by +∆(A, ν1) +p[d−m−1] +�▼ +▼ +▼ +▼ +▼ +▼ +▼ +▼ +▼ +▼ +Φ12 +� ∆(A, ν2) +p[d−m−1] +�qqqqqqqqqq +∆(A, ν1,2) +and the Euclidean lengths of the fibers of p[d−m−1] are equal. +Example 4.6. In our running example the maximal cone C ∈ GF(I) has two maximal prime cones +in Trop(I) as facets. Let τ1 ∈ Trop(I) be the cone generated by (2, 1, 1)T +mod LI (teal in Figure 1) +and τ2 be the cone generated by (2, 3, 0)T +mod LI. Then +∆(A, ν1) = conv +��1 +0 +� +, +�1 +3 +�� +and +∆(A, ν2) = conv +��1 +0 +� +, +�1 +1 +�� +. +The Newton–Okounkov polytope ∆(A, ν1,2) is simply the point {1} ∈ R. Hence, the piecewise linear +functions ϕi, ψi are constants: +∆(A, ν1) = {(1, z) : ϕ1(1) := 0 ≤ z ≤ 3 =: ψ1(1)}, +∆(A, ν2) = {(1, z) : ϕ2(1) := 0 ≤ z ≤ 1 =: ψ2(1)}. +The global constant can be computed from the volume of the Newton–Okounkov polytopes (with respect +to the ambient subspace where they are full-dimensional poyltopes). We have that κ1vol(∆(A, ν1)) = +κ2vol(∆(A, ν2)) = deg(y2z − x3 + z3) and κ = |κ1/κ2| = 1 +3, so +S12 : (1, z) �→ +� +1, z +3 +� +, +F12 : (1, z) �→ +� +1, 1 − z +3 +� +. +5. Families of Gröbner degenerations +In this section, we recall the main construction of the paper [BMNC21]. It gives a multi-parameter +flat family associated to a maximal cone C ∈ GF(I) where I ⊂ S is a homogeneous ideal. We will see +that this algebraic construction is closely related to the polyhedral objects from the previous section. +Let A be the quotient S/I. Recall the classical construction of a Gröbner degenerations associated +to w a weight vector w ∈ C◦ from §2.2 defined by the quotient S[t]/Ih;w. The ideal Ih;w defines the flat +family Spec(S[t]/Ih;w) → Spec(k[t]) whose fiber over the closed point (t) is isomorphic to Spec(Aw), +where Aw := S/ inw(I) and the fiber over any non-zero closed point (t − c) is isomorphic to Spec(A). +Both, the construction of Ih;w and [Eis13, Theorem 15.17] hold for arbitrary cones in GF(I). In what +follows, for simplicity, we focus on maximal cones as the generalization to lower dimensional ones is +straight forward. +To generalize the construction of Ih;w we fix vectors r1, . . . , rnC ∈ C such that {r1, . . . , rnC} is the +set of primitive ray generators for C, which is possible due to [BMNC21, Lemma 2.13]. Let M be +the (nC × n)-matrix whose rows are r1, . . . , rnC. Additionally, we write < for a monomial term order +compatible with C and denote by G the associated reduced Gröbner basis. +Definition 5.1. For f = � +α∈Zn +≥0 cαxα ∈ I set µM(f) := (maxcα̸=0{ri · α})i=1,...,nC ∈ ZnC×1, hence +µM(f) as a column vector with nC entries. Define the lift of f as the polynomial ˜fM ∈ S[t1, . . . , tnC] +12 + +given by the following formula +˜fM := ˜fM(t, x) := f(t−M·e1x1, . . . , t−M·enxn)tµM (f) = +� +α∈Zn +≥0 +cαxαt−M·α+µM(f). +Similarly, we define the lifted ideal as ˜IM := +� +˜fM : f ∈ I +� +⊂ S[t1, . . . , tnC] and the lifted algebra +as the quotient +(6) +˜AM := S[t1, . . . , tnC]/˜IM. +Although by construction the lifted algebra depends on the choice of ray matrix M it can be shown +that different choices yield the same algebra [BMNC21, Corollary 3.10]. Another useful result about +the lifted ideal ˜IM is an explicit construction of a Gröbner basis. On S[t1, . . . , tnC] we consider the +following term order induced by the term order < on S corresponding to C: +(7) +xαtλ ≪ xβtµ +if and only if +(i) xα < xβ +or +(ii) xα = xβ and tλ = 0.14 +F +(b) +8000 +8sim = 0.18 +&sim = 0.13 +0.10 + 0.1 +Tetrahedra +Tetrahedra +Grid points +Grid points +0.05 +6000 +0.0 +10-1 +10-2 +10-1 +counts +l +4000 +2000 +0 +-1.0 +-1.0 +-0.5 +0.0 +0.5 +-0.5 +0.0 +0.5 +1.0 +1.05 +solved over the more than 56,000 lag-space tetrahedra +provided by the Helioswarm constellation. The statisti- +cal agreement between the cascade rate measured using +the tetrahedra with that obtained from the exact evalu- +ation over the grid points is striking and very promising +for the ability of Helioswarm to determine accurate ap- +proximations of the solar wind turbulence cascade rate. +We expect that improved estimates will be obtained by +applying geometric quality factors [24] to the tetrahe- +dra. +Another detail that can be observed, is that the +histogram of ϵ estimates in the anisotropic case reflects +the variability of values in different directions where the +inertial ranges may have different extensions as shown by +the spectra in Fig. 3. Further experience with analysis of +cascade rates in simulations [20] will guide refinements of +this method, as well as extensions to properly define and +obtain directional cascade rates as well. +Note that the span of scale in the solar wind is much +larger than that available in the simulation. However, +only the largest virtual spacecraft separations approach +or exceed the scales within the inertial range. Since our +goal here is to evaluate inertial range statistics, the re- +sults are not severely affected. When applied to the mag- +netosheath [26] the range of scales is narrower and an +even closer correspondence can be found with the simu- +lation. +We note that higher-order polyhedra with vertices +> 4 might also be employed. +For this work, we used +tetrahedra to exploit well-tested routines that have +been validated in Cluster and MMS data [24]. +The +present demonstration provides guidance and confidence +concerning the evaluation of critical turbulence quan- +tities on the upcoming generation of multispacecraft +constellations beyond Helioswarm, including concepts +such as MagCon, Plasma Observatory, and Magnetore +[27]. +Accurate evaluations of cascade rates directly +support theories of dissipation, plasma heating, solar +wind acceleration, and cross-scale dynamics in general, +which through these missions may well revolutionize our +conception of the dynamics in these complex interplane- +tary and magnetosphere space plasmas. +ACKNOWLEDGMENTS +This research is supported in part by the MMS +Theory and Modeling program grant 80NSSC19K0284, +the Parker Solar prove Guest Investigator program +80NSSC21K1765, the PUNCH mission through SWRI +subcontract N99054DS, and the NSF/DOE program un- +der grant AGS-2108834 at the University of Delaware. +LP acknowledges support by EU FP7 2007-13 through +the MATERIA Project (PONa3 00370) and EU Hori- +zon 2020 through the STAR 2 Project (PON R&I 2014- +20, PIR01 00008) for running the simulations on the +“newton” cluster. Helioswarm sprites in Fig. 2 courtesy +of UNH https://eos.unh.edu/helioswarm/mission/ +flight-system. +[1] S. B. Pope, Turbulent Flows (Cambridge University +Press, Cambridge, UK, 2000). +[2] D. Biskamp, Magnetohydrodynamic turbulence (Cam- +bridge University Press, 2003). +[3] G. Comte-Bellot and S. Corrsin, Simple Eulerian time +correlation of full- and narrow-band velocity signals in +grid-generated, ‘isotropic’ turbulence, Journal of Fluid +Mechanics 48, 273 (1971). +[4] M. Yamada, Y. Ren, H. Ji, J. Breslau, S. Gerhardt, +R. Kulsrud, and A. Kuritsyn, Experimental study of two- +fluid effects on magnetic reconnection in a laboratory +plasma with variable collisionality, Physics of Plasmas +13, 052119 (2006). +[5] J. Credland, G. Mecke, and J. Ellwood, The cluster mis- +sion: Esa’s spacefleet to the magnetosphere, Space Sci- +ence Reviews 79, 33 (1997). +[6] J. L. Burch, T. E. Moore, R. B. Torbert, and B. L. Giles, +Magnetospheric multiscale overview and science objec- +tives, Space Science Reviews 199, 5 (2016). +[7] H. E. Spence, HelioSwarm: +Unlocking the Multiscale +Mysteries of Weakly-Collisional Magnetized Plasma Tur- +bulence and Ion Heating, in AGU Fall Meeting Abstracts, +Vol. 2019 (2019) pp. SH11B–04. +[8] S. A. Orszag, On the elimination of aliasing in finite- +difference schemes by filtering high-wavenumber compo- +nents, J. Atmos. Sci. 28, 1074 (1971). +[9] S. A. Orszag, Comparison of pseudospectral and spectral +approximation, Stud. Applied Math. 51, 253 (1972). +[10] S. A. Orszag and C.-M. Tang, Small-scale structure +of two-dimensional magnetohydrodynamic turbulence, J. +Fluid Mech. 90, 129 (1979). +[11] A. Pouquet, On two-dimensional magnetohydrodynamic +turbulence, J. Fluid Mech. 88, 1 (1978). +[12] S. Servidio, W. H. Matthaeus, and P. Dmitruk, Depres- +sion of Nonlinearity in Decaying Isotropic MHD Turbu- +lence, Physical Review Letters 100, 095005 (2008). +[13] H. Politano and A. Pouquet, Dynamical length scales for +turbulent magnetized flows, Geophysical Research Let- +ters 25, 273 (1998). +[14] K. T. Osman and T. S. Horbury, Multispacecraft mea- +surement of anisotropic correlation functions in solar +wind turbulence, Astrophys. J. 654, L103 (2007). +[15] W. H. Matthaeus and M. L. Goldstein, Measurement of +the rugged invariants of magnetohydrodynamic turbu- +lence in the solar wind, Journal of Geophysical Research +87, 6011 (1982). +[16] G. K. Batchelor, The theory of homogeneous turbulence +(Cambridge university press, 1953). +[17] L. Sorriso-Valvo, +F. Carbone, +S. Perri, +A. Greco, +R. Marino, and R. Bruno, On the statistical properties +of turbulent energy transfer rate in the inner heliosphere, +Solar Physics 293, 10 (2018). +[18] R. +Bandyopadhyay, +L. +Sorriso-Valvo, +A. +Chasapis, +P. Hellinger, W. H. Matthaeus, A. Verdini, S. Landi, + +6 +L. Franci, L. Matteini, B. L. Giles, D. J. Gershman, +T. E. Moore, C. J. Pollock, C. T. Russell, R. J. Strange- +way, R. B. Torbert, and J. L. Burch, In situ observation +of hall magnetohydrodynamic cascade in space plasma, +Phys. Rev. Lett. 124, 225101 (2020). +[19] R. Marino and L. Sorriso-Valvo, Scaling laws for the en- +ergy transfer in space plasma turbulence, Physics Reports +1006, 1 (2023). +[20] Y. Wang, R. Chhiber, S. Adhikari, Y. Yang, R. Bandy- +opadhyay, M. A. Shay, S. Oughton, W. H. Matthaeus, +and M. E. Cuesta, Strategies for Determining the Cas- +cade Rate in MHD Turbulence: +Isotropy, Anisotropy, +and Spacecraft Sampling, Astrophys. J. 937, 76 (2022), +arXiv:2209.00208 [physics.space-ph]. +[21] H. Politano, A. Pouquet, and V. Carbone, Determina- +tion of anomalous exponents of structure functions in +two-dimensional magnetohydrodynamic turbulence, Eu- +rophys. Lett. 43, 516 (1998). +[22] K. T. Osman, M. Wan, W. H. Matthaeus, J. M. Wey- +gand, and S. Dasso, Anisotropic third-moment estimates +of the energy cascade in solar wind turbulence using mul- +tispacecraft data, Phys. Rev. Lett. 107, 165001 (2011). +[23] R. Bandyopadhyay, M. L. Goldstein, B. A. Maruca, +W. +H. +Matthaeus, +T. +N. +Parashar, +D. +Ruffolo, +R. Chhiber, A. Usmanov, A. Chasapis, R. Qudsi, S. D. +Bale, J. W. Bonnell, T. Dudok de Wit, K. Goetz, P. R. +Harvey, R. J. MacDowall, D. M. Malaspina, M. Pulupa, +J. C. Kasper, K. E. Korreck, A. W. Case, M. Stevens, +P. Whittlesey, D. Larson, R. Livi, K. G. Klein, M. Velli, +and N. Raouafi, Enhanced Energy Transfer Rate in +Solar Wind Turbulence Observed near the Sun from +Parker Solar Probe, Astrophys. J. Suppl. 246, 48 (2020), +arXiv:1912.02959 [physics.space-ph]. +[24] M. Dunlop, A. Balogh, K.-H. Glassmeier, and P. Robert, +Four-point cluster application of magnetic field analysis +tools: The curlometer, Journal of Geophysical Research: +Space Physics 107, SMP (2002). +[25] A. Verdini, R. Grappin, P. Hellinger, S. Landi, and W. C. +M¨uller, Anisotropy of third-order structure functions in +mhd turbulence, The Astrophysical Journal 804, 119 +(2015). +[26] R. Bandyopadhyay, A. Chasapis, R. Chhiber, T. N. +Parashar, W. H. Matthaeus, M. A. Shay, B. A. Maruca, +J. L. Burch, T. E. Moore, C. J. Pollock, B. L. Giles, +W. R. Paterson, J. Dorelli, D. J. Gershman, R. B. Tor- +bert, C. T. Russell, and R. J. Strangeway, Incompressive +energy transfer in the earth’s magnetosheath: Magneto- +spheric multiscale observations, The Astrophysical Jour- +nal 866, 106 (2018). +[27] B. A. Maruca, J. A. Agudelo Rueda, R. Bandyopad- +hyay, F. B. Bianco, A. Chasapis, R. Chhiber, H. De- +Weese, W. H. Matthaeus, D. M. Miles, R. A. Qudsi, +M. J. Richardson, S. Servidio, M. A. Shay, D. Sund- +kvist, D. Verscharen, S. K. Vines, J. H. Westlake, and +R. T. Wicks, Magnetore: +Mapping the 3-d magnetic +structure of the solar wind using a large constellation +of nanosatellites, Frontiers in Astronomy and Space Sci- +ences 8, 10.3389/fspas.2021.665885 (2021). + diff --git a/otFPT4oBgHgl3EQf6zWU/content/tmp_files/load_file.txt b/otFPT4oBgHgl3EQf6zWU/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..52b799b2dd630fde69505ae0bbb2995cef118dab --- /dev/null +++ b/otFPT4oBgHgl3EQf6zWU/content/tmp_files/load_file.txt @@ -0,0 +1,579 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf,len=578 +page_content='Multipoint Turbulence Analysis with Helioswarm Francesco Pecora,1 Sergio Servidio,2 Leonardo Primavera,2 Antonella Greco,2 Yan Yang,1 and William H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Matthaeus1 1Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA∗ 2Universit`a della Calabria, Arcavacata di Rende, 87036, IT (Dated: February 1, 2023) Exploration of plasma dynamics in space, including turbulence, is entering a new era of multi- satellite constellation measurements that will determine fundamental properties with unprecedented precision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Familiar but imprecise approximations will need to be abandoned and replaced with more advanced approaches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' We present a preparatory study of the evaluation of second- and third-order statistics, using simultaneous measurements at many points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Here, for specificity, the orbital con- figuration of the NASA Helioswarm mission is employed in conjunction with three-dimensional magnetohydrodynamics numerical simulations of turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The Helioswarm 9-spacecraft constel- lation flies virtually through the turbulence to compare results with the exact numerical statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' We demonstrate novel increment-based techniques for the computation of (1) the multidimensional spectra and (2) the turbulent energy flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' This latter increment-space estimate of the cascade rate, based on the third-order Yaglom-Politano-Pouquet theory, uses numerous increment-space tetrahe- dra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Our investigation reveals that Helioswarm will provide crucial information on the nature of astrophysical turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Introduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='–Guidance from experiments remains a principal driver of progress in revealing the basic physics of turbulence, in spite of the difficulties inherent in di- agnosing complex multiscale turbulent motions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Ad- vances in this unsolved grand challenge problem imme- diately have beneficial impacts on numerous applications in space and astrophysical plasmas as well as geophysi- cal fluids [1, 2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Laboratory turbulence experiments [3, 4] have made great progress by employing numerous probes at multiple spatial positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' In contrast, investigations of space plasma turbulence are typically limited to single spacecraft measurements, with a few notable exceptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' However, current state- of-the-art multispacecraft probes have severe limitations in quantifying interplanetary turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The interspace- craft separations on the Cluster [5] mission are at a single scale, and too large for accurate computation of deriva- tives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The Magnetosphere Multiscale Mission (MMS) [6] probes very small sub-fluid scales, and cannot accurately respond to conditions in the “pristine” solar wind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The solution to these problems is, of course, a larger num- ber of spacecraft, providing true multipoint multiscale measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The upcoming Helioswarm mission [7] heralds several unprecedented advancements: nine space- craft flying in the pristine solar wind, arranged such that the 36 baselines – the separations between any two space- craft – range from a few tens to a thousand kilometers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' This configuration allows computing derivatives with un- rivaled precision and at several different scales centered on the turbulence inertial range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Here, we address the fundamental question of how to utilize such data from a turbulence theory perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Our conclusions impact not only Helioswarm but all future multipoint spacecraft constellations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The present work employs nominal orbital ∗ fpecora@udel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='edu Helioswarm trajectories transferred in numerically gener- ated turbulent fields, mimicking satellite flights through solar wind turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The purpose is to propose novel methods to unambiguously characterize the inertial range of plasma turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' We base our new technique on mul- tipoint increment analysis, extracting information about the spectra and the energy cascade rate of turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Numerical setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='–We model decaying plasma turbu- lence by using magnetohydrodynamics (MHD) simula- tions, with and without mean magnetic field B0 (along the z axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The simulations are carried out through a pseudo-spectral, incompressible, 3D numerical code that integrates the MHD equations in a three-periodic sim- ulation box of 10243 gridpoints, having lengths in each direction equal to 2πL0, where we use classic Alfv´enic units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The code uses a standard 2/3 dealiasing technique [8–10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Both viscosity and resistivity are chosen to be adequately small, namely ν = η = 5 · 10−5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The initial conditions consist of a superposition of fluctuations with random phases in the range of modes peaked at k = 3, with amplitude such that vrms = Brms = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' This initial condition is evolved in time up to the peak of energy dis- sipation rate, which happens after a few Alfv´en times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' At this instant of time, turbulence is in a quasi-steady state [11, 12] and we perform our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Helioswarm trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='–The nine-spacecraft constel- lation orbits the Earth, with a nominal period of two weeks, and with interspacecraft separations roughly rang- ing from 10 to 1000 km.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The nominal phase trajectories projected onto the x-y plane, are shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 1(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The time evolution of the interspacecraft separations rij = |ri−rj|, where i, j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' , 9, is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 1(b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Knowing that the time evolution of the turbulence in the solar wind is much faster than the timescale at which the spacecraft drift with respect to one another (few hours vs days), we can select and fix the separations at a sin- gle time, and then create virtual trajectories within the simulation volume of our MHD turbulence simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='13202v1 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='plasm-ph] 27 Jan 2023 2 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' (a) Nominal phase Helioswarm trajectories projected in the ecliptic plane, with Earth indicated as a blue dot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' (b) Interspacecraft separations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The vertical dashed line indicates one time at which Helioswarm separations are measured and transferred in the simulations (see text.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=') To do this, it is necessary to convert the relative posi- tions of the spacecraft in numerical units to fit in the simulation domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The conversion is made such that the minimal interspacecraft separation is set to be 50 km and then normalized to 10 times the Kolmogorov scale in the simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' This normalization grants that the in- terspacecraft separations lie in the inertial range, as the Kolmogorov scale roughly indicates the smallest scale of the inertial range, and is defined as λK = (ν3/ϵ)1/4 [13] where ν is the kinematic viscosity and ϵ = ⟨ηj2 + νω2⟩ is the total dissipation rate evaluated using the resistiv- ity η, the current density j, and the vorticity ω.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' With these assumptions, the trajectories are parallel lines that are then chosen to have a specified angle relative to the z axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' As the virtual spacecraft motion progresses, the tra- jectories span the simulation box several times as shown by the black lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 2(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The individual trajectories become visible when examined in zoomed-in regions, as shown by the dotted lines in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 2(b), where the shaded colors indicate a region of intense magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' For the analyses that follow, the simulation data is interpolated onto the satellite trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The Helioswarm 9-spacecraft configuration allows dif- ferent strategies for turbulence analyses based on incre- ments, such as δB(x, ℓ) ≡ B(x + ℓ) − B(x), for the magnetic field B, the position x and the spatial lag ℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Particular examples are: (I) evaluation of increments at the fixed separations given by the 36 baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' That is, B(x) = B(ri) and B(x + ℓ) = B(rj), where i, j is any pair of spacecraft and the lag vector is ℓ = rij;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' (II) employing Taylor hypothesis, computing quantities along the 9 individual time series, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=', B(x) = B(ri), B(x + ℓ) = B(ri − Vswδt) and ℓ = −Vswδt;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' (III) a combined scheme employing one spacecraft as a fixed point, and using the Taylor hypothesis, varying the lag relative to the paired partner [14]: B(x) = B(ri), B(x + ℓ) = B(rj − Vswδt) and ℓ = rij − Vswδt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Power spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='–We first carry out an increment-space estimation of the power spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The method relies on the Blackman-Tukey technique estimation of the second- FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' (a) Three-dimensional view of the simulation domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Shaded colors are regions where the magnetic field is more in- tense.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The black oblique lines are the virtual spacecraft tra- jectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' (b) Zoom into a region of very strong magnetic field, where individual spacecraft trajectories can be distinguished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' order structure function [15], after which the magnetic field power spectral density (PSD) is obtained via Fourier transform of the autocorrelation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Except for the total variance, the autocorrelation is readily obtained from the second-order structure function, as described below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' We proceed with the analysis of the magnetic field, but the same procedure can be applied to the den- sity and fluid velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The magnetic field second-order structure function is defined as S2 b (ℓ) = ⟨|B(x) − B(x + ℓ)|2⟩, where the averaging operation ⟨·⟩ is performed over a suitable volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' We have employed the above procedure (structure function, autocorrelation function, and Blackman-Tukey spectrum) to obtain second-order turbulence statistics using strategy III.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' We supplement this technique with repetitive passage through the simulation with varying angular orientations of the trajectories relative to the box.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The latter procedure emulates analyzing solar wind streams with the mean field being oriented in different directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' When the mean field is absent, the procedure gives a more ergodic sampling of turbulence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Generally, we find good correspondence between the methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' For example, the second-order structure functions obtained with strategy I (not shown) produce 36 points nicely scat- tered about the globally computed structure function for the isotropic case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' To populate correlations in a plane of parallel and per- pendicular increments, we generated several different sets of Helioswarm-like trajectories changing the angle with respect to the z axis: When the angle is smaller, more parallel coverage is obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Accordingly, for angles closer to π/2, more perpendicular coverage is realized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' We merged 6 different trajectory inclinations from 20◦ to 70◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The structure function in the perpendicular-parallel plane is shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 3(a, b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The 2D structure func- tions clearly show the effect of a mean field, the contours of the structure function being squashed in the perpen- dicular direction for the anisotropic case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' We can further look at directional properties by sampling the 2D struc- 400 a 103 200 [ueol] km 0 102 200 Analyzed configuration 101 200 200 15 0 400 Oct 15 Nov 15 Dec 15 UTC Dec 2026 x[103km](a) b3 FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' (Top) Structure functions (strategy III) for (a) isotropic and (b) anisotropic simulations in the parallel- perpendicular increment plane.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Dashed colored lines are di- rections along which 1D cuts are collected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The dotted line indicates the correlation length (of the isotropic case).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' (Bot- tom) PSDs obtained from 1D cuts compared with exact PSD obtained from simulation (dashed line), for isotropic (c) and anisotropic (d) cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' ture functions along 1D cuts in different directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' As expected, the 1D cuts in the isotropic case show no differ- ences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' On the other hand, in the anisotropic case, appre- ciable differences arise along different directions relative to the mean field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The directional dependence of the structure function translates directly into the directional anisotropy of the magnetic field power spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Indeed, the structure function and the correlation functions are related as C(ℓ) = Eb − 1 2S2 b (ℓ), where Eb = ⟨δb2⟩ is (twice) the energy density of the magnetic fluctuations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' This link between S2 b and C is important for at least two reasons: (I) the Fourier transform relates the correlation function to the power spectrum, and (II) the structure function has stronger convergence properties than the correlation function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Starting from S2 b , it is possible to recover C, then Fourier transform C and obtain the power spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' However, some care needs to be exercised.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The corre- lation function must be an even function of the lag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' This and formal periodicity properties are prescribed by re- flecting the correlation function about the origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' To avoid spurious oscillations at large lags due to low statis- tical weight, the correlation function is windowed with a cosine function that smooths the far edges gently to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' We zero-pad the correlation function to extend the do- main without adding any further information, with the aesthetic advantage of better-resolving modes to the in- ertial range [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Finally, the Fourier transform of the as- sembled correlation function yields the power spectrum of the magnetic field [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 3, the power spectra computed from the 1D cuts are shown for the (c) isotropic, and (d) anisotropic cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' These are shown together with the exact isotropic spec- trum obtained directly from the full simulation dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Several features can now be noticed: (I) different exten- sion in k between simulation and directional spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' For the latter, larger k’s appear because of a finer sampling of the second-order structure functions when collecting 1D information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Smaller k’s arise based on the total length of the trajectories “time series” that depends on how many times the trajectories sample the simulation domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' (II) In fact, the gray shaded area in panels (c) and (d) identi- fies k values related to separations smaller than the small- est spacecraft separation (that is 10λK).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' (III) The slope in the inertial range is overall consistent between all the different spectra (being isotropic, anisotropic, and exact).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' (IV) In the isotropic case, the spectral modes’ magni- tudes remain nearly constant regardless of the sampling direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' (V) In the anisotropic case, the nearly parallel 10◦ spectrum is of smaller magnitudes than the spectra at more oblique directions, and also has, one may argue, a shorter inertial range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' (VI) In passing, it is interesting to notice that, despite the structure functions not show- ing a neat inertial range (not shown here), their Fourier transforms (the spectra) do.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' This kind of analysis is of fundamental importance in order to predict what can be observed with constellations such as Helioswarm in the solar wind, where the exact spectrum is not available for comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Energy cascade rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='–The energy cascade rate is a fun- damental ingredient of turbulence theory, and below we measure it with a novel technique.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Numerous attempts have been made to estimate this number in space plas- mas [17–19].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' However, the lack of multipoint measure- ments in the appropriate environment or range of scales has made it necessary to rely on various simplifying ap- proximations that may provide potentially unrealistic es- timates (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=', [20]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' In the incompressible regime, the cascade rate ϵ is related to the increments of the Els¨asser variables via the von K´arm´an-Howarth equa- tions ∂ ∂t⟨|δz±|2⟩ = −∇ℓ·⟨δz∓|δz±|2⟩+2ν∇2 ℓ⟨|δz±|2⟩−4ϵ± where, δz±(x, ℓ) = z±(x + ℓ) − z±(x) are the increments of the Els¨asser variables z± = v ± b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Here v and b are the velocity and magnetic fields respectively, and the magnetic field is in Alfv´en speed units.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The averaging operation ⟨·⟩ is performed over a suitably large domain in real space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' These equations are exact for homogeneous turbulence, at any lag ℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' For a large, scale-separated system, the different terms separately dominate at different length-scales: Generally, the time derivative is large at very large scales, the dis- sipative term is large at very small scales, while the non- linear term, also called the Yaglom term, dominates in the intermediate inertial range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Therefore, when one fo- cuses on the inertial range, the full von K´arm´an-Howarth equation reduces to the Yaglom law [21], ∇ℓ · Y± = −4ϵ±, (1) Si 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='50 (b) (n) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='00 一10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='50 10-2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='25 10-1 10- 10 10-1 D10 2 k-5/3 k-5/3 Simulation Simulation 10-3 =10° = 10° = 40° = 40° = 70° = 70° 10-4 101 101 102 102 k k4 that involves only the third-order structure function (or Yaglom flux) Y± = ⟨δz∓|δz±|2⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The dissipation rate is finally given by ϵ = (ϵ+ + ϵ−)/2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' In the pre-Helioswarm era, even this simpler reduced form of the cascade law was relatively inaccessible via spacecraft measurements for the lack of viable multi- point measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Attempts were made with Clus- ter [22] and MMS [23] but these are obviously limited to four points and intrinsically to a single interspacecraft scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Helioswarm [7] introduces a novel configuration of 9 spacecraft that provides 36 baselines, most of which will lie in the inertial range where Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 1 is valid.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' It is im- mediately evident that the available data to solve Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 1 is a steeply increasing function of the number of simulta- neous measurement points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The 36 baselines are geomet- ric lines in the real space and become 36 points in the lag space where the divergence is to be computed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' This means that, in lag space, we have a swarm of 36 points, at each of which we have a value of Y ±.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Implementing FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' (inset) Nine spacecraft (red spheres) provide 36 base- lines (black lines) that correspond to 36 points in lag space (panel a, spheres).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Three possible tetrahedra are highlighted in colors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' (b) Tetrahedron in lag space with the Yaglom flux vectors at its vertices pointing roughly towards the origin (black dot on the left).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Arrow length is ∝ |Y |.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' the new approach, we sort the 36 points in permutations of 4 to form the astonishing number of 58905 tetrahedra (of which, we used 56718).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' To compute the required lag- space divergence, the tetrahedra are subjected to well- tested techniques based on the curlometer approach [24], that have been developed to analyze Cluster and MMS data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' This procedure is explicated in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 4 where the 9 spacecraft are represented in real space (inset) as (red) spheres with the 36 baselines drawn in black.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Panel (a) of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 4 shows the lag space, where the baselines transform into 36 points – represented as spheres –, and 3 sam- ple tetrahedra are color shaded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Note that only strategy I is used here to evaluate increments and only a single realization of the trajectories is employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Panel (b), instead, depicts a tetrahedron in lag space, where at each vertex the Yaglom vector Y = (Y+ + Y−)/2 is represented with length proportional to its magnitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The arrows do, indeed, point roughly to- ward the origin (black dot) with decreasing magnitude moving towards smaller scales in the expected fashion [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' This is expected from the general structure of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 1, from which, for ϵ± ∼ constant, the Yaglom flux is ex- pected to be ∼ ℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' We start by computing Yaglom’s FIG.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Estimations of cascade rate, for isotropic (a) and anisotropic (b) simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Insets show ϵ(ℓ, θ, φ) computed from Yaglom’s law Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' (1) over all grid points, plotted as a function of lag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The maximum value within the inertial range is highlighted with a dashed horizontal line and reported as ϵsim in the legend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Histograms are obtained from computing the divergence using tetrahedra in lag space (see text and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' We discarded values larger than ±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' law, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 1 in the simulation using spherical coordinates and all simulation grid points, to have the exact value as a reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The insets in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 5 show the values of ϵ(ℓ, θ, φ) as a function of the lag;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Panel (a) and (b) are for the isotropic and anisotropic cases, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The variability of ϵ(ℓ, θ, φ) at each lag ℓ, for varying θ and φ (the azimuthal and polar angles in the simulation domain), is indicated by the spread around the mean value (black curve).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' These variations are attributed to inhomogeneities and anisotropies (the latter is evidently more present in the simulation with the mean field).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The maximum of the average curve is identified as the “effec- tive” cascade rate: ϵsim = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='18 and ϵsim = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='13 for the isotropic and anisotropic simulations, respectively, which also indicates the points where the inertial range condi- tions are better attained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The histograms in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 5 represent the values of ϵ mea- sured by calculating the divergence over the tetrahedra in lag space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The effective and averaged values of ϵ are shown as vertical lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The agreement between the cas- cade rate obtained using the tetrahedra with the exact one is excellent as the relative errors are 7% and 15% for the anisotropic and isotropic cases, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Discussion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='– We have shown that sampling data from many spacecraft in a realistic constellation orbit can accurately describe statistics based on increments, in- cluding second and third orders statistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' These cru- cially lead to the detection of anisotropy, accurate in- ertial range spectra estimate, and perhaps most impor- tantly, the evaluation of the turbulence energy transfer rate in the inertial range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' This is accomplished here for the first time using nine-point sampling and nominal He- lioswarm orbits, scale-adjusted to a high-resolution MHD turbulence simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The accurate evaluation of the cascade rate is based on a novel strategy in which the von K´arm´an-Yaglom expression for the cascade rate is Z Axis 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='1 Y Ax 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='05 (a) 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='02 (b) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='06 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='06 U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='040 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='02 foos Z Axis Y_Axis AR04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='05 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='94xis 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='04 + fo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='03 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='0 Z Axis 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='02 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='9%xis 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='01 0 to X Axis o X Axis 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='011 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='01 t 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='02 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='02 +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='03 /0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='03 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='04 X Axis 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='03 /-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='04 t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='05 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='05V 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='05 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='1 ° 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='04 Z Axis 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='02 YAxis 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='08±-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='09 /-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='05 Y Axis 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='02 QO0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='08 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='050.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='15 (8) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='15 <ε>= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='14 F (b) 8000 8sim = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='18 &sim = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='1 Tetrahedra Tetrahedra Grid points Grid points 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='05 6000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='0 10-1 10-2 10-1 counts l 4000 2000 0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='05 solved over the more than 56,000 lag-space tetrahedra provided by the Helioswarm constellation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The statisti- cal agreement between the cascade rate measured using the tetrahedra with that obtained from the exact evalu- ation over the grid points is striking and very promising for the ability of Helioswarm to determine accurate ap- proximations of the solar wind turbulence cascade rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' We expect that improved estimates will be obtained by applying geometric quality factors [24] to the tetrahe- dra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Another detail that can be observed, is that the histogram of ϵ estimates in the anisotropic case reflects the variability of values in different directions where the inertial ranges may have different extensions as shown by the spectra in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Further experience with analysis of cascade rates in simulations [20] will guide refinements of this method, as well as extensions to properly define and obtain directional cascade rates as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Note that the span of scale in the solar wind is much larger than that available in the simulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' However, only the largest virtual spacecraft separations approach or exceed the scales within the inertial range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Since our goal here is to evaluate inertial range statistics, the re- sults are not severely affected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' When applied to the mag- netosheath [26] the range of scales is narrower and an even closer correspondence can be found with the simu- lation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' We note that higher-order polyhedra with vertices > 4 might also be employed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' For this work, we used tetrahedra to exploit well-tested routines that have been validated in Cluster and MMS data [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' The present demonstration provides guidance and confidence concerning the evaluation of critical turbulence quan- tities on the upcoming generation of multispacecraft constellations beyond Helioswarm, including concepts such as MagCon, Plasma Observatory, and Magnetore [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Accurate evaluations of cascade rates directly support theories of dissipation, plasma heating, solar wind acceleration, and cross-scale dynamics in general, which through these missions may well revolutionize our conception of the dynamics in these complex interplane- tary and magnetosphere space plasmas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' ACKNOWLEDGMENTS This research is supported in part by the MMS Theory and Modeling program grant 80NSSC19K0284, the Parker Solar prove Guest Investigator program 80NSSC21K1765, the PUNCH mission through SWRI subcontract N99054DS, and the NSF/DOE program un- der grant AGS-2108834 at the University of Delaware.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' LP acknowledges support by EU FP7 2007-13 through the MATERIA Project (PONa3 00370) and EU Hori- zon 2020 through the STAR 2 Project (PON R&I 2014- 20, PIR01 00008) for running the simulations on the “newton” cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Helioswarm sprites in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 2 courtesy of UNH https://eos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='unh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='edu/helioswarm/mission/ flight-system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Pope, Turbulent Flows (Cambridge University Press, Cambridge, UK, 2000).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [2] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Biskamp, Magnetohydrodynamic turbulence (Cam- bridge University Press, 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [3] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Comte-Bellot and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Corrsin, Simple Eulerian time correlation of full- and narrow-band velocity signals in grid-generated, ‘isotropic’ turbulence, Journal of Fluid Mechanics 48, 273 (1971).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [4] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Yamada, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Ren, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Ji, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Breslau, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Gerhardt, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Kulsrud, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Kuritsyn, Experimental study of two- fluid effects on magnetic reconnection in a laboratory plasma with variable collisionality, Physics of Plasmas 13, 052119 (2006).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [5] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Credland, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Mecke, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Ellwood, The cluster mis- sion: Esa’s spacefleet to the magnetosphere, Space Sci- ence Reviews 79, 33 (1997).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [6] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Burch, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Moore, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Torbert, and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Giles, Magnetospheric multiscale overview and science objec- tives, Space Science Reviews 199, 5 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [7] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Spence, HelioSwarm: Unlocking the Multiscale Mysteries of Weakly-Collisional Magnetized Plasma Tur- bulence and Ion Heating, in AGU Fall Meeting Abstracts, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 2019 (2019) pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' SH11B–04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [8] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Orszag, On the elimination of aliasing in finite- difference schemes by filtering high-wavenumber compo- nents, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Atmos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Sci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 28, 1074 (1971).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [9] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Orszag, Comparison of pseudospectral and spectral approximation, Stud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Applied Math.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 51, 253 (1972).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [10] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Orszag and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Tang, Small-scale structure of two-dimensional magnetohydrodynamic turbulence, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Fluid Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 90, 129 (1979).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [11] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Pouquet, On two-dimensional magnetohydrodynamic turbulence, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Fluid Mech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 88, 1 (1978).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [12] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Servidio, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Matthaeus, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Dmitruk, Depres- sion of Nonlinearity in Decaying Isotropic MHD Turbu- lence, Physical Review Letters 100, 095005 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [13] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Politano and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Pouquet, Dynamical length scales for turbulent magnetized flows, Geophysical Research Let- ters 25, 273 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [14] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Osman and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Horbury, Multispacecraft mea- surement of anisotropic correlation functions in solar wind turbulence, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 654, L103 (2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [15] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Matthaeus and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Goldstein, Measurement of the rugged invariants of magnetohydrodynamic turbu- lence in the solar wind, Journal of Geophysical Research 87, 6011 (1982).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [16] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Batchelor, The theory of homogeneous turbulence (Cambridge university press, 1953).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [17] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Sorriso-Valvo, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Carbone, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Perri, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Greco, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Marino, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Bruno, On the statistical properties of turbulent energy transfer rate in the inner heliosphere, Solar Physics 293, 10 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [18] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Bandyopadhyay, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Sorriso-Valvo, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Chasapis, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Hellinger, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Matthaeus, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Verdini, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Landi, 6 L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Franci, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Matteini, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Giles, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Gershman, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Moore, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Pollock, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Russell, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Strange- way, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Torbert, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Burch, In situ observation of hall magnetohydrodynamic cascade in space plasma, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 124, 225101 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [19] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Marino and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Sorriso-Valvo, Scaling laws for the en- ergy transfer in space plasma turbulence, Physics Reports 1006, 1 (2023).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [20] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Wang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Chhiber, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Adhikari, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Yang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Bandy- opadhyay, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Shay, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Oughton, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Matthaeus, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Cuesta, Strategies for Determining the Cas- cade Rate in MHD Turbulence: Isotropy, Anisotropy, and Spacecraft Sampling, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 937, 76 (2022), arXiv:2209.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='00208 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='space-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [21] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Politano, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Pouquet, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Carbone, Determina- tion of anomalous exponents of structure functions in two-dimensional magnetohydrodynamic turbulence, Eu- rophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 43, 516 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [22] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Osman, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Wan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Matthaeus, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Wey- gand, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Dasso, Anisotropic third-moment estimates of the energy cascade in solar wind turbulence using mul- tispacecraft data, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Lett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 107, 165001 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [23] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Bandyopadhyay, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Goldstein, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Maruca, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Matthaeus, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Parashar, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Ruffolo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Chhiber, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Usmanov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Chasapis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Qudsi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Bale, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Bonnell, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Dudok de Wit, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Goetz, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Harvey, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' MacDowall, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Malaspina, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Pulupa, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Kasper, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Korreck, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Case, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Stevens, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Whittlesey, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Larson, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Livi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Klein, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Velli, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Raouafi, Enhanced Energy Transfer Rate in Solar Wind Turbulence Observed near the Sun from Parker Solar Probe, Astrophys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Suppl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' 246, 48 (2020), arXiv:1912.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='02959 [physics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='space-ph].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [24] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Dunlop, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Balogh, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Glassmeier, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Robert, Four-point cluster application of magnetic field analysis tools: The curlometer, Journal of Geophysical Research: Space Physics 107, SMP (2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [25] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Verdini, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Grappin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Hellinger, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Landi, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' M¨uller, Anisotropy of third-order structure functions in mhd turbulence, The Astrophysical Journal 804, 119 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [26] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Bandyopadhyay, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Chasapis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Chhiber, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Parashar, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Matthaeus, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Shay, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Maruca, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Burch, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Moore, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Pollock, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Giles, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Paterson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Dorelli, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Gershman, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Tor- bert, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Russell, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Strangeway, Incompressive energy transfer in the earth’s magnetosheath: Magneto- spheric multiscale observations, The Astrophysical Jour- nal 866, 106 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' [27] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Maruca, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Agudelo Rueda, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Bandyopad- hyay, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Bianco, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Chasapis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Chhiber, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' De- Weese, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Matthaeus, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Miles, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Qudsi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Richardson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Servidio, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Shay, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Sund- kvist, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Verscharen, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Vines, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Westlake, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content=' Wicks, Magnetore: Mapping the 3-d magnetic structure of the solar wind using a large constellation of nanosatellites, Frontiers in Astronomy and Space Sci- ences 8, 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='3389/fspas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} +page_content='665885 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/otFPT4oBgHgl3EQf6zWU/content/2301.13202v1.pdf'} diff --git a/pdAzT4oBgHgl3EQfAfrM/content/tmp_files/2301.00928v1.pdf.txt b/pdAzT4oBgHgl3EQfAfrM/content/tmp_files/2301.00928v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..cdc86466aa306b409ad3b42270d14cfd580ea390 --- /dev/null +++ b/pdAzT4oBgHgl3EQfAfrM/content/tmp_files/2301.00928v1.pdf.txt @@ -0,0 +1,6078 @@ +AI-Driven Confidential Computing across Edge-to-Cloud Continuum +Sm Zobaed +A Dissertation presented to the Graduate Faculty +in Partial Fulfillment of the Requirements for the Degree +Doctor of Philosophy +University of Louisiana at Lafayette +Fall 2022 +APPROVED: +Mohsen Amini Salehi, Chair +The Center for Advanced Computer Studies +Sheng Chen +The Center for Advanced Computer Studies +Raju Gottumukkala +Informatics Research Institute +Xiali Hei +The Center for Advanced Computer Studies +Li Chen +The Center for Advanced Computer Studies +Mary Farmer-Kaiser +Dean of the Graduate School +arXiv:2301.00928v1 [cs.DC] 3 Jan 2023 + +© Sm Zobaed +2022 +All Rights Reserved + +Abstract +With the meteoric growth of technology, both individuals and organizations +are widely adopting cloud services to mitigate the burdens of maintenance. Despite +its scalability and ease of use, many potential cloud users who own sensitive data +refrain from fully utilizing cloud services due to valid confidentiality concerns. +Maintaining data confidentiality for data at rest and in transit has been widely +explored but data remains vulnerable in the cloud while it is in use. This +vulnerability is further elevated once the scope of computing spans across the +edge-to-cloud continuum. From the notion of safeguarding, confidential data needs +to be encrypted while offloading from users’ premises. Although adopting user-side +encryption ensures data confidentiality, it limits the ability to data processing. +Subsequently, we are limited to performing only low-level operations (e.g., string +pattern matching). Accordingly, the goal of this dissertation is to enable data +confidentiality by adopting confidential computing across the continuum. Towards +this goal, one approach we explore is to separate the intelligence aspect of data +processing from the pattern-matching aspect. We present our approach to make +confidential data clustering on the cloud, and then develop confidential search +service across edge-to-cloud for unstructured text data. Our proposed clustering +solution named ClusPr, performs topic-based clustering for static and dynamic +datasets that improves cluster coherency up to 30%-to-60% when compared with +other encryption-based clustering techniques. Our trusted enterprise search service +named SAED, provides context-aware and personalized semantic search over +iii + +confidential data across the continuum. Evaluation results, verified by human users, +demonstrates that SAED can improve the relevancy of the retrieved search results +by ≈ 24% for plain-text and 75% for encrypted datasets. We realized that enabling +confidential computing across edge-to-cloud requires major contribution from the +edge tiers particularly to run multiple Deep Learning (DL) services concurrently. +This raises memory contention on the edge tier. To resolve the contention, we +propose Edge-MultiAI framework to manage Neural Network (NN) models of DL +applications such that it can meet the latency constraints of the DL applications +without compromising inference accuracy. Our evaluation confirms that +Edge-MultiAI can stimulate the degree of multi-tenancy by 2× on the edge tier. +iv + +To my Creator, the Almighty Allah (SWT), my master prophet Muhammad (pbuh), +who taught us the purpose of life, my parents, Md Mazharul Islam and Jubaida +Naznin, who never stop providing support in countless ways, my enlighteners, Md +Fazle Rabby, Md Sazib Hasan who have provided enormous inspiration regardless of +the rainy or shiny days throughout the journey with the fullest and truest attention, +my pioneer since childhood, Jahid Md Mahabub Islam, who has been acting as a +LiDAR through the sea of darkness, my asymptotic remembrance, Farzana Hasan, +whom I am forever grateful, my mentors, Muhammad Usama Islam, Md Istiaq +Hossain, Jubair Yusuf, Farhan Tanvir, my only sister, Mantika Mahbuba, and to all +my friends and beloved ones. + +Acknowledgments +I sincerely thank my supervisor, Dr. Mohsen Amini Salehi, for his constant +encouragement since the inception of the journey. He has provided a plethora of +guidance, support, and cooperation. Thanks to my dissertation committee, Dr. +Raju Gottumukukkala, Dr. Li Chen, Dr. Xiali Hei, and Dr. Sheng Chen. Thanks to +Jason Woodworth, Razin Farhan Hussain, Davood Ghatreh Samani, and Chavit +Denninart for their assistance in the work of this dissertation. A special thanks goes +to Ali Mokhtari for his collaboration in the latest work. Finally, thanks goes to the +Center for Advanced Computer Studies and the Graduate School at the University +of Louisiana at Lafayette for their support and guidance. +vi + +Table of Contents +Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii +Dedication +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v +Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi +List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi +List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii +Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 +1.1 +Motivation: Data Confidentiality in the Current Age +. . . . . . . . 1 +1.2 +Essence of Maintaining Data Confidentiality +. . . . . . . . . . . . . . . . 1 +1.3 +Confidential Computing +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 +1.3.1 +Basic Definition +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 +1.3.2 +Confidential Computing across Edge-to-Cloud +Continuum +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 +1.3.3 +Confidential Computing of Unstructured data +. . . . . . . . 6 +1.4 +Research Problems and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . 8 +1.5 +Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 +1.6 +Dissertation Organization +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 +Chapter 2: Background and Literature Study . . . . . . . . . . . . . . . . . . . . . . 14 +2.1 +Background +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 +2.1.1 +Trusted Execution Environment +. . . . . . . . . . . . . . . . . . . 14 +2.1.2 +Trustworthy Infrastructure for Confidential +Computing +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 +2.1.3 +Cloud-based Enterprise Search Services over +Unstructured Text Data +. . . . . . . . . . . . . . . . . . . . . . . . . . . 18 +2.1.4 +Emergence of Edge-to-Cloud Continuum +. . . . . . . . . . . 19 +2.1.5 +Machine/Deep Learning for Unstructured +Data-driven Applications +. . . . . . . . . . . . . . . . . . . . . . . . . 20 +2.1.6 +Edge Multi-Tenancy for Latency-Sensitive +Processing +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 +2.2 +Prior Literature for Confidential Computing for +Unstructured Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 +2.2.1 +Privacy-preserving Unstructured Data Clustering +Schemes +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 +2.2.2 +Searchable Encryption and Encrypted Index +. . . . . . . . 25 +vii + +2.2.3 +Privacy-Preserving Cloud-based Search Systems +. . . . . 27 +2.2.4 +Edge Computing for Privacy-preserving +Unstructured Data Processing +. . . . . . . . . . . . . . . . . . . . . 30 +2.3 +Prior Literature on Multi-Tenant AI-based Executions on +Edge +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 +2.3.1 +Edge AI +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 +2.3.2 +Multi-tenant Execution on Edge +. . . . . . . . . . . . . . . . . . . 31 +2.3.3 +DNN Model Compression +. . . . . . . . . . . . . . . . . . . . . . . . . 32 +2.3.4 +Warm-Start vs Cold-Start DL Inference +. . . . . . . . . . . . 34 +2.4 +Summary and Positioning of this Dissertation +. . . . . . . . . . . . . 34 +Chapter 3: Privacy-Preserving Clustering for Unstructured Cloud +Data +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 +3.1 +Overview +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 +3.2 +Problem Statement +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 +3.3 +Positioning of the Proposed Clustering Works +. . . . . . . . . . . . . 37 +3.4 +Architecture to Facilitate Clustering in Secure Search +System +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 +3.4.1 +Architecture: ClustCrypt +. . . . . . . . . . . . . . . . . . . . . . . . . . 38 +3.4.2 +Architecture: ClusPr +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 +3.5 +ClustCrypt: Privacy-preserving Clustering Scheme for +Static Unstructured Data +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 +3.5.1 +Estimating the Number of Clusters for Static +Datasets +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 +3.5.2 +Determining Clusters’ Centers +. . . . . . . . . . . . . . . . . . . . 52 +3.5.3 +Clustering Tokens +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 +3.6 +S-ClusPr: Privacy-preserving Clustering Scheme For Static +Unstructured Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 +3.6.1 +Center Selection +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 +3.6.2 +Distributing Encrypted Tokens Across Clusters +. . . . . 59 +3.6.3 +Pruning Clusters to Expedite the Search Operation +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 +3.7 +Privacy-preserving Clustering Scheme For Dynamic +Unstructured datasets +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 +3.7.1 +Overview +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 +3.7.2 +Semi-Dynamic Data Clustering Scheme +(SD-ClusPr) +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 +3.7.3 +Fully-Dynamic Data Clustering Scheme +(FD-ClusPr) +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 +3.8 +Security Analysis of the Proposed Clustering Works +. . . . . . . . 69 +viii + +3.9 +Performance Evaluation of Clustering +. . . . . . . . . . . . . . . . . . . . . 73 +3.9.1 +Experimental Setup +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 +3.9.2 +Evaluation Metrics and Baselines from Prior +Works +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 +3.9.3 +Evaluation Results +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 +3.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 +Chapter 4: Edge-Based Intelligence for Privacy-Preserving +Enterprise Search on the Cloud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 +4.1 +Overview +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 +4.2 +Problem Statement +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 +4.3 +SAED: Smart Edge-Leveraged Enterprise Search System +. . . . 94 +4.3.1 +Architectural Overview +. . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 +4.3.2 +Query Context Identification +. . . . . . . . . . . . . . . . . . . . . . 96 +4.3.3 +Query Expansion Unit +. . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 +4.3.4 +User Interest Detection +. . . . . . . . . . . . . . . . . . . . . . . . . . 100 +4.3.5 +Weighting Unit +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 +4.3.6 +Ranking Unit +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 +4.4 +SAED As a Pluggable Module Enterprise Search +Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 +4.5 +Performance Evaluation of SAED . . . . . . . . . . . . . . . . . . . . . . . . 108 +4.5.1 +Experimental Set up +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 +4.5.2 +Benchmark Queries +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 +4.5.3 +Evaluation Metrics +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 +4.5.4 +Evaluating Search Relevancy +. . . . . . . . . . . . . . . . . . . . . 111 +4.5.5 +Relevancy of Privacy-Preserving Enterprise Search +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 +4.5.6 +Discussion of the Relevancy Results +. . . . . . . . . . . . . . 115 +4.5.7 +Evaluating the Search Time +. . . . . . . . . . . . . . . . . . . . . . 116 +4.6 +Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 +Chapter 5: Multi-Tenancy of Latency-Sensitive Deep Learning +Applications on Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 +5.1 +Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 +5.2 +Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 +5.3 +Solution Statement and Contributions . . . . . . . . . . . . . . . . . . . . 125 +5.4 +Architectural Overview & System Design of Edge-MultiAI . . . 126 +5.5 +Heuristics to Manage Models of Multi-tenant Applications . . . 128 +5.5.1 +Overview +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 +ix + +5.5.2 +Policy 1: Largest-First Model Eviction (LFE) +. . . . . . 131 +5.5.3 +Policy 2: Best-Fit Model Eviction (BFE) +. . . . . . . . . . 132 +5.5.4 +Policy 3: Warm-Start-aware Best-Fit Model +Eviction (WS-BFE) +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 +5.5.5 +Policy 4: Intelligent Warm-Start-aware Best-Fit +Eviction (iWS-BFE) +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 +5.6 +Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 +5.6.1 +Experimental Setup and Evaluation Metrics +. . . . . . . 137 +5.6.2 +Impact of Edge-MultiAI on the Degree of +Multi-tenancy +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 +5.6.3 +Impact of the Eviction Policies on the Cold-Start +Inference +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 +5.6.4 +Impact of the Eviction Policies on the Inference +Accuracy +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 +5.6.5 +Bi-Objective Analysis of NN Model Eviction +Policies +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 +5.6.6 +Analyzing Robustness against Uncertainties +. . . . . . . 144 +5.6.7 +Evaluating the Fairness of NN Model Eviction +Policies +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 +5.7 +Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 +Chapter 6: Conclusion and Future Research Directions +. . . . . . . . . . . 149 +6.1 +Discussion +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 +6.2 +Future Research Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 +6.2.1 +Hierarchical Clustering of unstructured Data +. . . . . . 151 +6.2.2 +Building Classifier from the Encrypted Clusters +. . . . 152 +6.2.3 +Introducing Elasticity in Confidential Search +. . . . . . 152 +6.2.4 +Adding Energy in Model Management Schemes +. . . . 153 +6.2.5 +Cloud Offloading for Latency-tolerant Applications +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 +Bibliography +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 +Biographical Sketch +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 +x + +List of Tables +Table 3.1. +Summary of the existing privacy-preserving clustering +approaches and positioning our proposed works (ClustCrypt and +ClusPr) with respect to them. +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 +Table 3.2. +Token-Document Frequency Matrix A, built based on the +index structure +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 +Table 3.3. +Normalized Token-Document matrix N +. . . . . . . . . . . . . . . . . . 47 +Table 3.4. +Matrix R is built based on normalized matrix N to +represent the importance of each token across all documents . . . . . . . . 48 +Table 3.5. +Matrix S is built from N to represent the importance of +each document with respect to each token +. . . . . . . . . . . . . . . . . . . . . . 49 +Table 3.6. +Cluster decision matrix Q is built based on the +multiplication of R and S matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 +Table 3.7. +Calinski-Harabasz Index for the datasets. +. . . . . . . . . . . . . . . . 81 +Table 3.8. +Benchmark queries for each one of the studied datasets. +. . . . . . . . 86 +Table 4.1. +Benchmark search queries developed for the RFC and BBC +datasets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 +Table 4.2. +Comparing the mean F-1 and the mean TSAP@10 scores +obtained from SAED-plugged enterprise search systems versus their +original forms. The highest resulted scores are shown in bold font. . . . . . . 115 +Table 5.1. +Load time, inference time, and accuracy of popular NN +models individually running on Samsung Galaxy S20+ as the edge +server. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 +Table 5.2. +Application-specific models with different precision variants +that are experimented. +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 +xi + +List of Figures +Figure 1.1. +High-level workflow diagram of performing confidential +computing on an edge-cloud system. The bottom arrow indicates +the degree of trust across the continuum. . . . . . . . . . . . . . . . . . . . . . . . . 5 +Figure 1.2. +A high-level diagram of user-edge-cloud based three-tier +architecture to facilitate smart and confidential enterprise search +service. +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 +Figure 1.3. +Interrelationship between chapters and related +contribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 +Figure 2.1. +High-level architectural overview of TEE building blocks. . . . . 16 +Figure 2.2. +A taxonomy of the scopes of confidential computing. . . . . . . . 17 +Figure 2.3. +Taxonomy of different types of search over encrypted big +data in the cloud. +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 +Figure 3.1. +High-level two-tiered (client-cloud) Search System +Architecture Integrating ClustCrypt Approach. +. . . . . . . . . . . . . . . . . . 40 +Figure 3.2. +Overview of the context where ClusPr is deployed in a +three-tier architecture (of client, edge, and cloud) to facilitate a +secure cloud-based search service. The edge tier is assumed to be on +the user premises and trusted. It is used to ease the computational +overheads imposed by privacy and clustering related processes. +. . . . . . 43 +Figure 3.3. +A bipartite graph representing the relatedness among centers +and remaining tokens. The weight of each edge represents the relatedness +of a token and a center. Solid lines show centers that offer the maximum +relatedness for a token. +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 +Figure 3.4. +Silhouette Coefficient (SC) metric for each dataset. The results +are obtained from S-ClusPr, HK-means++, ClustCrypt (that are +encrypted-based clustering schemes), W2V-Kmeans, and WordNet +clustering schemes (that operate on plain-text tokens). +. . . . . . . . . . . . . . 78 +Figure 3.5. +Davies-Bouldin Index (DI) for each dataset using different +clustering schemes. +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 +xii + +Figure 3.6. +Cluster coherency for each dataset. +. . . . . . . . . . . . . . . . . . . . . . 80 +Figure 3.7. +Comparing the impact of clustering using S-ClusPr against +original clustering of S3BD for the studied datasets. +. . . . . . . . . . . . . . . . . 84 +Figure 3.8. +Comparing the relevancy of search results using S-ClusPr vs +original S3BD clustering in BBC dataset. The value of relevancy is +calculated based on TSAP@10 scoring metric. +. . . . . . . . . . . . . . . . . . . . . 85 +Figure 3.9. +Search time of S3BD when S-ClusPr is used for clustering +versus when the original S3BD clustering is used. +. . . . . . . . . . . . . . . . . . . 88 +Figure 3.10. Clusters’ coherency for different updates of the three +studied datasets when SD-ClusPr is applied with and without +re-clustering option. +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 +Figure 4.1. +Architectural overview of the SAED system within edge +tier and as part of the three-tier enterprise search service. SAED +provides semantic search via identifying the query context and +combining that with the user’s interests. Then, Query Expansion +and Weighting unit of SAED, respectively, incorporate the semantic +and assure the relevancy of the results. Solid and dashed lines +indicate the interactions from user to the cloud tier and from the +cloud tier to the user respectively. +. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 +Figure 4.2. +Comparing TSAP@10 scores of SAED+S3BD and S3BD +systems. Horizontal axes show the benchmark queries. +. . . . . . . . . . . 112 +Figure 4.3. +Comparing TSAP@10 scores obtained from SAED+Kendra +versus AWS Kendra in searching benchmark queries. . . . . . . . . . . . . . 112 +Figure 4.4. +Comparing TSAP@10 scores obtained from SAED+Kendra +vs AWS Kendra systems in the encrypted domain. . . . . . . . . . . . . . . . 113 +Figure 4.5. +Search time comparison among S3BD, Kendra, +SAED+S3BD, and SAED+Kendra systems. +. . . . . . . . . . . . . . . . . . . 117 +Figure 5.1. +Bird-eye view of SmartSight, an IoT-based system that +continuously receives various inputs from the smartglass (IoT +device) sensors, and processes them via multi-tenant DL +applications running on the edge server. . . . . . . . . . . . . . . . . . . . . . . . 120 +xiii + +Figure 5.2. +Architectural overview of the Edge-MultiAI framework with +three tiers: Application, NN Model Manager, and Memory. . . . . . . . . . . . 126 +Figure 5.3. +A sample scenario of inference requests for five +multi-tenant applications, namely A1 to A5. Each pulse represents +the time window within which an inference request is expected. +Solid lines expresses the event that has already happened and +dashed lines after “now” are the request predictions. +. . . . . . . . . . . . . 130 +Figure 5.4. +The impact of Edge-MultiAI and its iWS-BFE eviction +policy on satisfying the requested multi-tenancy. The large graph +represents the summative analysis via increasing the mean of +multi-tenancy requested in the horizontal axis, and showing the +percentage of requests that were satisfied in the vertical axis. For +each case, the smaller graph more granularly represents the number +of concurrent requests issued and fulfilled during the simulation +time. +. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 +Figure 5.5. +Measuring the percentage of cold-start inferences of +multi-tenant applications resulted from the proposed eviction +policies. The horizontal axis shows the deviation between predicted +and actual inference request times. . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 +Figure 5.6. +Measuring the normalized inference accuracy of +applications resulted from employing the different eviction policies. . . . 141 +Figure 5.7. +Bi-objective analysis of the different model selection policies. +. . . 143 +Figure 5.8. +Robustness of the system against uncertainty in the +prediction of inference requests. +. . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 +Figure 5.9. +The percentage of cold-start inferences using different NN +model eviction policies versus no policy. . . . . . . . . . . . . . . . . . . . . . . . 146 +Figure 5.10. The inference accuracy obtained from the different policies. +The “maximum” is the benchmark, showing the accuracy of the +highest-precision model for each application. +. . . . . . . . . . . . . . . . . . . 147 +xiv + +Chapter 1: +Introduction +1.1 Motivation: Data Confidentiality in the Current Age +More than half of the world’s population is now connected to the internet +thanks to the proliferation of information and communication technologies that have +shaped today’s digital world. The expeditious growth of digitalization has been +producing a massive volume of data in various forms. It is estimated that every day +2.5 exabytes of data are being generated in which, over 80% of the data is in +unstructured (e.g., audio, streaming, text) form [1]. Data can range widely from a +person’s first and last name to sensitive (a.k.a. confidential) information such as +biometric information, law-enforcement records, healthcare reports, and so on. Such +confidential data must always be safeguarded to prevent unauthorized access. As an +example, most of the current smartphones are featured with biometric-based +security protocol and so, they retain biometric data for unlocking the device after +ensuring proper authorization. If this biometric information is compromised as a +result of a data breach, it could assist criminals in stealing identities, forging +documents, and committing crimes. +1.2 Essence of Maintaining Data Confidentiality +Maintaining data confidentiality while data is stored either on-premises +denoted as (data at rest) is a widely known problem with numerous established +encryption solutions [2, 3, 4, 5]. On another front, solutions like transport layer +security (TLS) protocol are globally adopted to tackle the challenge of maintaining +data confidentiality during node-to-node transmission (a.k.a. data at transit). +1 + +Another state of data that needs to be protected is known as data in use that refers +to preserving data confidentiality and security while it is being accessed and +processed by users. Although adopting an encryption technique can provide security +assurance while data is stored or transmitted, it does not guarantee data privacy +when the data is being used in memory. Compared to other two states, data is most +vulnerable during computing (i.e., when it is in use). The degree of data +vulnerability is further elevated when owners of confidential data are either +individuals or institutions that rely on cloud services for their storage demands. +Cloud providers (e.g., AWS, Azure, Google cloud) have come forward +offering various services for large-scale data storing and processing, however, +confidential data owners are hesitant to adopt cloud services due to the valid +data-privacy concerns [3, 6] on the cloud data centers. In fact, cloud adoption +increases the risks associated with ubiquitous access to the data. In fact, they +provide larger attack surface that can be exploited by intruders. That is why clouds +have been the target platform for numerous recent privacy violations incidents +[7, 8]. In one notable incident, confidential information of over three billion Yahoo +users were exposed [9]. In another incident, information of over 14 million Verizon +customer accounts were exposed from the company’s cloud system [10]. +Considering these incidents, currently, a large spectrum of applications +ranging from personalized healthcare, search, archives, and finance to social network +(e.g., Twitter, Facebook) and IoT industries are under similar cloud-based data +breaching threats [7]. Even if cloud providers can offer strict security control against +2 + +external threats, subscribers dealing with sensitive content are still concerned, +hence, cannot fully embrace cloud services due to potential of insider attacks. As +such, securing confidential data processing both within and across a wide range of +systems– from user devices to clouds and even multi-cloud environments– that is not +fully controlled by the data owner is the pressing need of the IT industry globally. +1.3 Confidential Computing +1.3.1 Basic Definition +There are numerous solutions to ensure data confidentiality for data at rest +and in transit. However, preserving confidentiality of data in use remains an open +problem that needs further attention. In this regard, the idea of confidential +computing has emerged over the recent years that has given birth to +hardware-enforced trusted execution environment (TEE) systems for secure +computing (e.g., data processing) without compromising data privacy. TEE allows +user-level code to allocate private regions of memory, called enclaves to +confidentially process data without trusting operating system or hypervisors [11, 12]. +Hence, it prevents unauthorized access or modification of applications and data +while they are “in use”. By that means, confidential computing enhances the data +security assurances. Recently, the use cases of confidential computing are getting +popular both in industry and academia, and the total market of the concept is +expected to grow at least 26× over the next five years [13]. +1.3.2 Confidential Computing across Edge-to-Cloud Continuum +Adoption of cloud services is virtually unavoidable to successfully store and +3 + +process large volume of data; nevertheless, due to simultaneous threats arriving +from both within and outside the cloud systems, confidential data owner cannot put +their faith in the cloud and liberally utilize its services. Accordingly, the goal of +confidential computing on the cloud is defined as to provide the users with the secure +access to third-party cloud computing services in a public domain. However, apart +from the security aspect, due to their centralized nature, clouds also suffer from +high communication latency that can be detrimental for many of the IoT-based +solutions that have latency constraints [14, 15, 16]. That is the reason for the +emergence of a new computing paradigm over the past few years that goes beyond +conventional cloud systems and encompasses a continuum of computing tiers—from +the device tier to edge, fog, and the cloud [14, 17, 15, 16]. +The device-to-cloud continuum increases the vulnerability surface beyond the +cloud, hence, confidential computing solutions have to be expanded across the entire +continuum to enable integrity of the IoT-based systems. Figure 1.1, represents a +computing continuum with applications span across the user-device to edge and +cloud. The data generated by the user is first pre-processed on the device-tier (e.g., +IoT devices); Then, it is processed by the services on the edge and cloud tiers, +depending on the on the low-latency and resources demands. +In our vision, confidential computing across edge-to-cloud continuum is +defined as protecting the integrity and confidentiality of the users’ data while are in +use by the applications span across the continuum. One challenge in providing +confidential computing to across the continuum is that both the device tier (e.g., +4 + +Figure 1.1. High-level workflow diagram of performing confidential computing on +an edge-cloud system. The bottom arrow indicates the degree of trust across the +continuum. +Storage +Computing +Cloud +HDD +SSD +Visualization +Machine Learning +Device +Edge +Services +Low-latency +services +Computing +Trust +UAV [18] and smartglasses [19]) and the edge tier (e.g., smartphones, companion +devices), often, are resource- and energy-limited and fall short in executing trusted +applications needed for confidential computing. Trustworthiness throughout the +continuum is another challenge that must be overcome. This is due to the fact that +as soon as data is transited away from the user’s end, the vulnerability surface +expands (Figure 1.1), and as a result, the degree of trust falls as data is sent to edge +and cloud tiers. In addition, various encryption techniques such as client side +encryption [20] are adopted to encrypt data at user-premise, thereby, ensure data +confidentiality while utilizing any cloud services. This is because, in this case, +clouds providers are not capable of decrypting the data. The inability to decrypt +data, however, prevents accessing the data. It is these challenges that we aim at +addressing in this dissertation. Specifically, this dissertation investigates ways to +5 + +enable confidential computing across edge-cloud while considering (a) the +trustworthiness level of each tier in the continuum; and (b) the low-latency +constraints of the applications. +1.3.3 Confidential Computing of Unstructured data +An organization with a massive volume of confidential unstructured +text-based data desires a trusted application that is executed on confidential +computing platform to provide secure semantic searchability over the data in +latency-sensitive manner. One instance of such organization is a law enforcement +agency with encrypted crime report data, with officers who would require to search +over the reports using their handheld devices while at the office or on the move in +low-latency. In the context of confidential unstructured data processing, various +searchable encryption systems (e.g., [21, 22, 23, 24]) have been developed to enable +secure search ability over the encrypted data. Upon using encrypted data, such +systems build an encrypted index, which is then traversed against a search query at +the search time to discover relevant documents. +Figure 1.2. A high-level diagram of user-edge-cloud based three-tier architecture to +facilitate smart and confidential enterprise search service. +Edge +User +Cloud +Compute +Storage +Enterprise Search + Service +~~ +~~ +SAED +Searching exhaustively over the whole index for a given search query +6 + +prohibits the low-latency constraint of the search operation. Therefore, index +partitioning (a.k.a. clustering) is required to prune the search space so that search +can be performed over a pruned index with minimal overhead. Clustering is one of +the crucial data analytics methods that are commonly used to group datapoints +based on their shared attributes. Therefore, upon applying clustering on the search +index, we can prune it into multiple subsets that can improve search time overhead +in orders of magnitudes [1, 3]. +It is possible that the user (e.g., law enforcement officers) do not remember +the specific keywords that are included in the documents they are looking for. +Hence, they need to retrieve documents semantically and contextually related to +their given search query. As example, if a officer searches for “robbery”, he/she can +also be interested in finding documents about “mugging”, “theft”, or “break in”. In +addition, since the officer performs the searches on their limited resourceful +handheld devices when he/she is on the move, the solution should incur a minimal +processing overhead and scale well to massive amount of unstructured text data. To +this end, a robust and secure enterprise search service in the form of a trusted +application is the need of the hour to search semantically over the encrypted +confidential data. In Figure 1.2, a high-level architecture of secure enterprise search +service is depicted. Such service can provide the secure search intelligence utilizing +the on-premises edge resources. The high-end storage and compute resources on the +cloud tier are utilized by the existing search systems to exhaustively carry out +pattern matching on the entire dataset. +7 + +1.4 Research Problems and Objectives +With the aim of facilitating confidential computing across edge-to-cloud +continuum, in this dissertation, we address the following research problems: +1. How to develop a trusted application to optimally, scalably, and securely +cluster keywords in an encrypted unstructured dataset? +2. How to cluster the data when there is dynamism in the dataset meaning that +the contents are being added to or removed from? +3. How to enable secure semantic search over encrypted data with minimum +overhead? +4. How to develop a trustworthy robust encrypted enterprise search service? +5. How to manage NN models of trustworthy DL applications to stimulate their +concurrent executions without compromising their inference accuracy? +1.5 Contributions +In light of the research topics outlined in the preceding section, this +dissertation makes the following significant contributions: +1. Proposing two trusted applications to enable confidential clustering of +encrypted unstructured data in the cloud: (1) ClustCrypt- cloud-only +architecture and (2) ClusPr- edge-cloud architecture. While ClustCrypt can +estimate the suitable number of clusters (K) and then cluster encrypted static +data only, by incorporating edge, ClusPr can go beyond by clustering data +8 + +that contain dynamism. ClusPr against other schemes in the literature, on +three different test datasets demonstrates between 30% to 60% improvement +on the cluster coherency. Moreover, we notice that employing ClusPr within a +privacy-preserving enterprise search system can reduce the search time by up +to 78%, while improving the search accuracy by up to 35%. +2. Proposing an open-source search mechanism (titled as SAED) that overcomes +the privacy problem by separating the intelligence aspect of the search from +its pattern matching aspect. In SAED, the search intelligence is provided by +an on-premises edge tier and the shared cloud tier only serves as an exhaustive +pattern matching search utility. Leveraging the edge tier, SAED offers +personalized semantic searchability on existing cloud-based enterprise search +services with low-latency constraint while maintaining data privacy. +Evaluation under real settings and verified by human users demonstrate that +SAED can improve the relevancy of the retrieved results by on ≈ 75% for +encrypted generic datasets with negligible search time overhead. +3. Proposing an NN model management framework, called Edge-MultiAI that +facilitates continuous execution of confidential DL applications on the +trustworthy edge server to avoid the risk of cloud execution. This is because, +NN models of the trusted applications cannot be outsourced to the public +clouds. With the help of approximate computing, Edge-MultiAI efficiently +utilizes the edge memory such that the multi-tenancy degree is maximized +9 + +without any major compromise on the inference operations. Edge-MultiAI +dynamically loads the high-precision NN model for the requester application, +while loading low-precision ones for others. The framework proposes iWS-BFE +policy along with three other baseline heuristic policies within Edge-MultiAI +to choose the suitable model for the application performing inference, and to +decide how to allocate memory for it. Experiment reveals that Edge-MultiAI +can stimulate the degree of multi-tenancy on the edge by at least 2× without +any major loss on the inference accuracy. +1.6 Dissertation Organization +Figure 1.3. Interrelationship between chapters and related contribution. +SAED +(Chapter 4) +ClustCrypt +(Chapter 3) +Edge-MultiAI +(Chapter 5) +ClusPr +(Chapter 3) +Device +Cloud +Edge +Figure 1.3 depicts the relationships between chapters and the contribution to +which they are related to. The core chapters of this dissertation are derived from +several research papers published during the course of the Ph.D. candidacy. +10 + +• Chapter 2 provides background for: emergence of edge-cloud continuum, +trustworthy compute tiers, enterprise search service, confidential machine +learning, and explores the related research works. +– Sm Zobaed, Mohsen Amini Salehi, Big Data in the Cloud published in +Encyclopedia of Big data, Springer, ISBN: 978-3-319-32009-0. +– Sm Zobaed, Md Enamul Haque, Md Fazle Rabby, Mohsen Amini +Salehi, Senspick: Sense Picking for Word Sense Disambiguation, +Published in proceedings of the 15th IEEE International Conference on +Semantic Computing (ICSC’21), Online, 2021. +– Sm Zobaed, Mohsen Amini Salehi, A Survey on Confidential +Computing over Edge-to-Cloud Continuum, Preparing to be submitted. +• Chapter 3 explores the Benefits of clustering privacy-preserving text-based big +data. The semantics of the data is lost after the encryption. However, the +data can be clustered topically by utilizing the statistical characteristics of the +data. This Chapter discusses our proposed approach of clustering encrypted +static and dynamic data. In addition, the Chapter compares the clusters +obtained by proposed approach and others in the measure of popular cluster +goodness metrics (e.g., Silhouette Coefficient, Davis-Boudin index). Finally, it +presents a set of experiments carried out in a realistic environment to show +the effectiveness of the clustering. +– Sm Zobaed, Sahan Ahmad, Raju Gottumukkala, Mohsen Amini Salehi, +11 + +Clustcrypt: Privacy-preserving clustering of unstructured big data in the +cloud, Published in proceedings of the 21st IEEE International +Conference on High Performance Computing and Communications +(HPCC’19), China, 2019. (Full code in Github repository: +https://github.com/hpcclab/ClustCrypt). +– Sahan Ahmad, Sm Zobaed, Raju Gottumukkala, Mohsen Amini Salehi, +Edge Computing for User-Centric Secure Search on Cloud-Based +Encrypted Big Data, Published in proceedings of the 21st IEEE +International Conference on High Performance Computing and +Communications (HPCC’19), China, 2019. +– Sm Zobaed, Mohsen Amini Salehi, Privacy-Preserving Clustering of +Unstructured Big Data for Cloud-Based Enterprise Search Solutions, +Published in Journal of Concurrency and Computation: Practice and +Experience (CCPE),Volume 34, Issue 22, 2022. (Full code in Github +repository: https://github.com/zobaed11/Jorunal-Version). +• Chapter 4 studies the significance of secure and personalized semantic search +over the encrypted data. This Chapter explains the workflow and mechanisms +of the proposed secure search service architecture. Finally, it presents a set of +experiments carried out in AWS Kendra service environment to show the +effectiveness of the search relevancy. +– Sm Zobaed, Mohsen Amini Salehi, Rajkumar Buyya, SAED: +12 + +Edge-Based Intelligence for Privacy-Preserving Enterprise Search on the +Cloud, Published in proceedings of the 21st ACM/IEEE International +Conference on Cluster Cloud and Grid Computing (CCGrid ’21), +Australia, 2021. (Full code in Github repository: +https://github.com/hpcclab/SAED-Security-At-Edge) +• Chapter 5 explores multi-tenant execution of latency-sensitive DL applications +on edge server. This Chapter explains the architectural overview of +Edge-MultiAI and the heuristics within Edge-MultiAI for managing models of +the multi-tenant DL applications. +– Sm Zobaed, Ali Mokhtari, Jaya Prakash Champati†, Mathieu +Kourouma, Mohsen Amini Salehi, Edge-MultiAI: Multi-Tenancy of +Latency-Sensitive Deep Learning Applications on Edge, Accepted in +proceedings of the 15th ACM/IEEE International Conference on Utility +and Cloud Computing (UCC’22), USA, 2022. (Full code in Github +repository: https://github.com/hpcclab/SAED-Security-At-Edge) +• Chapter 6 concludes the dissertation with a discussion of our major findings +and explores further research topics and directions that emerged during the +course of this research but have not discussed in this thesis. +13 + +Chapter 2: +Background and Literature Study +This chapter provides background and a survey of other research works +undertaken in the fields most related to the confidential computing across +edge-to-cloud. +2.1 Background +2.1.1 Trusted Execution Environment +A trusted execution environment (TEE) is a tamper-resistant processing +environment that are leveraged to run trustworthy applications, such as biometric +authentication, privacy-preserving search over encrypted data etc.with +hardware-enforced isolation via a trusted hardware (i.e., secure processor). TEEs +have their own memory regions where trusted applications (TAs) reside with +complete isolation aiming to prevent unauthorised accesses from generic (a.k.a. +untrusted) space, manipulation of software adversaries (e.g., malware, hacked OS) +or even hardware adversaries (e.g., channel attack) who have physical access to the +platform. TEE is considered as the kernel of confidential computing and so, recent +advancement in TEE technology has brought solution ranges from microcontrollers +to large servers. The widely adopted TEE technologies are Intel SGX, AMD SEV, +and ARM TrustZone. Intel SGX and AMD SEV provide TEE support for serverside +and personal computers, while ARM TrustZone-based TEEs are designed for +resource constraint devices (e.g., edge devices, smartphones and Raspberry Pis). +In Figure 2.1, we represent a high-level architectural overview of TEE +components. Generally, a TEE maintains two separate spaces for all trusted and +14 + +generic applications, namely trusted and untrusted world. The trusted world +contains a trusted OS or, kernel that communicates with TAs using the TEE +Internal API, whereas generic applications from the untrusted world communicate +with the trusted world via the TEE Client API. In addition, a TEE can offer secure +storage utilizing the sealing abstraction (e.g., GPTEE, SGX); a trusted +user-interface API for establishing secure paths between TAs and output display; a +secure provisioning API for initiating TEE network connections using POSIX-style +sockets. +15 + +Figure 2.1. High-level architectural overview of TEE building blocks. +Trusted Applications +TEE Client API +Untrusted World +Trusted World +TEE Comm- +unication +Secure +Provisioning +Trusted +I/O Path +User Applications +Hardware Layer +Secure +Storage +Generic (Rich) OS +Trusted Kernel +TEE Internal APIs +Secure +Boot +Secure Hardwares +Root of +Trust +Secure +Scheduling +Separation Kernel +Communication +2.1.2 Trustworthy Infrastructure for Confidential Computing +Towards deploying confidential computing pipeline, trust should be ensured +in hardware, middleware (OS), and application layer. Breaching confidentiality +while execution can be occurred due to tempering any of the layers. Figure 2.2 +represents a taxonomy of the scopes implementing confidential computing in +high-level. Dealing with big data size confidential data, confidential computing on +16 + +the cloud tier is crucial where the chance of breaching always remains peak. +Although confidential computing provides isolated execution environment, related +hardwares, OS, and applications should be attested locally or remotely via third +party (i.e., trusted authority) prior to any executions. In [25], Valadares +et al.provided different attestation mechanisms for preventing hardware attacks +(e.g., side -channel) on Intel SGX-enhanced edge-IoT systems. +Figure 2.2. A taxonomy of the scopes of confidential computing. +Confidential +Computing +Middleware +serverful +serverless +TPM +SE +VM +container +FaaS +BaaS +func. def. +VM +container +VM+container +bare metal +microVM +unikernel +Paradigm +Tier +device +edge +cloud +fog +Hardware +bare metal +Application +Partitioning +monolithic +Architecture +microservice +ML Engine +(Conf. ML) +federated learning +differential privacy + Encryption +discrete +secure space +memory encryption (AMD SEV) +hypervisor +integrated +firmware +software +Module +TEE +Intel SGX + ARM TrustZone +differential learning +Systems/ +func. invoc. +17 + +2.1.3 Cloud-based Enterprise Search Services over Unstructured Text +Data +Providing access and search ability over big data is essential and data +without these abilities is not much of use. However, organizations that deploy cloud +services for their big data are concerned about data exposure ([1, 3]). Hence, +accessing the data without exposure is required. Enterprise search cloud services +are becoming increasingly popular to enable searching over and providing legitimate +access to organizational big data ([26]). Enterprise search services often maintain a +dynamic index structure based on timely crawling in organizational documents. +Then, the user’s query is searched against the index structure and the result-set, +referencing the relevant documents, is displayed to the legitimate user. +Amazon cloud has provided a semantic enterprise search service named Kendra +by leveraging machine learning and natural language processing methods. Amazon +argues that their clients, such as Woodside, 3M, and Sage have improved the +accuracy and speed of searching and accessing their organizational documents, in +compared to other existing solutions([27]). Semantic searchability comes with the +cost of compromising the users’ data privacy [3, 17, 1]. This is, in fact, the trapdoor +that particularly internal attackers can misuse to breach the confidentiality or even +the integrity of the users’ data. It is this type of attack model that we try to make +the cloud-based enterprise search services resistant against. We note that, for +encrypted datasets, the current enterprise search services cannot offer anything +beyond na¨ıve string matching. +18 + +We note that currently Amazon Kendra does not support enterprise search +service over datasets encrypted by the user’s key (aka user-side encryption). This +leaves the organizational data privacy concern an open question in the cloud era. To +address this concern, multiple solutions are provided to enable semantic search over +user-side encrypted big data ([3],[1],[17]). These solutions aim at performing +real-time search operation without compromising data privacy. +Even for plain-text datasets, our investigations revealed that Kendra covers +only ontological semantics in the search and it falls short in providing context-aware +and personalized semantics. For instance, we tested Kendra to verify the ability of +capturing context-aware semantics by feeding soccer as a query and in the result +set, there were documents about rugby [15]. In another test, river bank query +returned documents about commercial bank that indicates the lack of +context-awareness in the search. +Microsoft Azure Cognitive Services provide different APIs for performing +various useful NLP tasks including sentiment analysis, conversational AI, and +translator on Azure cloud. Such services give the scopes of using both customizable +and pretrained models to deploy anywhere either on demand or spot instance +basis [28]. +2.1.4 Emergence of Edge-to-Cloud Continuum +The edge computing paradigm [12, 29, 30] becomes widely adopted because +of the latency-sensitive feature that ensures secure real-time data processing. +However, because of the constrained processing power, edge nodes are limited to +19 + +process small volume (i.e., light-weight) of data. Therefore, the edge paradigm is +not effective processing massive volume of sensitive data in standalone manner and +application developers and data owner adopt to cloud. Although a large body of +research regarding performance improvement in terms of real-time processing, +scalability, and output accuracy have been performed on edge-to-cloud continuum, +comparatively less attentions are paid to confidential data processing ability [12]. In +addition, edge computing is capable only for processing light-weight data and hence, +from big data aspect, no alternative exists except processing on the cloud. +Generally, edges are dispersedly distributed and have a large attack surface. +As a result, there is high chance that off-premises edge can be compromised. The +recent move of the hardware vendors who design dedicated hardware-assisted TEE +compatible to the both cloud and edge computing infrastructures. +2.1.5 Machine/Deep Learning for Unstructured Data-driven +Applications +Due to the volume and complexity of the data, conventional data analytics +tools (such as frameworks) are unable to handle unstructured data in an efficient +manner. We need to employ a variety of computer vision- and natural language +modeling (NLP)-based solutions that are founded on machine learning and deep +learning architecture so that we can carry out data analytics on unstructured data. +Recent advances in vision and natural language processing algorithms, such as +convolutional neural networks, autoencoders, generative adversarial networks, long +short-term memories (LSTM), transformers, and multi-headed attention +20 + +mechanisms, have made it possible to deal with unstructured text data in an +effective manner. +There have been several advancements made in cloud-based, AI-powered, +and specific use-case driven data analytics tools as a result of the availability of +artificial intelligence services from major cloud service providers such as AWS and +Azure. It is necessary to train a model by providing it with a curated dataset in +order to construct machine learning and deep learning-enhanced applications for +unstructured data. This is done so that the model can comprehend the underlying +intricate pattern, relation, or advanced features. It has been established, after +validating the validity of the model, that the model is prepared to carry out the +activity that has been stated. Following this, the model will move on to the +inference phase, where it will undertake predictive analysis based on live data in +order to produce results that may be acted upon. +2.1.6 Edge Multi-Tenancy for Latency-Sensitive Processing +An edge server is an indispensable part of an IoT-based edge-cloud system +that has to continuously execute multiple (a.k.a. multi-tenant) smart (e.g., deep +learning) applications with low-latency and high accuracy. However, due to memory +limitation, executing latency-sensitive multi-tenant applications on an edge server +can cause memory contention problem that decreases execution rate. This is +because, DL applications utilize bulky Neural Network (NN) models at their kernel +to infer on the inputs received from the sensors. The NN models have to be kept in +memory to enable low-latency (a.k.a. warm-start [31]) inference operations. +21 + +Otherwise, because the NN model size is often huge, loading it into the memory in +an on-demand manner (a.k.a. cold-start) is counterproductive and affects the +latency constraint of the DL applications. As the edge servers naturally have a +limited memory size (e.g., 4 GB in the case of Jetson Nano [32]), multi-tenant +execution of DL applications on them leads to a memory contention challenge across +the processes [14, 33]. To this point, in a multi-tenant execution environment, it is +crucial to dynamically load a suitable model in memory from the set of models +available to the application such that it neither interrupts the execution of other +applications, nor causes a cold-start inference for them. +22 + +2.2 +Prior Literature for Confidential Computing for Unstructured Data +2.2.1 Privacy-preserving Unstructured Data Clustering Schemes +Clustering is essential for various Natural Language Processing (NLP) tasks, +particularly a pre-requisite for most of the advance search systems. Once the data is +encrypted, only statistical characteristics of data remains. Therefore, secure data +clustering is performed based on considering only the statistical properties of the +cipher-texts of the document set. +A large body of research has been undertaken to enable processing of the +encrypted data (ciphertext). Zhou et al. proposed a linear transformation-based +solution for matching queries against encrypted data while ensuring data privacy on +the cloud without any intervention of the data owner [34]. However, linear +transformation methods support secure K-nearest neighbor (KNN)-based query +matching approaches but not the clustering. This is because clustering is not +invariant to linearly transformed data. The optimal linear transformation has a +prerequisite of knowing the true cluster means, which is not possible to obtain +before generating the cluster [35]. In addition, we assume that the data are +tokenized and encrypted before transferring to the cloud. Therefore, unlike [34], +where the entirety of encrypted data is queried using time-consuming cryptographic +calculations, we use the statistical properties of the data without revealing any +meaningful part of it to the cloud. Sun et al. proposed a searchable encryption +method by forming a tree index structure that operates based on the cosine +similarity and TF × IDF [36, 4] measures. However, the solution is not scalable for +23 + +big data, because the search index can become large to the extent that it impacts +timeliness of the search operation. We believe that our proposed clustering approach +can be a complement to [36, 4] where the central index is partitioned topically into +multiple small size index structures that can improve the search time and efficiency. +Homomorphic encryption has become a popular method to perform +computation over the encrypted data. Several variations of the homomorphic +encryption such as fully or partially Homomorphic encryption [37, 38] have been +proposed to enable privacy-preserving data processing on the cloud. Zhu et al. [5] +proposed a secure aggregation and division protocol based on homomorphic +encryption to securely compute clusters without tampering with the privacy of +individual peers in a peer-to-peer system. However, their clustering technique does +not consider data dynamism. Pang and Wang proposed a homomorphic scheme that +provides security to outsourced data uploaded from multiple parties in a twin-cloud +system [39] that is assumed to be a semi-honest environment, whereas, we assume +cloud to be untrusted in terms of storing/processing sensitive data [40]. +Wang et al. proposed HK-Means++ that combines K-Means clustering with +finding the suitable cluster numbers [41]. In addition, the work leverages +homomorphic encryption scheme to solve the encrypted data manipulation, +distance, and convergence calculation. Although our work is comparable to +HK-Means++, it can only cluster static datasets. Moreover, the experiments were +performed only on one dataset and it is not clear how the method performs on other +datasets. We note that the current implementations of the homomorphic encryption +24 + +technique imply a high computational overhead [42] which affects the real-time +response of a search system, particularly, for big datasets [5]. +Vaidya and Clifton [43] proposed a solution to cluster encrypted datasets in +which different data attributes are stored in distinct storage systems. Then, the +clustering was carried out in each one of the data storage systems individually. +However, this solution is time consuming and cannot serve the real-time constraint +we consider in this work. +Very few research have been undertaken in the context of privacy-preserving +big data processing in real-time. S3BD, proposed by Woodworth et al. [3] is one of +them. S3BD is a cloud-based secure semantic search system that performs searching +over big data using cloud services without exposing any data to cloud providers. To +maintain the constraint of real-time search on big data, S3BD proactively prunes +the search space to a subset of the whole dataset. For the sake of pruning, they +proposed a method to cluster the encrypted big data. Once the clustering is done, +an abstract (a representative set) of each cluster is maintained on the client-end to +navigate the search operation to appropriate clusters at the search time. +2.2.2 Searchable Encryption and Encrypted Index +Several research works have been undertaken recently to initiate different +types of search over encrypted data in the cloud. Most of the searchable encryption +based solutions generate cipher-text of the search query and search over encrypted +text in a na´ıve straightforward way. Particularly, each word in a given document is +encrypted independently and later, the document set is sequentially scanned while +25 + +searching for getting match with the queried cipher-text (encrypted query) [44, 45]. +These solutions are generally chosen as they require no storage overhead on the +server but they are commonly slower [3, 44]. +Figure 2.3 provides a high-level taxonomy of research works on the search +over encrypted data in the cloud. Privacy-Preserving query over encrypted +graph-structured data ([46]), cryptDB ([47]), and dragonfruit ([48]) are the +instances of search over encrypted structured data. SecureNoSQL ([49]), SemiLD +([50], and XSnippets ([51]) are the instances of search over encrypted +semi-structured data. REseED ([24]), SSE ([52]) S3C ([53]) are tools developed for +regular expression (Regex), keyword, and semantic searching respectively over +unstructured big data in the cloud. +Figure 2.3. Taxonomy of different types of search over encrypted big data in the +cloud. +Searcheable +Encryption +Structured +Data +Unstructured + Data +Semantic +Keyword +Regular +Expression +Format-preserving +Encryption +Property-preserving +Encryption +SQL-aware Encryption + NoSQL-aware +Encryption +Keyword +Semi-Structured +Data +26 + +Some of the searchable encryption based solutions maintains central index +structure to store store selected data from each document for the sake of making the +search operation relatively quicker and well adapted to big data +aspects [53, 3, 52, 1, 54]. +2.2.3 Privacy-Preserving Cloud-based Search Systems +In addition to plain-text data, searching is performed on privacy-preserving +data ensuring negligible chances of data leakage. Therefore, various searchable +encryption-based solutions are adopted to facilitate search over such data. Few +works at the time of writing have combined the ideas of semantic searching and +searchable encryption. Works that attempt to provide a semantic search often only +consider word similarity instead of true semantics. Li et al. [55] proposed a system +which could handle minor user typos through a fuzzy keyword search. +Moataz et al. [56] use various stemming approaches on terms in the index and query +to provide more general matching. Sun et al. [57] present a system that used an +indexing approach over encrypted file metadata and data mining techniques to +capture the semantics of queries. This approach, however, builds a semantic +network only using the documents that are given to the set and only considers +words that are likely to co-occur as semantically related, leaving out many possible +synonyms or categorically related terms. S3BD [3], a secure semantic search system +that could search semantically over encrypted confidential big data. +They expand their search query by incorporating semantic data extracted +blindly from an ontological network.They do not consider context-aware query +27 + +expansion that created confusion for the search system while processing ambiguous +or multi-context keywords in a query. To perform query processing in client devices, +they end up requiring additional computational overhead in the client tier. +28 + +2.2.3.1 Semantic Representation of Search Query Keywords. Query +expansion is a process to seek keywords that are semantically related to a given +query and fill the lexical gap between the user queries and the searchable +documents. One of the widely-used methods of query expansion is Pseudo-Relevance +Feedback (PRF) [58, 59] that extends an unsuccessful query with various related +keywords and then re-ranks the search results to increase the likelihood of retrieving +relevant documents. Although the PRF-based approach generally improves the +retrieval effectiveness, it is sensitive to the quality of the original search results. +Latent semantic analysis [60], latent dirichlet analysis [61], and neural-based +linguistic models [59, 62] are some of the query expansion methods that can obtain +the semantic representation of a given query. In these methods, vectors are +commonly referred to as word embeddings that represent words into a +low-dimensional semantic space, where the vicinity of words demonstrates the +syntactic or semantic similarity between them [63]. However, pre-trained word +embedding models, such as Word2vec [63], always generate the same vector +representation for an input word, regardless of the context in which the word has +appeared in. Hence, if any ambiguous keyword(s) present in a query, the underlying +topic of the query could not be detected. +WordNet [64] is one of the widely-used and lexically-rich resources in English +that is utilized to infer the sense of ambiguous words in a given corpus. In WordNet, +words containing similar meanings are grouped into synonym sets, whereby each set +has a semantic and conceptual relationship with the other sets. Song et al. [65] and +29 + +Nakade et al. [66] evaluate the effectiveness of utilizing WordNet for query +expansion in National Institute of Standards and Technology (NIST) and Twitter +datasets. They identify important key-phrases of the query and use WordNet to +obtain the relevant synonym sets. Later, they utilize the synonym sets to construct +the expanded query. Nevertheless, in most of the prior research on query expansion +using WordNet (e.g., [67]), the elements of the expanded query set are considered +uniformly that undermines the relevancy and ranking of the result set. +2.2.4 Edge Computing for Privacy-preserving Unstructured Data +Processing +To facilitate secure personalized search, most of the enterprise search services +rely on the computational capability of the client devices. Therefore, it imposes a +significant overhead on the user devices (i.e., thin client) to perform a secure query +processing or to encrypt/decrypt user documents. To this regard, on-premises edge +computing has potential to perform personalized search based on the historical +search data stored in the client devices and also perform encryption/decryption on +demand. To this context, it is ensured that the on-premises edge is fully trusted and +offer uninterrupted confidential computing environment. Prior work S3BD [3] +imposes overhead to the client device while performing secure search over encrypted +big data. On-premises edge computing is an appropriate approach for such system. +By extending their two-tiered architecture with an on-premises/trusted edge can +reduce a significant overhead from the client devices. +30 + +2.3 Prior Literature on Multi-Tenant AI-based Executions on Edge +2.3.1 Edge AI +Numerous research have been undertaken to explore the applications, scopes, +and benefits of edge-based AI for the seamless execution of latency-sensitive smart +applications [68, 69, 14, 70]. Murshed et al.discussed different DNN-based practical +applications such as video analytics and image recognition for enabling edge AI [69]. +Zhou et al.surveyed on various training and inference techniques for NN models on +edge devices [70]. Chen and Ran discussed different techniques that can help to +accelerate the DL training and inference on the edge-based systems [68]. +Han et al.explored the ways to accelerate the training convergence for the +edge-based architectures [14]. Wang et al.surveyed the development of DL +applications on edge from the latency and bandwidth perspectives [71]. Zhou +et al. [70] claimed that although higher edge intelligence reduces data offloading and +improves the privacy, the latency and energy consumption overhead can increase. +2.3.2 Multi-tenant Execution on Edge +Prior studies investigated AI multi-tenancy on the edge servers. +Mao et al.proposed a mobile computing framework, MoDNN, to execute DL +applications simultaneously on resource-constrained devices [72]. MoDNN can +partition pre-trained DNN models across several mobile devices to accelerate tensor +processing with reduced device-level computing cost and memory usage while +achieving 2.17×—4.28× speedup. +Multi-tenant execution across edge servers can lead to undesirable latency in +31 + +application execution. Ko et al.proposed DisCo, a multi-tenant DL application +execution offloading framework that enables execution of both the compute- and +data-intensive parts of applications either on the device or on the edge [73]. +Hadidi et al.discussed that complex DNN models are sensitive to data loss as they +depend more on the nuances in the data [74]. They mentioned losing one layer of +the Inception V3 model can deteriorate the accuracy by more than 50%. They +utilized distributed DNN models on IoT systems to reduce the processing and the +memory footprints. +The aforementioned research works addressed the problem of accelerating +multi-tenant applications without considering the memory constraint of the edge +servers. The only exception, to the best of our knowledge is [75], in which the +authors explored the executing the obstacle detection application in an autonomous +vehicle with ultra low-latency constraint upon compromising with other executing +applications. They proposed a reinforcement learning-based technique to scavenge +memory from a non-priority application, hence, executing the obstacle detection +application immediately and avoid accidents. Although their technique is effective +to serve the latency-sensitive task, multi-tenant executions is out of their scope [75]. +In contrast to these works, we investigate the problem of memory management to +increase the degree of multi-tenancy and the number of warm-start inferences, +thereby, improving the practical usability of IoT-based systems. +2.3.3 DNN Model Compression +Model compression techniques allow for running a model on different +32 + +resource-constrained devices. There are mainly two techniques to reduce the +complexity of a given DNN model: making use of a fewer bit widths (a.k.a. +quantization) and using fewer weights (a.k.a. pruning). These techniques have been +considered individually and together to serve the purpose of model compression. +Quantization reduces the computational resource demand at the expense of a +diminutive loss in accuracy. By default, the model weights are float32 type variables +which means 4 bytes are associated with each model weight with a significant +amount of memory requirements. Model weights can be reduced from 32 bits to 8 +bits (or even shorter [33]) to accelerate inference operation. +Pruning technique is applied to reduce the memory consumption of the model to +accelerate the inference operations. An effective pruning technique removes +redundant connections and/or reduces the width of a layer while ensuring a slight +impact on the inference accuracy. Therefore, the pruned models are retrained to +compensates the loss in accuracy. Failure of selecting proper pruning candidates +affects inference tasks and make the pruned model futile. Some studies have also +been conducted on the selection of appropriate pruning candidates. +For compatibility with the IoT devices, Yao et al.proposed DeepIoT [76], a +reinforcement learning pruning technique for DNN models in the IoT devices. +However, during pruning the model parameters, they only considered the execution +time speed-up, hence, the technique inevitably exhibits inferior inference accuracy +performance. As noted above, aggressive pruning often substantially degrades the +inference accuracy. Training and inference with high pruning with negligible impact +33 + +on the accuracy is still an open research problem [33]. +2.3.4 Warm-Start vs Cold-Start DL Inference +Provided the increasing complexity of DNN models, loading even compressed +models to the edge memory is a burden. The problem is further complicated in +scenarios where the edge server has to continuous maintain multiple applications in +its memory (i.e., multi-tenancy) which is cost-prohibitive. Nonetheless, cold-start +inferences should be avoided as they bring about a remarkable inference latency (see +loading time in Table 5.1 for more details). Some research works have been +accomplished to avoid cold-start inferences. For instance, to support +latency-sensitive applications, in [77], the authors proposed cold-start of a DNN +model in the background while the user is browsing a specific web page. By utilizing +system resources, their technique tracks the user’s browsing activity and loads the +task-specific model in parallel during browsing activity to avoid the cold-start. +2.4 +Summary and Positioning of this Dissertation +Prior literatures neither provided a confidential computing-enabled system +design for confidential unstructured data processing, nor low-latency constraint and +multi-tenacy requirements on the resource limited edge computing systems. For the +confidential computing, we propose to logically partition the system to perform +intelligence within the on-premise edge tier and use the cloud tier to perform simple +and large scale processing. There has been much research accomplished in the fields +of confidential computing, clustering, searchable encryption, and enterprise +searching. However, there has been little done in the intersection of these fields. +34 + +It is this intersection that we position our contributions. In this regard, we +develop (1) Data clustering for confidential static and dynamic unstructured data +that can be used in delay sensitive systems such as cloud-based search systems (2) +Enabling trusted enterprise semantic searching over encrypted confidential data +across edge-to-cloud (3) Stimulating the ability of edge systems to execute +multi-tenant DL applications with low-latency without the help of unstructured +cloud systems. +35 + +Chapter 3: +Privacy-Preserving Clustering for Unstructured Cloud Data +3.1 Overview +Our preliminary research depicted in the previous chapter has confirmed that +clustering is possible in encrypted data. Topic-based clustering can improve the +performance of various NLP tasks, particularly, in the context of secure search +system. However, forming topic-based clusters with encrypted text data is a +challenge. To overcome this challenge, clustering is achieved based on statistical +semantics. The idea is to locate tokens that are semantically close to each other in +the same cluster. To achieve this, we first need to know the number of clusters (k) +that should be created to cover topics exist in token of a given dataset. Then, we +find the central tokens for each cluster and assign the rest of tokens to the most +topically related clusters. We develop the proposed clustering solutions, namely +ClustCrypt [1] and ClusPr [54]. We replace the existing clustering policy of S3BD +with the proposed schemes. +This chapter presents data-characteristics specific different clustering schemes +and the architectural overview of the context where the proposed clustering schemes +can be deployed. Note that, we consider that the frequency and co-occurrences of +all tokens in the dataset are available in the proposed clustering works. +3.2 Problem Statement +The prior clustering schemes of S3BD and other works require to specify +number of clusters to initiate partitioning that is detrimental to optimal clustering +of tokens (keywords) in the most appropriate cluster. We cannot predetermine the +36 + +same number of clusters and cluster size regardless of any sized datasets. In +addition, if the data contains dynamism, the clustering scheme needs to +accommodate new tokens added to the dataset. On the contrary, the clusters can be +shrunk due to the deletion of some documents from the document set. Therefore, in +this chapter, we investigate how to optimally and scalably cluster keywords in an +encrypted unstructured dataset. The outcome of this research enhances clustering +of encrypted keywords by estimating the appropriate (k) and distributing keywords +across the clusters. We highlight the importance of probabilistical semantic +similarity among the encrypted tokens for clustering to measure the tendency for +each token to be separate from others. +3.3 Positioning of the Proposed Clustering Works +Our proposed works are motivated from Woodworth et al.method for +topic-based clustering on encrypted tokens (aka keywords) over the central index +using K-means method [3]. The cluster-wise token distribution function was +determined based on the statistical data of each encrypted token. The authors used +a predefined K value. Such K value is inefficient, because the appropriate number +of clusters could be varied based on the dataset characteristics. Moreover, as the +authors only considered static/unchanged data, the proposed scheme is not capable +of processing dynamic data. On the other hand, proposed solutions provides a +heuristic to approximate the suitable number of clusters and then, clustering the +data while maintaining the data privacy on the cloud. For a dynamic dataset, where +documents are added or removed over time, because of the re-clustering operation, +37 + +clusters are shrunk or expanded to reflect the dynamism of the dataset. +Note that, ClustCrypt can effectively cluster the encrypted static data only +and hence, it is not capable to manage the cluster set if dynamism exists in the +data. Our next solution ClusPr can work with static, semi-dynamic, and also fully +dynamic encrypted unstructured data. Particularly, we propose three different +clustering schemes namely S-ClusPr, SD-ClusPr, and FD-ClusPr for compatibility +with respect to static, semi-dynamic, and fully-dynamic datasets. Table 3.1 +summarizes the notable related studies in the literature and positions the +contribution of the proposed clustering works with respect to them. +Table 3.1. Summary of the existing privacy-preserving clustering approaches and +positioning our proposed works (ClustCrypt and ClusPr) with respect to them. +Research Works +Estimating +#Clusters +Encryption +Approach +Cloud’s +Trustworthiness +Using Edge +Computing +Real-time +Support +Dynamic Data +Clustering +Multiple +Data Owners +Wang et al. [41] +No +Homomorphic +Semi-honest +No +No +No +No +Valdiya & Clifton [43] +No +Homomorphic +Semi-honest +No +Yes +No +Yes +Pang & Wang [39] +No +Homomorphic +Semi-honest +No +Yes +No +Yes +Sun et al. [36, 4] +No +User-side +Honest-but-curious +No +Yes +No +No +Zhu et al. [34] +No +Homomorphic +Honest +No +No +No +Yes +Woodworth et al. [3] +No +User-side +Honest-but-curious +No +Yes +No +Yes +ClustCrypt (Proposed) et al. [1] +Yes +User-side +Honest-but-curious +No +Yes +No +Yes +ClusPr (proposed) et al. [54] +Yes +User-side +Honest-but-curious +Yes +Yes +Yes +Yes +3.4 Architecture to Facilitate Clustering in Secure Search System +3.4.1 Architecture: ClustCrypt +Although we implemented ClustCrypt in the context of S3BD, the approach +is generic and can be deployed in other systems that require clustering of encrypted +data (e.g., [78, 79]). Figure 3.1 presents where ClustCrypt is positioned within the +S3BD system. We can see that S3BD is composed of a client tier and a cloud +tier [3]. The client tier is considered trusted and it provides upload and search +functionalities for the users. The cloud tier is considered honest but curious, +38 + +therefore, all the documents and their indexed tokens are stored in encrypted form. +To enable real-time searching, the encrypted indexed tokens have to be clustered. +The illustrated system consists of “Client tier” for the user (who can be the data +owner as well) and “Cloud Tier” where the index and clusters reside. Users are able +to upload documents to cloud or input search queries to look for documents that are +semantically relevant to the queries. In this setup, if a user wants to upload +documents, first, the keywords or tokens are extracted from the original documents, +then the documents and tokens are both encrypted and sent to the cloud tier. RSA +deterministic encryption technique [80] is used to encrypt documents and extracted +tokens. Individual data users (e.g., law-enforcement agent) who want to perform +search share the same RSA key. +The Cloud Tier maintains a central index structure with a key-value pairs. +Each key-value pair represents, respectively, an encrypted token, and the list of +documents (locations) where the token appears in, plus the frequency of the token +in each one of those documents. Homomorphic encryption [37] can be used to +encrypt the token frequency information. However, due to the slow down imposed +by processing homomorphically encrypted data [42] and to practically maintain the +real-time search quality, currently, the frequency information is stored in +unencrypted form. Upon issuing a search query by a user, the search keywords are +encrypted and searched against the central index in the Cloud Tier to retrieve the +relevant documents. Upon receiving the list of matching documents, the user can +download and decrypt them utilizing his/her private key. +39 + +Clusters c1...cn are constructed based on the tokens of the index structure +and to mitigate exhaustively searching the whole index structure for every single +search query. The clusters are topic-based and they are constructed so that the +union of the k clusters is equivalent to the index structure. For a given search query, +instead of searching the whole index, the search space is pruned and gets limited to +only those clusters that are topically related to the search query. The pruning is +achieved based on a set of Abstract structures (denoted a1...an) that are sampled +from each one of the clusters and reside either on the Client tier or possibly on a +trusted edge server. In our prior research, we proposed to formulate user-centric +Abstract for personalized search [17]. Details of the ways sampling can be +accomplished are mentioned in [3]. Upon issuing a search query, the most similar +abstracts to the search query are chosen and then, their corresponding clusters are +searched. +Figure 3.1. High-level two-tiered (client-cloud) Search System Architecture Inte- +grating ClustCrypt Approach. +Search Query +𝑎" +𝑎# +𝑎$ +Key Phrase +Extractor +Document +Unencrypted +Abstract Form +Of Clusters +Uploads +Central Index +𝑐"𝑐# +𝑐& +Clustered +Data +Client Tier +Cloud Tier +Encryption +Encryption +Storage +𝑎& +3.4.2 Architecture: ClusPr +40 + +Figure 3.2 presents an architectural overview of the context where ClusPr is +developed. The architecture represents applying ClusPr for S3BD, a cloud-based +secure semantic search system that requires clustering over encrypted data [3]. The +architecture represents a three-tier system based on a client device, edge system, +and the central cloud system unlike original S3BD [3] and ClustCrypt [1] leveraged +architecture of S3BD. The edge tier resides on the user’s premises (hence, is +considered trusted) to relieve the client tier from processing computationally +intensive tasks. This is particularly important for non-static (i.e., semi-, +fully-dynamic) datasets where documents have to be processed as they are uploaded +to the cloud tier over time. +In the specific context of S3BD, upon uploading a document by the user, the +document is passed through Token Extractor on the edge tiers to retrieve the +keywords (aka tokens) semantically representing the document. For dynamic +datasets, a temporary index structure is used to store the extracted tokens +representing the occurrences of each new token in different documents. Next, the +document is encrypted by the user’s key and is securely stored on the cloud +repository. Next, a Temporary Index structure is formed based on the extracted +tokens of the documents in question before encrypting and uploading them to the +cloud. The Temporary Index structure shows the tokens, their frequency, and their +appearances across the uploaded batch. Tokens of the Temporary Index are +encrypted by the Encryptor using the user’s key. By encrypting documents as well +as the extracted tokens, Encryptor preserves the data privacy on the cloud. Note +41 + +that, although we can technically use homomorphic encryption to maintain the +statistical properties (frequency and co-appearances), for efficiency reasons, in the +current implementation, we keep the properties unencrypted. We assume that such +properties do not reveal meaningful information about the data. In fact, in [41], +K-means clustering was used over homomorphically encrypted big data and showed +that the time overhead of clustering can be prohibitively expensive. In the next +step, the Temporary Index is fed to the Cluster Manager to make the suitable +clustering decision on the cloud. Cluster Manager may decide to keep the existing +clusters and only update them by the entries of the Temporary Index. Alternatively, +upon observing a major update in the Temporary Index, the Cluster Manager +decides to exhaustively re-cluster all of the tokens. Though a few of the +aforementioned prior works can cluster encrypted data, they fall-short in clustering +dynamic datasets, whereas, ClusPr can cluster both static and dynamic data while +ensuring privacy. We explain the updating and re-clustering procedures ClusPr in +Section 3.7. Cluster Manager is also in charge of generating and maintaining +Abstracts. Each abstract ai is a sampled summary of a corresponding cluster Ci on +the cloud tier [17]. Abstracts are to prune the search operation and navigate the +search only to clusters that are topically-related to the query. Further details about +Abstracts are described in Section 3.6.3. +42 + +Figure 3.2. Overview of the context where ClusPr is deployed in a three-tier archi- +tecture (of client, edge, and cloud) to facilitate a secure cloud-based search service. +The edge tier is assumed to be on the user premises and trusted. It is used to ease +the computational overheads imposed by privacy and clustering related processes. +Cloud Tier +Token +Extractor +Docs +Encrypted +Docs +Clusters {c1…cn} +c1 +c2 +cn +Users +Edge Tier +Index +Query +Pre-processor +Encryptor +E(Docs) +≈ +Search Query +Upload +Client Tier +Cluster +Manager +Abstracts +a1 +a2 +an +≈ +Temp. Index +E(tokens) +For static datasets, the architecture is streamlined such that the extracted +tokens are encrypted and directly fed into the Index structure on the cloud tier. +Once the data uploading procedure is completed, the cloud tier initiates the +clustering procedure. As there is no re-clustering procedures defined for static +clusters, the Cluster Manager is only in charge of generating and maintaining the +abstracts [17]. It is noteworthy that, in the architecture of Figure 3.2, the dashed +arrows located in the edge tier are to highlight the differences for dynamic datasets. +Further details of the proposed static (S-Cluspr) and dynamic (SD-, FD-Cluspr) +data clustering schemes are presented in Section 3.6and 3.7respectively. +Similar to ClustCrypt, ClusPr uses RSA encryption technique for the +encryption purpose and forms the Abstract set from the clusters. As an use case of +the clustering policy in the context of a search system, upon issuing a search query +by the user, the abstracts with the highest similarity to the search query are +43 + +identified. Then, only the clusters associated with the abstracts are searched. +44 + +3.5 ClustCrypt: Privacy-preserving Clustering Scheme for Static Unstruc- +tured Data +In this part, first (in Section 3.5.1), we elaborate on how to estimate the +appropriate number of clusters that should be formed to represent a static big +dataset. Second, in Section 3.5.2, we provide an algorithm to form the center of +each cluster. Then, in Section 3.5.3, we explain methods to distribute the indexed +terms across clusters. Finally, in Section 3.6.3, we describe the way pruning is +achieved, i.e., the method that navigates a search query to relevant cluster(s). +3.5.1 Estimating the Number of Clusters for Static Datasets +Depending on the characteristics of a dataset and distribution of tokens in its +documents, the appropriate number of clusters (K) can vary significantly. However, +optimally determining K directly impacts the accuracy of topic-based clustering +and, subsequently, the efficiency of the system (e.g., search application) that uses +the clusters. Encrypted tokens and their metadata, including documents they +appear in and their frequency, are the only available parameters to estimate K. The +tokens and their metadata are generated by a keyword extractor that retrieves n +single or multi-phrase tokens from each document. We assume that all documents +are treated equally and the value of n is the same across all documents in a given +static dataset. +Estimating K for the static dataset is performed based on the following two +steps: (1) building Token-Document Frequency Matrix; and (2) constructing +Normalized Matrix. +45 + +Step-1: Building Token-Document Frequency Matrix. To be able to +follow the scheme, we consider an example using five tokens and six documents in +Table 3.2. We initialize a token-document matrix A from the index structure. In +the matrix, each row represents a token and each column represents a document. +Although our approach does not deal with plain-text tokens, just for further +readability, in the Table 3.2, we redundantly show the plain-text tokens (in “Word” +column) along with their encrypted forms (in “Hash” column). Each entry ai,j of +matrix A represents the frequency of ith token in jth document (denoted as f(i, j)). +Table 3.2. Token-Document Frequency Matrix A, built based on the index structure +Word +Hash +d1 +d2 +d3 +d4 +d5 +d6 +Book +Uh5W +30 +0 +23 +4 +40 +0 +Solve +/Vdn +5 +0 +0 +60 +34 +0 +Traffic +oR1r +0 +23 +0 +30 +0 +0 +Net +vJHZ +52 +49 +0 +23 +0 +26 +Enter +tH7c +0 +45 +68 +0 +3 +5 +For a big dataset, the matrix size can be prohibitively large and sparse. To +avoid this, we trim the matrix to include only the tokens that are influential in +building clusters. We define document co-occurrences as the number of documents +containing a particular token. Then, to build the token-document frequency matrix +A, we only take into account tokens whose document co-occurrences are either +greater than or equal to the mean value of the document co-occurrences across the +whole dataset. +Step-2: Constructing Normalized Matrix. To make the relationship among +tokens and documents quantifiable and comparable, we need to normalize the +46 + +token-document frequency matrix. Considering that ai,j represents the strength of +association between token ti and document dj, the maximum value in column j of +the token-document frequency matrix represents the token with the highest +association with document dj. Hence, for normalization, we divide the value of each +entry of A to the highest value in the corresponding column of the matrix and the +result is stored in a new matrix, called matrix N. The value for each entry ni,j is +formally calculated based on Equation 3.1. +ni,j = +ai,j +max +∀i ai,j +(3.1) +For the example provided in Table 3.2, the normalized matrix N is presented +in Table 3.3. +Table 3.3. Normalized Token-Document matrix N +Word +Hash +d1 +d2 +d3 +d4 +d5 +d6 +Book +Uh5W +0.58 +0 +0.34 +0.07 +1 +0 +Solve +/Vdn +0.1 +0 +0 +1 +0.85 +0 +Traffic +oR1r +0 +0.47 +0 +0.5 +0 +0 +Net +vJHZ +1 +1 +0 +0.38 +0 +1 +Enter +tH7c +0 +0.92 +1 +0 +0.08 +0.2 +Step-3: Building Probabilistic Matrices R and S The goal, in this step, is to +calculate the topic similarity among encrypted tokens. For that purpose, we need to +calculate the probability that topic of a token shares similarity with other tokens. +We hypothesize that tokens that co-occur across documents are likely to share the +same topic. Besides, the magnitude of similarity between two tokens could be +influenced by the tokens’ distribution across the dataset. For instance, specific +terms appear only in a few documents and are not widely distributed throughout +47 + +the dataset. Such sparsely distributed tokens have low co-occurrences with other +tokens which increases the diversity of topics in a dataset and potentially raises the +required number of clusters (K). We leverage the normalized matrix (N) to perform +a two-phase probability calculation that yields a matrix (denoted as Q) representing +token-to-token topic similarity. +Table 3.4. Matrix R is built based on normalized matrix N to represent the impor- +tance of each token across all documents +Word +Hash +d1 +d2 +d3 +d4 +d5 +d6 +Book +Uh5W +0.29 +0 +0.17 +0.04 +0.50 +0 +Solve +/Vdn +.05 +0 +0 +0.51 +0.43 +0 +Traffic +oRir +0 +0.48 +0 +0.52 +0 +0 +Net +vJHZ +0.29 +0.29 +0 +0.11 +0 +0.29 +Enter +tH7c +0 +0.42 +0.45 +0 +0.03 +0.09 +In the first phase, we calculate the importance of each token to each +document. The importance of token ti, in document dj, denoted as τi,j, is defined +based on Equation 3.2. +τi,j = +ni,j +� +∀k +ni,k +(3.2) +Considering Equation 3.2 and matrix N, we generate matrix R whose entries +represent the importance of each token across all documents. In fact, each entry ri,j +of R represents the probability of choosing a document dj, having token ti. That is, +ri,j = P(ti, dj). In our example, Table 3.4 shows the matrix R obtained from the +matrix N (shown in Table 3.3). +In the second phase, we calculate the importance of each document to each +token. The importance of document dj for term ti, denoted by δj,i and is defined +48 + +based on Equation 3.3. +δj,i = +nj,i +� +∀q +nq,i +(3.3) +Table 3.5. Matrix S is built from N to represent the importance of each document +with respect to each token +Docs +Book +Uh5W +Solve +/Vdn +Traffic +oRir +Net +vJHZ +Enter +tH7c +d1 +0.34 +0.06 +0 +0.60 +0 +d2 +0 +0 +0.19 +0.49 +0.38 +d3 +0.17 +0 +0 +0 +0.45 +d4 +.04 +0.51 +0.25 +0.19 +0 +d5 +0.52 +0.44 +0 +0 +0.04 +d6 +0 +0 +0 +0.84 +0.16 +Considering each δj,i and N, we generate S whose entries represent the +importance of each document with respect to each token. In fact, each entry si,j +represents the probability of choosing ti from dj (i.e., we have si,j = P(dj, ti)). In +our example, Table 3.5 shows S obtained from N. +Step 4- Constructing Matrix Q to Determine the Number of Clusters +Recall that R is a token-to-document matrix and S is a document-to-token +matrix. To identify the similarity among the encrypted tokens, we multiply R and +S. As the number of columns and rows of R and S are equal, it is possible to +multiply matrix R with S. The resultant matrix, denoted as Q, is a token-to-token +matrix and serves as the base to determine the number of required clusters. Each +entry qi,j denotes the topic similarity between token i and j. More specifically, qi,j +indicates the magnitude to which token i shares similar topic with token j for i ̸= j +49 + +and is calculated as qi,j = +� +∀i,j +ri,j· sj,i. Table 3.6 shows matrix Q for the example we +discuss in this section. +Table 3.6. Cluster decision matrix Q is built based on the multiplication of R and +S matrices +Word-Hash +Book +Uh5W +Solve +/Vdn +Traffic +oRir +Net +vJHZ +Enter +tH7c +Book- Uh5W +0.39 +0.25 +0.01 +0.18 +0.09 +Solve- /Vdn +0.26 +0.45 +0.12 +0.12 +0.02 +Traffic- oRir +0.02 +0.26 +0.21 +0.33 +0.18 +Net- vJHZ +0.10 +0.07 +0.08 +0.58 +0.15 +Enter- tH7c +0.09 +0.01 +0.08 +0.28 +0.37 +Diagonal entries of Q signify the topic similarity of each token with itself and +dissimilarity (i.e., separation) from other topics. More specifically, the value of qi,i +indicates the magnitude that term ti does not share its topic with other terms. +Therefore, we define diagonal entries (qi,i) as separation factor, because for each +token, it represents the token’s tendency to stay separate from other topics. As +such, summation of the separation factors can approximate the number of clusters +(K) needed to partition topics of a dataset. Let m denote the total number of +tokens in Q. Then, Equation 3.4 is used to approximate K for a given dataset. We +use the ceiling function to make K an integer value. +k = ⌈ +m +� +i=1 +qi,i⌉ +(3.4) +Correctness of K is verified using a hypothesis that states K for a set should +be higher if individual elements of the set are dissimilar, otherwise K should be +low [81, 82]. Equation 3.4 is the core of approximating K. According to this +50 + +equation, the maximum K value can reach to M, when the documents are highly +distinct and each individual token of the documents represents a unique topic, +otherwise it is lower than M. Hence, our approach conforms with the clustering +hypothesis. +51 + +3.5.2 Determining Clusters’ Centers +In k-means clustering, generally, the clusters’ centers are arbitrarily +chosen [83, 84]. Then, based on a distance measure function (e.g., Euclidean +distance [83] or semantic graph [84]), dataset elements are distributed into clusters. +K-means operates based on iteratively shifting clusters’ centers until convergence. +However, we realized that the extremely large number of tokens make the iterative +center shifting step (and therefore k-means clustering) prohibitively time consuming +for big data [85]. Accordingly, in this part, we are to propose a big-data-friendly +method to cluster encrypted tokens. +The key to our clustering method is to dismiss the iterative center shifting +step. This change entails initial clusters’ centers not to be chosen arbitrarily, +instead, they have to be chosen proactively so that they cover various topics of the +dataset. For that purpose, a na¨ıve method can be choosing the top k tokens that +have the highest number of associated documents. Although this approach chooses +important (highly associated) tokens, it ends up selecting centers that have high +document and topical overlap. To choose appropriate center tokens, we propose to +choose tokens that not only have highly document association, but also cover +diverse topics exist in the dataset. +We define centrality of a token i, denoted Φi, as a measure to represent a +topic and relatedness to other tokens of the same topic. Assume that tokens are +sorted descendingly based on the degree of document association. Let U represent +the union of documents associated to the currently chosen centers. Also, for token i, +52 + +let Ai represent the set of documents associated to i. Then, uniqueness [3] of token +i, denoted ωi, is defined as the ratio of the number of documents associated to i but +not present in U (i.e., |Ai − U|) to the number of documents associated to i and are +present in U (i.e., |Ai ∩ U|). Uniqueness indicates the potential of a token to +represent a topic that has not been identified by other tokens already chosen as +centers. Particularly, tokens with uniqueness value greater than 1 have high +association to documents that are not covered by the currently chosen centers, +hence, can be chosen as new centers. +Recall that each entry ci,j of matrix C represents the topic similarity between +tokens i and j. Besides, diagonal entry ci,i measures separation of token i from +others. Therefore, the total similarity token i shares with others can be obtained by +Σ∀j|j̸=ici,j. Note that for token i, we have Σ∀jci,j = 1, hence, the total similarity for +token i is equal to 1 − ci,i. Centrality of a token is measured by the uniqueness of +the token, the magnitude of similarity the token shares with others, and the +magnitude of it being isolated. That is, for token i, centrality is defined as +Φi = ωi × ci,i × (1 − ci,i). +Algorithm 1 shows the high-level pseudo-code to select maximum of k +centers from the set of indexed tokens of a dataset. In addition to k, the algorithm +receives the central index and the C matrix as inputs. The algorithm returns a set +of at most k center tokens, denoted centers, as output. In the beginning, the output +set is initialized to null. U represents the set of documents covered with the chosen +centers. A heap structure, denoted Θ, is used to store a pair for each token and its +53 + +Algorithm 1: Pseudo-code to determine clusters’ centers +Input +: k, C matrix, and central index (with tokens sorted descendingly +based on the degree of document association) +Output: Set centers that includes at most k center tokens +1 Function +Choose Center(k, C, Index): +2 +centers ← ∅ +3 +U ← ∅ +4 +Θ ← {(∅, ∅)} //Pairs of tokens and centrality values +5 +foreach token i ∈ index do +6 +ωi ← CalculateUniqueness(i, U) +7 +if ωi > 1 then +8 +U ← U ∪ Ui +9 +Φi ← (ωi × ci,i × (1 − ci,i)) +10 +Add pair (i, Φi) to max-heap Θ based on Φi +11 +end +12 +end +13 +centers ← Extract k max pairs from Θ heap +14 +return centers +15 end +centrality value. For each token i, the uniqueness and centrality values are +calculated (Steps 5 to 12) and the corresponding pair is inserted to the heap. Note +that tokens with uniqueness lower than one do not have the potential to serve as a +cluster center. In the next step, we select at most k center tokens that have the +highest centrality values. +3.5.3 Clustering Tokens +Once k tokens are chosen as cluster centers, the tokens are distributed among +the clusters. The distribution is performed based on the relatedness (aka distance) +between the center tokens and remaining tokens. Established techniques exist to +calculate such relatedness, however, most of them (e.g., semantic graph [84] and +Euclidean distance [83]) are not suitable for tokens sparsely distributed across the +54 + +dataset [83]. Besides, these are not designed to apply on encrypted data [84]. +In S3BD [3], a method based on document co-occurrence is proposed to +measure relatedness and cluster encrypted tokens. In this method, if two tokens are +present in the same set of documents, they are considered related [3]. We utilize +that to measure the relatedness of tokens with cluster centers and distribute tokens +to the most related cluster. To determine the relatedness between a particular token +and a center, we need to calculate the contribution and co-occurrences metrics for +the token. Let t be a token in document d of dataset D with frequency denoted as +f(t, d). Then, contribution of d to t, denoted as κ(d, t), is defined based on +Equation 3.5. +κ(d, t) = +f(t, d) +� +j∈D +f(t, j) +(3.5) +Co-occurrence of token t with center token γx in document d (denoted +ρ(t, d, γx) ) is defined as a ratio of the sum of frequencies of t and center γx in d to +the total frequencies of t and γx throughout the dataset. The formal presentation of +co-occurrence is provided in Equation 3.6. +ρ(t, d, γx) = +f(t, d) + f(γx, d) +� +j∈D +(f(t, j) + f(γx, j)) +(3.6) +Based on the contribution and co-occurrence metrics, relatedness between +token t and γx (denoted r(γx, t)), is defined as multiplication of these two metrics +(i.e., r(γx, t) = +� +j∈D +κ(j, t)· log (ρ(t, γx, j))). +55 + +3.6 S-ClusPr: Privacy-preserving Clustering Scheme For Static Unstruc- +tured Datasets +In this section, we provide a detailed description of S-ClusPr scheme to +cluster privacy-preserving static big datasets. Note that S-ClusPr uses similar +method to estimate suitable number of clusters (k) that is used in ClustCrypt in +Section 3.5.1. However, we proposed more robust heuristics for the center selection +and token distribution method in ClusPr to obtain more topically segmented +clusters. In Section 3.6.1 and 3.6.2, we explain the center selection and token +distribution method respectively. +3.6.1 Center Selection +In K-means clustering, generally, the clusters’ centers are arbitrarily +chosen [83, 84]. Then, based on a distance measure function (e.g., Euclidean +distance [83] or semantic graph citeLiuCroft), dataset elements are distributed into +the clusters. K-means operates based on iteratively shifting clusters’ centers until it +converges. However, we realized that the extremely large number of tokens make +the iterative center shifting step (and therefore K-means clustering) prohibitively +time-consuming for big data [85]. Accordingly, in this part, we are to propose a +big-data-friendly method to cluster encrypted tokens. +The key to our clustering method is to dismiss the iterative center shifting +step. This change entails initial clusters’ centers not to be chosen arbitrarily, +instead, they have to be chosen proactively so that they cover various topics of the +dataset. For that purpose, a na¨ıve method can choose the top K tokens that have +56 + +the highest number of associated documents. Although this approach chooses +important (highly associated) tokens, it ends up selecting centers that have a high +topical overlap. We propose to choose tokens that not only have high document +association but also cover diverse topics exist in the dataset. +We define centrality of a token i, denoted Φi, as a measure to represent a +topic and relatedness to other tokens of the same topic. Assume that tokens are +sorted in a descending manner, based on the degree of document association. Let U +represent the union of documents associated to the currently chosen centers. Also, +for token i, let Ai represent the set of documents associated to i. Then, +uniqueness [3] of token i, denoted ωi, is defined as the ratio of the number of +documents associated to i but not present in U (i.e., |Ai − U|) to the number of +documents associated to i and are present in U (i.e., |Ai ∩ U|). Uniqueness indicates +the potential of a token to represent a topic that has not been identified by other +tokens already chosen as centers. Particularly, tokens with uniqueness value greater +than 1 have high association to documents that are not covered by the currently +chosen centers, hence, can be chosen as new centers. +Recall that each entry qi,j of matrix Q represents the topic similarity +between tokens i and j. Besides, diagonal entry qi,i measures separation of token i +from others. Therefore, the total similarity token i shares with others can be +obtained by Σ∀j|j̸=iqi,j. Note that for token i, we have Σ∀jqi,j = 1, hence, the total +similarity for token i is equal to 1 − qi,i. Centrality of a token is measured by the +uniqueness of the token, the magnitude of similarity the token shares with others, +57 + +and the magnitude of it being isolated. That is, for token i, centrality is defined as: +Φi = ωi × qi,i × (1 − qi,i). +Algorithm 2: Pseudo-code to determine clusters’ centers +Input +: K, C matrix, and Index (with tokens sorted descendingly based on +the degree of document association) +Output: centers set that includes at most K center tokens +1 Function +Choose Center(k, Q, Index): +2 +centers ← ∅ +3 +U ← ∅ +4 +Θ ← {(∅, ∅)} //Pairs of tokens and centrality values +5 +foreach token i ∈ Index do +6 +ωi ← CalculateUniqueness(i, U) +7 +if ωi > 1 then +8 +Ai ← CalculateDocumentAssoc(i, Index) +9 +U ← U ∪ Ai +10 +Φi ← (ωi × qi,i × (1 − qi,i)) +11 +Add pair (i, Φi) to max-heap Θ based on Φi +12 +end +13 +end +14 +centers ← Extract K max pairs from Θ heap +15 +return centers +16 end +Algorithm 2 shows the high-level pseudo-code to select maximum of K +centers from the set of indexed tokens of a dataset. In addition to K, the algorithm +receives the central index and the Q as inputs. The algorithm returns a set of at +most K center tokens, denoted centers, as output. In the beginning, the output set +is initialized to null. U represents the set of documents covered with the chosen +centers. A heap structure, denoted Θ, is used to store a pair for each token and its +centrality value. For each token i, the uniqueness and centrality values are +calculated (Steps 5 − 13) and the corresponding pair is inserted to the heap. Note +that tokens with uniqueness lower than one do not have the potential to serve as a +58 + +cluster center. In the next step, we select at most K center tokens that have the +highest centrality values. +3.6.2 Distributing Encrypted Tokens Across Clusters +Once K tokens are nominated as cluster centers, the remaining tokens of the +index are distributed across the clusters with respect to their relatedness (aka +distance) with the center tokens. +Because there is no intersection between the non-center tokens and members +of the centers set, we can model the token distribution across the clusters as a +weighted bipartite graph where the weight of each edge represents the relatedness +between a token and a center. Figure 3.3 depicts an example of a bipartite graph to +show the relationship of each token and centers. Solid lines show the edge with the +highest weight for each token that represent the cluster that a token should be +distributed to. Established techniques (e.g., semantic graph [84], Euclidean +distance [83]) are to calculate the relatedness, however, these methods are not +appropriate for encrypted tokens that are sparsely distributed [83] [84]. +As encrypted tokens lose their semantics, we ought to define the relatedness +between tokens based on their statistical characteristics and then leverage it to +distribute each token to the cluster that offers the maximum relatedness. +Intuitively, the relatedness measure between tokens ti and tj, denoted +r(ti, tj), is defined based on the magnitude of their co-occurrences, i.e., the number +of documents where the two tokens appear together [3, 1]. Let Fi and Fj +respectively denote the sets of documents that ti and tj are appeared in. Then, the +59 + +Figure 3.3. A bipartite graph representing the relatedness among centers and remaining +tokens. The weight of each edge represents the relatedness of a token and a center. Solid +lines show centers that offer the maximum relatedness for a token. +School +Car +Book +0.28 +0.63 +0.07 +0.07 +0.04 +0.19 +0.06 +0.76 +0.02 +0.15 +0.13 +0.63 +0.48 +0.78 +Cluster centers +Tokens +Teach +Pen +Kia +Gear +Story +0.03 +intuitive co-occurrence of the two tokens is Fco = Fi ∩ Fj. However, a deeper +analysis reveals that quantifying the relatedness only based on the cardinality of +co-occurrence (i.e., |Fco|) can be misleading for the two following reasons: +First, intuitive co-occurrence ignores the magnitude of disparity across Fi +and Fj that negatively impacts the relatedness between ti and tj. The disparity is +determined based on the symmetric difference (i.e., we have Fdis = Fi ⊕ Fj). +Accordingly, to consider the impact of both co-occurrence and disparity, we define a +new measure, called relative co-occurrence, and leverage it to determine the +relatedness between ti and tj. +Second, intuitive co-occurrence ignores the importance of ti and tj in each +60 + +document d ∈ Fco. Accordingly, to measure the co-occurrence value in each +document d, denoted υ(ti, tj, d), we consider the importance of each one of the +tokens relative to their importance across all documents of Fco. We use frequency of +a token in a document to measure its importance in that document. Formally, in +document d, we calculate the value of co-occurrence based on Equation 3.7. +υ(ti, tj, d) = +f(ti, d) +� +∀m∈Fco +f(ti, m)· +f(tj, d) +� +∀m∈Fco +f(tj, m) +(3.7) +Similarly, we utilize Equation 3.8 to measure the impact of disparity between +two tokens in each document d ∈ Fdis, denoted ϕ(ti, tj, d). +ϕ(ti, tj, d) = +f(ti, d) +� +∀m∈Fdis +f(ti, m) + +f(tj, d) +� +∀m∈Fdis +f(tj, m) +(3.8) +In document d, once we know the co-occurrence and disparity between ti and +tj, we can calculate the relative co-occurrence as ρ(ti, tj, d) = υ(ti, tj, d) − ϕ(ti, tj, d). +Then, the relative co-occurrence across all documents of the two tokens (i.e., +Fi ∪ Fj) is leveraged to calculate the relatedness between them. +Assuming c as the token that represents center of a given cluster (i.e., +ti = c ∈ centers), we define relatedness between c and token t, according to +Equation 3.9. Token t is distributed to the cluster whose center offers the maximum +relatedness. Note that, in this equation, to emphasize the importance of token t in +document d, we also consider its frequency ratio. +61 + +r(c, t) = +� +d∈(Ft∪Fc) +ρ(t, c, d)· +f(t, d) +� +∀m∈Ft +f(t, m) +(3.9) +3.6.3 Pruning Clusters to Expedite the Search Operation +The purpose of building topic-based clusters is to achieve scalable search over +big data via limiting (pruning) the search scope based on the query topic, instead of +exhaustively traversing the whole index structure. For pruning, we need to identify +the clusters that are semantically relevant to the search query and discard the +irrelevant ones. However, pruning is a challenging task when we operate on the +encrypted data in the cloud. +To overcome the challenge, we require the topic of each cluster in plain-text, +such that we can identify the clusters whose topics are semantically related to the +search query and only consider those clusters for searching. For that purpose, in our +previous work [17], we established a method to represent the topic of each cluster +Cx (denoted αx) by considering the top-n most-frequent tokens of Cx. The tokens of +αx are decrypted and maintained on the edge tier of ClusPr in a structure called +Abstract. Abstracts are leveraged to measure the topic similarity between a query +and their corresponding clusters. In the next step, the search is conducted on the +clusters that are most relevant to the query. For further details about creating +abstracts and pruning operation, interested readers can refer to our earlier +study [17, 3]. +62 + +3.7 Privacy-preserving Clustering Scheme For Dynamic Unstructured datasets +3.7.1 Overview +In the previous section, we explained clustering of static (e.g., archive) +encrypted big datasets. However, many big datasets are dynamic (e.g., healthcare +data, criminal records) [86] and their contents change over time. In this section, we +deal with clustering and subsequently searching over such datasets. We consider two +types of dynamic datasets: First is the semi-dynamic datasets whose contents are +updated in batch over time (e.g., Museum of Modern Art (MoMA) dataset [87]); +Second is fully-dynamic datasets whose contents are constantly updated (e.g., +Twitter streams [88]). +The latest changes on the dataset have to be reflected in the clusters. +Otherwise, altered documents are not retrieved by the search system, even if they +include relevant contents. In fact, the updates on the dataset affect the tokens’ +co-occurrences and, subsequently, the clustering arrangement. As such, the +challenge is to know how the addition or deleting documents change the topics and +number of clusters. +Given the size of big datasets, reconstructing clusters (called re-clustering) +upon arrival of every single document or a small batch of documents is +time-prohibitive. Moreover, the small updates generally cause negligible changes in +the co-occurrences of tokens that are unlikely to modify the arrangement of clusters. +Only significant updates can cause decisive changes on the magnitude of +63 + +co-occurrence and relatedness that entail re-clustering. Accordingly, the two +followup questions are: when to perform re-clustering? and how to re-cluster the +tokens? To address these questions, based on the type of dynamic datasets, we +propose two clustering schemes in ClusPr: Semi-dynamic data clustering scheme +(SD-ClusPr) and Fully-dynamic data clustering scheme (FD-ClusPr). +3.7.2 Semi-Dynamic Data Clustering Scheme (SD-ClusPr) +In semi-dynamic datasets, topic-based clustering can be initially achieved on +the first batch of documents in the dataset according to the method described in the +previous section. Then, the re-clustering decisions are made depending on the +changes caused by the new batch of documents. That is, we need to determine +whether the change caused by the extracted tokens of the new batch is significant or +not. +To determine the significance of changes caused by the tokens of the new +batch, we utilize χ2 (chi-square) distribution test [89] that can identify significant +changes observed in a variable of a given population. The χ2 test is known as +testing goodness of fit and it is represented by Equation 3.10, where Oi is the +observed and Ei is the expected value of a particular variable in K trials. +χ2 = +k +� +i=1 +[(Oi − Ei)2/Ei] +(3.10) +We consider the number of the extracted tokens in the new batch and the +number of tokens in the existing clusters. Our null hypothesis (H0) is to perform +re-clustering and χ2 test is employed to check the validity of H0. If the difference +64 + +between the number of new tokens and existing tokens is small, a low value of χ2 is +obtained. For one degree of freedom with 95% confidence interval, the value of +χ2 = 3.841 fails to reject H0. Alternatively, if the number of tokens in the new batch +is significantly smaller than the number of existing tokens, χ2 value becomes higher +that denotes significant deviation from H0. Then, the decision is to reject H0 and +keep the existing clusters. +Once the re-clustering decision is made, we use the method explained in +Section 3.6 to cluster tokens of the updated dataset. In the event that re-clustering +is not achieved, the new tokens are accumulated with the of tokens of the next +batches. As a result, the total number of new tokens becomes significant that leads +to a lower χ2 value and subsequently acceptance of H0. +3.7.2.1 Updating Clusters. Let U1 a new batch of documents that +introduces a set of new tokens T = {t1, t2, ..., tn} that does not exist in the existing +clusters. Assume that based on the re-clustering decision method, mentioned in the +previous part, we determine to keep the existing clusters {C1, C2, ..., Cn} to +accommodate T. +To distribute ti ∈ T to a cluster, we can measure the relatedness as explained +in Section 3.5.3. Alternatively, we can leverage the set of abstracts {A1, A2, ..., An}. +As they are in the plain-text format, a more accurate relatedness measurement can +be conducted using the semantic similarity, as opposed to inferring the relatedness +based on token co-occurrences in documents. In this case, we use Word2Vec [63] +model to calculate the relatedness of ti and abstract Aj. Then, ti is assigned to a +65 + +cluster that offers the highest relatedness. To avoid poor assignments, we define θ as +the relatedness threshold that should be reached to assign ti to Cj. In the event +that ti cannot join any cluster, a new cluster, called Cnew ∈ C, is formed and ti is +considered as its center. The above procedure is repeated for all ti ∈ T. +Algorithm 3: Pseudo-code to update clusters in SD-ClusPr. +Input +: set of abstracts A, tempIndex , θ +Output: H, map of new tokens to clusters +1 Function +SD-ClusPr(A, tempIndex, θ): +2 +T ← tempIndex \ CentralIndex +3 +H ← ∅ +4 +A ← ∪n +i=1Ai +5 +Φ ← ∅ +6 +//Max-heap to find the abstract with highest similarity +7 +foreach token t ∈ T do +8 +foreach aij ∈ A do +9 +s ← sim (aij, t) +10 +if +s > θ then +11 +Add (s, i) to Φ +12 +end +13 +end +14 +if Φ ̸= ∅ then +15 +//Allocate t to existing cluster +16 +(t, i) ← Extract max pair from Φ +17 +Add (t, i) to H +18 +end +19 +else +20 +//Forming a new abstract and cluster and add it to H +21 +An+1 ← {t} +22 +A ← ∪n+1 +i=1 Ai +23 +Add (t, n + 1) to H +24 +end +25 +end +26 +Encrypt H and push it to the cloud tier +27 end +3.7.2.2 Determining the value of θ Threshold. We estimate the value +of θ threshold by leveraging the abstracts {A1, A2, ...An}. Recall that the elements +66 + +of abstract Ai are the ones that best represent the topic of its corresponding cluster +Ci. We define coherency of Ai as the average similarity distance across pairs of its +elements. Let {ai1, ..., aip} be the set of elements of Ai. Then, coherency of Ai, +denoted Ki, is defined based on Equation 3.11 where sim(x, y) shows the similarity +distance between (x, y) ∈ Ai × Ai. +Ki = +� +∀(x,y)∈Ai×Ai|x̸=y +Sim(x, y) +�p +2 +� +(3.11) +Then, we define θ as the global minimum across all abstracts (i.e., +θ = min +∀i Ki). This implies that a new token can join a cluster only if its distance +does not worsen the coherency of current clusters. Otherwise, the new token forms +its own cluster. +Algorithm 3 shows the pseudo-code of how to update clusters in SD-ClusPr, +in case we choose not to perform re-clustering. In addition to the set of abstracts +(A) and θ, the algorithm receives the set of tokens for a new document batch, which +is stored in form of a temporary index. The algorithm returns the H structure that +includes the mapping of new tokens to their respective clusters. In Steps 7 − 9, for +each new token, we calculate the similarity distance with respect to all abstract +elements aij and check whether the similarity distance exceeds θ or not. If it +exceeds θ, we make a pair of similarity distance and corresponding abstract number, +denoted as (aij, t) and build max-heap Φ based on the distance (in Step 10 − 12). If +Φ contains any value, we extract from it the pair that has the largest value (i.e., the +abstract that offers the most topic similarity for t). Then, in Step 17, the pair of +67 + +(t, i) is added to H. On the contrary, if Φ is null, it implies that no cluster offers a +considerable similarity to t, and so, in Steps 19 − 24, we build a new abstract and +cluster using t. Finally, we encrypt the tokens of H and push it to the cloud tier. +On the cloud end, cluster manager updates its clusters based on H. +3.7.3 Fully-Dynamic Data Clustering Scheme (FD-ClusPr) +Unlike SD-ClusPr, for fully-dynamic datasets, clusters have to be formed or +updated upon arrival of the documents. That is, continuous or burst arrival of new +documents should trigger FD-ClusPr. Accordingly, in FD-ClusPr, we consider two +cases in forming clusters: (A) initial case that occurs when first document arrives +and there is no existing cluster and (B) update case, where the existing clusters have +to be updated based on the new changes in the dataset. +In the initial case, the edge tier extracts the set of new tokens from the +uploaded document(s). We designate the token with the highest frequency to +represent the topic and choose it as the cluster center too. Then, the second most +frequent token is clustered based on its similarity distance with the designated +cluster center, according to the method discussed in Section 3.7.2. Also, to +determine joining the existing cluster or forming a new one, we initialize the +threshold to θ = 0.1. This procedure continues until all tokens are clustered. In the +update case, we apply the same method as SD-ClusPr. That is, upon uploading a +document, the system decides to either perform re-clustering or updating existing +clusters. +68 + +3.8 Security Analysis of the Proposed Clustering Works +In this section, we only cover the security analysis of ClusPr. In this regard, +explaining security analysis of the three-tiered architecture also covers the analysis +of two-tiered ClustCrypt. +The proposed clustering schemes are applicable in the context of searchable +encryption and document retrieval systems. According to the three-tier +architecture, described in Figure 3.2, client- and edge tiers are in the user premises, +hence, the activities conducted and the user’s key on these tiers are considered safe +and trusted. The Abstract structures are kept on the edge tier in plain-text to +enable us to measure the similarity with the search phrase and performing pruning. +On the other hand, activities performed on the cloud-tier are considered as +dishonest and prone to different types of attacks. We are concerned about both +internal (i.e., affiliated parties) and external (i.e., unaffiliated outside intruders) +attackers who desire to learn the encrypted clustered tokens and documents. To +explain the threats of the attackers, we provide the following preliminaries: View: +This term denotes the portion that is visible to the cloud during any given +interaction among client, edge, and server. The central index and the set of clusters +C1...Cn, the trapdoor of the given encrypted search query Q +′, and the collection of +encrypted documents D +′. In some models, Q +′ also contains a particular weight for +each term. The search results related to Q +′ are considered as Ic. The view of +expanded Q +′ and Ic are symbolized as V (Q +′) and V (Ic) respectively. +Trace: This term denotes the information exposed about Ic. Our aim is to +69 + +allow the attacker to infer the information of Ic as little as possible. +The View and Trace enclose all the information that the attacker would gain. +To encrypt the document set we use probabilistic encryption model that is +considered to be one of the most secure encryption techniques [3, 90]. This does not +utilize one-to-one mapping and so, D +′ is not prone to dictionary-based attacks [91]. +Each token in a cluster is deterministically encrypted. Thus, each cluster in the +View, only shows an encrypted mapping of the tokens and their co-occurrences in +the plain-text format. +If any type of attacker can gain access to the cloud, he/she could only +understand the importance of a particular encrypted token by observing the +co-occurrences. It is technically possible to encrypt co-occurrences using +homomorphic encryption [37] and perform computation on the co-occurrences while +it is in the encrypted form. However, in Section 2.2.1, we discuss that this technique +practically falls short on performance [92] and affects the real-time behavior of the +search system. As such, in the current implementation, we use co-occurrence +information in the plain-text format. Note that, even when the co-occurrences are +not encrypted, the attacker cannot decrypt the token. +An attacker could obtain a Trace regarding V (Q +′). From that view, the +attacker could only understand the importance of each search term from Q +′ by +analyzing the associated weights of the query terms. Similar to the previous +consideration, the attacker is not able to reveal the search terms from Q +′. In spite of +a minimally trusted computing base, an attacker may still intend to access the +70 + +system through man-in-the-middle, either honest but compromised or untrusted +cloud providers to attack the confidentiality of the user data. By any means, if the +attacker successfully performs a man-in-the-middle attack, he/she can access the +document list V (Ic) resulting from searching Q +′ with Trace. At this point, the +attacker may only obtain the documents’ names with encrypted contents that are +unreadable. +There are methods (e.g., [93]) that can be used to tackle frequency attacks +when the searches and cluster updates are predictable. Theoretically, an attacker +could build a dictionary considering all the clusters’ tokens by performing frequency +attack. Eventually, the attacker tries to build a clone document set D′ utilizing the +dictionary. Although all of the tokens extracted from a particular document are +sufficient to learn the topic of the document, it is not possible to unveil the whole +document as we do not use all of the keywords of the document set to build the +encrypted index. Besides, we encrypt the whole document at once instead of word +level encryption before outsourcing it to the cloud. This procedure ensures that +even if the document set is compromised on the cloud tier, it is impossible to +perform a dictionary attack. +Even if the attacker knows the trace, he/she cannot understand what exactly +the retrieved encrypted documents convey. Moreover, attacks can be occurred in the +communication between the edge and cloud tiers. In this case, by monitoring the +search process, an attacker could obtain the resultant document list for Q′. +However, the attacker is not able to decrypt the documents, since they can be +71 + +decrypted only when they are downloaded on the edge system. +An attacker could also attempt to modify data (e.g., encrypted tokens and +documents) in the clusters. Such attacks can potentially tamper with the integrity +of user data. However, this type of attack could be detected, because neither the +edge will be able to decrypt the modified tokens to form or update Abstracts, nor +the user will be able to decrypt the retrieved documents in the original plain-text +form. This is because of applying symmetric encryption (e.g., AES encryption) on +the user’s data with keys managed by the user. Hence, in the event that the +encrypted data are altered by an attacker, such data cannot be decrypted by the +users’ keys. Actually, protecting the user’s key is crucial to restrain possible attacks. +If the key is compromised, the system cannot detect the attacker and, therefore, +both tokens and documents can be exposed. +72 + +3.9 Performance Evaluation of Clustering +3.9.1 Experimental Setup +We developed working versions of ClustCrypt and ClusPr and made it +available publicly in our Githuba,b. We evaluate the performance of ClusPr using +three distinct datasets that have different properties and volumes. We compare and +analyze the clustering quality with other approaches that operate in encrypted or +unencrypted domains. The experiments were conducted on a machine with two +10-core 2.8 GHz E5 Intel Xeon processors and 64 GB of memory. +To evaluate the performance of ClusPr in handling big data, we used a +subset of Amazon Common Crawl Corpus (ACCC) dataset [94]. The whole dataset +size ≈ 150 terabytes that contains different web-based contents, such as blogs and +social media contents. We randomly selected 6, 119 documents that collectively form +a ≈ 500 GB document set. The second dataset, named Request For Comments +(RFC) [95], is domain- specific and includes documents about the internet and +communication networks. RFC includes 2, 000 documents and its total size is ≈ 247 +MB. The third dataset is BBC [96] that is not domain-specific and includes news in +certain categories such as technology, politics, sports, entertainments, and business. +It contains 2, 225 documents and is ≈ 5 MB. The reason for choosing this small +dataset is that, unlike ACCC and RFC, each document of BBC is short and we can +verify clusters’ coherency manually. For each dataset, the documents are passed +through Maui keyword extractor [97] to identify keywords semantically represent +ahttps://git.io/fjDsq +bhttps://github.com/hpcclab/ClustCrypt +73 + +the document. +3.9.2 Evaluation Metrics and Baselines from Prior Works +For performance evaluation of the proposed works, we compare them against +four other schemes, where two schemes cluster plain-text data and the other two +schemes cluster encrypted data. Among the first two, one of the schemes W2V +Kmeans) is based on K-means clustering [98] where feature extraction is done based +on Word2Vec [63] embedding. +Another scheme, WordNet [99], is an enhanced version of K-means that +generates synonym set based on the input data and then, applies K-means +clustering on the sets. Token distribution in WordNet is performed based on edge +counting method, proposed by Wu and Palmer [99]. +Two encrypted clustering schemes that have been used in the comparison are +namely, S3BD [3], and HK-means++ [41]. We have discussed S3BD +and HK-means++ in Section 2.2.1 +. ClustCrypt is the preliminary version of S-ClusPr. +Their difference mainly lies in the way tokens are distributed across the clusters. In +ClustCrypt, the relatedness is simply calculated based on contribution and +co-occurrences metrics, whereas in S-ClusPr, the magnitude of both similarity and +disparity are considered to measure the relatedness (see Section 3.6.2for further +details). +The goodness of clusters set can be quantified by a number of evaluation +metrics. However, evaluating the performance of a clustering scheme is not as +simple as counting errors in classification algorithm. Specifically, instead of +74 + +considering the absolute values of cluster labels, cluster evaluation metrics either +measure the separation of clustered data similar to ground truth set of classes or +internal cluster validation. Internal cluster validation denotes that members belong +to the same class should be more similar than members of other classes and vice +versa. In practice, class label information is not always available in most of the +application scenarios and, therefore, internal validation metrics are the only option +for validation in such situation [100, 101]. +As there is no ground truth for the considered datasets, we choose evaluation +metrics that evaluate the clusters based on statistical analysis of the cluster +members. We evaluate three widely-adopted clustering metrics, namely Silhouette +coefficient (SC), Calinski-Harabasz index (CI), and Davies-Bouldin index (DI). +Silhouette Coefficient (SC) score interprets and validates intra-cluster +consistency. In particular, the metric signifies how similar a cluster member is to its +own cluster compared to the other clusters. The value of the SC score ranges from +−1 to +1, where a high value indicates that a given member is well matched to its +own cluster and poorly matched to the other ones. Calinski-Harabasz Index (CI) +denotes how well-defined (i.e., well-separated) the clusters are. The CI value of +clusters is calculated based on the ratio of the sum of between-clusters dispersion to +the sum of inter-cluster dispersion. A higher CI value indicates a more topically +separated (i.e., less overlapping) clustering and vice versa. Similar to the CI metric, +Davies Bouldin Index (DI) is used to measure the goodness of separation across +clusters and the reason we consider it in our evaluation is to verify the CI metric +75 + +evaluation for the clusters. DI is calculated based on the ratio of within-cluster +distances to the between-cluster distances. A lower DI value indicates a more +topically-separated clustering and it is preferred. In addition to these metrics, we +measure the clusters’ coherency to evaluate the quality of the topic-based clustering +within each cluster. This is a similarity-based evaluation metric to calculate the +average of all possible pair-wise token similarity for a given cluster. In fact, +Coherency represents how the tokens in a cluster are related to a certain topic. +Then, the average of coherency across all clusters is calculated to represent the +overall quality of a certain clustering method. +We instrument the pre-trained Google News Word2vec model [63] to +determine the similarity between any two given keywords. The model is a +300-dimension vector representation of three million phrases. The model requires a +text dataset as input to build a vocabulary from the input dataset and learns vector +representation of the words in the dataset. The model uses cosine similarity and +provides the score (−1 ≤ similarity score ≤ 1) for any two given tokens. We note +that, the pre-trained Word2vec model operates only on plain-text tokens. +Subsequently, we do not encrypt the tokens while uploading for evaluation purposes. +However, the proposed schemes assume tokens to be encrypted and do not use the +properties of plain-text tokens. +3.9.3 Evaluation Results +3.9.3.1 Evaluating Silhouette Coefficient (SC) Score. Figure 3.4 shows the +results of SC score evaluation on the three datasets and for varying number of +76 + +clusters (in the horizontal axis). We note that, for this experiment, the value of K +in W2V Kmeans, WordNet, and HK-means++ is randomly chosen and iteratively +evolves. As such, we calculate the SC score for all the considered K values and show +them in multiple data points in the figure. However, other schemes (namely, +S-ClusPr, ClustCrypt, S3BD) are not iterative and provide only one SC score for +their determined K values. +As the procedure of estimating the number of clusters is similar in +ClustCrypt and S-ClusPr schemes, we can see that both of the schemes generate 69, +65, and 133 clusters for the BBC, RFC, and ACCC datasets, respectively. As ACCC is +the largest and broadest (i.e., not domain-specific) dataset, it yields the highest K +value. RFC is not the smallest dataset, however, due to its domain-specific nature, it +yields the lowest K value. +Figure 3.4 represents SC metric outcomes for ClustCrypt, S-ClusPr and the +four other compared schemes. According to the figure, considering all of the +datasets, overall top performers are: WordNet and S-ClusPr. Moreover, S-ClusPr +outperforms others in the RFC dataset. On the contrary, HK-means++ and S3BD +underperform in most of the situation. The experiment indicates that the cluster +sets generated by HK-means++ and S3BD contain less intra-cluster similarity. +WordNet and S-ClusPr provide the highest intra-cluster similarity and hence, +outperform others in all datasets. +3.9.3.2 Evaluating Calinski-Harabasz Index (CI). Table 3.7 represents CI +metric outcomes for S-ClusPr and the four other schemes. According to the table, +77 + +Figure 3.4. Silhouette Coefficient (SC) metric for each dataset. The results are obtained +from S-ClusPr, HK-means++, ClustCrypt (that are encrypted-based clustering schemes), +W2V-Kmeans, and WordNet clustering schemes (that operate on plain-text tokens). +50 +100 +150 +200 +250 +Number of clusters +4 +6 +Davies-Bouldin Index +BBC +S-ClusPr +ClustCrypt +WordNet +W2V Kmeans +S3BD +HK-Means++ +50 +100 +150 +200 +250 +Number of clusters +2 +4 +6 +8 +Davies-Bouldin Index +RFC +50 +100 150 200 250 300 +Number of clusters +4 +6 +Davies-Bouldin Index +ACCC +78 + +Figure 3.5. Davies-Bouldin Index (DI) for each dataset using different clustering schemes. +50 +100 +150 +200 +250 +Number of clusters +4 +6 +Davies-Bouldin Index +BBC +S-ClusPr +ClustCrypt +WordNet +W2V Kmeans +S3BD +HK-Means++ +50 +100 +150 +200 +250 +Number of clusters +2 +4 +6 +8 +Davies-Bouldin Index +RFC +50 +100 150 200 250 300 +Number of clusters +4 +6 +Davies-Bouldin Index +ACCC +79 + +Figure 3.6. Cluster coherency for each dataset. +50 +100 +150 +200 +250 +Number of clusters +0.10 +0.15 +Coherence +BBC +S-ClusPr +ClustCrypt +WordNet +W2V Kmeans +S3BD +HK-Means++ +50 +100 +150 +200 +250 +Number of clusters +0.15 +0.20 +RFC +50 +100 150 200 250 300 +Number of clusters +0.10 +0.15 +Coherence +ACCC +80 + +Table 3.7. Calinski-Harabasz Index for the datasets. +(a) BBC +Approaches +No. of +Cluster +HK- +means++ +WordNet +W2V +Kmeans +S3BD +ClustCrypt +S-ClusPr +10 +- +- +- +8.7 +- +- +50 +25.43 +277.53 +11.16 +- +- +- +69 +18.47 +253.60 +9.22 +- +11.70 +13.58 +100 +11.13 +203.87 +7.37 +- +- +- +150 +14.05 +164.43 +5.81 +- +- +- +200 +10.17 +122.51 +4.93 +- +- +- +250 +12.02 +97.15 +4.38 +- +- +- +(b) RFC +Approaches +No. of +Cluster +HK- +means++ +WordNet +W2V +Kmeans +S3BD +ClustCrypt +S-ClusPr +10 +- +- +- +1247.20 +- +- +50 +1730.26 +4320.63 +60380.05 +- +- +- +65 +1945.42 +3980.75 +51564.61 +- +23760.64 +29439.30 +100 +1834.64 +3660.78 +24374.17 +- +- +- +150 +1684.47 +3110.25 +18684.33 +- +- +- +200 +846.71 +2572.89 +16746.74 +- +- +- +250 +436.43 +1834.58 +15139.11 +- +- +- +the RFC clusters provide large CI values compared to the BBC dataset, regardless +of the employed clustering scheme. It is noteworthy that, we had the same +observation for the ACCC dataset, however, we do not show its table due to the +shortage of space. The superiority of RFC is because it is a domain-specific dataset +with a few topics compared to the other two. Within Table 3.7b, we can see that +although W2V-Kmeans significantly outperforms the other schemes for most of the +K values, WordNet, ClustCrypt, and S-ClusPr also provide satisfactory CI values +that imply well-partitioned clusters. +81 + +3.9.3.3 Evaluating Davies Bouldin Index (DI). The DI values for the clusters, +obtained by S-ClusPr and the compared schemes are expressed in Figure 3.5. In +most of the scenarios, we observe that increasing the number of clusters reduces the +DI value. This is because, typically, configuring clustering schemes to build more +clusters on a given dataset leads to a higher coherency within each of the clusters. +According to the figure, we observe that WordNet scheme outperforms +others. The DI value for S-ClusPr is in the acceptable range, which indicates that +the scheme can offer a competitive goodness of separation across clusters in +compared to the most of other schemes. On the other hand, higher DI value yielded +by HK-means++ signifies poor cluster separation. +3.9.3.4 Evaluating Cluster Coherency. Figure 3.6 shows the clusters’ coherency +on the three datasets using various clustering schemes. Using S-ClusPr, 69, 65, and +133 clusters are created for the BBC, RFC, and ACCC datasets, respectively. As ACCC is +the largest and broadest (i.e., not domain-specific) dataset, it yields the highest K +value. RFC is not the smallest dataset, however, due to its domain-specific nature, it +yields the lowest K value. For the same reason, across the three datasets, S-ClusPr +offers the highest coherency value (≈ 0.16) for the RFC dataset. +In compare to ClustCrypt, we notice that S-ClusPr offers a negligible +coherency improvement (≈ 6%) for the BBC and RFC datasets. However, for the +ACCC dataset, S-ClusPr improves the coherency by approximately 31%. +Analysis of the plain-text-based schemes reveal that, WordNet clusters offer +the highest coherency value. This is expected, because it is difficult for an encrypted +82 + +clustering scheme (e.g., S-ClusPr) to outperform the unencrypted ones, since they +do not have access to the semantics of the tokens [99] to build the clusters. +However, we observe that the coherency offered by S-ClusPr competes with the one +offered by the K-means scheme. In particular, S-ClusPr provides a higher coherency +value than K-means for the RFC and BBC datasets. +To evaluate the suitability of estimated number of clusters (K) by S-ClusPr, +we configure both K-means and WordNet to use the estimated K number of +clusters for the studied datasets. According to the figure, for RFC and BBC, S-ClusPr +suggested sets of K clusters offer a higher coherency than K-means and a +comparable one to WordNet. In the case of ACCC, S-ClusPr even outperforms +WordNet in terms of coherency. +83 + +Figure 3.7. Comparing the impact of clustering using S-ClusPr against original clustering +of S3BD for the studied datasets. +BBC +RFC +ACCC +0.00 +0.02 +0.04 +0.06 +0.08 +0.10 +0.12 +0.14 +0.16 +Coherence +S-ClusPr +Original S3BD +3.9.3.5 Analyzing the Impact of S-ClusPr on Searchable Encryption +Systems. One objective of this research is to enhance the performance of S3BD +secure search system. As such, we instrumented S-ClusPr in S3BD and compared +the coherency of resulting clusters with its original clustering scheme that +predetermines a value for k = 10. Moreover, its center selection only considers the +co-occurrences. In this experiment, we intend to evaluate the improvement that +S-ClusPr achieves within S3BD on the three studied datasets. In this experiment, +the estimated values of K for BBC, RFC, and ACCC are 69, 65, and 133, respectively. +Impact on the Clustering Coherency of S3BD. Figure 3.7 shows that for all +the studied datasets, clusters generated by S-ClusPr have remarkably higher +coherency than the original clustering scheme of S3BD. This shows determining +number of clusters based on dataset characteristics and choosing center tokens +84 + +Figure 3.8. Comparing the relevancy of search results using S-ClusPr vs original S3BD +clustering in BBC dataset. The value of relevancy is calculated based on TSAP@10 scoring +metric. +News Update +Top Movies +Recent Attacks +Extinct Animal +Score Updates +Champions League +World Health Issue +People & Busi. +China Market +Europe. Stock Ex +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +Relevance Score +S-ClusPr +Original S3BD +based on the centrality concept is effective. Our hypothesis is that, such efficiency +improves the accuracy and offers more relevant semantic search results. This is +because tokens of the clusters are more congruent to the clusters’ topics, hence, +more effective pruning is accomplished. For further evaluation of this hypothesis, +next experiments concentrate on the impact of S-ClusPr on the search quality. +Impact on the Search Accuracy of S3BD. The purpose of improving the +clusters’ coherency in this study is to ultimately enhance the search accuracy by +85 + +Table 3.8. Benchmark queries for each one of the studied datasets. +ACCC Dataset +BBC Dataset +RFC Dataset +Orlando Magic +News Update +Internet +Samsung Galaxy +Top Movies +TCP +Baseball +routine +Recent Attacks +Fiber Doctor +Recommendation +Endangered +Animals +Wifi +North America +Score Updates +IoT +Tennis +Tournament +Champions +League +Radio +Frequency +Holy Martyr +World Health +Issue +UDP +Library +People and +Business +Edge Computing +Stardock +China Market +Encryption +Schemes +Orthodox Church +European Stock +Exchange +Broadcasting +retrieving more relevant documents. To evaluate the impact of such improvement, +in this part, we compare and analyze how the search accuracy of S3BD system is +affected by utilizing S-ClusPr’s clusters against the circumstance where its original +clustering method is utilized.For the evaluation, we generated a set of 10 benchmark +search queries that are listed in Table 3.8. +To measure the relevancy of search results for each query, we use TREC-Style +Average Precision scoring method [102]. This method works based on the +recall-precision concept and the score is calculated by +N +� +i=0 +ri/N, where ri denotes the +86 + +score for ith retrieved document and N is the cutoff number (number of elements in +the search results) that we consider as 10. Therefore, we call it TSAP@10. +We measure TSAP@10 score only for the RFC dataset and its benchmark +queries. The reason is that it is domain-specific and feasible to determine the +relevancy of the retrieved documents. To compare the relevancy provided by +S-ClusPr against the original S3BD clustering, we apply the benchmark queries to +the S3BD search system. In Figure 3.8, the relevancy score of the results for each +query when the two clustering schemes are applied are measured and presented. +According to the Figure, for most of the queries, S-ClusPr clustering offers a higher +relevancy score. For the two queries that have identical TSAP@10 score, their +retrieved document lists are equivalent. Also, S-ClusPr clusters provide score for +News Update and China Market benchmark queries, whereas original S3BD clusters +do not retrieve any relevant documents for these queries. +Impact on the Search Time of S3BD. Figure 3.9 presents the total search +time of the benchmark queries for each dataset. The search time is measured as the +turnaround time of searching each query—from the time a query is issued until the +result set is received. To eliminate the impact of any randomness in the computing +system, we searched each set of benchmarks 10 times and reported the results in +form of box plots. The figure indicates that when S-ClusPr clustering is utilized, the +search time is significantly shorter than the circumstance where the original S3BD +clustering is used. Longer search time impacts the scalability and real-time quality +of the search operation on big data. Analyzing Figures 3.7 to 3.9 reveals that +87 + +Figure 3.9. Search time of S3BD when S-ClusPr is used for clustering versus when the +original S3BD clustering is used. +BBC +RFC +ACCC +0 +5 +10 +15 +20 +25 +Search Time (ms) +S-ClusPr +Original S3BD +integrating S-ClusPr in the search system, not only makes it more accurate, but +makes it faster and more scalable too. +Figure 3.10. Clusters’ coherency for different updates of the three studied datasets +when SD-ClusPr is applied with and without re-clustering option. +Update1 +Update2 +Update3 +Update4 +Update5 +0.00 +0.02 +0.04 +0.06 +0.08 +0.10 +0.12 +0.14 +0.16 +Coherence +Baseline +SD-ClusPr +(a) BBC Dataset +Update1 +Update2 +Update3 +Update4 +Update5 +0.00 +0.02 +0.04 +0.06 +0.08 +0.10 +0.12 +0.14 +0.16 +Coherence +Baseline +SD-ClusPr +(b) RFC Dataset +Update1 +Update2 +Update3 +Update4 +Update5 +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +Coherence +Baseline +SD-ClusPr +(c) ACCC Dataset +3.9.3.6 Evaluation of Clustering Coherency for Dynamic Schemes. +In this part, we analyze the effectiveness of dynamic clustering schemes (SD-ClusPr +and FD-ClusPr). We mention in Section 3.7 that FD-ClusPr is a specific case of +SD-ClusPr. Hence, we only consider the SD-ClusPr scheme for evaluation. To this +end, we leverage the three studied datasets and build subsets that each one serves as +a batch update. Specifically, we consider an existing set of clusters based on 500 +88 + +documents for each dataset. Then, we sample five times to create a list of five +updates that each one includes a set of documents. List U includes the pairs of +update names and the size of each update as follows: +U =< (U1, 25), (U2, 50), (U3, 100), (U4, 20), (U5, 200) >. To assure that the results are +not biased to any particular sample, we performed the sampling procedure 10 +independent times and report the mean and 95% confidence interval of the analysis +in the results. The reason we designated U3 and U5 to be larger is to examine +SD-ClusPr decision in re-clustering. To evaluate the scheme in terms of the cluster +coherency, we build a baseline version from SD-ClusPr that does not consider +re-clustering. The baseline only performs clustering based on existing clusters (as +explained in Algorithm 3) to accommodate the new updates. +Figures 3.10a, 3.10b, and 3.10c, respectively, present cluster coherency of five +different batch updates of BBC, RFC, and ACCC respectively applying SD-ClusPr +scheme. In Figure 3.10a, we observe that the coherency of clusters are decreased in +baseline for U3 whereas the coherency obtained for SD-ClusPr beats the previous by +around 105%. We observe the similar pattern of coherency variation for U5. For +baseline, the lowest coherency is obtained in U5. On the contrary, in SD-ClusPr, we +observe around 115% improvement in coherency for U5. +According to Figure 3.6, clusters formed for the RFC dataset shows the +highest coherency. Similarly, in Figure 3.10b, we observe the highest coherency for +all updates in compare with other datasets. With respect to baseline, we observe +that SD-ClusPr causes minor improvements in coherency of both U3 and U5. Since +89 + +the documents are more domain-specific, clusters do not lose coherency significantly +from one update to the other. As such, we do not observe significant improvements +by SD-ClusPr. Similar to BBC and RFC, in Figure 3.10c, we observe improvement in +the coherency for ACCC dataset. In particular, the improvement in coherency for U3 +and U5 is approximately 45% and 35%, respectively. +From these experiments, we conclude that ClusPr scheme can improve the +coherency of clustering even for dynamic datasets. Specifically, we observed that for +sufficiently large batches, such as U3 and U5, SD-ClusPr decides to re-cluster that +remarkably improves the clustering coherency. +90 + +3.10 Summary +In this chapter, we propose two secure clustering solutions, namely +ClustCrypt and ClusPr in the form of trusted applications for three forms of +unstructured datasets, namely static, semi-dynamic, and dynamic. The proposed +clustering functions based on statistical characteristics of the datasets to: (A) +determine the suitable number of clusters; (B) populate the clusters with topically +relevant tokens; and (C) adapt the cluster set based on the dynamism of the +underlying dataset. Experimental results, obtained from evaluating ClusPr against +other schemes in the literature, on three different test datasets demonstrate between +30% to 60% improvement on the cluster coherency. Moreover, we notice that +employing ClusPr within a privacy-preserving enterprise search system can reduce +the search time by up to 78%, while improving the search accuracy by up to 35%. +In the next chapter, we explore how to enable secure enterprise search over +unstructured data without jeopardizing its confidentiality. +91 + +Chapter 4: +Edge-Based Intelligence for Privacy-Preserving Enterprise +Search on the Cloud +4.1 Overview +Cloud-based enterprise search services (e.g., AWS Kendra) have been +entrancing big data owners by offering convenient and real-time search solutions to +them. However, to offer an intelligent search over the privacy-preserving data, these +services have to access the user’s search history that further jeopardizes his/her +privacy. To overcome the privacy problem, the main idea of this research is to +separate the intelligence aspect of the search from its pattern matching aspect. +According to this idea, the search intelligence is provided by an on-premises edge +tier and the shared cloud tier only serves as an exhaustive pattern matching search +utility. We propose Smartness at Edge (SAED mechanism) that offers intelligence +in the form of semantic and personalized search at the edge tier while maintaining +privacy of the search on the cloud tier. At the edge tier, SAED uses a +knowledge-based lexical database to expand the query and cover its semantics. +SAED personalizes the search via an RNN model that can learn the user’s interest. +A word embedding model is used to retrieve documents based on their semantic +relevance to the search query. +4.2 Problem Statement +Ideally, data owners desire a privacy-preserving cloud service that offers +semantic and personalized searchability in a real-time manner, without +overwhelming their resource-constrained (thin) client devices (e.g., smartphones). A +92 + +large body of research has been undertaken on privacy-preserving enterprise search +services in the cloud [55, 57, 103, 53, 3] whose goals are to protect user’s sensitive +data from internal and external attackers. However, most of these works fall short +in retrieving search results that are semantically relevant to the context and user’s +interest (i.e., personalized search) [3, 53]. In addition, these works often rely on the +client device and impose significant overhead on it to perform a secure query +processing or to encrypt/decrypt user documents. +To satisfy all of the aforementioned desires of a particular user, our main +idea in this research is to separate the intelligence aspect of the enterprise search +from its pattern matching aspect. +93 + +4.3 SAED: Smart Edge-Leveraged Enterprise Search System +4.3.1 Architectural Overview +In this part, we provide a bird-eye view of the SAED system, that enables +intelligent and secure enterprise search on the cloud. The system is structured +around three tiers, shown in Figure 1.2, and explained as follows: +• Client tier (e.g., smartphone, tablet) contains a lightweight application that +provides a user interface for uploading documents and to search over them in +the cloud. Datasets are either uploaded by the user or by the organization +that owns the data. +• Edge tier extracts representative keywords of the documents being uploaded +to the cloud tier and builds an index on the cloud tier. Upon receiving a +search query from the client tier, the SAED system on the edge tier offers +intelligence by considering the query semantics and the user’s interest. The +edge tier is located in the client’s premises, hence, deemed as an honest and +secure system. To offer a secure enterprise search service, the edge tier +encrypts both the uploaded data and the search query. In addition, it +decrypts the result set before delivering it back to the client tier. +• Cloud tier contains numerous high-end servers that are utilized for storing +(encrypted) data and performing the large-scale computation required to +exhaustively search against the index [53, 3]. The index can be clustered +based on the underlying topics of its keywords (please refer to our prior +94 + +works [3, 1] for further details). +Figure 4.1. +Architectural overview of the SAED system within edge tier and as +part of the three-tier enterprise search service. SAED provides semantic search via +identifying the query context and combining that with the user’s interests. Then, +Query Expansion and Weighting unit of SAED, respectively, incorporate the semantic +and assure the relevancy of the results. Solid and dashed lines indicate the interactions +from user to the cloud tier and from the cloud tier to the user respectively. +Query +Handler +Interest +Detector +Weighting Unit +Query +History +Context +Identifier +Query +Expansion +Ranking +Unit +         +Enterprise Search + Service +Cloud Tier +User +Edge Tier +SAED +~~ +~~ +In Figure 4.1, we depict the components of SAED and show the interactions +between them. At first, a user-provided search query is received by the Query +Handler that keeps track of the user’s search history and initializes the Context +Identifier unit whose job is to extract the context and disambiguate the query +phrase. Then, according to the extracted context, the query is proactively expanded +by the Query Expansion unit and a query set is constructed. To achieve the +personalized search, the Interest Detector unit of SAED leverages the user’s search +history to recognize his/her interest and weight each element of the query set (i.e., +expanded queries) based on its relatedness to the user interest. Once the pattern +matching phase is accomplished on the cloud tier, the resulted documents are +returned to SAED on the edge tier. Next, the Ranking Unit utilizes the assigned +95 + +Xweights to order the retrieved documents based on their relevance to the user’s +interest and generates a retrieved document list, denoted as Dθ, that is sent to the +user’s device. In the next parts, we elaborate on each unit of the SAED system. +4.3.2 Query Context Identification +Identifying the context of a given search phrase is vital to navigate the +search to the semantics intended by the user. Considering the example of cloud +computing as the search query, without a proper context identification the returned +document set can potentially include documents about sky and climate, whereas, +an efficient context identifier can recognize the right semantic and navigate the +search to the topics around distributed, edge, fog, and cloud computing. In +fact, identifying the context helps the Query Expansion unit to form a query set +diversified around relevant keywords that semantically represent the search query +and subsequently improve the relevancy of the results. +Prior context identification works (e.g., [104, 105, 62]) have the following +shortcomings: first, they often assume each keyword has the same importance in the +query and recognize the query context via averaging the embeddings of its +keywords. However, not all keywords in a query necessarily help in identifying the +context. For example, the keyword various in various cloud providers does not +bring any significance to the context and can be eliminated. Second, the embedding +methods used by the existing works always provide the same representation for a +given keyword, irrespective of the underlying context. This is particularly +problematic for ambiguous keywords whose meaning vary based on the query +96 + +context. For instance, the embedding of cloud in the aforementioned example +should be different when it is used along with the computing as opposed to when it +is used along with the weather in a given query. Third, existing methods only +consider the embeddings of the common keywords, while discarding most of the +name-entities (e.g., names and locations) that do not exist in the vocabulary of +Word2Vec [64, 106]. For instance, consider best selling books of J.K. Rowling +as the query; Book and Sell are identified as the query context and J.K. Rowling +is discarded. However, our analysis suggests that the context of a short query +phrase often has contextual association with the discarded name-entities. +To overcome the shortcomings and identify the actual context of a given +query, we propose to take a holistic approach and extract the semantic across query +keywords, proportionate to the importance of each keyword. The main output of the +Context Identification unit is a set of keywords, denoted as C, that collectively +represent the context of the query. +Specifically, to eliminate unimportant keywords that do not contribute to the +semantic of query Q, the Context Identification unit utilizes Yake [107], which is a +unsupervised keyword extractor that discards unimportant keywords of the query. +The remaining keywords (i.e., the trimmed query, denoted as the Q′ set) are +considered for context identification. To learn the true semantic of Q′, the unit +leverages the Lesk algorithm [106] of WordNet to disambiguate each keyword +q ∈ Q′. Lesk algorithm works based on the fact that keywords in a given sentence +(query) tend to imply a certain topic. For keyword q, Lesk can determine its true +97 + +semantics via comparing the dictionary definitions of q against other keywords in Q′ +(i.e., Q′ − {q}). Let cq be the set of keywords representing the context of q. Then, +the context of Q is determined as C = ∪∀q∈Q′cq. Lastly, the Context Identifier +recognizes name-entities from Q using WordNet and considers them as part of the +context, but in a separate set, denoted as N. The reason for considering a separate +set is that we apply a different treatment on N and C in the other units of SAED. +Algorithm 4: Pseudo-code to detect the context of a given query in the +Context Identification unit of SAED. +Input +: query Q +Output: C: set of keywords representing context of Q, +N: set of name-entity in Q +1 Function contextIdentification(Q): +2 +Q′ ← extract keywords from Q using Yake alg. +3 +foreach q ∈ Q do +4 +if q ∈ Name-entity then +5 +N ← N ∪ {q} +6 +end +7 +else +8 +if q ∈ Q′ then +9 +Eq ← define q based on Q′ − q using Lesk alg. +10 +c ← extract set of keywords of Eq using Yake alg. +11 +C ← C ∪ c +12 +end +13 +end +14 +end +15 +return C, N +16 end +Algorithm 4 provides a pseudo-code for identifying the context of incoming +query Q. The outputs of the pseudo-code are two sets, namely C and N, that +collectively represent the context of Q. In Step 2 of the pseudo-code, Yake +algorithm is used to filter Q by extracting its important keywords and generate the +98 + +Q′ set. Name-entities of Q are identified by checking against WordNet and form the +set N (Steps 4–6). Next, in Steps 8–12, for each keyword q ∈ Q′, the Lesk algorithm +is employed to disambiguate q and find its true definition with respect to the rest of +keywords in Q′. Important keywords of the definitions form the context set (C) for +Q. +4.3.3 Query Expansion Unit +The Query Expansion unit is in charge of proactively expanding the query +keywords based on their relevant synonyms that are in line with their identified +context. Neglecting the query context and blindly considering all the synonyms, as +achieved in [104, 105, 62, 3], leads to finding irrelevant documents. Accordingly, the +unit leverages the context of Q (i.e., C and N) to only find the set of synonyms, +denoted as P, that are semantically close to the query context. +Word2Vec [63] is a shallow neural network model that can be trained to +generate vector representation of keywords, such that the cosine similarity of two +given keywords indicates the semantic similarity between them. Accordingly, to +proactively expand each keyword q ∈ Q, the Query Expansion unit instruments +Word2Vec, pre-trained with Google News dataset [108], to form the set of +nominated synonyms, denoted as sq. Let si +q be a synonym of q (i.e., si +q ∈ sq). Then, +the similarity of si +q and the query context, denoted as sim(si +q, C), is defined based +on the sum of similarities with each element of C, as shown in Equation 4.1. +99 + +sim(si +q, C) = +� +∀Cj∈C +sim(si +q, Cj) +(4.1) +Then, si +q is chosen as an element of P, only if it is semantically close enough +to the query context. To determine the sufficient closeness, we consider sim(si +q, C) +to be greater than the mean of the pair-wise similarity across all members of sq +(i.e., sim(si +q, C) > µ∀q∀j(sim(sj +q, C))). We note that because the elements of C and +N represent the context of Q, they as well are added to P. +Algorithm 5 provides a high level pseudo-code for generating the expanded +query set P. In Steps 2–7 of the pseudo-code, the synonym set for each q is +generated. Next, the similarity between each word si +q and C is calculated. The +similarity values are used to calculate the mean similarity of all nominated queries +in Step 8. In Steps 9–15, expanded query set P is formed by including nominated +synonyms whose semantic closeness is greater than µ. Lastly, in Step 16, set P is +expanded by including context set and name-entities. +4.3.4 User Interest Detection +Detecting the user’s search interest is essential to deliver personalized search. +In SAED, interest detection is achieved by analyzing two factors: (A) the user’s +search history; and (B) the user’s reaction to the retrieved results of prior search +queries. This can be detected based on the results chosen by the user or the time +spent for browsing them. +Let ∆′ represent the whole resulted documents that are sent to the user and +τ represent the documents where the user is interested in. We have τ ⊆ ∆′. +100 + +Algorithm 5: Pseudo-code to expand query based on the context in the +Query Expansion unit of SAED +Input +: Q, C, N +Output: P: the expanded query set +1 Function +QueryExpansion(Q, C, N) +2 +foreach q ∈ Q do +3 +sq ← use WordNet to obtain synonym set of q +4 +foreach si +q ∈ sq do +5 +sim(si +q, C) ← +� +∀Cj∈C +sim(si +q, Cj) +6 +end +7 +end +8 +µ ← calculate mean sim(sj +q, C) across all q ∈ Q, ∀sj +q ∈ sq +9 +foreach q ∈ Q do +10 +foreach si +q ∈ sq do +11 +if sim(si +q, C) > µ then +12 +Add si +q to set P +13 +end +14 +end +15 +end +16 +P ← P ∪ C ∪ N +17 +return P +18 end +101 + +Accordingly, the user’s interest can be derived from the topics of τ. The Interest +Detector unit uses an existing document classification model [109], operating based +on Na¨ıve Biased (NB) method, to determine the topics of τ, denoted as tτ. We also +perform majority voting on tτ to find the user’s main interest. The process is +repeated to store n-prior search interests data of the user. The data is characterized +as sequential as it is harvested from each successful search. By analyzing the user’s +prior search interests, the edge tier trains a recurrent neural network-based +prediction model [110] that can predict the user’s search interest. In case of SAED, +as the data does not contain long dependency and to keep the model simple and to +maintain real-timeliness, instead of a stacked (i.e., deeper) model, we feed the +harvested user-specific historical search data to train a many-to-one vanilla RNN +model [111]. +4.3.5 Weighting Unit +Once SAED learns the user interest, the next step to accomplish a +context-aware and personalized enterprise search is to determine the closeness of +contextually-expanded queries (i.e., elements of P) to the user’s interest. In fact, +not all expanded queries have the same significance in the interpretation of the +query. Accordingly, the objective of the Weighting unit is defined as quantifying the +closeness of each expanded query to the user’s interest. Later, upon completion of +the search operation on the cloud tier, the weights are used by the Ranking unit of +SAED to prune and sort the result set. +Prior weighting schemes (e.g., [53, 3, 62, 59, 105]) often use the word +102 + +frequency-based approach (e.g., TF-IDF [3]) and discard the user interests. +Alternatively, the weighting procedure of SAED quantifies the importance of each +expanded query p ∈ P based on two factors: (A) The type of p, which means if it +directly belongs to the context (C and N sets) or is derived from them; and (B) The +semantic similarity of p to the user interest. +In particular, those elements of P that directly represent the query context +or name-entities (i.e., ∀p|p ∈ P ∩ (C ∪ N)) explicitly indicate the user’s search +intention, hence, weighting them should be carried out irrespective of the user +interest. A deeper analysis indicates that name-entities that potentially exist in a +query represent the search intention, thus, biasing the search results to them can +lead to a higher user satisfaction. As such, the highest weight is assigned to +∀p|p ∈ (P ∩ N). The highest weight is determined by the domain expert, however, +in the experiments we consider it as ηmax = 1. We define the contribution of q ∈ Q +as the ratio of the number of keywords added to C because of q (denoted Cq) to the +cardinality of C. Let ηp denote the weight of p ∈ P. Then, for those elements of P +that are in the query context (i.e., ∀p ∈ (P ∩ C)), ηp is calculated based on the +contribution of the query keyword q corresponding to p. Equation 4.2 formally +represents how ηp is calculated. +ηp = ηmax· |Cq| +|C| +(4.2) +The weight assignment for those p that are derived from elements of C, as +explained in Section 4.3.3 +, (i.e., ∀p|p ∈ P − (C ∪ N)) is carried out via considering +semantic similarity of p with the user interest θ. That is, ηp = sim(p, θ). +103 + +Algorithm 6 provides the high level pseudo-code for distributing weight to +the expanded query set P. The algorithm considers P, C, N, and highest weight +value η as the inputs. After assigning weights to ∀p iteratively, it returns the +weights mapped with corresponding p as a hash map denoted as ϖ. In Step 2 of the +pseudo code, θ gets the user’s search interest that is identified by leveraging a +pre-trained document classifier and a vanilla RNN model. In the following Step, +hash map ϖ is initialized to contain the weights that mapped with corresponding p. +Overall, in Steps 4–15, weight of each p denoted as ϖp is calculated according +to its type. Specifically, in Steps 5–7, ϖp, where p ∈ (P ∩ N) is set by directly +assigned η. In Steps 8–11, p, where p ∈ (P ∩ C) is weighted based on its contribution +towards context C. At first, q is determined that generates p and weight ϖp of p is +calculated by the ratio between η and total number of keywords added in C for the +corresponding q. In the following Steps (12–14), ϖp, where p ∈ P − (C ∪ N) is +calculated by its semantic similarity with θ. Lastly, the algorithm is finished by +returning hash map ϖ filled with weights corresponding to their q (Step 16). +4.3.6 Ranking Unit +Once the expanded query set P is formed, the cloud tier performs string +matching for each p ∈ P across the index structure. We note that, if the user +chooses to perform a secure search, the elements of P are encrypted before delivered +to the cloud tier. In addition, in our prior works [1], we proposed methods for the +cloud tier to cluster the index structure and perform the pattern matching only on +the clusters that are relevant to the query. +104 + +Algorithm 6: Pseudo-code to weight expanded query +Input +: P, C, N, η +Output: ϖ +1 Function +weighting(P, C, N, η) +2 +θ ← predict a user’s search interest +3 +ϖ ← initialize hash map to store weights mapped with their +corresponding keywords +4 +foreach p ∈ P do +5 +if p ∈ N then +6 +ϖp ← η +7 +end +8 +else if p ∈ C then +9 +ϖp ← ηmax· |Cq| +|C| +10 +end +11 +else +12 +ϖp ← sim(p, θ) /*Compute similarity and store it in hash map */ +13 +end +14 +end +15 +return ϖ +16 end +105 + +The cloud tier returns the resulted document set, denoted as ∆, to the edge +tier where the Ranking unit of SAED ranks them based on the relevance and the +user’s interest and generates a document list, called ∆′ to show to the user. For a +document δi ∈ ∆, the ranking score, denoted as γi, is calculated by aggregating the +importance values of each p ∈ P within δi and with respect to its weight (ηp). The +importance of p in δi is conventionally measured based on the TF-IDF score [112]. +Accordingly, γi is formally calculated based on Equation 4.3. +γi = +� +∀p∈P +� +ηp · TF-IDF(p, δi) +� +(4.3) +The TF-IDF score of p in δi is defined based on the frequency of p in δi +versus the inverse document frequency of p across all documents in ∆. Details of +calculating the tf-idf score can be found in [112]. Once the Ranking unit calculates +the ranking score for all δi ∈ ∆, then the documents are sorted in the descending +order based on their ranks and thus, the document list ∆′ are formed with each δi +and displayed to the user. +106 + +4.4 SAED As a Pluggable Module Enterprise Search Solutions +The advantage of SAED is to be independent from the enterprise search +service deployed on the cloud tier. That is, using SAED neither interferes with nor +implies any change on the cloud-based enterprise search service. SAED can be +plugged into any enterprise search solution. It provides the search smartness on the +on-premises edge tier and leaves the cloud tier only for large-scale pattern matching. +The whole SAED solution reforms the enterprise search to be semantic, +personalized, and confidential services. +In this work, we set SAED to work both with AWS Kendra and S3BD. In +the case of using AWS Kendra, the Query Expansion unit sends the expanded query +set P to Kendra to search each keyword p against the dataset on the Amazon cloud. +The resulted documents are received by SAED and ranked before being delivered to +the client tier. In the implementation, we only show top 10 documents from the +resulted list to the user. Similarly, we plugged SAED to S3BD to perform +confidential semantic search on the cloud. Because S3BD maintains an encrypted +index structure that has to be traversed against each search query, the elements of +P had to be encrypted before handing them over to the cloud tier. We also verified +SAED when it is used along with AWS Kendra where the dataset was encrypted. +We noticed that SAED can achieve smart search even when Kendra is set to work +with encrypted dataset. The performance measurement and analysis of using SAED +along with AWS Kendra and S3BD are elaborated in the next Section. +107 + +4.5 Performance Evaluation of SAED +4.5.1 Experimental Set up +We have developed a fully working version of SAED and made it available +publicly in our Githuba page. To conduct a comprehensive performance evaluation +of SAED on the enterprise search solutions, we developed it to work with both +S3BD [3] and AWS Kendra [113]. S3BD already has the query expansion and +weighting mechanisms, but we deactivated them and set it to use the expanded +queries generated by SAED. In the experiments, the combination of SAED and +S3BD is shown as SAED+S3BD. Likewise, the combination of SAED and AWS +Kendra is shown as SAED+Kendra. +We evaluated SAED using two different datasets, namely Request For +Comments (RFC) and BBC that have distinct properties and volume. The reason we +chose the RFC dataset is that it is domain-specific and includes 4, 951 documents +about the Internet and wireless communication network. Alternatively, the BBC +dataset is more diverse. It includes 2, 224 news documents in five distinct categories, +including politics, entertainment, business, sports, and technology. +To conduct a comprehensive evaluation, we used both systematic metrics and +human-based feedback as elaborated in Section 4.5.3 +. We deployed and experimented +SAED on a Virtual Machine (VM) within our local edge computing system. The +VM had two 10-core 2.8 GHz E5 Xeon processors with 64 GB memory and Ubuntu +18.4 operating system. +ahttps://github.com/hpcclab/SAED-Security-At-Edge +108 + +Table 4.1. Benchmark search queries developed for the RFC and BBC datasets. +BBC Dataset +RFC Dataset +European Commission (EC) +Network Information (NI) +Parliament Archives (PA) +Host Network Configuration (HNC) +Top Camera Phones 2020 (TCP) +Data Transfer (DT) +Credit Card Fraud (CCF) +Service Extension(SE) +Animal Welfare Bill (AWB) +Transport Layer (TL) +Piracy and Copyright Issues (PCI) +Message Authentication (MA) +Car and Property Market (CPM) +Network Access (NA) +Rugby Football League (RFL) +Internet Engineering (IE) +Opera in Vienna (OV) +Fibre Channel (FC) +Windows Operating System (WOS) +Streaming Media Service (SMS) +4.5.2 Benchmark Queries +The datasets that we use to carry out the experiments are not featured with +any benchmark. Therefore, we required to develop benchmark queries for the +datasets before evaluating the performance of SAED. We developed 10 benchmark +queries, shown in Table 4.1, for each one of the two datasets. The benchmark +queries are proactively designed to explore the breadth and depth of the datasets in +question. In addition, some of the queries intentionally contain ambiguous keywords +to enable us examining the context detection capability of SAED. For the sake of +brevity, we provide one acronym for each benchmark query (see Table 4.1). For each +benchmark query, we collected at most the top-20 retrieved documents. Then, the +quality of the retrieved documents were measured via both automated script and +human-based users. +4.5.3 Evaluation Metrics +We have to measure the search relevancy metric to understand how related +109 + +the resulted documents are with respect to the user’s query and how they meet the +his/her interests. For the measurement, we use TREC-Style Average Precision +(TSAP) score, described by Mariappan et al. [102]. TSAP provides a qualitative +score in a relatively fast manner and without the knowledge of the entire dataset [3]. +It works based on the precision-recall concept that is commonly used for judging +text retrieval systems. The TSAP score is calculated based on +N +� +i=0 +ri/N, where ri +denotes score for ith retrieved document and N denotes the cutoff number (total +number of retrieved documents). Since we consider N = 10, we call the scoring +metric as TSAP@10. +To determine ri for retrieved document δ′ +i ∈ ∆′, we conducted a +human-based evaluation. We engaged five volunteer students to judge the relevancy +of each retrieved document. For every search query, the volunteers labeled each +retrieved document as highly relevant, partially relevant, or irrelevant. +After performing majority voting based on the provided responses for document i, +the value of ri is determined as follows: +• ri = 1/i if a document is highly relevant +• ri = 1/2i if a document is partially relevant +• ri = 0 if a document is irrelevant +We report TSAP@10 score to show the relevancy of results for each +benchmark query. In addition, mean TSAP score is reported to show the overall +relevancy across each dataset. As we set the top 10 documents to be retrieved for +110 + +each search, the highest possible for TSAP@10 score can be 0.292 [102]. +In addition to the TSAP score, we measure Mean F-1 score too to compare +the search quality offered by the SAED-plugged enterprise search solutions against +the original enterprise search solutions (i.e., without SAED in place). The F-1 score +maintains a balance between the precision and recall metrics, which is useful for +unstructured datasets with non-uniform topic distribution. +4.5.4 Evaluating Search Relevancy +The purpose of this experiment is to evaluate the search relevancy of +enterprise search systems that have SAED plugged into them and compare them +against the original (unmodified) systems. To evaluate the personalized search, we +set (assumed) technology as the user’s interest for both datasets. We note that, in +this part, the enterprise search solutions (S3BD and AWS Kendra) are set to work +in the plain-text datasets. +S3BD vs SAED+S3BD. +Figure 4.2a shows the TSAP@10 score for the RFC +and BBC datasets for the original S3BD and SAED+S3BD. The horizontal axes in +both subfigures show the benchmark queries and the vertical axes show the search +relevancy based on the TSAP@10 score. +In both Figure 4.2a and 4.2b, we observe that for all queries in both +datasets, SAED+S3BD outperforms the S3BD system. In addition, we observe that +S3BD produces less relevant results for the BBC dataset compared to the RFC +dataset. This is because, unlike the RFC dataset, in several cases, the exact +keywords of the benchmark queries do not exist in the BBC dataset. The worst case +111 + +Figure 4.2. Comparing TSAP@10 scores of SAED+S3BD and S3BD systems. Hor- +izontal axes show the benchmark queries. +EC +PA +TCP +CCF +AWB +PCI +CPM +RFL +OV +WOS +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +0.30 +TSAP@10 Score +SEA+S3BD +S3BD +(a) BBC dataset +NI +HNC +DT +SE +TL +MA +NA +IE +FC +SMS +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +0.30 +TSAP@10 Score +SEA+S3BD +S3BD +(b) RFC dataset +Figure 4.3. Comparing TSAP@10 scores obtained from SAED+Kendra versus AWS +Kendra in searching benchmark queries. +EC +PA +TCP +CCF +AWB +PCI +CPM +RFL +OV +WOS +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +0.30 +TSAP@10 Score +SAED+Kendra +Kendra +(a) BBC dataset +NI +HNC +DT +SE +TL +MA +NA +IE +FC +SMS +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +0.30 +TSAP@10 Score +SAED+Kendra +Kendra +(b) RFC dataset +of these issues has occurred for the PCI query in S3BD, because its query expansion +procedure could not capture the complete semantics. In contrast, SAED+S3BD is +able to handle the cases where the exact keyword does not exist in the dataset, +thus, we see that it yields to a remarkably higher relevancy. +Even if we consider PCI as an outlier and exclude that from the analysis, in +Figure 4.2a, we still notice that the TSAP@10 score of SAED+S3BD is on average +41.2% higher than S3BD. Although the difference between S3BD and SAED+S3BD +is less significant for the RFC dataset (in Figure 4.2b), we still notice some 17% +improvement in TSAP@10 score. This is because RFC is a domain-specific dataset +112 + +Figure 4.4. +Comparing TSAP@10 scores obtained from SAED+Kendra vs AWS +Kendra systems in the encrypted domain. +EC +PA +TCP +CCF +AWB +PCI +CPM +RFL +OV +WOS +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +0.30 +TSAP@10 Score +SAED+Kendra +Kendra +(a) Encrypted BBC dataset +NI +HNC +DT +SE +TL +MA +NA +IE +FC +SMS +0.00 +0.05 +0.10 +0.15 +0.20 +0.25 +0.30 +TSAP@10 Score +SAED+Kendra +Kendra +(b) Encrypted RFC dataset +and the exact keywords of queries can be found in the dataset, hence, making use of +smart methods to extract the semantic is not acute to earn relevant results. From +these results, we can conclude that SAED can be specifically effective for generic +datasets where numerous topics exist in the documents. +AWS Kendra vs SAED+Kendra. +In Figures 4.3a and 4.3b, we report +TSAP@10 score obtained from AWS Kendra versus SAED+Kendra for BBC and +RFC datasets, respectively. Specifically, in Figure 4.3a (BBC dataset), a significant +improvement (on average 26.5%) is noticed in the TSAP@10 score of +SAED+Kendra. However, unlike SAED+S3BD, SAED+Kendra does not beat +Kendra for all the queries. The reason Kendra outperforms SAED+Kendra for AWB +and CPM queries is that SAED injects extra keywords and sends the expanded query +set to AWS Kendra. Then, Kendra returns documents that are related to the +queries and to the expanded keywords. We realized that the Ranking unit of SAED +occasionally prioritizes documents that include keywords of the expanded queries +instead of those with the query keywords. +113 + +Similar to the S3BD experiment, we observe that the relevancy resulted from +Kendra and SAED+Kendra is less significant for RFC. However, we still obtain +around 12% improvement in TSAP@10 score according to Figure 4.3b. +4.5.5 Relevancy of Privacy-Preserving Enterprise Search +To examine the efficiency of SAED for privacy-preserving enterprise search +systems, we conducted experiments using encrypted BBC and RFC datasets. The +encrypted datasets were uploaded to the cloud tier and the expanded queries were +also encrypted and searched on the cloud tier via Kendra. +We use the TSAP@10 score, as shown in Figure 4.4a and 4.4b, for the BBC +and RFC datasets, respectively. Figure 4.4a indicates that SAED+Kendra +substantially outperforms Kendra for all the benchmark queries. We can see that +for encrypted dataset Kendra cannot do anything except pattern matching and +returning documents that exactly include the encrypted query. Therefore, searching +for several queries (e.g., PA,TCP, CPM, etc.) does not retrieve any documents. We +notice that, in both systems, the highest TSAP@10 score is in searching EC. The +reason is the high number of documents in BBC that contain the exact phrase +European commission. +The reported TSAP@10 scores for the RFC dataset in Figure 4.4b shows a +clear improvement in compared with the BBC dataset. We observe that seven out +of ten queries provide an equal TSAP@10 scores in both systems. The reason that +makes Kendra competitive to SAED+Kendra is the exact availability of the +benchmark queries in RFC. However, for HNC and FC, the exact query keywords are +114 + +not present in the dataset, hence, Kendra fails to find any results. +4.5.6 Discussion of the Relevancy Results +In Table 4.2, we report mean F-1 and mean TSAP@10 scores for the +SAED-plugged enterprise search systems along with their original versions upon +utilizing the datasets both in the plain-text and encrypted forms. From the table, +we notice that, regardless of the enterprise search system being employed, a higher +search relevancy is consistently achieved for the RFC dataset as opposed to the +BBC dataset. +The search relevancy is consistently improved when SAED+Kendra is used +and it provides on average of 23% improvement in mean F-1 score and 21% in the +mean TSAP@10 score. Although original S3BD is the underperformer, using +SAED+S3BD improves its mean F-1 and mean TSAP@10 scores by on average of +40% and 32%, respectively. +Table 4.2. +Comparing the mean F-1 and the mean TSAP@10 scores obtained from +SAED-plugged enterprise search systems versus their original forms. The highest resulted +scores are shown in bold font. +BBC +RFC +Systems +Mean +F-1 +Mean +TSAP@10 +Mean +F-1 +Mean +TSAP@10 +S3BD +0.50 +0.17 +0.80 +0.24 +SAED+S3BD +0.82 +0.25 +0.92 +0.28 +Kendra +0.67 +0.20 +0.88 +0.26 +SAED+Kendra +0.90 +0.27 +0.93 +0.28 +Kendra (Encry.) +0.31 +0.09 +0.75 +0.22 +SAED+Kendra (Encry.) +0.73 +0.22 +0.90 +0.27 +In the encrypted domain, we notice that SAED+Kendra offers a +115 + +substantially higher (up to 130%) search relevancy for BBC dataset. As the exact +keywords of the given search queries are not present in the encrypted form of BBC +dataset, AWS Kendra fails to perform semantic search, rather does only a pattern +matching, which makes it an underperformer for this dataset. On the other hand, +search relevancy is improved for RFC dataset since mean F-1 and mean TSAP@10 +scores are improved by at least 20%. This is because, most of the queries are +present exactly in the dataset and Kendra retrieves most of the relevant documents +by relying only on pattern matching. +4.5.7 Evaluating the Search Time +Figure 4.5 presents the total incurred search time of the experimented +queries for each dataset. The search time is calculated as the summation of the +elapsed time taken by a query to be processed (e.g., expansion, weighting) and +turnaround time until the result set is received. To eliminate the impact of any +randomness in the computing system, we searched each set of experimented queries +10 times and reported the results in the form of box plots. The figure indicates that +S3BD system has the highest search time overhead for both datasets which could +impact real-time searchability in case of big data. SAED+S3BD incurs less query +processing time overhead compared to the original (unmodified) S3BD system. +On the other hand, AWS Kendra causes the lowest time overhead for both +datasets compared to SAED+Kendra. SAED+Kendra causes around 4 times more +time overhead compared to original Kendra. However, in the prior set of +experiments, we determine that SAED+Kendra achieves a substantially higher +116 + +search relevancy for most of the queries and, particularly, for datasets with privacy +constraints. +Figure 4.5. +Search time comparison among S3BD, Kendra, SAED+S3BD, and +SAED+Kendra systems. +BBC +RFC +0 +2 +4 +6 +8 +10 +Search Time (S) +S3BD +Kendra +SAED+S3BD +SAED+Kendra +117 + +4.6 Summary +A context-aware, personalized, and privacy-preserving enterprise search +service is the need of the hour for data owners who wish to use cloud services. Our +approach to address this demand was to separate the search intelligence and privacy +aspects from the pattern matching aspect. We developed SAED that achieves +privacy and intelligence at the edge tier and leaves the large-scale pattern matching +for the cloud tier. SAED is pluggable and can work with any enterprise search +solution (e.g., AWS Kendra and S3BD) without dictating any change on them. +Utilizing edge computing on the user’s premises preserves the user’s privacy and +makes SAED a lightweight solution. Leveraging recurrent neural network-based +prediction models, WordNet database, and Word2Vec, SAED proactively expands a +search query in a proper contextual direction and weights the expanded query set +based on the user’s interest. In addition, SAED provides the ability to perform +semantic search while the data are stored in the encrypted form on the cloud. In +this case, the existing enterprise search solutions just perform the pattern matching +without knowing the underlying data. Evaluation results, verified by human users, +show that SAED can improve the relevancy of the retrieved results by on average +≈ 24% for plain-text and ≈ 75% for encrypted generic datasets. +118 + +Chapter 5: +Multi-Tenancy of Latency-Sensitive Deep Learning +Applications on Edge +5.1 Overview +In the prior chapter, we propose an enterprise search application, namely +SAED in the form of a trusted application for enabling secure search over +confidential data in the cloud. The SAED application spans across edge-to-cloud +continuum and consists of several microservices that run on edge to perform the +intelligent aspects of searching (i.e., query processing, personalization, and ranking). +Our investigation indicates that running a number of microservices on the edge +consumes a significant percentage of resource, specifically, edge memory is exhausted +and service(s) can either be killed or failed to execute. Prior studies quantized the +NN models to make them lighter but without model management, the system +cannot get actual advantage of multi-tenant processing. Edge-MultiAI leverages NN +model compression techniques, such as model quantization, and dynamically loads +NN models for DL applications to stimulate multi-tenancy on the edge server. We +consider the problem and scale it up in order to come across a unified solution of it. +Due to the robust uses of smart IoT-based systems, various application +requests (i.e., object detection, face recognition, NLP, and motion capture) +incoming from users’ devices execute on edge tier with low-latency constraint on a +daily basis. An exemplar use case of such IoT-based systems is SmartSight [19], +illustrated in Figure 5.1, that aims at providing ambient perception for the blind +and visually impaired people. The system operates based on a smartglass (IoT +119 + +Figure 5.1. Bird-eye view of SmartSight, an IoT-based system that continuously +receives various inputs from the smartglass (IoT device) sensors, and processes them +via multi-tenant DL applications running on the edge server. +IoT device +speech rec. +NLP +face rec. +memory +edge system +processors +multi-tenant DL +applications +object det. +video +camera +voice +storage +device) and a companion edge server (e.g., smartphone). The smartglass +continuously captures the inputs via its sensors (e.g., camera and microphone) and +requests the edge server to process DL-based applications, such as object detection +to identify obstacles; face recognition to identify acquainted people; speech +recognition, and NLP to understand and react to the user’s commands. To make +SmartSight usable, the edge server has to continuously execute multiple (a.k.a. +multi-tenant) DL application to process incoming requests with low-latency and +high accuracy. It is noteworthy that, although cloud datacenters can mitigate the +inherent resource limitations of the edge, due to the network latency overhead and +data confidentiality [14, 15, 16], offloading the latency-sensitive service requests to +the cloud is not a tractable approach in many use cases. +DL applications utilize bulky Neural Network (NN) models at their kernel to +120 + +315Table 5.1. Load time, inference time, and accuracy of popular NN models individ- +ually running on Samsung Galaxy S20+ as the edge server. +NN Models +Bit +Width +Size +(MB) +Loading +Time (ms) +Inference +Time (ms) +Accu- +racy (%) +InceptionV3 +FP32 +105 +650 +100 +78.50 +INT8 +24 +380 +80 +77.20 +VGG16 +FP32 +528 +820 +52 +71.30 +INT8 +132 +185 +40 +70.18 +MobileNetV1 +FP32 +89 +600 +15 +70.56 +INT8 +23 +192 +8 +65.70 +MobileNetV2 +FP32 +26 +110 +10 +72.08 +INT8 +9 +65 +7.5 +63.70 +MobileNetV3 +FP32 +14 +80.3 +7.80 +74.04 +INT8 +8 +47.45 +6.21 +71.32 +MobileBERT +FP32 +96 +1100 +62 +81.23 +INT8 +26 +890 +40 +77.08 +infer on the inputs received from the sensors. The NN models have to be kept in +memory to enable low-latency (a.k.a. warm-start [31]) inference operations. +Otherwise, because the NN model size is often huge, loading it into the memory in +an on-demand manner (a.k.a. cold-start) is counterproductive and affects the +latency constraint of the DL applications. As the edge servers naturally have a +limited memory size (e.g., 4 GB in the case of Jetson Nano [32]), multi-tenant +execution of DL applications on them leads to a memory contention challenge across +the processes [14, 33]. +Accordingly, the main challenge of this study is to resolve the memory +contention across multi-tenant DL applications without compromising their latency +and accuracy constraints. +In the deep learning context, there are techniques based on the idea of +approximate computing, such as quantization [114], that make the model +121 + +edge-friendly via compressing its NN model, hence, reducing its inference time and +accuracy. To understand the impact of such approximations, we conducted a +preliminary experiment using a Samsung Galaxy S20+ as the edge server; and five +popular DNN models, namely InceptionV3, VGG16, MobileNetV1, MobileNetV2, +MobileNetV3, MobileBERT, each one at two quantization (precision) levels, namely +FP32 and INT8 bit widths. In Table 5.1, we report the average loading time, +inference time, and accuracy for their individual executions. We observe that: (A) +for all the models, the loading time is 8—17× more than its inference time; (B) +Loading the high-precision model (FP32 bit width) occupies ≈3.5× more memory +than the low-precision (INT8 bit width) one; and (C) Loading a low-precision model +can reduce the inference accuracy by around 3—6%. These results demonstrate that +the model compression has a considerable potential to mitigate the memory +footprint of the DL applications. Moreover, the model loading time invariably +dominates the inference time [115]. Accordingly, our hypothesis is that the efficient +use of model compression and the edge memory can enhance the multi-tenancy and +inference time of DL applications without any major loss on their inference accuracy. +We propose each DL application to be equipped with multiple NN models +with different precision levels. The low-precision models have a small memory +footprint, hence, allowing for a higher multi-tenancy of DL applications with their +models loaded into the memory (i.e., warm-start inference) that enhances the +service latency. However, loading overly low-precision (over-quantized) models to +maximize multi-tenancy and warm-start inference is not viable, because it reduces +122 + +the inference accuracy and renders the multi-tenant DL applications to be futile. +On the contrary, loading high-precision (large) NN models on a memory-limited +edge system for an indefinite time period unnecessarily occupies an excessive +memory space that is detrimental for the multi-tenancy and warm-start inference of +other tenants. That is, other tenants face a significant slow down (as noted in +Table 5.1), because they cannot keep their NN model in memory and have to load it +from the storage (i.e., cold-start) to perform the inference operation. Therefore, an +ideal solution for a multi-tenant edge system should be able to dynamically load a +suitable model from the set of models available to the application (a.k.a. model +zoo), such that it neither interrupts the execution of other applications, nor causes a +cold-start inference for them. +5.2 Problem Statement +The research question that we investigate is: how to maximize the number of +warm-start inferences for multi-tenant DL applications on edge without +compromising the inference accuracy? The question indicates a trade-off between +two objectives: fulfilling the latency constraint of DL applications and maintaining +their inference accuracy. The former objective entails having the NN models of DL +applications loaded into the memory (i.e., warm-start inference), whereas, the latter +entails retaining high-precision NN models in the memory. +For application Ai ∈ A with Mi = {mk +i | 1 ≤ k ≤ qi} as its model zoo, let +ri(t) be a Boolean function that represents an inference request for Ai at time t with +value 1. Also, let m∗ +i ⊆ Mi be an NN model of Ai with size of s∗ +i that is currently +123 + +loaded in the memory. This means that, for application Aj that does not have any +of its NN models currently in the memory, we have m∗ +j = ∅ and s∗ +j = 0. Then, +M ∗ = +n� +i=1 +m∗ +i represents the set of currently loaded NN models that occupy +S∗ = +n +� +i=1 +s∗ +i of the memory space. A cold start event for the request arrives at time t +for Ai, denoted Ci(M ∗, t) and shown in Equation (5.1), occurs when there is no NN +model in memory for Ai (i.e., Mi ∩ M ∗ = ∅). +Ci(M ∗, t) = +� +ri(t) +Mi ∩ M ∗ = ∅ +0 +otherwise +(5.1) +Assume that utilizing m∗ +i ∈ Mi results in an inference accuracy that we +denote it as χ∗ +i . Then, based on Equation (5.2), for n multi-tenant DL applications, +we can formally state the objective function as minimizing the total number of +cold-start inferences, while maximizing the accuracy of the inferences. In this case, +the total memory size available for the NN models (denoted S) serves as the +constraint. +min +�� ∞ +t +n +� +i=1 +Ci(M ∗, t) dt +� +, +max +�� ∞ +t +n +� +i=1 +χ∗ +i (t) dt +� +subject to: +∀t, +n +� +i=1 +s∗ +i ≤ S +(5.2) +Note that optimal NN model management decisions do not have a greedy +nature. That is, minimizing the number of cold-start inferences at a given time t +does not necessarily lead to the minimum total number of cold-starts with +maximum accuracy during the entire applications’ lifetime. In other words, the +system may experience a cold-start at time t to prevent multiple ones at a later +124 + +time. That is why, the objective function of Equation 5.2 includes integrals over t to +the ∞ to encompass the impacts of the decisions at t on the future cold-starts and +accuracy levels. In the objectives, the NN models of application Ai are only chosen +from its model zoo (Mi), thus, the accuracy (µi(t)) and size functions (si) are +discrete functions. It is needless to say that minimizing the number of cold-start +inferences is equivalent to maximizing the number of warm-start events [116]. In the +rest of this chapter, we use these two interchangeably. +5.3 Solution Statement and Contributions +To stimulate multi-tenancy on the limited edge memory, we develop a +framework, called Edge-MultiAI, that takes advantage of a model zoo for each DL +application and can dynamically swap the NN models of the applications. To +maximize the number of warm-starts with high inference accuracy across +multi-tenant DL applications, our approach is to proactively load the high-precision +NN models for the applications that are expected to receive inference requests, +while loading low-precision models for the others. We utilize the recent memory +usage information to predict the memory availability for the next executions while +not interrupting other active applications. We develop model management heuristic +policies that make use of the expected memory availability and the usage pattern of +multi-tenant DL applications to choose a suitable NN model for the requester +application right before the inference operation, thereby, both the latency and +inference accuracy of the application are fulfilled. +125 + +Figure 5.2. +Architectural overview of the Edge-MultiAI framework with three tiers: +Application, NN Model Manager, and Memory. +logic +business +model +loader +NN Model +Manager +N +A +B +model +m1 +m2 +m3 +m4 +app request +C +predictor +memory +predictor +Tier +Memory +multi-tenant DL +processes +manager +memory +A +B +C +N +memory +optimizer +memory space of DL processes +zoo +Application + Tier +5.4 Architectural Overview & System Design of Edge-MultiAI +Figure 5.2 illustrates the architectural overview of Edge-MultiAI that +facilitates multi-tenancy of DL applications on a resource-limited edge system via +enabling the applications to only swap their NN models, instead of the entire +application. The framework consists of three tiers: (i) Application tier, (ii) NN +model manager, and (iii) Memory tier. +Application Tier. The incoming multi-modal inputs from the connected IoT +devices trigger execution of multi-tenant DL applications in the application tier. +The model zoo for each DL application acts as a repository that contains NN models +126 + +with different compression levels (sizes) and inference accuracy (a.k.a. various +precision levels). The model loader is responsible for loading the chosen NN model +from the model zoo into the edge memory. +NN Model Manager. NN model manager comprises of three components: (i) +application request predictor, (ii) memory predictor, and (iii) memory optimizer. +“Application request predictor” collects historical requests to each application and +trains a lightweight (edge-friendly) many-to-one vanilla recurrent neural network +(RNN) time series prediction model, similar to the one in [110], to periodically +foresee the inference request arrivals for each application. Upon arrival of each +request, “memory predictor” is in charge of predicting the memory availability +based on the recent memory allocations in the entire edge system. We leverage the +historical memory allocation data and train another many-to-one vanilla RNN +time-series prediction model to predict the available memory. +Memory optimizer interacts with the application “request predictor” and +“memory predictor” to receive: (A) the request arrival time for different applications +plus the information of their model zoo; and (B) the memory availability +information. Then, the memory optimizer feeds the received information to an NN +model management policy that determines the highest possible precision NN model +that can be loaded to serve the inference request of a DL application with the +minimum impact (in terms of the prediction accuracy or latency) on the execution +of other applications. Upon facing memory shortage for an arriving inference +request, the memory optimizer scavenges the memory allocated to the NN models of +127 + +other applications via either loading a lower-precision model or forcing them to +cold-start. After procuring adequate memory, the memory optimizer informs the +“model loader” to load the appropriate NN model of the requested application. +Memory Tier. The tier includes the “memory spaces” allocated to the +applications; and a “memory manager” that keeps track of the currently loaded +models, the available memory spaces, and the current status of the applications. +The memory manager communicates these information to the NN Model Manager +to efficiently allocates them to the arriving requests. +5.5 Heuristics to Manage Models of Multi-tenant Applications +5.5.1 Overview +Recall that the aim of NN model management policy is to minimize the +number of cold-start inferences and maximize the inference accuracy for +multi-tenant DL applications on the edge servers. To that end, the memory +optimizer strives to maximize the time to retain the loaded models in the edge +memory. However, due to limitations in the available memory space, it is not +possible to retain the highest precision NN model of all applications in the memory. +To resolve this memory contention, the NN models of the applications that are +unlikely to be requested in the near future should be assigned a lower priority to +remain in the memory. Furthermore, Edge-MultiAI makes it possible to +dynamically load NN models for the applications. This means that, upon predicting +time t as the inference request time for a given DL application, Edge-MultiAI can +be instructed to load the high-precision NN model of that application immediately +128 + +before performing the inference. Similarly, in the face of a memory shortage, for the +application(s) that are unlikely to be requested at time t, Edge-MultiAI can be +instructed to unload their NN models or, more interestingly, replace them with a +lower precision one. +However, we know that the request arrivals are inherently uncertain [19] and +no prediction model can precisely capture the exact request time for an application. +To capture the uncertainty, we consider a request time window, denoted as ∆, +around each predicted request time. The value of ∆ is obtained from profiling past +request predictions and calculating the mean difference of actual arrival time and +the predicted ones across all applications. In addition, there is a time overhead, +denoted as θi, to load the chosen NN model of an application Ai into the memory. +In sum, to prevent a cold-start for Ai that is predicted to perform inference at time +t, as shown in Figure 5.3, the NN model has to be loaded at time (ti − ∆ − θi) and +kept in memory until (ti + ∆). Furthermore, there is uncertainty in predictions of +“no request” for an application at a given time. That is, at time t, there can be an +inference request for an application that was predicted not to have an request at +that time. To make the system robust against this type of uncertainty and to avoid +cold-start inferences in these circumstances, an ideal policy should load +low-precision NN models for these applications. Hence, an unpredicted inference +request can be still served as a warm-start by the low-precision model and the +latency constraint is maintained. +In this work, the set of applications whose NN models are retained in +129 + +Figure 5.3. A sample scenario of inference requests for five multi-tenant applications, +namely A1 to A5. Each pulse represents the time window within which an inference +request is expected. Solid lines expresses the event that has already happened and +dashed lines after “now” are the request predictions. +request time +window +A1 +A2 +A5 +A3 +A4 +now +history window (H) +time +memory outside of their predicted request time window are called the minimalist +set, and denoted as A′. Similarly, the set of applications that are in their request +time window and we load a high-precision model for them are called maximalist, +and denoted as A∗. To resolve the memory contention, the policy can be based on +scavenging memory from the minimalist applications to procure the required +memory space for the maximalist ones. That is, in the event that application Ai is +predicted to have an inference at time ti, it becomes a member of A∗ set at time +ti − ∆ − θi, and then becomes a member of A′ set after ti + ∆; thus, its model can +be evicted from the memory in the event the memory space is needed for another +maximalist application. The NN model eviction is only permitted from A′ set and +we aim at retaining a low-precision model for the applications in this set. However, +130 + +due to high inference demand, A′ have to unload their models (i.e., switch to +cold-start) to free space for the model of the applications that are in the maximalist +set. In an extreme situation, if A′ is empty, or the scavenged memory from A′ +cannot procure sufficient space to load the suitable model for application Ai, the +next (smaller) model for Ai is considered, and the aforementioned steps are +repeated. Ultimately, if the scavenged memory space is inadequate for the lowest +precision model of Ai, an inference failure occurs. +The memory contention problem can be reduced to the classic binary +Knapsack optimization problem [117] where from a collection of items, each one +with a weight and a value, we need to select items such that the total value is +maximized, while the total weight is bounded to a limit. This problem is known to +be NP-Complete,hence, we can rely on the heuristic-based solutions for it [118]. In +the next part, we discuss four NN model management (a.k.a. NN model eviction) +policies to manage the memory for multi-tenant DL applications such that the +number of warm-start inferences is maximized without any major impact on the +inference accuracy. +5.5.2 Policy 1: Largest-First Model Eviction (LFE) +In this policy, to allocate memory for the NN model of a maximalist process, +we first evict NN models from set (A′ that occupy the highest memory space, until +there is enough space to allocate the high-precision NN model of A∗. For that +purpose, members of A′ are sorted based on the size of their currently loaded NN +model in the descending order. In the event that evicting all the NN models of A′ +131 + +does not free enough memory space to allocate the NN model of the request, a lower +precision NN model (smaller in size) is tried for allocation. This procedure +continues until a model from the model zoo can be allocated in the memory; +otherwise, the edge system is not able to serve that request at that time. +5.5.3 Policy 2: Best-Fit Model Eviction (BFE) +The limitation of LFE is to evict the largest NN models of the minimalist +applications, irrespective of the exact memory requirement. This means that +adopting LFE can free more memory space than the actual requirement. To tackle +the issue, we implement the BFE policy where applications in the minimalist set are +sorted based on the difference between their model sizes and the actual memory +requirement. Then, the NN model with a minimum difference is chosen for eviction. +The memory requirement for a maximalist application is first calculated based on +its highest precision (largest) NN model to gain the highest inference accuracy. +However, in the event that evicting the NN models of all the minimalist applications +do not free enough memory space to allocate the desired NN model, BFE iteratively +selects the next high-precision model from the model zoo of the requested +application. +5.5.4 Policy 3: Warm-Start-aware Best-Fit Model Eviction (WS-BFE) +Let Ai ∈ A∗ an application that is currently in the maximalist set, and +Aj ∈ A′ an application that is currently in the minimalist set. It is technically +possible that the predicted request time window of Ai overlaps with the one for Aj. +In this case, LFE and BFE policies potentially choose to evict the NN model of Aj +132 + +in favor of the Ai model. This is because both of these policies are backward-looking +and ignore the fact that Aj can be requested soon after evicting its NN model. Such +an eviction decision increases the likelihood of a cold-start inference and to avoid +that, we develop WS-BFE that assigns the lowest eviction priority to those +applications in A′ that have overlapping time window with Ai. +In our early experiments, we realized that another reason for cold-start +inferences is due to uncertain nature of request arrivals. That is, a minimalist +application is unexpectedly requested. To minimize the likelihood of cold-start +inference in these circumstances, we implement WS-BFE to replace the evicted NN +model with the lowest-precision (i.e., smallest) NN model of that application. As +such, in the event of an unpredicted request the minimalist applications, there is a +low-precision model available to carry out a warm-start inference. +5.5.5 Policy 4: Intelligent Warm-Start-aware Best-Fit Eviction +(iWS-BFE) +To make WS-BFE robust against uncertainties in the application request +time prediction, we enhance it by applying the Bayesian theory and proposing a +new policy, called iWS-BFE. This policy is inspired from the widely-adopted +LRU-K cache management policy [119] that considers the least recently used (i.e., +requested) applications are not likely to be requested in the near future. Similarly, +iWS-BFE only considers members of A′ as eviction candidates, denoted by E′, that +are not recently requested. Figure 5.3, shows a scenario of predicted request times +for A1—A5. To procure memory for A1, we have A′ = {A2, A3, A5}. Because A3 was +133 + +requested during the “history window” (H), it is likely to be requested in the near +future. Hence, iWS-BFE, chooses E′ = {A2, A5} for eviction. The value of H is +determined based on the mean request inter-arrival time of all applications. +In addition to considering LRU, iWS-BFE also makes use of the request +prediction, provided by Edge-MultiAI. That is, it considers the most appropriate +application for eviction as the one that has not been recently requested, and is +predicted to be requested the latest in future. However, the request time predictions +are uncertain, and the system can receive an unexpected request from members of E′ +in the current request window. To make iWS-BFE robust against such uncertainty, +we calculate the probability of an unexpected request. For application Aj ∈ E′, let +rj denote an unexpected request. Then, the probability of rj occurring during the +current request window (i.e., [t, t + ∆]) is defined as P(rj|Ai ∈ A∗). The application +that is likely to be requested unexpectedly is not an optimal choice for eviction. +Therefore, in Equation 5.3, to calculate the fitness score of Aj for eviction (denoted +Score(Aj)), we consider 1 − P(rj|Ai ∈ A∗). To take the predicted request time of Aj +into consideration, we calculate the distance between its predicted request time and +the current time (i.e., tj − ti). To confine the value between [0,1], we normalize the +distance based on the latest predicted distance across all k applications. +Score(Aj) = +tj − ti +max +k∈E′(tk − ti)· +� +1 − P(rj|Ai ∈ A∗) +� +(5.3) +The pseudo-code of the iWS-BFE policy is provided in Algorithm 7. It +begins with an initial set of eviction candidates, called τ ⊆ A′, that is formed based +134 + +on the applications that were not requested during the history window (H). From +τ, in Step 3, a list of eviction candidates (denoted E) whose elements do not overlap +with the request window of active application (Ai) is derived. Next, in Step 4, we +use Equation 5.3 to calculate the fitness score for each Ek ∈ E and then, build a +max-heap tree of E based on the fitness scores (Step 5). In Steps 6—10, the policy +iteratively retrieves the application with the highest fitness score (i.e., the max-heap +root, denoted w) and foresees the amount of memory that can be scavenged upon +replacing its loaded model with the lowest-precision one. Once the policy finds +enough memory to be scavenged such that the NN model of Ai (denoted mi) can be +loaded, in Step 13, it enacts all the NN model replacement decisions and then loads +mi in Step 14. In the event that the scavenged memory is insufficient, the policy +switches to the next NN model for Ai that has a lower size and accuracy (Step 17). +In the worst case that even the smallest NN model of Ai cannot fit in the memory, +the inference request fails (Step 17) [120]. +135 + +Algorithm 7: Pseudo-code for iWS-BFE NN model eviction policy +1 Function iWS-BFE(A′, A∗, Ai, H) +2 +τ ← Select ∀A′ +j ∈ A′ not requested during H +3 +E ← Determine ∀A′ +j ∈ τ non-overlapping with request window of Ai +4 +∀Ek ∈ E calculate fitness score using Equation 5.3 +5 +Build max-heap tree of E based on fitness score +6 +while size(mi) > available memory do +7 +w ← Extract root of the max-heap tree +8 +If w = ∅ then break the loop +9 +Measure memory scavenged by replacing model of w with its +lowest-precision one +10 +Add scavenged amount to available memory +11 +end +12 +if size(mi) ≤ available memory then +13 +Enact NN model replacement(s) decisions +14 +Scavenge the leftover memory to load mi +15 +end +16 +else +17 +If there is no model left to check then the inference request fails +18 +Repeat Step 6—10 with the next (smaller) model +19 +end +20 end +136 + +Table 5.2. +Application-specific models with different precision variants that are +experimented. +Application +NN Model +Bit +Width +Size +(MB) +Accuracy +(%) +Face recognition +VGG-Face +FP32 +535.1 +90.2 +FP16 +378.8 +82.5 +INT8 +144.2 +71.8 +Image classification +VIT-base-patch16 +FP32 +346.4 +94.5 +FP16 +242.2 +81.3 +INT8 +106.7 +72.2 +Speech recognition +S2T-librisspeech +FP32 +285.2 +89.7 +FP16 +228.0 +77.2 +INT8 +78.4 +68.0 +Sentence prediction +Paraphrase-Mini +LM-L12-v2 +FP32 +471.3 +88.2 +FP16 +377.6 +81.7 +INT8 +98.9 +76.2 +Text classification +Roberta-base +FP32 +499.0 +91.1 +FP16 +392.2 +82.4 +INT8 +132.3 +76.6 +5.6 Performance Evaluation +5.6.1 Experimental Setup and Evaluation MetricsTo evaluate the efficacy of +Edge-MultiAI and its NN model eviction policies, we benchmarked five different DL +applications, namely face recognition, speech recognition, image classification, next +sentence prediction, and text classification, and recorded their real characteristics, +including the model size, and the inference accuracy (shown in Table 5.2). We have +developed the E2C simulator that enables modeling the IoT-based systems with +different characteristics and configurations, and is available publicly for the +community access through our Github pagea. The simulator has implemented all of +the NN model eviction policies, and the user can quickly deploy and examine any +one of them. +The simulator also enables us to generate workload traces that include the +aGithub page of the E2C simulator: https://github.com/hpcclab/E2C-Sim.git +137 + +Figure 5.4. The impact of Edge-MultiAI and its iWS-BFE eviction policy on satis- +fying the requested multi-tenancy. The large graph represents the summative analysis +via increasing the mean of multi-tenancy requested in the horizontal axis, and showing +the percentage of requests that were satisfied in the vertical axis. For each case, the +smaller graph more granularly represents the number of concurrent requests issued +and fulfilled during the simulation time. +1.8 +3.6 +5.0 +mean requested degree of multi-tenancy +0 +20 +40 +60 +80 +100 +multi-tenancy satisfication rate (%) +0 +1000 +2000 +simulation time +0 +1 +2 +degree of multi-tenancy +#of request +iWS-BFE +no policy +0 +1000 +2000 +0 +2 +4 +0 +1000 +2000 +0 +2 +4 +5 +0 +1000 +2000 +simulation time +0 +1 +2 +degree of multi-tenancy +#of request +iWS-BFE +no policy +0 +1000 +2000 +0 +2 +4 +0 +1000 +2000 +0 +2 +4 +5 +0 +1000 +2000 +simulation time +0 +1 +2 +degree of multi-tenancy +#of request +iWS-BFE +no policy +0 +1000 +2000 +0 +2 +4 +0 +1000 +2000 +0 +2 +4 +5 +0 +1000 +2000 +simulation time +0 +1 +2 +degree of multi-tenancy +#of request +iWS-BFE +no policy +0 +1000 +2000 +0 +2 +4 +0 +1000 +2000 +0 +2 +4 +5 +0 +1000 +2000 +simulation time +0 +1 +2 +degree of multi-tenancy +#of request +iWS-BFE +no policy +0 +1000 +2000 +0 +2 +4 +0 +1000 +2000 +0 +2 +4 +5 +0 +1000 +2000 +simulation time +0 +1 +2 +degree of multi-tenancy +#of request +iWS-BFE +no policy +0 +1000 +2000 +0 +2 +4 +0 +1000 +2000 +0 +2 +4 +5 +request arrival times for each application during the simulation time. We configure +the actual workload to include an equal number of requests for the five applications, +and the inter-arrival times between requests for each application are distributed +exponentially within the workload. To study the uncertainty exists in the inference +request predictions, in the evaluations, we generate two sets of workloads, one +includes the predicted arrival times for the multi-tenant applications, and the other +one includes the actual arrival times of the applications. The distribution of request +arrivals in the actual workload deviates from the distribution of requests in the +predicted workload. The degree of deviation between the two is measured based on +the Kullback-Leibler (KL) [121] divergence. We explore the impact of this deviation +in the experiments of next subsections. +138 + +Our evaluation metrics are: (A) The degree of multi-tenancy under different +request arrival intensity; (B) The inference latency; (C) the inference accuracy; and +(D) The robustness metric to measure the tolerance of different eviction policies +against the uncertainty exists in the request predictions. +5.6.2 Impact of Edge-MultiAI on the Degree of Multi-tenancy +This experiment is to examine the efficacy of Edge-MultiAI in satisfying the +incoming requests to the edge server. To that end, as shown in Figure 5.4, we +increased the workload intensity, via the mean number of concurrent requests +issued, and in each case measured the multi-tenancy satisfaction rate, which is the +percentage of warm-start inferences out of the total incoming requests during the +simulation time. We examined two cases: (A) without any solution to stimulate +multi-tenancy (called, no policy); and (B) with Edge-MultiAI and its iWS-BFE +policy in place. The experiment was repeated 10 times and the average rate and +95% confidence intervals for each data point is reported. +The experiment shows that the degree of multi-tenancy achieved by adopting +Edge-MultiAI and its iWS-BFE is remarkably higher than the situation where +Edge-MultiAI is not in place. The smaller graphs show that this superiority occurs +consistently during the simulation time. We also notice that the impact of +employing Edge-MultiAI is more effective for higher degrees of multi-tenancy. In +particular, we can see that with the mean degree of multi-tenancy is 5, using +Edge-MultiAI and its iWS-BFE policy achieves ≈130% higher satisfaction rate than +no policy when mean requested degree of multi-tenancy is larger than 2. This +139 + +Figure 5.5. Measuring the percentage of cold-start inferences of multi-tenant appli- +cations resulted from the proposed eviction policies. The horizontal axis shows the +deviation between predicted and actual inference request times. +0% +20% +30% +60% +90% +deviation of actual workload from prediction (%) +0 +10 +20 +30 +40 +50 +60 +70 +cold-start inferences (%) +LFE +BFE +WS-BFE +iWS-BFE +experiment justifies the efficacy of Edge-MultiAI and the NN model management in +stimulating multi-tenancy of DL applications. +5.6.3 Impact of the Eviction Policies on the Cold-Start Inference +The purpose of this experiment is to analyze the impact of different NN +model eviction policies on the number of cold-start inferences. For that purpose, we +measure percentage of cold-start inferences caused by employing different eviction +policies, particularly, upon varying the deviation of request prediction from the +actual requests. +The results, illustrated in Figure 5.5, show that LFE and BFE perform +poorly and cause a remarkable number of cold-start inferences, whereas, WS-BFE +and iWS-BFE mitigate the cold-start inferences by at least 65%. This is because, in +140 + +Figure 5.6. Measuring the normalized inference accuracy of applications resulted +from employing the different eviction policies. +0% +20% +30% +60% +90% +deviation of actual workload from prediction (%) +0 +10 +20 +30 +40 +50 +60 +70 +80 +normalized inference accuracy (%) +LFE +BFE +WS-BFE +iWS-BFE +LFE and BFE, upon evicting an NN model, its corresponding application suffers +from a cold-start inference in the event of an unpredicted request. In contrast, in +WS-BFE and iWS-BFE, the evicted model is replaced with a low-precision one, +hence, unpredicted calls to the corresponding application do not lead to cold-start +inferences. It is noteworthy that, regardless of the employed policy, the percentage +of cold-start inferences rises upon increasing the deviation between predicted and +actual request times. Nonetheless, we see that even under 90% deviation, iWS-BFE +still substantially outperforms other policies. On average, it yields 102% less +cold-start in compare to LFE and BFE, and 40% less than WS-BFE. +5.6.4 Impact of the Eviction Policies on the Inference Accuracy +In this experiment, we analyze the average inference accuracy caused by +employing different model eviction policies. Because the accuracy largely varies +141 + +across different applications, we perform min-max normalization on the accuracy +values. Also, for the cold-start inferences, in the accuracy measurements, we +consider the accuracy provided by the NN model after it is loaded into the memory. +Figure 5.6 shows the normalized mean inference accuracy obtained from +employing different NN model eviction policies upon changing the deviation +between predicted and actual request times. According to the figure, LFE and BFE +policies outperform WS-BFE. This is because, these two policies do not retain the +low-precision models in the memory. Therefore, their inference requests either lead +to a cold-start (that was explored in the previous experiment), or they load +high-precision models that provide a high inference accuracy. Nonetheless, we +observe that iWS-BFE outperforms LFE and BFE in most of the cases, except the +one with 90% deviation. The reason for the higher inference accuracy of iWS-BFE +is that, it nominates cold-start candidates intelligently, based on their probability of +future invocations. This results indicate the importance of the scoring (described in +Equation 5.3) on efficiently nominating cold-start candidates. It is noteworthy that +the higher inference accuracy of LFE and BFE at 90% deviation comes with the +cost of substantially higher cold-start inferences that are detrimental to the +“usability” of the IoT-based systems. +5.6.5 Bi-Objective Analysis of NN Model Eviction Policies +Recall that the NN model management for multi-tenant applications in a +resource-limited edge system is a bi-objective optimization problem that aims at +minimizing the number of cold-start inferences and maximizing the inference +142 + +Figure 5.7. Bi-objective analysis of the different model selection policies. +accuracy. However, these two are generally conflicting objectives and there is not a +single optimal solution that can satisfy both objectives. Instead, there could be a +range of solutions that dominate other solutions. To analyze which one of the +studied policies dominate others, in Figure 5.7, we plot the percentage of cold-start +inferences versus the model error (defined as 100-accuracy) for different policies and +∆ values. Let D and σ be the mean and standard deviation of residuals of predicted +versus actual request times. Then, ∆ = D ± α· σ ranges by changing the value of +0 ≤ α ≤ 2. The deviation of actual versus predicted workload in this experiment is +30%. +For each policy, the colored area shows the cold-start inferences and model +error rate that are dominated by that policy. An ideal policy should approach the +graph origin (i.e., resulting in zero cold-start and zero model error). In Figure 5.7, +we observe that Edge-MultiAI dominates other policies and form the Pareto-front, +143 + +100 +cold-start inference (%) +80 +60 +LFE +BFE +40 +20 +WS-BFE +iWS-BFE +α= 1.02 +0 +0 +20 +40 +60 +08 +100 +model error (%)particularly with α = 1.02. We can conclude that the iWS-BFE policy can +significantly improve the usability of the systems via causing fewer cold-start +inferences and offering a higher inference accuracy. +5.6.6 Analyzing Robustness against Uncertainties +The goal of this experiment is to study how the eviction policies of +Edge-MultiAI make the IoT-based system robust against the uncertainty exists +between the predicted and actual application request predictor. We define the +robustness metric, shown in Equation 5.4, to encompass the ratio of warm-start +inferences (denoted ϖi) to the total number of requests (denoted γi), and the mean +prediction accuracy (ψi) of each application i throughout the simulation period. +R = 1 +n· +n +� +i=1 +�ϖi +γi +· ψi +� +(5.4) +Figure 5.8 represents the robustness score achieved by adopting the proposed +policies and no policy (a.k.a. baseline) against uncertainties in the inference request +prediction. We observe that deploying Edge-MultiAI with any policy provides more +robustness than the circumstance where Edge-MultiAI is not in place (no policy). +We also notice that the robustness value consistently drops because the rate of +inference failure and cold-starts rise for higher deviations. We observe that WS-BFE +and iWS-BFE are more robust against deviation than the LFE and BFE. This is +because, LFE and BFE do not replace their NN models with a lower-precision one +upon eviction, which leads to cold-start inferences for the applications. +144 + +Figure 5.8. Robustness of the system against uncertainty in the prediction of infer- +ence requests. +0 +20% +30% +60% +90% +deviation of actual workload from prediction (%) +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +robustness +LFE +BFE +WS-BFE +iWS-BFE +no policy +5.6.7 Evaluating the Fairness of NN Model Eviction Policies +In this experiment, our goal is to examine whether the achievements of +Edge-MultiAI and its policies, explored in the previous experiments, is fairly +distributed across all applications, or some applications benefit more than the +others. To that end, we analyze the distribution of cold-start inference and accuracy +across different DL applications. The name and the NN model characteristics of the +examined DL applications are listed in Table 5.2. Figures 5.9 and 5.10, respectively, +express the percentage of cold-start inferences and inference accuracy for each +application upon using various NN model eviction policies. It is noteworthy that in +Figure 5.9, “no policy” indicates the situation where Edge-MultiAI is not in place, +and in Figure 5.10, “maximum” serve as the benchmark, by showing the use of +highest-precision NN model for each application. While Figure 5.9 shows that +145 + +Figure 5.9. The percentage of cold-start inferences using different NN model eviction +policies versus no policy. +face recog. +speech recog. +image class. +sent. pred. +text class. +0 +20 +40 +60 +80 +cold-start inferences (%) +LFE +BFE +WS-BFE +iWS-BFE +no policy +WS-BFE and iWS-BFE remarkably outperform the other policies across all the +applications, Figure 5.10 illustrates that, particularly for iWS-BFE, the +outperformance does not come with the cost of lower inference accuracy for the +applications. More importantly, in both figures, we observe that, for each policy, the +percentage of cold-start inferences and accuracy do not fluctuate significantly from +one application to the other. This shows that policies are not biased to any +particular DL application. Specifically, the rate of cold-start inferences and the +accuracy are fairly distributed across different applications. +146 + +Figure 5.10. +The inference accuracy obtained from the different policies. +The +“maximum” is the benchmark, showing the accuracy of the highest-precision model +for each application. +face recog. +speech recog. +image class. +sent. pred. +text class. +0 +20 +40 +60 +80 +normalized inference accuracy (%) +maximum +LFE +BFE +WS-BFE +iWS-BFE +147 + +5.7 Summary +Smart IoT-based systems often desire continuous execution of multiple +latency-sensitive Deep Learning (DL) applications. The edge servers serve as the +cornerstone of such IoT-based systems, however, their resource limitations hamper +the continuous execution of multiple (multi-tenant) DL applications. The research +aims to stimulate the degree of multi-tenancy of such applications without +compromising their latency and accuracy objectives. +We developed a framework, called Edge-MultiAI, to facilitate multi-tenancy +of DL applications via enabling swapping only their NN models. The framework was +also equipped with model management policies, particularly iWS-BFE, to choose +suitable models for eviction and loading to edge memory, such that the percentage of +warm-start inferences is maximized without any major loss in the inference accuracy +of the applications. Evaluation results indicate that Edge-MultiAI can improve the +degree of multi-tenancy by 2×, and iWS-BFE can increase warm-start inferences by +60%. They also show how different policies are robust against uncertainty in the +inference request predictions. Last but not the least, the experiments show that the +policies are not biased to a certain application in their decisions. +148 + +Chapter 6: +Conclusion and Future Research Directions +This chapter summarizes the research and major findings of this dissertation. +Additionally, research topics that have surfaced during this research but have not +been covered in this dissertation are brought up and discussed. These potential +pathways for the future can be investigated further by other researchers working in +this field. +6.1 Discussion +In this dissertation, our main objective was to enable confidential computing +across edge-to-cloud continuum by maintaining data integrity and confidentiality +during executions that span across the continuum. We provide three trusted +applications to perform secure clustering and semantic searching over confidential +data without revealing any meaningful information to any off-premise tiers. In +addition, for model management of DL applications, we develop a framework that +can effectively facilitate multi-tenancy of DL applications via enabling swapping +only their NN models. +In Chapter 3, we developed solutions for topic-based clustering of both static +(ClustCrypt and S-ClusPr) and dynamic unstructured encrypted big datasets +(SD-ClusPr and FD-ClusPr). The proposed solutions approximate the number of +clusters for a dataset within a feasible time complexity. For that purpose, they +leverage the tokens’ co-occurrences to measures the tendency of each token to stay +with or segregate from other tokens and use that to estimate the number of clusters. +Next, we develop a probabilistic approach to determine the center of each cluster +149 + +and disseminate encrypted tokens to the most topically related cluster. +Experimental evaluations reveal that for static datasets, S-ClusPr can improve the +clustering coherency on average by 65%. Similarly, for semi-dynamic and dynamic +datasets, SD-ClusPr and FD-ClusPr can improve the coherency by 55%. By +incorporating ClustCrypt and ClusPr within the context of a secure semantic search +system, we learned that the more coherent and accurate topic-based clustering can +improve the relevancy of search results. +In Chapter 4, we propose an open-source generic pluggable module, namely +SAED into existing search services (e.g., AWS kendra, S3BD) to perform +context-aware, personalized, and secure search without dictating any change on +them. SAED can search over the data that is either plain-text or encrypted using +client side encryption before outsourcing to the cloud (i.e., AWS S3). Upon verified +by human users, experimental evaluations indicate SAED can improve the relevancy +of the retrieved results by on average ≈ 24% for plain-text and ≈ 75% for encrypted +datasets. +Our solution in Chapter 4 entailed continuously and simultaneously +maintaining multiple DL models that process confidential user data on the trusted +edge tier. This was challenging considering the memory limitations on the edge tier. +Moreover, such ML models could not be outsourced to Clouds because of the user’s +privacy. As such in Chapter 5, we propose a framework, namely Edge-MultiAI that +that operates based on the idea of approximate computing and ushers the NN +models of the DL applications into the edge memory such that the degree of +150 + +multi-tenancy and the number of warm-starts are maximized. +Edge-MultiAI leverages NN model compression techniques, such as model +quantization, and dynamically loads NN models for DL applications to stimulate +multi-tenancy on the edge server. We also devise a model management heuristic for +Edge-MultiAI, called iWS-BFE, that functions based on the Bayesian theory to +predict the inference requests for multi-tenant applications, and uses it to choose +the appropriate NN models for loading, hence, increasing the number of warm-start +inferences. We evaluate the efficacy and robustness of Edge-MultiAI under various +configurations. Evaluation results indicate that Edge-MultiAI can improve the +degree of multi-tenancy by 2×, and iWS-BFE can increase warm-start inferences by +60%. They also show how different policies are robust against uncertainty in the +inference request predictions. Last but not the least, the experiments show that the +policies are not biased to a certain application in their decisions. +6.2 Future Research Directions +Based on our findings during the exploration of AI-driven confidential +computing paradigm across the edge-to-cloud continuum, there are several points +where the work could be expanded upon that were not covered in this dissertation. +6.2.1 Hierarchical Clustering of unstructured Data +We can employ active learning to enable the automatic hierarchical +clustering of tokens with similar topics [122, 123, 124]. The active learning +paradigm was inspired by situations in which it is simple to collect enormous +quantities of unlabeled data (i.e., pictures and videos downloaded from the internet, +151 + +speech signals obtained from recordings made with microphones, and so on), but it +is difficult or expensive to gain their labels. +We can exploit the meaning of the deciphered tokens and their distributions +in the available clusters. With this information, we incorporate Wikipedia +knowledge to formulate hierarchical relationships among the tokens across the +confidential dataset. Later, for new a token, we measure the relatedness between the +token and the representation of each topic to propagate the hierarchy. +6.2.2 Building Classifier from the Encrypted Clusters +Clustering is a classic unsupervised learning that groups a massive amount of +unlabeled data. We can employ active learning on the clusters to build a classifier +that potentially increases the use-cases in trusted computing for unstructured data +paradigm. Active learning can leverage the knowledge while querying on cluster to +measure the relatedness with the new token to form a decision boundary of a +classifier. The resultant classifier offers substantially lower cost than traditional +supervised learning [122]. +6.2.3 Introducing Elasticity in Confidential SearchThe current +implementation of SAED framework needs dependency of a connected edge server +to facilitate the searching. One idea is to including flexibility in the framework +which will reduce the burden of edge communication with acceptable performance +degradation. For instance, when the user is on the move and does not have access to +the edge, SAED should shrink to the bare minimum search intelligence and vice +versa. +152 + +6.2.4 Adding Energy in Model Management Schemes +In Edge-MultiAI, NN model management for multi-tenant applications in a +resource-limited edge system is a bi-objective optimization problem that aims at +minimizing the number of cold-start inferences and maximizing the inference +accuracy. Since the edge servers have limited energy, often use battery, considering +energy is crucial to assign a job on an edge. Otherwise, due to dead battery, the +system could be abruptly switched off that leads to execution failure. Subsequently, +we can add the energy as a third objective into the problem. In this way, we frame +the problem as maximizing the warm-starts and total accuracy with memory size +and energy budget as constraints. +6.2.5 Cloud Offloading for Latency-tolerant Applications +We only consider low-latency applications in Edge-MultiAI. We can also add +offloading option to the cloud tier in the framework. In this way, the system could +decide whether processing a task locally (probably with a few cold-starts) is more +beneficial (in terms of latency and energy consumption) or offloading it to the cloud +server. +153 + +Bibliography +[1] S. Zobaed, S. Ahmad, R. Gottumukkala, and M. A. Salehi, “Clustcrypt: +Privacy-preserving clustering of unstructured big data in the cloud,” in +Proceedings of the 21st International Conference on High Performance +Computing and Communications (HPCC), 2019, pp. 609–616. +[2] B. Seth, S. Dalal, V. Jaglan, D.-N. Le, S. Mohan, and G. Srivastava, +“Integrating encryption techniques for secure data storage in the cloud,” +Transactions on Emerging Telecommunications Technologies, vol. 33, no. 4, p. +e4108, 2022. +[3] W. Jason and M. A. Salehi, “S3BD: secure semantic search over encrypted big +data in the cloud,” Journal of Concurrency and Computation:Practice and +Experience (CCPE), vol. 28, no. 11, December 2018. +[4] W. Sun, W. Lou, Y. T. Hou, and H. Li, “Privacy-preserving keyword search +over encrypted data in cloud computing,” in Secure cloud computing. +Springer, 2014, pp. 189–212. +[5] Y. Zhu and X. Li, “Privacy-preserving k-means clustering with local +synchronization in peer-to-peer networks,” Journal of Peer-to-Peer +Networking and Applications, vol. 13, no. 6, 2020. +[6] J. Al-Muhtadi, B. Shahzad, K. Saleem, W. Jameel, and M. A. Orgun, +“Cybersecurity and privacy issues for socially integrated mobile healthcare +applications operating in a multi-cloud environment,” Jounral of Health +informatics journal, vol. 25, no. 2, pp. 315–329, May 2019. +[7] “The 15 biggest data breaches of the 21st century,” +www.csoonline.com/article/2130877/data-breach/ +the-biggest-data-breaches-of-the-21st-century.html, November, 2021. +[8] S. Zobaed and M. A. Salehi, “Big data in the cloud,” in Encyclopedia of Big +Data, L. A. Schintler and C. L. McNeely, Eds. +Springer, 2018. +[9] “Every Single Yahoo Account Was Hacked,” www.money.cnn.com/2017/10/ +03/technology/business/yahoo-breach-3-billion-accounts/index.html, Accessed +May, 2020. +[10] “Cloud leak: How a verizon partner exposed millions of customer accounts,” +www.upguard.com/breaches/verizon-cloud-leak, Accessed April, 2020. +[11] C. Shepherd, G. Arfaoui, I. Gurulian, R. P. Lee, K. Markantonakis, R. N. +Akram, D. Sauveron, and E. Conchon, “Secure and trusted execution: Past, +present, and future-a critical review in the context of the internet of things +154 + +and cyber-physical systems,” in 2016 IEEE Trustcom/BigDataSE/ISPA, 2016, +pp. 168–177. +[12] Z. Ning, J. Liao, F. Zhang, and W. Shi, “Preliminary study of trusted +execution environments on heterogeneous edge platforms,” in Proceedings of +Symposium on Edge Computing (SEC), 2018, pp. 421–426. +[13] “Confidential computing – the next frontier in data security,” +https://confidentialcomputing.io/wp-content/uploads/sites/85/2021/10/ +Everest Group - Confidential Computing - The Next Frontier in Data +Security - 2021-10-19.pdf, Accessed July 5, 2022. +[14] S. Deng, H. Zhao, W. Fang, J. Yin, S. Dustdar, and A. Y. Zomaya, “Edge +intelligence: The confluence of edge computing and artificial intelligence,” +Journal of IEEE Internet of Things, vol. 7, no. 8, pp. 7457–7469, 2020. +[15] S. M. Zobaed, M. A. Salehi, and R. Buyya, “Saed: Edge-based intelligence for +privacy-preserving enterprise search on the cloud,” in 2021 IEEE/ACM 21st +International Symposium on Cluster, Cloud and Internet Computing +(CCGrid). +IEEE, 2021, pp. 366–375. +[16] R. F. Hussain, A. Pakravan, and M. A. Salehi, “Analyzing the performance of +smart industry 4.0 applications on cloud computing systems,” in proceeginds +of 22nd IEEE International Conference on High Performance Computing and +Communications (HPCC), 2020, pp. 11–18. +[17] S. Ahmad, S. Zobaed, R. Gottumukkala, and M. A. Salehi, “Edge computing +for user-centric secure search on cloud-based encrypted big data,” in +Proceedings of the 21st International Conference on High Performance +Computing and Communications (HPCC), August 2019, pp. 662–669. +[18] F. Almalki, S. H. Alsamhi, R. Sahal, J. Hassan, A. Hawbani, N. Rajput, +A. Saif, J. Morgan, J. Breslin et al., “Green iot for eco-friendly and +sustainable smart cities: future directions and opportunities,” Mobile +Networks and Applications, pp. 1–25, 2021. +[19] A. Mokhtari, M. A. Hossen, P. Jamshidi, and M. A. Salehi, “FELARE: fair +scheduling of machine learning applications on heterogeneous edge systems,” +in Proceedings of International Conference On Cloud Computing, July 2022. +[20] “Protecting data using client-side encryption,” https://docs.aws.amazon.com/ +AmazonS3/latest/userguide/UsingClientSideEncryption.html, Accessed +November, 2022. +[21] H. Pham, J. Woodworth, and M. Amini Salehi, “Survey on secure search over +encrypted data on the cloud,” Journal of Concurrency and Computation: +Practice and Experience, vol. 31, no. 17, p. e5284, 2019. +155 + +[22] K. Zhang, J. Long, X. Wang, H.-N. Dai, K. Liang, and M. Imran, +“Lightweight searchable encryption protocol for industrial internet of things,” +Transactions on Industrial Informatics, vol. 17, no. 6, pp. 4248–4259, 2020. +[23] M. Zhang, Y. Chen, and J. Huang, “Se-ppfm: A searchable encryption scheme +supporting privacy-preserving fuzzy multikeyword in cloud systems,” Journal +of Systems, vol. 15, no. 2, pp. 2980–2988, 2020. +[24] M. A. Salehi, T. Caldwell, A. Fernandez, E. Mickiewicz, E. W. Rozier, +S. Zonouz, and D. Redberg, “RESeED: a secure regular-expression search tool +for storage clouds,” Journal of Software: Practice and Experience, vol. 47, +no. 9, pp. 1221–1241, September 2017. +[25] D. C. G. Valadares, M. S. L. da Silva, A. E. M. Brito, and E. M. Salvador, +“Achieving data dissemination with security using fiware and intel software +guard extensions (sgx),” in Proceedings of IEEE Symposium on Computers +and Communications (ISCC). +IEEE, 2018, pp. 1–7. +[26] M. Kehoe, “Mapping security requirements to enterprise search - part 1: +Defining specific security requirements,” +http://www.ideaeng.com/security-eprise-search-p1-0304, 2009, [Online; +accessed 16-February-2020]. +[27] “Announcing amazon kendra: Reinventing enterprise search with machine +learning,” https://aws.amazon.com/about-aws/whats-new/2019/12/ +announcing-amazon-kendra-reinventing-enterprise-search-with-machine-learning/, +2019, [Online; accessed 16-February-2020]. +[28] “Azure cognitive services,” +https://azure.microsoft.com/en-us/services/cognitive-services, Accessed April, +2022. +[29] W. Yu, F. Liang, X. He, W. G. Hatcher, C. Lu, J. Lin, and X. Yang, “A +survey on the edge computing for the internet of things,” Journal of IEEE +access, vol. 6, pp. 6900–6919, 2017. +[30] C. Gong, F. Lin, X. Gong, and Y. Lu, “Intelligent cooperative edge computing +in internet of things,” Journal of Internet of Things, vol. 7, no. 10, pp. +9372–9382, 2020. +[31] Q.-V. Dang and C.-L. Ignat, “dtrust: a simple deep learning approach for +social recommendation,” in proceedings of 3rd International Conference on +Collaboration and Internet Computing (CIC), 2017, pp. 209–218. +[32] “Jetson nano developer kit,” +https://developer.nvidia.com/embedded/jetson-nano-developer-kit, Accessed +November, 2022. +156 + +[33] A. Gholami, S. Kim, Z. Dong, Z. Yao, M. W. Mahoney, and K. Keutzer, “A +survey of quantization methods for efficient neural network inference,” in +Journal of Low-Power Computer Vision. +Chapman and Hall/CRC, 2021, pp. +291–326. +[34] L. Zhou, Y. Zhu, and A. Castiglione, “Efficient k-nn query over encrypted +data in cloud with limited key-disclosure and offline data owner,” Computers +& Security, vol. 69, pp. 84–96, 2017. +[35] T. Tarpey, “Linear transformations and the k-means clustering algorithm: +applications to clustering curves,” Journal of the american statistician, +vol. 61, no. 1, pp. 34–40, 2007. +[36] W. Sun, B. Wang, N. Cao, M. Li, W. Lou, Y. T. Hou, and H. Li, +“Privacy-preserving multi-keyword text search in the cloud supporting +similarity-based ranking,” in Proceedings of the 8th symposium on +Information, computer and communications security, ser. SIGSAC’13, May +2013, pp. 71–82. +[37] K. Gai and M. Qiu, “Blend arithmetic operations on tensor-based fully +homomorphic encryption over real numbers,” Transactions on Industrial +Informatics, vol. 14, no. 8, pp. 3590–3598, August 2018. +[38] K. Xing, C. Hu, J. Yu, X. Cheng, and F. Zhang, “Mutual privacy preserving +k-means clustering in social participatory sensing,” Transactions on Industrial +Informatics, vol. 13, no. 4, pp. 2066–2076, 2017. +[39] H. Pang and B. Wang, “Privacy-preserving association rule mining using +homomorphic encryption in a multikey environment,” Systems Journal, +vol. 15, no. 2, pp. 3131–3141, 2020. +[40] P. Li, J. Li, Z. Huang, C.-Z. Gao, W.-B. Chen, and K. Chen, +“Privacy-preserving outsourced classification in cloud computing,” Journal of +Cluster Computing, vol. 21, no. 1, pp. 277–286, March 2018. +[41] C. Wang, A. Wang, X. Liu, and J. Xu, “Research on k-means clustering +algorithm over encrypted data,” in Proceedings of International Symposium on +Cyberspace Safety and Security, December 2019, pp. 182–191. +[42] L. Ducas and D. Micciancio, “FHEW: Bootstrapping homomorphic +encryption in less than a second,” in Advances in Cryptology, ser. +EUROCRYPT’15, April 2015, pp. 617–640. +[43] J. Vaidya and C. Clifton, “Privacy-preserving k-means clustering over +vertically partitioned data,” in Proceedings of the 9th international conference +on Knowledge discovery and data mining, 2003, pp. 206–215. +157 + +[44] D. X. Song, D. Wagner, and A. Perrig, “Practical techniques for searches on +encrypted data,” in Proceedings of international symposium on security and +privacy. S&P 2000. +IEEE, 2000, pp. 44–55. +[45] D. Boneh, G. D. Crescenzo, R. Ostrovsky, and G. Persiano, “Public key +encryption with keyword search,” in Proceedings of international conference +on the theory and applications of cryptographic techniques. +Springer, 2004, +pp. 506–522. +[46] N. Cao, Z. Yang, C. Wang, K. Ren, and W. Lou, “Privacy-preserving query +over encrypted graph-structured data in cloud computing,” in Proceedings of +the 31st International Conference on Distributed Computing Systems, ser. +ICDCS ’11, Washington, DC, USA, 2011, pp. 393–402. +[47] R. A. Popa, C. M. Redfield, N. Zeldovich, and H. Balakrishnan, “Cryptdb: +processing queries on an encrypted database,” Journal of Communications of +the ACM, vol. 55, no. 9, pp. 103–111, 2012. +[48] E. W. Rozier, S. Zonouz, and D. Redberg, “Dragonfruit: Cloud +provider-agnostic trustworthy cloud data storage and remote processing,” in +Proceedings of 19th Pacific Rim International Symposium on Dependable +Computing. +IEEE, 2013, pp. 172–177. +[49] M. Ahmadian, F. Plochan, Z. Roessler, and D. C. Marinescu, “Securenosql: +An approach for secure search of encrypted nosql databases in the public +cloud,” Jounal of International Journal of Information Management, vol. 37, +no. 2, pp. 63–74, 2017. +[50] M. Kettouch, C. Luca, and M. Hobbs, “Semild: mediator-based framework for +keyword search over semi-structured and linked data,” Journal of Intelligent +Information Systems, vol. 52, no. 2, pp. 311–335, 2019. +[51] M. Naseriparsa, M. S. Islam, C. Liu, and L. Chen, “Xsnippets: Exploring +semi-structured data via snippets,” Journal of Data & Knowledge +Engineering, vol. 124, p. 101758, 2019. +[52] R. Curtmola, J. Garay, S. Kamara, and R. Ostrovsky, “Searchable symmetric +encryption: improved definitions and efficient constructions,” in Proceedings of +the 13th ACM conference on Computer and communications security, ser. +CCS ’06, 2006, pp. 79–88. +[53] J. Woodworth, M. A. Salehi, and V. Raghavan, “S3c: An architecture for +space-efficient semantic search over encrypted data in the cloud,” in +Proceedings of the 4th International Conference on Big Data, ser. Big Data’16, +December 2016, pp. 3722–3731. +158 + +[54] S. Zobaed and M. Amini Salehi, “Privacy-preserving clustering of unstructured +big data for cloud-based enterprise search solutions,” Journal of Concurrency +and Computation: Practice and Experience, vol. 34, no. 22, p. e7160, 2022. +[55] J. Li, Q. Wang, C. Wang, N. Cao, K. Ren, and W. Lou, “Fuzzy keyword +search over encrypted data in cloud computing,” in Proceedings of the 29th +International Conference on Computer Communications, ser. INFOCOM ’10, +March 2010, pp. 1–5. +[56] T. Moataz, A. Shikfa, N. Cuppens-Boulahia, and F. Cuppens, “Semantic +search over encrypted data,” in Proceedings of International Conference on +Telecommunications (ICT), May 2013, pp. 1–5. +[57] X. Sun, Y. Zhu, Z. Xia, and L. Chen, “Privacy preserving keyword based +semantic search over encrypted cloud data,” Journal of Security and Its +Applications, vol. 8, no. 3, May 2014. +[58] F. Liang, R. Qiang, and J. Yang, “Exploiting real-time information retrieval +in the microblogosphere,” in Proceedings of the 12th ACM/IEEE-CS joint +conference on Digital Libraries, June 2012, pp. 267–276. +[59] Y. Wang, H. Huang, and C. Feng, “Query expansion with local conceptual +word embeddings in microblog retrieval,” IEEE Transactions on Knowledge +and Data Engineering, October 2019. +[60] S. Deerwester, S. T. Dumais, G. W. Furnas, T. K. Landauer, and +R. Harshman, “Indexing by latent semantic analysis,” Journal of the American +society for information science, vol. 41, no. 6, pp. 391–407, September 1990. +[61] K. Albishre, Y. Li, and Y. Xu, “Effective pseudo-relevance for microblog +retrieval,” in Proceedings of the Australasian Computer Science Week +Multiconference, January 2017, pp. 1–6. +[62] F. Diaz, B. Mitra, and N. Craswell, “Query expansion with locally-trained +word embeddings,” in Proceedings of the 54th Annual Meeting of the +Association for Computational Linguistics (Volume 1: Long Papers), August +2016, pp. 367–377. +[63] T. Mikolov, K. Chen, G. Corrado, and J. Dean, “Efficient estimation of word +representations in vector space,” www.pub-tools-public-publication-data. +storage.googleapis.com/pdf/41224.pdf, 2013. +[64] G. A. Miller, “Wordnet: a lexical database for english,” Journal of +Communications of the ACM, vol. 38, no. 11, pp. 39–41, 1995. +[65] M. Song, I.-Y. Song, X. Hu, and R. B. Allen, “Integration of association rules +and ontologies for semantic query expansion,” Journal of Data & Knowledge +Engineering, vol. 63, no. 1, pp. 63–75, October 2007. +159 + +[66] V. Nakade, A. Musaev, and T. Atkison, “Preliminary research on +thesaurus-based query expansion for twitter data extraction,” in Proceedings +of the Southeast Regional Conference, ser. ACMSE’18, March 2018, pp. 1–4. +[67] C. H. Leung, Y. Li, A. Milani, and V. Franzoni, “Collective evolutionary +concept distance based query expansion for effective web document retrieval,” +in Proceedings of the International Conference on Computational Science and +Its Applications, June 2013, pp. 657–672. +[68] J. Chen and X. Ran, “Deep learning with edge computing: A review,” +Proceedings of the IEEE, vol. 107, no. 8, pp. 1655–1674, 2019. +[69] M. S. Murshed, C. Murphy, D. Hou, N. Khan, G. Ananthanarayanan, and +F. Hussain, “Machine learning at the network edge: A survey,” Journal of +ACM Computing Surveys (CSUR), vol. 54, no. 8, pp. 1–37, 2021. +[70] Z. Zhou, X. Chen, E. Li, L. Zeng, K. Luo, and J. Zhang, “Edge intelligence: +Paving the last mile of artificial intelligence with edge computing,” Journal of +the IEEE Access, vol. 107, no. 8, pp. 1738–1762, 2019. +[71] X. Wang, Y. Han, V. C. Leung, D. Niyato, X. Yan, and X. Chen, +“Convergence of edge computing and deep learning: A comprehensive survey,” +IEEE Communications Surveys & Tutorials, vol. 22, no. 2, pp. 869–904, 2020. +[72] J. Mao, X. Chen, K. W. Nixon, C. Krieger, and Y. Chen, “Modnn: Local +distributed mobile computing system for deep neural network,” in Proceedings +of Design, Automation & Test in Europe Conference & Exhibition (DATE). +IEEE, 2017, pp. 1396–1401. +[73] K. Ko, Y. Son, S. Kim, and Y. Lee, “Disco: A distributed and concurrent +offloading framework for mobile edge cloud computing,” in Proceedings of 9th +international conference on ubiquitous and future networks (ICUFN), 2017, +pp. 763–766. +[74] R. Hadidi, J. Cao, M. Woodward, M. S. Ryoo, and H. Kim, “Distributed +perception by collaborative robots,” IEEE Robotics and Automation Letters, +vol. 3, no. 4, pp. 3709–3716, 2018. +[75] L. Xie, S. Wang, A. Markham, and N. Trigoni, “Towards monocular vision +based obstacle avoidance through deep reinforcement learning,” arXiv preprint +arXiv:1706.09829, 2017. +[76] S. Yao, Y. Zhao, A. Zhang, L. Su, and T. Abdelzaher, “DeepIoT: Compressing +deep neural network structures for sensing systems with a compressor-critic +framework,” in Proceedings of the 15th ACM Conference on Embedded +Network Sensor Systems, 2017, pp. 1–14. +160 + +[77] Y. Ma, D. Xiang, S. Zheng, D. Tian, and X. Liu, “Moving deep learning into +web browser: How far can we go?” in Proceedings of the 19th World Wide +Web Conference (WWW), May 2019, pp. 1234–1244. +[78] S. R. Paladhi, R. M. Kumar, A. D. Reddy, C. Vinayak, and T. Pusphavathi, +“Enhanced possibilistic c-means clustering on big data while ensuring +security,” in International Conference on Computer Networks and +Communication Technologies. +Springer, 2019, pp. 583–588. +[79] P. K. Samantaray, N. K. Randhawa, and S. L. Pati, “An efficient +multi-keyword text search over outsourced encrypted cloud data with ranked +results,” in Computational Intelligence in Data Mining. +Springer, 2019, pp. +31–40. +[80] W. Diffie and M. Hellman, “New directions in cryptography,” Transactions on +Information Theory, vol. 22, no. 6, pp. 644–654, November 1976. +[81] F. Can and E. A. Ozkarahan, “Concepts and effectiveness of the +cover-coefficient-based clustering methodology for text databases,” Journal of +ACM Trans. Database Syst., vol. 15, no. 4, pp. 483–517, December 1990. +[82] D. R. Cutting, D. R. Karger, J. O. Pedersen, and J. W. Tukey, +“Scatter/gather: A cluster-based approach to browsing large document +collections,” in ACM SIGIR Forum, vol. 51, no. 2, August 2017, pp. 148–159. +[83] S. Aggarwal, N. Agarwal, and M. Jain, “Performance analysis of uncertain +k-means clustering algorithm using different distance metrics,” in +Computational Intelligence: Theories, Applications and Future +Directions-Volume I. +Springer, 2019, pp. 237–245. +[84] X. Liu and W. B. Croft, “Cluster-based retrieval using language models,” in +Proceedings of the 27th International ACM SIGIR Conference on Research and +Development in Information Retrieval, ser. SIGIR ’04, July 2004, pp. 186–193. +[85] C. C. Aggarwal, A. Hinneburg, and D. A. Keim, “On the surprising behavior +of distance metrics in high dimensional space,” in Proceedings of the 8th +International conference on database theory, ser. ICDT ’01, January 2001, pp. +420–434. +[86] A. L. Mary and K. S. Kumar, “A density based dynamic data clustering +algorithm based on incremental dataset,” Journal of Computer Science, vol. 8, +no. 5, pp. 656–664, 2012. +[87] “The Museum of Modern Art Data,” +tapoueh.org/blog/2018/07/batch-updates-and-concurrency, Accessed May +,2020. +161 + +[88] “Twitter stream api dataset,” +github.com/shreybatra/Twitter-Stream-API-Dataset, Accessed March, 2020. +[89] “Statistics Solution,” +www.statisticssolutions.com/using-chi-square-statistic-in-research/, Accessed +July 15, 2020. +[90] R. A. Popa, C. M. S. Redfield, N. Zeldovich, and H. Balakrishnan, “Cryptdb: +Protecting confidentiality with encrypted query processing,” in Proceedings of +the 23rd ACM Symposium on Operating Systems Principles, ser. SOSP ’11, +October 2011, pp. 85–100. +[91] D. Wang and P. Wang, “Offline dictionary attack on password authentication +schemes using smart cards,” in Information Security. +Springer International +Publishing, 2015, pp. 221–237. +[92] M. Naehrig, K. Lauter, and V. Vaikuntanathan, “Can homomorphic +encryption be practical?” in Proceedings of the 3rd ACM Workshop on Cloud +Computing Security Workshop, ser. CCSW ’11, October 2011, pp. 113–124. +[93] M. George, S. Kamara, and T. Moataz, “Structured encryption and dynamic +leakage suppression,” in Proceedings of Annual International Conference on +the Theory and Applications of Cryptographic Techniques, October 2021, pp. +370–396. +[94] “Common Crawl on Amazon Web Services (AWS),” +https://aws.amazon.com/public-datasets/common-crawl/, Accessed February, +2021. +[95] “RFC (request for comments) series,” old.datahub.io/dataset/rfcs, Accessed +March, 2020. +[96] “BBC news classification,” www.kaggle.com/c/learn-ai-bbc, Accessed March, +2020. +[97] O. Medelyan, E. Frank, and I. H. Witten, “Human-competitive tagging using +automatic keyphrase extraction,” in Proceedings of the 14th Conference on +Empirical Methods in Natural Language, ser. EMNLP ’09, August 2009, pp. +1318–1327. +[98] P. Berkhin, “A survey of clustering data mining techniques,” in Grouping +multidimensional data. +Springer, 2006, pp. 25–71. +[99] G. A. Miller, “Wordnet: a lexical database for english,” Journal of +Communications of the ACM, vol. 38, no. 11, pp. 39–41, November 1995. +162 + +[100] M. Z. Rodriguez, C. H. Comin, D. Casanova, O. M. Bruno, D. R. Amancio, +L. d. F. Costa, and F. A. Rodrigues, “Clustering algorithms: A comparative +approach,” Journal of PloS one, vol. 14, no. 1, p. e0210236, 2019. +[101] B. C. Kwon, B. Eysenbach, J. Verma, K. Ng, C. De Filippi, W. F. Stewart, +and A. Perer, “Clustervision: Visual supervision of unsupervised clustering,” +IEEE transactions on visualization and computer graphics, vol. 24, no. 1, pp. +142–151, 2017. +[102] A. K. Mariappan, R. M. Suresh, and V. S. Bharathi, “A comparative study on +the effectiveness of semantic search engine over keyword search engine using +tsap measure,” Journal of Computer Applications EGovernance and Cloud +Computing Services, pp. 4–6, December 2012. +[103] M. Amini Salehi, T. Caldwell, A. Fernandez, E. Mickiewicz, D. Redberg, +E. W. D. Rozier, and S. Zonouz, “RESeED: Regular Expression Search over +Encrypted Data in the Cloud,” in Proceedings of the 7th International Cloud +conference, ser. Cloud ’14, June 2014, pp. 673–680. +[104] A. Silva and M. Mendoza, “Improving query expansion strategies with word +embeddings,” in Proceedings of the ACM Symposium on Document +Engineering, September 2020. +[105] S. Kuzi, A. Shtok, and O. Kurland, “Query expansion using word +embeddings,” in Proceedings of the 25th international on conference on +information and knowledge management, 2016. +[106] C. Fellbaum, “Wordnet: An electronic lexical resource,” in The Oxford +Handbook of Cognitive Science. +Routledge, 2017, pp. 301–314. +[107] R. Campos, V. Mangaravite, A. Pasquali, A. M. Jorge, C. Nunes, and +A. Jatowt, “YAKE! collection-independent automatic keyword extractor,” in +Proceedings of the 40th European Conference on Information Retrieval, March +2018, pp. 806–810. +[108] A. Khatua, A. Khatua, and E. Cambria, “A tale of two epidemics: Contextual +word2vec for classifying twitter streams during outbreaks,” Journal of +Information Processing & Management, vol. 56, no. 1, pp. 247–257, 2019. +[109] Z. Kastrati, A. S. Imran, and S. Y. Yayilgan, “The impact of deep learning on +document classification using semantically rich representations,” Journal of +Information Processing & Management, vol. 56, no. 5, pp. 1618–1632, 2019. +[110] X. Pang, Y. Zhou, P. Wang, W. Lin, and V. Chang, “An innovative neural +network approach for stock market prediction,” The Journal of +Supercomputing, vol. 76, no. 3, pp. 2098–2118, 2020. +163 + +[111] “Vanilla recurrent neural network,” +http://calvinfeng.gitbook.io/machine-learning-notebook/supervised-learning/ +recurrent-neural-network/recurrent neural networks, Accessed +September,2020. +[112] F. Viegas, S. Canuto, C. Gomes, W. Luiz, T. Rosa, S. Ribas, L. Rocha, and +M. Gon¸calves, “Cluwords: exploiting semantic word clustering representation +for enhanced topic modeling,” in Proceedings of the 12th International +Conference on Web Search and Data Mining, January 2019, pp. 753–761. +[113] “Amazon Kendra,” www.aws.amazon.com/kendra, Accessed April 10, 2020. +[114] Y. Zhou, S.-M. Moosavi-Dezfooli, N.-M. Cheung, and P. Frossard, “Adaptive +quantization for deep neural network,” in Proceedings of the AAAI Conference +on Artificial Intelligence, vol. 32, no. 1, 2018. +[115] D. G. Samani and M. A. Salehi, “Exploring the impact of virtualization on +the usability of deep learning applications,” in Proceedings of 22nd IEEE +International Symposium on Cluster, Cloud and Internet Computing +(CCGrid), 2022, pp. 442–451. +[116] J. Manner, M. Endreß, T. Heckel, and G. Wirtz, “Cold start influencing +factors in function as a service,” in Proceedings of the 12th IEEE/ACM +International Conference on Utility and Cloud Computing Companion (UCC), +2018, pp. 181–188. +[117] X. Chen, Y. Wu, and Y. Han, “Fepim: Contention-free in-memory computing +based on ferroelectric field-effect transistors,” in Proceedings of 26th IEEE +Asia and South Pacific Design Automation Conference (ASP-DAC), 2021, pp. +114–119. +[118] T. V. Christensen, “Heuristic algorithms for np-complete problems,” Project +report, Institute of Informatics and mathematical Modelling, Technical +University of Denmark, 2007. +[119] E. J. O’neil, P. E. O’neil, and G. Weikum, “The LRU-K page replacement +algorithm for database disk buffering,” Journal of Acm Sigmod Record, +vol. 22, no. 2, pp. 297–306, 1993. +[120] A. Mokhtari, C. Denninnart, and M. A. Salehi, “Autonomous task dropping +mechanism to achieve robustness in heterogeneous computing systems,” in +Proceedings of International Parallel and Distributed Processing Symposium +Workshops (IPDPSW), 2020, pp. 17–26. +[121] T. Van Erven and P. Harremos, “R´enyi divergence and kullback-leibler +divergence,” IEEE Transactions on Information Theory, vol. 60, no. 7, pp. +3797–3820, 2014. +164 + +[122] S. Dasgupta and D. Hsu, “Hierarchical sampling for active learning,” in +Proceedings of the 25th international conference on Machine learning, 2008, +pp. 208–215. +[123] P. Kumar and A. Gupta, “Active learning query strategies for classification, +regression, and clustering: a survey,” Journal of Computer Science and +Technology, vol. 35, no. 4, pp. 913–945, 2020. +[124] F. Min, S.-M. Zhang, D. Ciucci, and M. Wang, “Three-way active learning +through clustering selection,” International Journal of Machine Learning and +Cybernetics, vol. 11, no. 5, pp. 1033–1046, 2020. +165 + +Biographical Sketch +Sm Zobaed received his Bachelor of Science in computer science and +engineering in the fall of 2015 from Islamic University of Technology (IUT), +Bangladesh. He started his professional career in December of 2015, as a System +Engineer in one of the top tech giants named “Huawei Technologies Ltd”. After +around a year and half, he planned to enrich his academic knowledge by pursuing +higher education. Hence, Sm Zobaed started his Ph.D. journey in computer science +in the fall of 2017 at the University of Louisiana at Lafayette. Sm Zobaed received +his M.Sc. degree in computer science in the spring of 2019 during his Ph.D. journey. +His research interests are: Natural language processing, Data analytics, and Cloud +computing. +166 + diff --git a/pdAzT4oBgHgl3EQfAfrM/content/tmp_files/load_file.txt b/pdAzT4oBgHgl3EQfAfrM/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..3828585a2bbd34b66fe318a495a9bc8be664a36b --- /dev/null +++ b/pdAzT4oBgHgl3EQfAfrM/content/tmp_files/load_file.txt @@ -0,0 +1,8318 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf,len=8317 +page_content='AI-Driven Confidential Computing across Edge-to-Cloud Continuum Sm Zobaed A Dissertation presented to the Graduate Faculty in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy University of Louisiana at Lafayette Fall 2022 APPROVED: Mohsen Amini Salehi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chair The Center for Advanced Computer Studies Sheng Chen The Center for Advanced Computer Studies Raju Gottumukkala Informatics Research Institute Xiali Hei The Center for Advanced Computer Studies Li Chen The Center for Advanced Computer Studies Mary Farmer-Kaiser Dean of the Graduate School arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='00928v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='DC] 3 Jan 2023 © Sm Zobaed 2022 All Rights Reserved Abstract With the meteoric growth of technology, both individuals and organizations are widely adopting cloud services to mitigate the burdens of maintenance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Despite its scalability and ease of use, many potential cloud users who own sensitive data refrain from fully utilizing cloud services due to valid confidentiality concerns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Maintaining data confidentiality for data at rest and in transit has been widely explored but data remains vulnerable in the cloud while it is in use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This vulnerability is further elevated once the scope of computing spans across the edge-to-cloud continuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' From the notion of safeguarding, confidential data needs to be encrypted while offloading from users’ premises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Although adopting user-side encryption ensures data confidentiality, it limits the ability to data processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Subsequently, we are limited to performing only low-level operations (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', string pattern matching).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Accordingly, the goal of this dissertation is to enable data confidentiality by adopting confidential computing across the continuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Towards this goal, one approach we explore is to separate the intelligence aspect of data processing from the pattern-matching aspect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We present our approach to make confidential data clustering on the cloud, and then develop confidential search service across edge-to-cloud for unstructured text data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Our proposed clustering solution named ClusPr, performs topic-based clustering for static and dynamic datasets that improves cluster coherency up to 30%-to-60% when compared with other encryption-based clustering techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Our trusted enterprise search service named SAED, provides context-aware and personalized semantic search over iii confidential data across the continuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Evaluation results, verified by human users, demonstrates that SAED can improve the relevancy of the retrieved search results by ≈ 24% for plain-text and 75% for encrypted datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We realized that enabling confidential computing across edge-to-cloud requires major contribution from the edge tiers particularly to run multiple Deep Learning (DL) services concurrently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This raises memory contention on the edge tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To resolve the contention, we propose Edge-MultiAI framework to manage Neural Network (NN) models of DL applications such that it can meet the latency constraints of the DL applications without compromising inference accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Our evaluation confirms that Edge-MultiAI can stimulate the degree of multi-tenancy by 2× on the edge tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' iv To my Creator,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' the Almighty Allah (SWT),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' my master prophet Muhammad (pbuh),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' who taught us the purpose of life,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' my parents,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Md Mazharul Islam and Jubaida Naznin,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' who never stop providing support in countless ways,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' my enlighteners,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Md Fazle Rabby,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Md Sazib Hasan who have provided enormous inspiration regardless of the rainy or shiny days throughout the journey with the fullest and truest attention,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' my pioneer since childhood,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Jahid Md Mahabub Islam,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' who has been acting as a LiDAR through the sea of darkness,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' my asymptotic remembrance,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Farzana Hasan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' whom I am forever grateful,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' my mentors,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Muhammad Usama Islam,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Md Istiaq Hossain,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Jubair Yusuf,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Farhan Tanvir,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' my only sister,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Mantika Mahbuba,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' and to all my friends and beloved ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Acknowledgments I sincerely thank my supervisor, Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Mohsen Amini Salehi, for his constant encouragement since the inception of the journey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' He has provided a plethora of guidance, support, and cooperation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Thanks to my dissertation committee, Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Raju Gottumukukkala, Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Li Chen, Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Xiali Hei, and Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Sheng Chen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Thanks to Jason Woodworth, Razin Farhan Hussain, Davood Ghatreh Samani, and Chavit Denninart for their assistance in the work of this dissertation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A special thanks goes to Ali Mokhtari for his collaboration in the latest work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Finally, thanks goes to the Center for Advanced Computer Studies and the Graduate School at the University of Louisiana at Lafayette for their support and guidance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' vi Table of Contents Abstract .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' iii Dedication .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' v Acknowledgments .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' vi List of Tables .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' xi List of Figures .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' xii Chapter 1: Introduction .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Motivation: Data Confidentiality in the Current Age .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Essence of Maintaining Data Confidentiality .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Confidential Computing .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Basic Definition .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Confidential Computing across Edge-to-Cloud Continuum .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Confidential Computing of Unstructured data .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Research Problems and Objectives .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Contributions .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 Dissertation Organization .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 10 Chapter 2: Background and Literature Study .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 14 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Background .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 14 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Trusted Execution Environment .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 14 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Trustworthy Infrastructure for Confidential Computing .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 16 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Cloud-based Enterprise Search Services over Unstructured Text Data .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 18 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Emergence of Edge-to-Cloud Continuum .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 19 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Machine/Deep Learning for Unstructured Data-driven Applications .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 20 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 Edge Multi-Tenancy for Latency-Sensitive Processing .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 21 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Prior Literature for Confidential Computing for Unstructured Data .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 23 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Privacy-preserving Unstructured Data Clustering Schemes .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 23 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Searchable Encryption and Encrypted Index .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 25 vii 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Privacy-Preserving Cloud-based Search Systems .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 27 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Edge Computing for Privacy-preserving Unstructured Data Processing .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 30 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Prior Literature on Multi-Tenant AI-based Executions on Edge .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 31 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Edge AI .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 31 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Multi-tenant Execution on Edge .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 31 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 DNN Model Compression .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 32 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Warm-Start vs Cold-Start DL Inference .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 34 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Summary and Positioning of this Dissertation .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 34 Chapter 3: Privacy-Preserving Clustering for Unstructured Cloud Data .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 36 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Overview .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 36 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Problem Statement .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 36 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Positioning of the Proposed Clustering Works .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 37 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Architecture to Facilitate Clustering in Secure Search System .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 38 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Architecture: ClustCrypt .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 38 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Architecture: ClusPr .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 40 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 ClustCrypt: Privacy-preserving Clustering Scheme for Static Unstructured Data .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 45 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Estimating the Number of Clusters for Static Datasets .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 45 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Determining Clusters’ Centers .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 52 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Clustering Tokens .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 54 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 S-ClusPr: Privacy-preserving Clustering Scheme For Static Unstructured Datasets .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 56 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Center Selection .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 56 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Distributing Encrypted Tokens Across Clusters .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 59 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Pruning Clusters to Expedite the Search Operation .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 62 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 Privacy-preserving Clustering Scheme For Dynamic Unstructured datasets .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 63 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Overview .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 63 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Semi-Dynamic Data Clustering Scheme (SD-ClusPr) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 64 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Fully-Dynamic Data Clustering Scheme (FD-ClusPr) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 68 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8 Security Analysis of the Proposed Clustering Works .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 69 viii 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9 Performance Evaluation of Clustering .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 73 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Experimental Setup .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 73 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Evaluation Metrics and Baselines from Prior Works .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 74 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Evaluation Results .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 76 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 Summary .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 91 Chapter 4: Edge-Based Intelligence for Privacy-Preserving Enterprise Search on the Cloud .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 92 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Overview .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 92 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Problem Statement .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 92 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 SAED: Smart Edge-Leveraged Enterprise Search System .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 94 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Architectural Overview .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 94 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Query Context Identification .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 96 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Query Expansion Unit .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 99 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 User Interest Detection .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 100 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Weighting Unit .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 102 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 Ranking Unit .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 104 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 SAED As a Pluggable Module Enterprise Search Solutions .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 107 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Performance Evaluation of SAED .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 108 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Experimental Set up .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 108 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Benchmark Queries .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 109 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Evaluation Metrics .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 109 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Evaluating Search Relevancy .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 111 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Relevancy of Privacy-Preserving Enterprise Search .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 114 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 Discussion of the Relevancy Results .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 115 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 Evaluating the Search Time .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 116 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 Summary .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 118 Chapter 5: Multi-Tenancy of Latency-Sensitive Deep Learning Applications on Edge .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 119 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Overview .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 119 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Problem Statement .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 123 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Solution Statement and Contributions .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 125 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Architectural Overview & System Design of Edge-MultiAI .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 126 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Heuristics to Manage Models of Multi-tenant Applications .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 128 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Overview .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 128 ix 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Policy 1: Largest-First Model Eviction (LFE) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 131 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Policy 2: Best-Fit Model Eviction (BFE) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 132 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Policy 3: Warm-Start-aware Best-Fit Model Eviction (WS-BFE) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 132 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Policy 4: Intelligent Warm-Start-aware Best-Fit Eviction (iWS-BFE) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 133 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 Performance Evaluation .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 137 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Experimental Setup and Evaluation Metrics .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 137 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Impact of Edge-MultiAI on the Degree of Multi-tenancy .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 139 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Impact of the Eviction Policies on the Cold-Start Inference .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 140 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Impact of the Eviction Policies on the Inference Accuracy .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 141 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Bi-Objective Analysis of NN Model Eviction Policies .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 142 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 Analyzing Robustness against Uncertainties .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 144 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 Evaluating the Fairness of NN Model Eviction Policies .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 145 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 Summary .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 148 Chapter 6: Conclusion and Future Research Directions .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 149 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Discussion .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 149 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Future Research Directions .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 151 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Hierarchical Clustering of unstructured Data .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 151 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Building Classifier from the Encrypted Clusters .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 152 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Introducing Elasticity in Confidential Search .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 152 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Adding Energy in Model Management Schemes .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 153 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Cloud Offloading for Latency-tolerant Applications .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 153 Bibliography .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 154 Biographical Sketch .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 166 x List of Tables Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Summary of the existing privacy-preserving clustering approaches and positioning our proposed works (ClustCrypt and ClusPr) with respect to them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 38 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Token-Document Frequency Matrix A, built based on the index structure .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 46 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Normalized Token-Document matrix N .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 47 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Matrix R is built based on normalized matrix N to represent the importance of each token across all documents .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 48 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Matrix S is built from N to represent the importance of each document with respect to each token .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 49 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cluster decision matrix Q is built based on the multiplication of R and S matrices .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 50 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Calinski-Harabasz Index for the datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 81 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Benchmark queries for each one of the studied datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 86 Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Benchmark search queries developed for the RFC and BBC datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 109 Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Comparing the mean F-1 and the mean TSAP@10 scores obtained from SAED-plugged enterprise search systems versus their original forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The highest resulted scores are shown in bold font.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 115 Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Load time, inference time, and accuracy of popular NN models individually running on Samsung Galaxy S20+ as the edge server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 121 Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Application-specific models with different precision variants that are experimented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 137 xi List of Figures Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' High-level workflow diagram of performing confidential computing on an edge-cloud system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The bottom arrow indicates the degree of trust across the continuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A high-level diagram of user-edge-cloud based three-tier architecture to facilitate smart and confidential enterprise search service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 6 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Interrelationship between chapters and related contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 10 Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' High-level architectural overview of TEE building blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 16 Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A taxonomy of the scopes of confidential computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 17 Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Taxonomy of different types of search over encrypted big data in the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 26 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' High-level two-tiered (client-cloud) Search System Architecture Integrating ClustCrypt Approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 40 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Overview of the context where ClusPr is deployed in a three-tier architecture (of client, edge, and cloud) to facilitate a secure cloud-based search service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The edge tier is assumed to be on the user premises and trusted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It is used to ease the computational overheads imposed by privacy and clustering related processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 43 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A bipartite graph representing the relatedness among centers and remaining tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The weight of each edge represents the relatedness of a token and a center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Solid lines show centers that offer the maximum relatedness for a token.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 60 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Silhouette Coefficient (SC) metric for each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The results are obtained from S-ClusPr, HK-means++, ClustCrypt (that are encrypted-based clustering schemes), W2V-Kmeans, and WordNet clustering schemes (that operate on plain-text tokens).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 78 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Davies-Bouldin Index (DI) for each dataset using different clustering schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 79 xii Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cluster coherency for each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 80 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Comparing the impact of clustering using S-ClusPr against original clustering of S3BD for the studied datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 84 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Comparing the relevancy of search results using S-ClusPr vs original S3BD clustering in BBC dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The value of relevancy is calculated based on TSAP@10 scoring metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 85 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Search time of S3BD when S-ClusPr is used for clustering versus when the original S3BD clustering is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 88 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Clusters’ coherency for different updates of the three studied datasets when SD-ClusPr is applied with and without re-clustering option.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 88 Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Architectural overview of the SAED system within edge tier and as part of the three-tier enterprise search service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' SAED provides semantic search via identifying the query context and combining that with the user’s interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, Query Expansion and Weighting unit of SAED, respectively, incorporate the semantic and assure the relevancy of the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Solid and dashed lines indicate the interactions from user to the cloud tier and from the cloud tier to the user respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 95 Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Comparing TSAP@10 scores of SAED+S3BD and S3BD systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Horizontal axes show the benchmark queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 112 Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Comparing TSAP@10 scores obtained from SAED+Kendra versus AWS Kendra in searching benchmark queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 112 Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Comparing TSAP@10 scores obtained from SAED+Kendra vs AWS Kendra systems in the encrypted domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 113 Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Search time comparison among S3BD, Kendra, SAED+S3BD, and SAED+Kendra systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 117 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Bird-eye view of SmartSight, an IoT-based system that continuously receives various inputs from the smartglass (IoT device) sensors, and processes them via multi-tenant DL applications running on the edge server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 120 xiii Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Architectural overview of the Edge-MultiAI framework with three tiers: Application, NN Model Manager, and Memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 126 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A sample scenario of inference requests for five multi-tenant applications, namely A1 to A5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Each pulse represents the time window within which an inference request is expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Solid lines expresses the event that has already happened and dashed lines after “now” are the request predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 130 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The impact of Edge-MultiAI and its iWS-BFE eviction policy on satisfying the requested multi-tenancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The large graph represents the summative analysis via increasing the mean of multi-tenancy requested in the horizontal axis, and showing the percentage of requests that were satisfied in the vertical axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For each case, the smaller graph more granularly represents the number of concurrent requests issued and fulfilled during the simulation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 138 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Measuring the percentage of cold-start inferences of multi-tenant applications resulted from the proposed eviction policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The horizontal axis shows the deviation between predicted and actual inference request times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 140 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Measuring the normalized inference accuracy of applications resulted from employing the different eviction policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 141 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Bi-objective analysis of the different model selection policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 143 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Robustness of the system against uncertainty in the prediction of inference requests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 145 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The percentage of cold-start inferences using different NN model eviction policies versus no policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 146 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The inference accuracy obtained from the different policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The “maximum” is the benchmark, showing the accuracy of the highest-precision model for each application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 147 xiv Chapter 1: Introduction 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Motivation: Data Confidentiality in the Current Age More than half of the world’s population is now connected to the internet thanks to the proliferation of information and communication technologies that have shaped today’s digital world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The expeditious growth of digitalization has been producing a massive volume of data in various forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It is estimated that every day 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 exabytes of data are being generated in which, over 80% of the data is in unstructured (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', audio, streaming, text) form [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Data can range widely from a person’s first and last name to sensitive (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' confidential) information such as biometric information, law-enforcement records, healthcare reports, and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Such confidential data must always be safeguarded to prevent unauthorized access.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As an example, most of the current smartphones are featured with biometric-based security protocol and so, they retain biometric data for unlocking the device after ensuring proper authorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' If this biometric information is compromised as a result of a data breach, it could assist criminals in stealing identities, forging documents, and committing crimes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Essence of Maintaining Data Confidentiality Maintaining data confidentiality while data is stored either on-premises denoted as (data at rest) is a widely known problem with numerous established encryption solutions [2, 3, 4, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' On another front, solutions like transport layer security (TLS) protocol are globally adopted to tackle the challenge of maintaining data confidentiality during node-to-node transmission (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' data at transit).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1 Another state of data that needs to be protected is known as data in use that refers to preserving data confidentiality and security while it is being accessed and processed by users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Although adopting an encryption technique can provide security assurance while data is stored or transmitted, it does not guarantee data privacy when the data is being used in memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Compared to other two states, data is most vulnerable during computing (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', when it is in use).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The degree of data vulnerability is further elevated when owners of confidential data are either individuals or institutions that rely on cloud services for their storage demands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cloud providers (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', AWS, Azure, Google cloud) have come forward offering various services for large-scale data storing and processing, however, confidential data owners are hesitant to adopt cloud services due to the valid data-privacy concerns [3, 6] on the cloud data centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In fact, cloud adoption increases the risks associated with ubiquitous access to the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In fact, they provide larger attack surface that can be exploited by intruders.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is why clouds have been the target platform for numerous recent privacy violations incidents [7, 8].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In one notable incident, confidential information of over three billion Yahoo users were exposed [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In another incident, information of over 14 million Verizon customer accounts were exposed from the company’s cloud system [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Considering these incidents, currently, a large spectrum of applications ranging from personalized healthcare, search, archives, and finance to social network (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', Twitter, Facebook) and IoT industries are under similar cloud-based data breaching threats [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Even if cloud providers can offer strict security control against 2 external threats, subscribers dealing with sensitive content are still concerned, hence, cannot fully embrace cloud services due to potential of insider attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As such, securing confidential data processing both within and across a wide range of systems– from user devices to clouds and even multi-cloud environments– that is not fully controlled by the data owner is the pressing need of the IT industry globally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Confidential Computing 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Basic Definition There are numerous solutions to ensure data confidentiality for data at rest and in transit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, preserving confidentiality of data in use remains an open problem that needs further attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this regard, the idea of confidential computing has emerged over the recent years that has given birth to hardware-enforced trusted execution environment (TEE) systems for secure computing (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', data processing) without compromising data privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' TEE allows user-level code to allocate private regions of memory, called enclaves to confidentially process data without trusting operating system or hypervisors [11, 12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hence, it prevents unauthorized access or modification of applications and data while they are “in use”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' By that means, confidential computing enhances the data security assurances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Recently, the use cases of confidential computing are getting popular both in industry and academia, and the total market of the concept is expected to grow at least 26× over the next five years [13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Confidential Computing across Edge-to-Cloud Continuum Adoption of cloud services is virtually unavoidable to successfully store and 3 process large volume of data;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' nevertheless, due to simultaneous threats arriving from both within and outside the cloud systems, confidential data owner cannot put their faith in the cloud and liberally utilize its services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Accordingly, the goal of confidential computing on the cloud is defined as to provide the users with the secure access to third-party cloud computing services in a public domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, apart from the security aspect, due to their centralized nature, clouds also suffer from high communication latency that can be detrimental for many of the IoT-based solutions that have latency constraints [14, 15, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is the reason for the emergence of a new computing paradigm over the past few years that goes beyond conventional cloud systems and encompasses a continuum of computing tiers—from the device tier to edge, fog, and the cloud [14, 17, 15, 16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The device-to-cloud continuum increases the vulnerability surface beyond the cloud, hence, confidential computing solutions have to be expanded across the entire continuum to enable integrity of the IoT-based systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1, represents a computing continuum with applications span across the user-device to edge and cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The data generated by the user is first pre-processed on the device-tier (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', IoT devices);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, it is processed by the services on the edge and cloud tiers, depending on the on the low-latency and resources demands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In our vision, confidential computing across edge-to-cloud continuum is defined as protecting the integrity and confidentiality of the users’ data while are in use by the applications span across the continuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' One challenge in providing confidential computing to across the continuum is that both the device tier (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', 4 Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' High-level workflow diagram of performing confidential computing on an edge-cloud system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The bottom arrow indicates the degree of trust across the continuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Storage Computing Cloud HDD SSD Visualization Machine Learning Device Edge Services Low-latency services Computing Trust UAV [18] and smartglasses [19]) and the edge tier (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', smartphones, companion devices), often, are resource- and energy-limited and fall short in executing trusted applications needed for confidential computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Trustworthiness throughout the continuum is another challenge that must be overcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is due to the fact that as soon as data is transited away from the user’s end, the vulnerability surface expands (Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1), and as a result, the degree of trust falls as data is sent to edge and cloud tiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, various encryption techniques such as client side encryption [20] are adopted to encrypt data at user-premise, thereby, ensure data confidentiality while utilizing any cloud services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is because, in this case, clouds providers are not capable of decrypting the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The inability to decrypt data, however, prevents accessing the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It is these challenges that we aim at addressing in this dissertation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Specifically, this dissertation investigates ways to 5 enable confidential computing across edge-cloud while considering (a) the trustworthiness level of each tier in the continuum;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' and (b) the low-latency constraints of the applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Confidential Computing of Unstructured data An organization with a massive volume of confidential unstructured text-based data desires a trusted application that is executed on confidential computing platform to provide secure semantic searchability over the data in latency-sensitive manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' One instance of such organization is a law enforcement agency with encrypted crime report data, with officers who would require to search over the reports using their handheld devices while at the office or on the move in low-latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the context of confidential unstructured data processing, various searchable encryption systems (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', [21, 22, 23, 24]) have been developed to enable secure search ability over the encrypted data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Upon using encrypted data, such systems build an encrypted index, which is then traversed against a search query at the search time to discover relevant documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A high-level diagram of user-edge-cloud based three-tier architecture to facilitate smart and confidential enterprise search service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Edge User Cloud Compute Storage Enterprise Search Service ~~ ~~ SAED Searching exhaustively over the whole index for a given search query 6 prohibits the low-latency constraint of the search operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, index partitioning (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' clustering) is required to prune the search space so that search can be performed over a pruned index with minimal overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Clustering is one of the crucial data analytics methods that are commonly used to group datapoints based on their shared attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, upon applying clustering on the search index, we can prune it into multiple subsets that can improve search time overhead in orders of magnitudes [1, 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It is possible that the user (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', law enforcement officers) do not remember the specific keywords that are included in the documents they are looking for.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hence, they need to retrieve documents semantically and contextually related to their given search query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As example, if a officer searches for “robbery”, he/she can also be interested in finding documents about “mugging”, “theft”, or “break in”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, since the officer performs the searches on their limited resourceful handheld devices when he/she is on the move, the solution should incur a minimal processing overhead and scale well to massive amount of unstructured text data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To this end, a robust and secure enterprise search service in the form of a trusted application is the need of the hour to search semantically over the encrypted confidential data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2, a high-level architecture of secure enterprise search service is depicted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Such service can provide the secure search intelligence utilizing the on-premises edge resources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The high-end storage and compute resources on the cloud tier are utilized by the existing search systems to exhaustively carry out pattern matching on the entire dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Research Problems and Objectives With the aim of facilitating confidential computing across edge-to-cloud continuum, in this dissertation, we address the following research problems: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' How to develop a trusted application to optimally, scalably, and securely cluster keywords in an encrypted unstructured dataset?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' How to cluster the data when there is dynamism in the dataset meaning that the contents are being added to or removed from?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' How to enable secure semantic search over encrypted data with minimum overhead?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' How to develop a trustworthy robust encrypted enterprise search service?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' How to manage NN models of trustworthy DL applications to stimulate their concurrent executions without compromising their inference accuracy?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Contributions In light of the research topics outlined in the preceding section, this dissertation makes the following significant contributions: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Proposing two trusted applications to enable confidential clustering of encrypted unstructured data in the cloud: (1) ClustCrypt- cloud-only architecture and (2) ClusPr- edge-cloud architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' While ClustCrypt can estimate the suitable number of clusters (K) and then cluster encrypted static data only, by incorporating edge, ClusPr can go beyond by clustering data 8 that contain dynamism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' ClusPr against other schemes in the literature, on three different test datasets demonstrates between 30% to 60% improvement on the cluster coherency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Moreover, we notice that employing ClusPr within a privacy-preserving enterprise search system can reduce the search time by up to 78%, while improving the search accuracy by up to 35%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Proposing an open-source search mechanism (titled as SAED) that overcomes the privacy problem by separating the intelligence aspect of the search from its pattern matching aspect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In SAED, the search intelligence is provided by an on-premises edge tier and the shared cloud tier only serves as an exhaustive pattern matching search utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Leveraging the edge tier, SAED offers personalized semantic searchability on existing cloud-based enterprise search services with low-latency constraint while maintaining data privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Evaluation under real settings and verified by human users demonstrate that SAED can improve the relevancy of the retrieved results by on ≈ 75% for encrypted generic datasets with negligible search time overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Proposing an NN model management framework, called Edge-MultiAI that facilitates continuous execution of confidential DL applications on the trustworthy edge server to avoid the risk of cloud execution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is because, NN models of the trusted applications cannot be outsourced to the public clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' With the help of approximate computing, Edge-MultiAI efficiently utilizes the edge memory such that the multi-tenancy degree is maximized 9 without any major compromise on the inference operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Edge-MultiAI dynamically loads the high-precision NN model for the requester application, while loading low-precision ones for others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The framework proposes iWS-BFE policy along with three other baseline heuristic policies within Edge-MultiAI to choose the suitable model for the application performing inference, and to decide how to allocate memory for it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Experiment reveals that Edge-MultiAI can stimulate the degree of multi-tenancy on the edge by at least 2× without any major loss on the inference accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 Dissertation Organization Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Interrelationship between chapters and related contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' SAED (Chapter 4) ClustCrypt (Chapter 3) Edge-MultiAI (Chapter 5) ClusPr (Chapter 3) Device Cloud Edge Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 depicts the relationships between chapters and the contribution to which they are related to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The core chapters of this dissertation are derived from several research papers published during the course of the Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' candidacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 10 Chapter 2 provides background for: emergence of edge-cloud continuum, trustworthy compute tiers, enterprise search service, confidential machine learning, and explores the related research works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' – Sm Zobaed, Mohsen Amini Salehi, Big Data in the Cloud published in Encyclopedia of Big data, Springer, ISBN: 978-3-319-32009-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' – Sm Zobaed, Md Enamul Haque, Md Fazle Rabby, Mohsen Amini Salehi, Senspick: Sense Picking for Word Sense Disambiguation, Published in proceedings of the 15th IEEE International Conference on Semantic Computing (ICSC’21), Online, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' – Sm Zobaed, Mohsen Amini Salehi, A Survey on Confidential Computing over Edge-to-Cloud Continuum, Preparing to be submitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chapter 3 explores the Benefits of clustering privacy-preserving text-based big data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The semantics of the data is lost after the encryption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, the data can be clustered topically by utilizing the statistical characteristics of the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This Chapter discusses our proposed approach of clustering encrypted static and dynamic data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, the Chapter compares the clusters obtained by proposed approach and others in the measure of popular cluster goodness metrics (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', Silhouette Coefficient, Davis-Boudin index).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Finally, it presents a set of experiments carried out in a realistic environment to show the effectiveness of the clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' – Sm Zobaed, Sahan Ahmad, Raju Gottumukkala, Mohsen Amini Salehi, 11 Clustcrypt: Privacy-preserving clustering of unstructured big data in the cloud, Published in proceedings of the 21st IEEE International Conference on High Performance Computing and Communications (HPCC’19), China, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' (Full code in Github repository: https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/hpcclab/ClustCrypt).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' – Sahan Ahmad, Sm Zobaed, Raju Gottumukkala, Mohsen Amini Salehi, Edge Computing for User-Centric Secure Search on Cloud-Based Encrypted Big Data, Published in proceedings of the 21st IEEE International Conference on High Performance Computing and Communications (HPCC’19), China, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' – Sm Zobaed, Mohsen Amini Salehi, Privacy-Preserving Clustering of Unstructured Big Data for Cloud-Based Enterprise Search Solutions, Published in Journal of Concurrency and Computation: Practice and Experience (CCPE),Volume 34, Issue 22, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' (Full code in Github repository: https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/zobaed11/Jorunal-Version).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chapter 4 studies the significance of secure and personalized semantic search over the encrypted data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This Chapter explains the workflow and mechanisms of the proposed secure search service architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Finally, it presents a set of experiments carried out in AWS Kendra service environment to show the effectiveness of the search relevancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' – Sm Zobaed, Mohsen Amini Salehi, Rajkumar Buyya, SAED: 12 Edge-Based Intelligence for Privacy-Preserving Enterprise Search on the Cloud, Published in proceedings of the 21st ACM/IEEE International Conference on Cluster Cloud and Grid Computing (CCGrid ’21), Australia, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' (Full code in Github repository: https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/hpcclab/SAED-Security-At-Edge) Chapter 5 explores multi-tenant execution of latency-sensitive DL applications on edge server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This Chapter explains the architectural overview of Edge-MultiAI and the heuristics within Edge-MultiAI for managing models of the multi-tenant DL applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' – Sm Zobaed, Ali Mokhtari, Jaya Prakash Champati†, Mathieu Kourouma, Mohsen Amini Salehi, Edge-MultiAI: Multi-Tenancy of Latency-Sensitive Deep Learning Applications on Edge, Accepted in proceedings of the 15th ACM/IEEE International Conference on Utility and Cloud Computing (UCC’22), USA, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' (Full code in Github repository: https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/hpcclab/SAED-Security-At-Edge) Chapter 6 concludes the dissertation with a discussion of our major findings and explores further research topics and directions that emerged during the course of this research but have not discussed in this thesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 13 Chapter 2: Background and Literature Study This chapter provides background and a survey of other research works undertaken in the fields most related to the confidential computing across edge-to-cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Background 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Trusted Execution Environment A trusted execution environment (TEE) is a tamper-resistant processing environment that are leveraged to run trustworthy applications, such as biometric authentication, privacy-preserving search over encrypted data etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='with hardware-enforced isolation via a trusted hardware (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', secure processor).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' TEEs have their own memory regions where trusted applications (TAs) reside with complete isolation aiming to prevent unauthorised accesses from generic (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' untrusted) space, manipulation of software adversaries (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', malware, hacked OS) or even hardware adversaries (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', channel attack) who have physical access to the platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' TEE is considered as the kernel of confidential computing and so, recent advancement in TEE technology has brought solution ranges from microcontrollers to large servers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The widely adopted TEE technologies are Intel SGX, AMD SEV, and ARM TrustZone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Intel SGX and AMD SEV provide TEE support for serverside and personal computers, while ARM TrustZone-based TEEs are designed for resource constraint devices (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', edge devices, smartphones and Raspberry Pis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1, we represent a high-level architectural overview of TEE components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Generally, a TEE maintains two separate spaces for all trusted and 14 generic applications, namely trusted and untrusted world.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The trusted world contains a trusted OS or, kernel that communicates with TAs using the TEE Internal API, whereas generic applications from the untrusted world communicate with the trusted world via the TEE Client API.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, a TEE can offer secure storage utilizing the sealing abstraction (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', GPTEE, SGX);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' a trusted user-interface API for establishing secure paths between TAs and output display;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' a secure provisioning API for initiating TEE network connections using POSIX-style sockets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 15 Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' High-level architectural overview of TEE building blocks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Trusted Applications TEE Client API Untrusted World Trusted World TEE Comm- unication Secure Provisioning Trusted I/O Path User Applications Hardware Layer Secure Storage Generic (Rich) OS Trusted Kernel TEE Internal APIs Secure Boot Secure Hardwares Root of Trust Secure Scheduling Separation Kernel Communication 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Trustworthy Infrastructure for Confidential Computing Towards deploying confidential computing pipeline, trust should be ensured in hardware, middleware (OS), and application layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Breaching confidentiality while execution can be occurred due to tempering any of the layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 represents a taxonomy of the scopes implementing confidential computing in high-level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Dealing with big data size confidential data, confidential computing on 16 the cloud tier is crucial where the chance of breaching always remains peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Although confidential computing provides isolated execution environment, related hardwares, OS, and applications should be attested locally or remotely via third party (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', trusted authority) prior to any executions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In [25], Valadares et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='provided different attestation mechanisms for preventing hardware attacks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', side -channel) on Intel SGX-enhanced edge-IoT systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A taxonomy of the scopes of confidential computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Confidential Computing Middleware serverful serverless TPM SE VM container FaaS BaaS func.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' def.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' VM container VM+container bare metal microVM unikernel Paradigm Tier device edge cloud fog Hardware bare metal Application Partitioning monolithic Architecture microservice ML Engine (Conf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' ML) federated learning differential privacy Encryption discrete secure space memory encryption (AMD SEV) hypervisor integrated firmware software Module TEE Intel SGX ARM TrustZone differential learning Systems/ func.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' invoc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 17 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Cloud-based Enterprise Search Services over Unstructured Text Data Providing access and search ability over big data is essential and data without these abilities is not much of use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, organizations that deploy cloud services for their big data are concerned about data exposure ([1, 3]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hence, accessing the data without exposure is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Enterprise search cloud services are becoming increasingly popular to enable searching over and providing legitimate access to organizational big data ([26]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Enterprise search services often maintain a dynamic index structure based on timely crawling in organizational documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, the user’s query is searched against the index structure and the result-set, referencing the relevant documents, is displayed to the legitimate user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Amazon cloud has provided a semantic enterprise search service named Kendra by leveraging machine learning and natural language processing methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Amazon argues that their clients, such as Woodside, 3M, and Sage have improved the accuracy and speed of searching and accessing their organizational documents, in compared to other existing solutions([27]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Semantic searchability comes with the cost of compromising the users’ data privacy [3, 17, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is, in fact, the trapdoor that particularly internal attackers can misuse to breach the confidentiality or even the integrity of the users’ data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It is this type of attack model that we try to make the cloud-based enterprise search services resistant against.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We note that, for encrypted datasets, the current enterprise search services cannot offer anything beyond na¨ıve string matching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 18 We note that currently Amazon Kendra does not support enterprise search service over datasets encrypted by the user’s key (aka user-side encryption).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This leaves the organizational data privacy concern an open question in the cloud era.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To address this concern, multiple solutions are provided to enable semantic search over user-side encrypted big data ([3],[1],[17]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' These solutions aim at performing real-time search operation without compromising data privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Even for plain-text datasets, our investigations revealed that Kendra covers only ontological semantics in the search and it falls short in providing context-aware and personalized semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For instance, we tested Kendra to verify the ability of capturing context-aware semantics by feeding soccer as a query and in the result set, there were documents about rugby [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In another test, river bank query returned documents about commercial bank that indicates the lack of context-awareness in the search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Microsoft Azure Cognitive Services provide different APIs for performing various useful NLP tasks including sentiment analysis, conversational AI, and translator on Azure cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Such services give the scopes of using both customizable and pretrained models to deploy anywhere either on demand or spot instance basis [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Emergence of Edge-to-Cloud Continuum The edge computing paradigm [12, 29, 30] becomes widely adopted because of the latency-sensitive feature that ensures secure real-time data processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, because of the constrained processing power, edge nodes are limited to 19 process small volume (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', light-weight) of data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, the edge paradigm is not effective processing massive volume of sensitive data in standalone manner and application developers and data owner adopt to cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Although a large body of research regarding performance improvement in terms of real-time processing, scalability, and output accuracy have been performed on edge-to-cloud continuum, comparatively less attentions are paid to confidential data processing ability [12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, edge computing is capable only for processing light-weight data and hence, from big data aspect, no alternative exists except processing on the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Generally, edges are dispersedly distributed and have a large attack surface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As a result, there is high chance that off-premises edge can be compromised.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The recent move of the hardware vendors who design dedicated hardware-assisted TEE compatible to the both cloud and edge computing infrastructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Machine/Deep Learning for Unstructured Data-driven Applications Due to the volume and complexity of the data, conventional data analytics tools (such as frameworks) are unable to handle unstructured data in an efficient manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We need to employ a variety of computer vision- and natural language modeling (NLP)-based solutions that are founded on machine learning and deep learning architecture so that we can carry out data analytics on unstructured data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Recent advances in vision and natural language processing algorithms, such as convolutional neural networks, autoencoders, generative adversarial networks, long short-term memories (LSTM), transformers, and multi-headed attention 20 mechanisms, have made it possible to deal with unstructured text data in an effective manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' There have been several advancements made in cloud-based, AI-powered, and specific use-case driven data analytics tools as a result of the availability of artificial intelligence services from major cloud service providers such as AWS and Azure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It is necessary to train a model by providing it with a curated dataset in order to construct machine learning and deep learning-enhanced applications for unstructured data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is done so that the model can comprehend the underlying intricate pattern, relation, or advanced features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It has been established, after validating the validity of the model, that the model is prepared to carry out the activity that has been stated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Following this, the model will move on to the inference phase, where it will undertake predictive analysis based on live data in order to produce results that may be acted upon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 Edge Multi-Tenancy for Latency-Sensitive Processing An edge server is an indispensable part of an IoT-based edge-cloud system that has to continuously execute multiple (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' multi-tenant) smart (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', deep learning) applications with low-latency and high accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, due to memory limitation, executing latency-sensitive multi-tenant applications on an edge server can cause memory contention problem that decreases execution rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is because, DL applications utilize bulky Neural Network (NN) models at their kernel to infer on the inputs received from the sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The NN models have to be kept in memory to enable low-latency (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' warm-start [31]) inference operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 21 Otherwise, because the NN model size is often huge, loading it into the memory in an on-demand manner (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' cold-start) is counterproductive and affects the latency constraint of the DL applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As the edge servers naturally have a limited memory size (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', 4 GB in the case of Jetson Nano [32]), multi-tenant execution of DL applications on them leads to a memory contention challenge across the processes [14, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To this point, in a multi-tenant execution environment, it is crucial to dynamically load a suitable model in memory from the set of models available to the application such that it neither interrupts the execution of other applications, nor causes a cold-start inference for them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 22 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Prior Literature for Confidential Computing for Unstructured Data 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Privacy-preserving Unstructured Data Clustering Schemes Clustering is essential for various Natural Language Processing (NLP) tasks, particularly a pre-requisite for most of the advance search systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Once the data is encrypted, only statistical characteristics of data remains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, secure data clustering is performed based on considering only the statistical properties of the cipher-texts of the document set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A large body of research has been undertaken to enable processing of the encrypted data (ciphertext).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' proposed a linear transformation-based solution for matching queries against encrypted data while ensuring data privacy on the cloud without any intervention of the data owner [34].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, linear transformation methods support secure K-nearest neighbor (KNN)-based query matching approaches but not the clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is because clustering is not invariant to linearly transformed data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The optimal linear transformation has a prerequisite of knowing the true cluster means, which is not possible to obtain before generating the cluster [35].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, we assume that the data are tokenized and encrypted before transferring to the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, unlike [34], where the entirety of encrypted data is queried using time-consuming cryptographic calculations, we use the statistical properties of the data without revealing any meaningful part of it to the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Sun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' proposed a searchable encryption method by forming a tree index structure that operates based on the cosine similarity and TF × IDF [36, 4] measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, the solution is not scalable for 23 big data, because the search index can become large to the extent that it impacts timeliness of the search operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We believe that our proposed clustering approach can be a complement to [36, 4] where the central index is partitioned topically into multiple small size index structures that can improve the search time and efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Homomorphic encryption has become a popular method to perform computation over the encrypted data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Several variations of the homomorphic encryption such as fully or partially Homomorphic encryption [37, 38] have been proposed to enable privacy-preserving data processing on the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [5] proposed a secure aggregation and division protocol based on homomorphic encryption to securely compute clusters without tampering with the privacy of individual peers in a peer-to-peer system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, their clustering technique does not consider data dynamism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Pang and Wang proposed a homomorphic scheme that provides security to outsourced data uploaded from multiple parties in a twin-cloud system [39] that is assumed to be a semi-honest environment, whereas, we assume cloud to be untrusted in terms of storing/processing sensitive data [40].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' proposed HK-Means++ that combines K-Means clustering with finding the suitable cluster numbers [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, the work leverages homomorphic encryption scheme to solve the encrypted data manipulation, distance, and convergence calculation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Although our work is comparable to HK-Means++, it can only cluster static datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Moreover, the experiments were performed only on one dataset and it is not clear how the method performs on other datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We note that the current implementations of the homomorphic encryption 24 technique imply a high computational overhead [42] which affects the real-time response of a search system, particularly, for big datasets [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Vaidya and Clifton [43] proposed a solution to cluster encrypted datasets in which different data attributes are stored in distinct storage systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, the clustering was carried out in each one of the data storage systems individually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, this solution is time consuming and cannot serve the real-time constraint we consider in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Very few research have been undertaken in the context of privacy-preserving big data processing in real-time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' S3BD, proposed by Woodworth et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [3] is one of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' S3BD is a cloud-based secure semantic search system that performs searching over big data using cloud services without exposing any data to cloud providers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To maintain the constraint of real-time search on big data, S3BD proactively prunes the search space to a subset of the whole dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For the sake of pruning, they proposed a method to cluster the encrypted big data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Once the clustering is done, an abstract (a representative set) of each cluster is maintained on the client-end to navigate the search operation to appropriate clusters at the search time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Searchable Encryption and Encrypted Index Several research works have been undertaken recently to initiate different types of search over encrypted data in the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Most of the searchable encryption based solutions generate cipher-text of the search query and search over encrypted text in a na´ıve straightforward way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Particularly, each word in a given document is encrypted independently and later, the document set is sequentially scanned while 25 searching for getting match with the queried cipher-text (encrypted query) [44, 45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' These solutions are generally chosen as they require no storage overhead on the server but they are commonly slower [3, 44].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 provides a high-level taxonomy of research works on the search over encrypted data in the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Privacy-Preserving query over encrypted graph-structured data ([46]), cryptDB ([47]), and dragonfruit ([48]) are the instances of search over encrypted structured data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' SecureNoSQL ([49]), SemiLD ([50], and XSnippets ([51]) are the instances of search over encrypted semi-structured data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' REseED ([24]), SSE ([52]) S3C ([53]) are tools developed for regular expression (Regex), keyword, and semantic searching respectively over unstructured big data in the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Taxonomy of different types of search over encrypted big data in the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Searcheable Encryption Structured Data Unstructured Data Semantic Keyword Regular Expression Format-preserving Encryption Property-preserving Encryption SQL-aware Encryption NoSQL-aware Encryption Keyword Semi-Structured Data 26 Some of the searchable encryption based solutions maintains central index structure to store store selected data from each document for the sake of making the search operation relatively quicker and well adapted to big data aspects [53,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 52,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Privacy-Preserving Cloud-based Search Systems In addition to plain-text data, searching is performed on privacy-preserving data ensuring negligible chances of data leakage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, various searchable encryption-based solutions are adopted to facilitate search over such data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Few works at the time of writing have combined the ideas of semantic searching and searchable encryption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Works that attempt to provide a semantic search often only consider word similarity instead of true semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [55] proposed a system which could handle minor user typos through a fuzzy keyword search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Moataz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [56] use various stemming approaches on terms in the index and query to provide more general matching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Sun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [57] present a system that used an indexing approach over encrypted file metadata and data mining techniques to capture the semantics of queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This approach, however, builds a semantic network only using the documents that are given to the set and only considers words that are likely to co-occur as semantically related, leaving out many possible synonyms or categorically related terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' S3BD [3], a secure semantic search system that could search semantically over encrypted confidential big data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' They expand their search query by incorporating semantic data extracted blindly from an ontological network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='They do not consider context-aware query 27 expansion that created confusion for the search system while processing ambiguous or multi-context keywords in a query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To perform query processing in client devices, they end up requiring additional computational overhead in the client tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 28 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Semantic Representation of Search Query Keywords.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Query expansion is a process to seek keywords that are semantically related to a given query and fill the lexical gap between the user queries and the searchable documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' One of the widely-used methods of query expansion is Pseudo-Relevance Feedback (PRF) [58, 59] that extends an unsuccessful query with various related keywords and then re-ranks the search results to increase the likelihood of retrieving relevant documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Although the PRF-based approach generally improves the retrieval effectiveness, it is sensitive to the quality of the original search results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Latent semantic analysis [60], latent dirichlet analysis [61], and neural-based linguistic models [59, 62] are some of the query expansion methods that can obtain the semantic representation of a given query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In these methods, vectors are commonly referred to as word embeddings that represent words into a low-dimensional semantic space, where the vicinity of words demonstrates the syntactic or semantic similarity between them [63].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, pre-trained word embedding models, such as Word2vec [63], always generate the same vector representation for an input word, regardless of the context in which the word has appeared in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hence, if any ambiguous keyword(s) present in a query, the underlying topic of the query could not be detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' WordNet [64] is one of the widely-used and lexically-rich resources in English that is utilized to infer the sense of ambiguous words in a given corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In WordNet, words containing similar meanings are grouped into synonym sets, whereby each set has a semantic and conceptual relationship with the other sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Song et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [65] and 29 Nakade et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [66] evaluate the effectiveness of utilizing WordNet for query expansion in National Institute of Standards and Technology (NIST) and Twitter datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' They identify important key-phrases of the query and use WordNet to obtain the relevant synonym sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Later, they utilize the synonym sets to construct the expanded query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Nevertheless, in most of the prior research on query expansion using WordNet (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', [67]), the elements of the expanded query set are considered uniformly that undermines the relevancy and ranking of the result set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Edge Computing for Privacy-preserving Unstructured Data Processing To facilitate secure personalized search, most of the enterprise search services rely on the computational capability of the client devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, it imposes a significant overhead on the user devices (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', thin client) to perform a secure query processing or to encrypt/decrypt user documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To this regard, on-premises edge computing has potential to perform personalized search based on the historical search data stored in the client devices and also perform encryption/decryption on demand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To this context, it is ensured that the on-premises edge is fully trusted and offer uninterrupted confidential computing environment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Prior work S3BD [3] imposes overhead to the client device while performing secure search over encrypted big data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' On-premises edge computing is an appropriate approach for such system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' By extending their two-tiered architecture with an on-premises/trusted edge can reduce a significant overhead from the client devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 30 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Prior Literature on Multi-Tenant AI-based Executions on Edge 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Edge AI Numerous research have been undertaken to explore the applications, scopes, and benefits of edge-based AI for the seamless execution of latency-sensitive smart applications [68, 69, 14, 70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Murshed et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='discussed different DNN-based practical applications such as video analytics and image recognition for enabling edge AI [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='surveyed on various training and inference techniques for NN models on edge devices [70].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chen and Ran discussed different techniques that can help to accelerate the DL training and inference on the edge-based systems [68].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Han et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='explored the ways to accelerate the training convergence for the edge-based architectures [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='surveyed the development of DL applications on edge from the latency and bandwidth perspectives [71].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhou et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [70] claimed that although higher edge intelligence reduces data offloading and improves the privacy, the latency and energy consumption overhead can increase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Multi-tenant Execution on Edge Prior studies investigated AI multi-tenancy on the edge servers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Mao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='proposed a mobile computing framework, MoDNN, to execute DL applications simultaneously on resource-constrained devices [72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' MoDNN can partition pre-trained DNN models across several mobile devices to accelerate tensor processing with reduced device-level computing cost and memory usage while achieving 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='17×—4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='28× speedup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Multi-tenant execution across edge servers can lead to undesirable latency in 31 application execution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ko et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='proposed DisCo, a multi-tenant DL application execution offloading framework that enables execution of both the compute- and data-intensive parts of applications either on the device or on the edge [73].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hadidi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='discussed that complex DNN models are sensitive to data loss as they depend more on the nuances in the data [74].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' They mentioned losing one layer of the Inception V3 model can deteriorate the accuracy by more than 50%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' They utilized distributed DNN models on IoT systems to reduce the processing and the memory footprints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The aforementioned research works addressed the problem of accelerating multi-tenant applications without considering the memory constraint of the edge servers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The only exception, to the best of our knowledge is [75], in which the authors explored the executing the obstacle detection application in an autonomous vehicle with ultra low-latency constraint upon compromising with other executing applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' They proposed a reinforcement learning-based technique to scavenge memory from a non-priority application, hence, executing the obstacle detection application immediately and avoid accidents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Although their technique is effective to serve the latency-sensitive task, multi-tenant executions is out of their scope [75].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In contrast to these works, we investigate the problem of memory management to increase the degree of multi-tenancy and the number of warm-start inferences, thereby, improving the practical usability of IoT-based systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 DNN Model Compression Model compression techniques allow for running a model on different 32 resource-constrained devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' There are mainly two techniques to reduce the complexity of a given DNN model: making use of a fewer bit widths (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' quantization) and using fewer weights (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' pruning).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' These techniques have been considered individually and together to serve the purpose of model compression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Quantization reduces the computational resource demand at the expense of a diminutive loss in accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' By default, the model weights are float32 type variables which means 4 bytes are associated with each model weight with a significant amount of memory requirements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Model weights can be reduced from 32 bits to 8 bits (or even shorter [33]) to accelerate inference operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Pruning technique is applied to reduce the memory consumption of the model to accelerate the inference operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' An effective pruning technique removes redundant connections and/or reduces the width of a layer while ensuring a slight impact on the inference accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, the pruned models are retrained to compensates the loss in accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Failure of selecting proper pruning candidates affects inference tasks and make the pruned model futile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Some studies have also been conducted on the selection of appropriate pruning candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For compatibility with the IoT devices, Yao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='proposed DeepIoT [76], a reinforcement learning pruning technique for DNN models in the IoT devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, during pruning the model parameters, they only considered the execution time speed-up, hence, the technique inevitably exhibits inferior inference accuracy performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As noted above, aggressive pruning often substantially degrades the inference accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Training and inference with high pruning with negligible impact 33 on the accuracy is still an open research problem [33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Warm-Start vs Cold-Start DL Inference Provided the increasing complexity of DNN models, loading even compressed models to the edge memory is a burden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The problem is further complicated in scenarios where the edge server has to continuous maintain multiple applications in its memory (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', multi-tenancy) which is cost-prohibitive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Nonetheless, cold-start inferences should be avoided as they bring about a remarkable inference latency (see loading time in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 for more details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Some research works have been accomplished to avoid cold-start inferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For instance, to support latency-sensitive applications, in [77], the authors proposed cold-start of a DNN model in the background while the user is browsing a specific web page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' By utilizing system resources, their technique tracks the user’s browsing activity and loads the task-specific model in parallel during browsing activity to avoid the cold-start.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Summary and Positioning of this Dissertation Prior literatures neither provided a confidential computing-enabled system design for confidential unstructured data processing, nor low-latency constraint and multi-tenacy requirements on the resource limited edge computing systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For the confidential computing, we propose to logically partition the system to perform intelligence within the on-premise edge tier and use the cloud tier to perform simple and large scale processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' There has been much research accomplished in the fields of confidential computing, clustering, searchable encryption, and enterprise searching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, there has been little done in the intersection of these fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 34 It is this intersection that we position our contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this regard, we develop (1) Data clustering for confidential static and dynamic unstructured data that can be used in delay sensitive systems such as cloud-based search systems (2) Enabling trusted enterprise semantic searching over encrypted confidential data across edge-to-cloud (3) Stimulating the ability of edge systems to execute multi-tenant DL applications with low-latency without the help of unstructured cloud systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 35 Chapter 3: Privacy-Preserving Clustering for Unstructured Cloud Data 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Overview Our preliminary research depicted in the previous chapter has confirmed that clustering is possible in encrypted data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Topic-based clustering can improve the performance of various NLP tasks, particularly, in the context of secure search system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, forming topic-based clusters with encrypted text data is a challenge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To overcome this challenge, clustering is achieved based on statistical semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The idea is to locate tokens that are semantically close to each other in the same cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To achieve this, we first need to know the number of clusters (k) that should be created to cover topics exist in token of a given dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, we find the central tokens for each cluster and assign the rest of tokens to the most topically related clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We develop the proposed clustering solutions, namely ClustCrypt [1] and ClusPr [54].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We replace the existing clustering policy of S3BD with the proposed schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This chapter presents data-characteristics specific different clustering schemes and the architectural overview of the context where the proposed clustering schemes can be deployed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Note that, we consider that the frequency and co-occurrences of all tokens in the dataset are available in the proposed clustering works.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Problem Statement The prior clustering schemes of S3BD and other works require to specify number of clusters to initiate partitioning that is detrimental to optimal clustering of tokens (keywords) in the most appropriate cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We cannot predetermine the 36 same number of clusters and cluster size regardless of any sized datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, if the data contains dynamism, the clustering scheme needs to accommodate new tokens added to the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' On the contrary, the clusters can be shrunk due to the deletion of some documents from the document set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, in this chapter, we investigate how to optimally and scalably cluster keywords in an encrypted unstructured dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The outcome of this research enhances clustering of encrypted keywords by estimating the appropriate (k) and distributing keywords across the clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We highlight the importance of probabilistical semantic similarity among the encrypted tokens for clustering to measure the tendency for each token to be separate from others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Positioning of the Proposed Clustering Works Our proposed works are motivated from Woodworth et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='method for topic-based clustering on encrypted tokens (aka keywords) over the central index using K-means method [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The cluster-wise token distribution function was determined based on the statistical data of each encrypted token.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The authors used a predefined K value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Such K value is inefficient, because the appropriate number of clusters could be varied based on the dataset characteristics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Moreover, as the authors only considered static/unchanged data, the proposed scheme is not capable of processing dynamic data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' On the other hand, proposed solutions provides a heuristic to approximate the suitable number of clusters and then, clustering the data while maintaining the data privacy on the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For a dynamic dataset, where documents are added or removed over time, because of the re-clustering operation, 37 clusters are shrunk or expanded to reflect the dynamism of the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Note that, ClustCrypt can effectively cluster the encrypted static data only and hence, it is not capable to manage the cluster set if dynamism exists in the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Our next solution ClusPr can work with static, semi-dynamic, and also fully dynamic encrypted unstructured data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Particularly, we propose three different clustering schemes namely S-ClusPr, SD-ClusPr, and FD-ClusPr for compatibility with respect to static, semi-dynamic, and fully-dynamic datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 summarizes the notable related studies in the literature and positions the contribution of the proposed clustering works with respect to them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Summary of the existing privacy-preserving clustering approaches and positioning our proposed works (ClustCrypt and ClusPr) with respect to them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Research Works Estimating #Clusters Encryption Approach Cloud’s Trustworthiness Using Edge Computing Real-time Support Dynamic Data Clustering Multiple Data Owners Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [41] No Homomorphic Semi-honest No No No No Valdiya & Clifton [43] No Homomorphic Semi-honest No Yes No Yes Pang & Wang [39] No Homomorphic Semi-honest No Yes No Yes Sun et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [36, 4] No User-side Honest-but-curious No Yes No No Zhu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [34] No Homomorphic Honest No No No Yes Woodworth et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [3] No User-side Honest-but-curious No Yes No Yes ClustCrypt (Proposed) et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [1] Yes User-side Honest-but-curious No Yes No Yes ClusPr (proposed) et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [54] Yes User-side Honest-but-curious Yes Yes Yes Yes 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Architecture to Facilitate Clustering in Secure Search System 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Architecture: ClustCrypt Although we implemented ClustCrypt in the context of S3BD, the approach is generic and can be deployed in other systems that require clustering of encrypted data (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', [78, 79]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 presents where ClustCrypt is positioned within the S3BD system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We can see that S3BD is composed of a client tier and a cloud tier [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The client tier is considered trusted and it provides upload and search functionalities for the users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The cloud tier is considered honest but curious, 38 therefore, all the documents and their indexed tokens are stored in encrypted form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To enable real-time searching, the encrypted indexed tokens have to be clustered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The illustrated system consists of “Client tier” for the user (who can be the data owner as well) and “Cloud Tier” where the index and clusters reside.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Users are able to upload documents to cloud or input search queries to look for documents that are semantically relevant to the queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this setup, if a user wants to upload documents, first, the keywords or tokens are extracted from the original documents, then the documents and tokens are both encrypted and sent to the cloud tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' RSA deterministic encryption technique [80] is used to encrypt documents and extracted tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Individual data users (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', law-enforcement agent) who want to perform search share the same RSA key.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The Cloud Tier maintains a central index structure with a key-value pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Each key-value pair represents, respectively, an encrypted token, and the list of documents (locations) where the token appears in, plus the frequency of the token in each one of those documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Homomorphic encryption [37] can be used to encrypt the token frequency information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, due to the slow down imposed by processing homomorphically encrypted data [42] and to practically maintain the real-time search quality, currently, the frequency information is stored in unencrypted form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Upon issuing a search query by a user, the search keywords are encrypted and searched against the central index in the Cloud Tier to retrieve the relevant documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Upon receiving the list of matching documents, the user can download and decrypt them utilizing his/her private key.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 39 Clusters c1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='cn are constructed based on the tokens of the index structure and to mitigate exhaustively searching the whole index structure for every single search query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The clusters are topic-based and they are constructed so that the union of the k clusters is equivalent to the index structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For a given search query, instead of searching the whole index, the search space is pruned and gets limited to only those clusters that are topically related to the search query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The pruning is achieved based on a set of Abstract structures (denoted a1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='an) that are sampled from each one of the clusters and reside either on the Client tier or possibly on a trusted edge server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In our prior research, we proposed to formulate user-centric Abstract for personalized search [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Details of the ways sampling can be accomplished are mentioned in [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Upon issuing a search query, the most similar abstracts to the search query are chosen and then, their corresponding clusters are searched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' High-level two-tiered (client-cloud) Search System Architecture Inte- grating ClustCrypt Approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Search Query 𝑎" 𝑎# 𝑎$ Key Phrase Extractor Document Unencrypted Abstract Form Of Clusters Uploads Central Index 𝑐"𝑐# 𝑐& Clustered Data Client Tier Cloud Tier Encryption Encryption Storage 𝑎& 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Architecture: ClusPr 40 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 presents an architectural overview of the context where ClusPr is developed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The architecture represents applying ClusPr for S3BD, a cloud-based secure semantic search system that requires clustering over encrypted data [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The architecture represents a three-tier system based on a client device, edge system, and the central cloud system unlike original S3BD [3] and ClustCrypt [1] leveraged architecture of S3BD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The edge tier resides on the user’s premises (hence, is considered trusted) to relieve the client tier from processing computationally intensive tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is particularly important for non-static (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', semi-, fully-dynamic) datasets where documents have to be processed as they are uploaded to the cloud tier over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the specific context of S3BD, upon uploading a document by the user, the document is passed through Token Extractor on the edge tiers to retrieve the keywords (aka tokens) semantically representing the document.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For dynamic datasets, a temporary index structure is used to store the extracted tokens representing the occurrences of each new token in different documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Next, the document is encrypted by the user’s key and is securely stored on the cloud repository.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Next, a Temporary Index structure is formed based on the extracted tokens of the documents in question before encrypting and uploading them to the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The Temporary Index structure shows the tokens, their frequency, and their appearances across the uploaded batch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Tokens of the Temporary Index are encrypted by the Encryptor using the user’s key.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' By encrypting documents as well as the extracted tokens, Encryptor preserves the data privacy on the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Note 41 that, although we can technically use homomorphic encryption to maintain the statistical properties (frequency and co-appearances), for efficiency reasons, in the current implementation, we keep the properties unencrypted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We assume that such properties do not reveal meaningful information about the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In fact, in [41], K-means clustering was used over homomorphically encrypted big data and showed that the time overhead of clustering can be prohibitively expensive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the next step, the Temporary Index is fed to the Cluster Manager to make the suitable clustering decision on the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cluster Manager may decide to keep the existing clusters and only update them by the entries of the Temporary Index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Alternatively, upon observing a major update in the Temporary Index, the Cluster Manager decides to exhaustively re-cluster all of the tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Though a few of the aforementioned prior works can cluster encrypted data, they fall-short in clustering dynamic datasets, whereas, ClusPr can cluster both static and dynamic data while ensuring privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We explain the updating and re-clustering procedures ClusPr in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cluster Manager is also in charge of generating and maintaining Abstracts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Each abstract ai is a sampled summary of a corresponding cluster Ci on the cloud tier [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Abstracts are to prune the search operation and navigate the search only to clusters that are topically-related to the query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Further details about Abstracts are described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 42 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Overview of the context where ClusPr is deployed in a three-tier archi- tecture (of client, edge, and cloud) to facilitate a secure cloud-based search service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The edge tier is assumed to be on the user premises and trusted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It is used to ease the computational overheads imposed by privacy and clustering related processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cloud Tier Token Extractor Docs Encrypted Docs Clusters {c1…cn} c1 c2 cn Users Edge Tier Index Query Pre-processor Encryptor E(Docs) ≈ Search Query Upload Client Tier Cluster Manager Abstracts a1 a2 an ≈ Temp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Index E(tokens) For static datasets, the architecture is streamlined such that the extracted tokens are encrypted and directly fed into the Index structure on the cloud tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Once the data uploading procedure is completed, the cloud tier initiates the clustering procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As there is no re-clustering procedures defined for static clusters, the Cluster Manager is only in charge of generating and maintaining the abstracts [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It is noteworthy that, in the architecture of Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2, the dashed arrows located in the edge tier are to highlight the differences for dynamic datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Further details of the proposed static (S-Cluspr) and dynamic (SD-, FD-Cluspr) data clustering schemes are presented in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Similar to ClustCrypt, ClusPr uses RSA encryption technique for the encryption purpose and forms the Abstract set from the clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As an use case of the clustering policy in the context of a search system, upon issuing a search query by the user, the abstracts with the highest similarity to the search query are 43 identified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, only the clusters associated with the abstracts are searched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 44 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 ClustCrypt: Privacy-preserving Clustering Scheme for Static Unstruc- tured Data In this part, first (in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1), we elaborate on how to estimate the appropriate number of clusters that should be formed to represent a static big dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Second, in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2, we provide an algorithm to form the center of each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3, we explain methods to distribute the indexed terms across clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Finally, in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3, we describe the way pruning is achieved, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', the method that navigates a search query to relevant cluster(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Estimating the Number of Clusters for Static Datasets Depending on the characteristics of a dataset and distribution of tokens in its documents, the appropriate number of clusters (K) can vary significantly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, optimally determining K directly impacts the accuracy of topic-based clustering and, subsequently, the efficiency of the system (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', search application) that uses the clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Encrypted tokens and their metadata, including documents they appear in and their frequency, are the only available parameters to estimate K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The tokens and their metadata are generated by a keyword extractor that retrieves n single or multi-phrase tokens from each document.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We assume that all documents are treated equally and the value of n is the same across all documents in a given static dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Estimating K for the static dataset is performed based on the following two steps: (1) building Token-Document Frequency Matrix;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' and (2) constructing Normalized Matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 45 Step-1: Building Token-Document Frequency Matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To be able to follow the scheme, we consider an example using five tokens and six documents in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We initialize a token-document matrix A from the index structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the matrix, each row represents a token and each column represents a document.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Although our approach does not deal with plain-text tokens, just for further readability, in the Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2, we redundantly show the plain-text tokens (in “Word” column) along with their encrypted forms (in “Hash” column).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Each entry ai,j of matrix A represents the frequency of ith token in jth document (denoted as f(i, j)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Token-Document Frequency Matrix A, built based on the index structure Word Hash d1 d2 d3 d4 d5 d6 Book Uh5W 30 0 23 4 40 0 Solve /Vdn 5 0 0 60 34 0 Traffic oR1r 0 23 0 30 0 0 Net vJHZ 52 49 0 23 0 26 Enter tH7c 0 45 68 0 3 5 For a big dataset, the matrix size can be prohibitively large and sparse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To avoid this, we trim the matrix to include only the tokens that are influential in building clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We define document co-occurrences as the number of documents containing a particular token.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, to build the token-document frequency matrix A, we only take into account tokens whose document co-occurrences are either greater than or equal to the mean value of the document co-occurrences across the whole dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Step-2: Constructing Normalized Matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To make the relationship among tokens and documents quantifiable and comparable, we need to normalize the 46 token-document frequency matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Considering that ai,j represents the strength of association between token ti and document dj, the maximum value in column j of the token-document frequency matrix represents the token with the highest association with document dj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hence, for normalization, we divide the value of each entry of A to the highest value in the corresponding column of the matrix and the result is stored in a new matrix, called matrix N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The value for each entry ni,j is formally calculated based on Equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' ni,j = ai,j max ∀i ai,j (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1) For the example provided in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2, the normalized matrix N is presented in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Normalized Token-Document matrix N Word Hash d1 d2 d3 d4 d5 d6 Book Uh5W 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='58 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='34 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='07 1 0 Solve /Vdn 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 0 0 1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='85 0 Traffic oR1r 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='47 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 0 0 Net vJHZ 1 1 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='38 0 1 Enter tH7c 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='92 1 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Step-3: Building Probabilistic Matrices R and S The goal, in this step, is to calculate the topic similarity among encrypted tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For that purpose, we need to calculate the probability that topic of a token shares similarity with other tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We hypothesize that tokens that co-occur across documents are likely to share the same topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Besides, the magnitude of similarity between two tokens could be influenced by the tokens’ distribution across the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For instance, specific terms appear only in a few documents and are not widely distributed throughout 47 the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Such sparsely distributed tokens have low co-occurrences with other tokens which increases the diversity of topics in a dataset and potentially raises the required number of clusters (K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We leverage the normalized matrix (N) to perform a two-phase probability calculation that yields a matrix (denoted as Q) representing token-to-token topic similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Matrix R is built based on normalized matrix N to represent the impor- tance of each token across all documents Word Hash d1 d2 d3 d4 d5 d6 Book Uh5W 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='29 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='50 0 Solve /Vdn .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='05 0 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='51 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='43 0 Traffic oRir 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='48 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='52 0 0 Net vJHZ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='29 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='29 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='11 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='29 Enter tH7c 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='42 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='45 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='09 In the first phase, we calculate the importance of each token to each document.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The importance of token ti, in document dj, denoted as τi,j, is defined based on Equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' τi,j = ni,j � ∀k ni,k (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2) Considering Equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 and matrix N, we generate matrix R whose entries represent the importance of each token across all documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In fact, each entry ri,j of R represents the probability of choosing a document dj, having token ti.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is, ri,j = P(ti, dj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In our example, Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 shows the matrix R obtained from the matrix N (shown in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the second phase, we calculate the importance of each document to each token.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The importance of document dj for term ti, denoted by δj,i and is defined 48 based on Equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' δj,i = nj,i � ∀q nq,i (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3) Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Matrix S is built from N to represent the importance of each document with respect to each token Docs Book Uh5W Solve /Vdn Traffic oRir Net vJHZ Enter tH7c d1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='34 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='06 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='60 0 d2 0 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='49 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='38 d3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='17 0 0 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='45 d4 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='51 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='19 0 d5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='52 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='44 0 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='04 d6 0 0 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='84 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='16 Considering each δj,i and N, we generate S whose entries represent the importance of each document with respect to each token.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In fact, each entry si,j represents the probability of choosing ti from dj (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', we have si,j = P(dj, ti)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In our example, Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 shows S obtained from N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Step 4- Constructing Matrix Q to Determine the Number of Clusters Recall that R is a token-to-document matrix and S is a document-to-token matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To identify the similarity among the encrypted tokens, we multiply R and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As the number of columns and rows of R and S are equal, it is possible to multiply matrix R with S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The resultant matrix, denoted as Q, is a token-to-token matrix and serves as the base to determine the number of required clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Each entry qi,j denotes the topic similarity between token i and j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' More specifically, qi,j indicates the magnitude to which token i shares similar topic with token j for i ̸= j 49 and is calculated as qi,j = � ∀i,j ri,j· sj,i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 shows matrix Q for the example we discuss in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cluster decision matrix Q is built based on the multiplication of R and S matrices Word-Hash Book Uh5W Solve /Vdn Traffic oRir Net vJHZ Enter tH7c Book- Uh5W 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='39 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='09 Solve- /Vdn 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='26 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='45 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='02 Traffic- oRir 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='26 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='21 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='33 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='18 Net- vJHZ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='58 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='15 Enter- tH7c 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='09 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='28 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='37 Diagonal entries of Q signify the topic similarity of each token with itself and dissimilarity (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', separation) from other topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' More specifically, the value of qi,i indicates the magnitude that term ti does not share its topic with other terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, we define diagonal entries (qi,i) as separation factor, because for each token, it represents the token’s tendency to stay separate from other topics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As such, summation of the separation factors can approximate the number of clusters (K) needed to partition topics of a dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Let m denote the total number of tokens in Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, Equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 is used to approximate K for a given dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We use the ceiling function to make K an integer value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' k = ⌈ m � i=1 qi,i⌉ (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4) Correctness of K is verified using a hypothesis that states K for a set should be higher if individual elements of the set are dissimilar, otherwise K should be low [81, 82].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 is the core of approximating K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' According to this 50 equation, the maximum K value can reach to M, when the documents are highly distinct and each individual token of the documents represents a unique topic, otherwise it is lower than M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hence, our approach conforms with the clustering hypothesis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 51 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Determining Clusters’ Centers In k-means clustering, generally, the clusters’ centers are arbitrarily chosen [83, 84].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, based on a distance measure function (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', Euclidean distance [83] or semantic graph [84]), dataset elements are distributed into clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' K-means operates based on iteratively shifting clusters’ centers until convergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, we realized that the extremely large number of tokens make the iterative center shifting step (and therefore k-means clustering) prohibitively time consuming for big data [85].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Accordingly, in this part, we are to propose a big-data-friendly method to cluster encrypted tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The key to our clustering method is to dismiss the iterative center shifting step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This change entails initial clusters’ centers not to be chosen arbitrarily, instead, they have to be chosen proactively so that they cover various topics of the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For that purpose, a na¨ıve method can be choosing the top k tokens that have the highest number of associated documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Although this approach chooses important (highly associated) tokens, it ends up selecting centers that have high document and topical overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To choose appropriate center tokens, we propose to choose tokens that not only have highly document association, but also cover diverse topics exist in the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We define centrality of a token i, denoted Φi, as a measure to represent a topic and relatedness to other tokens of the same topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Assume that tokens are sorted descendingly based on the degree of document association.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Let U represent the union of documents associated to the currently chosen centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Also, for token i, 52 let Ai represent the set of documents associated to i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, uniqueness [3] of token i, denoted ωi, is defined as the ratio of the number of documents associated to i but not present in U (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', |Ai − U|) to the number of documents associated to i and are present in U (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', |Ai ∩ U|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Uniqueness indicates the potential of a token to represent a topic that has not been identified by other tokens already chosen as centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Particularly, tokens with uniqueness value greater than 1 have high association to documents that are not covered by the currently chosen centers, hence, can be chosen as new centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Recall that each entry ci,j of matrix C represents the topic similarity between tokens i and j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Besides, diagonal entry ci,i measures separation of token i from others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, the total similarity token i shares with others can be obtained by Σ∀j|j̸=ici,j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Note that for token i, we have Σ∀jci,j = 1, hence, the total similarity for token i is equal to 1 − ci,i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Centrality of a token is measured by the uniqueness of the token, the magnitude of similarity the token shares with others, and the magnitude of it being isolated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is, for token i, centrality is defined as Φi = ωi × ci,i × (1 − ci,i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Algorithm 1 shows the high-level pseudo-code to select maximum of k centers from the set of indexed tokens of a dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition to k, the algorithm receives the central index and the C matrix as inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The algorithm returns a set of at most k center tokens, denoted centers, as output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the beginning, the output set is initialized to null.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' U represents the set of documents covered with the chosen centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A heap structure,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' denoted Θ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' is used to store a pair for each token and its 53 Algorithm 1: Pseudo-code to determine clusters’ centers Input : k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' C matrix,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' and central index (with tokens sorted descendingly based on the degree of document association) Output: Set centers that includes at most k center tokens 1 Function Choose Center(k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Index): 2 centers ← ∅ 3 U ← ∅ 4 Θ ← {(∅,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' ∅)} //Pairs of tokens and centrality values 5 foreach token i ∈ index do 6 ωi ← CalculateUniqueness(i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' U) 7 if ωi > 1 then 8 U ← U ∪ Ui 9 Φi ← (ωi × ci,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='i × (1 − ci,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='i)) 10 Add pair (i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Φi) to max-heap Θ based on Φi 11 end 12 end 13 centers ← Extract k max pairs from Θ heap 14 return centers 15 end centrality value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For each token i, the uniqueness and centrality values are calculated (Steps 5 to 12) and the corresponding pair is inserted to the heap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Note that tokens with uniqueness lower than one do not have the potential to serve as a cluster center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the next step, we select at most k center tokens that have the highest centrality values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Clustering Tokens Once k tokens are chosen as cluster centers, the tokens are distributed among the clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The distribution is performed based on the relatedness (aka distance) between the center tokens and remaining tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Established techniques exist to calculate such relatedness, however, most of them (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', semantic graph [84] and Euclidean distance [83]) are not suitable for tokens sparsely distributed across the 54 dataset [83].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Besides, these are not designed to apply on encrypted data [84].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In S3BD [3], a method based on document co-occurrence is proposed to measure relatedness and cluster encrypted tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this method, if two tokens are present in the same set of documents, they are considered related [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We utilize that to measure the relatedness of tokens with cluster centers and distribute tokens to the most related cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To determine the relatedness between a particular token and a center, we need to calculate the contribution and co-occurrences metrics for the token.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Let t be a token in document d of dataset D with frequency denoted as f(t, d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, contribution of d to t, denoted as κ(d, t), is defined based on Equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' κ(d, t) = f(t, d) � j∈D f(t, j) (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5) Co-occurrence of token t with center token γx in document d (denoted ρ(t, d, γx) ) is defined as a ratio of the sum of frequencies of t and center γx in d to the total frequencies of t and γx throughout the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The formal presentation of co-occurrence is provided in Equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' ρ(t, d, γx) = f(t, d) + f(γx, d) � j∈D (f(t, j) + f(γx, j)) (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6) Based on the contribution and co-occurrence metrics, relatedness between token t and γx (denoted r(γx, t)), is defined as multiplication of these two metrics (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', r(γx, t) = � j∈D κ(j, t)· log (ρ(t, γx, j))).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 55 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 S-ClusPr: Privacy-preserving Clustering Scheme For Static Unstruc- tured Datasets In this section, we provide a detailed description of S-ClusPr scheme to cluster privacy-preserving static big datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Note that S-ClusPr uses similar method to estimate suitable number of clusters (k) that is used in ClustCrypt in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, we proposed more robust heuristics for the center selection and token distribution method in ClusPr to obtain more topically segmented clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2, we explain the center selection and token distribution method respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Center Selection In K-means clustering, generally, the clusters’ centers are arbitrarily chosen [83, 84].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, based on a distance measure function (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', Euclidean distance [83] or semantic graph citeLiuCroft), dataset elements are distributed into the clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' K-means operates based on iteratively shifting clusters’ centers until it converges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, we realized that the extremely large number of tokens make the iterative center shifting step (and therefore K-means clustering) prohibitively time-consuming for big data [85].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Accordingly, in this part, we are to propose a big-data-friendly method to cluster encrypted tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The key to our clustering method is to dismiss the iterative center shifting step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This change entails initial clusters’ centers not to be chosen arbitrarily, instead, they have to be chosen proactively so that they cover various topics of the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For that purpose, a na¨ıve method can choose the top K tokens that have 56 the highest number of associated documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Although this approach chooses important (highly associated) tokens, it ends up selecting centers that have a high topical overlap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We propose to choose tokens that not only have high document association but also cover diverse topics exist in the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We define centrality of a token i, denoted Φi, as a measure to represent a topic and relatedness to other tokens of the same topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Assume that tokens are sorted in a descending manner, based on the degree of document association.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Let U represent the union of documents associated to the currently chosen centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Also, for token i, let Ai represent the set of documents associated to i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, uniqueness [3] of token i, denoted ωi, is defined as the ratio of the number of documents associated to i but not present in U (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', |Ai − U|) to the number of documents associated to i and are present in U (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', |Ai ∩ U|).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Uniqueness indicates the potential of a token to represent a topic that has not been identified by other tokens already chosen as centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Particularly, tokens with uniqueness value greater than 1 have high association to documents that are not covered by the currently chosen centers, hence, can be chosen as new centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Recall that each entry qi,j of matrix Q represents the topic similarity between tokens i and j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Besides, diagonal entry qi,i measures separation of token i from others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, the total similarity token i shares with others can be obtained by Σ∀j|j̸=iqi,j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Note that for token i, we have Σ∀jqi,j = 1, hence, the total similarity for token i is equal to 1 − qi,i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Centrality of a token is measured by the uniqueness of the token, the magnitude of similarity the token shares with others, 57 and the magnitude of it being isolated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is, for token i, centrality is defined as: Φi = ωi × qi,i × (1 − qi,i).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Algorithm 2: Pseudo-code to determine clusters’ centers Input : K,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' C matrix,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' and Index (with tokens sorted descendingly based on the degree of document association) Output: centers set that includes at most K center tokens 1 Function Choose Center(k,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Index): 2 centers ← ∅ 3 U ← ∅ 4 Θ ← {(∅,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' ∅)} //Pairs of tokens and centrality values 5 foreach token i ∈ Index do 6 ωi ← CalculateUniqueness(i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' U) 7 if ωi > 1 then 8 Ai ← CalculateDocumentAssoc(i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Index) 9 U ← U ∪ Ai 10 Φi ← (ωi × qi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='i × (1 − qi,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='i)) 11 Add pair (i,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Φi) to max-heap Θ based on Φi 12 end 13 end 14 centers ← Extract K max pairs from Θ heap 15 return centers 16 end Algorithm 2 shows the high-level pseudo-code to select maximum of K centers from the set of indexed tokens of a dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition to K, the algorithm receives the central index and the Q as inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The algorithm returns a set of at most K center tokens, denoted centers, as output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the beginning, the output set is initialized to null.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' U represents the set of documents covered with the chosen centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A heap structure, denoted Θ, is used to store a pair for each token and its centrality value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For each token i, the uniqueness and centrality values are calculated (Steps 5 − 13) and the corresponding pair is inserted to the heap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Note that tokens with uniqueness lower than one do not have the potential to serve as a 58 cluster center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the next step, we select at most K center tokens that have the highest centrality values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Distributing Encrypted Tokens Across Clusters Once K tokens are nominated as cluster centers, the remaining tokens of the index are distributed across the clusters with respect to their relatedness (aka distance) with the center tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Because there is no intersection between the non-center tokens and members of the centers set, we can model the token distribution across the clusters as a weighted bipartite graph where the weight of each edge represents the relatedness between a token and a center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 depicts an example of a bipartite graph to show the relationship of each token and centers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Solid lines show the edge with the highest weight for each token that represent the cluster that a token should be distributed to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Established techniques (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', semantic graph [84], Euclidean distance [83]) are to calculate the relatedness, however, these methods are not appropriate for encrypted tokens that are sparsely distributed [83] [84].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As encrypted tokens lose their semantics, we ought to define the relatedness between tokens based on their statistical characteristics and then leverage it to distribute each token to the cluster that offers the maximum relatedness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Intuitively, the relatedness measure between tokens ti and tj, denoted r(ti, tj), is defined based on the magnitude of their co-occurrences, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', the number of documents where the two tokens appear together [3, 1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Let Fi and Fj respectively denote the sets of documents that ti and tj are appeared in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, the 59 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A bipartite graph representing the relatedness among centers and remaining tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The weight of each edge represents the relatedness of a token and a center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Solid lines show centers that offer the maximum relatedness for a token.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' School Car Book 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='28 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='63 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='76 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='13 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='63 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='48 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='78 Cluster centers Tokens Teach Pen Kia Gear Story 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='03 intuitive co-occurrence of the two tokens is Fco = Fi ∩ Fj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, a deeper analysis reveals that quantifying the relatedness only based on the cardinality of co-occurrence (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', |Fco|) can be misleading for the two following reasons: First, intuitive co-occurrence ignores the magnitude of disparity across Fi and Fj that negatively impacts the relatedness between ti and tj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The disparity is determined based on the symmetric difference (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', we have Fdis = Fi ⊕ Fj).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Accordingly, to consider the impact of both co-occurrence and disparity, we define a new measure, called relative co-occurrence, and leverage it to determine the relatedness between ti and tj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Second, intuitive co-occurrence ignores the importance of ti and tj in each 60 document d ∈ Fco.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Accordingly, to measure the co-occurrence value in each document d, denoted υ(ti, tj, d), we consider the importance of each one of the tokens relative to their importance across all documents of Fco.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We use frequency of a token in a document to measure its importance in that document.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Formally, in document d, we calculate the value of co-occurrence based on Equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' υ(ti, tj, d) = f(ti, d) � ∀m∈Fco f(ti, m)· f(tj, d) � ∀m∈Fco f(tj, m) (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7) Similarly, we utilize Equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8 to measure the impact of disparity between two tokens in each document d ∈ Fdis, denoted ϕ(ti, tj, d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' ϕ(ti, tj, d) = f(ti, d) � ∀m∈Fdis f(ti, m) + f(tj, d) � ∀m∈Fdis f(tj, m) (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8) In document d, once we know the co-occurrence and disparity between ti and tj, we can calculate the relative co-occurrence as ρ(ti, tj, d) = υ(ti, tj, d) − ϕ(ti, tj, d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, the relative co-occurrence across all documents of the two tokens (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', Fi ∪ Fj) is leveraged to calculate the relatedness between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Assuming c as the token that represents center of a given cluster (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', ti = c ∈ centers), we define relatedness between c and token t, according to Equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Token t is distributed to the cluster whose center offers the maximum relatedness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Note that, in this equation, to emphasize the importance of token t in document d, we also consider its frequency ratio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 61 r(c, t) = � d∈(Ft∪Fc) ρ(t, c, d)· f(t, d) � ∀m∈Ft f(t, m) (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Pruning Clusters to Expedite the Search Operation The purpose of building topic-based clusters is to achieve scalable search over big data via limiting (pruning) the search scope based on the query topic, instead of exhaustively traversing the whole index structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For pruning, we need to identify the clusters that are semantically relevant to the search query and discard the irrelevant ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, pruning is a challenging task when we operate on the encrypted data in the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To overcome the challenge, we require the topic of each cluster in plain-text, such that we can identify the clusters whose topics are semantically related to the search query and only consider those clusters for searching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For that purpose, in our previous work [17], we established a method to represent the topic of each cluster Cx (denoted αx) by considering the top-n most-frequent tokens of Cx.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The tokens of αx are decrypted and maintained on the edge tier of ClusPr in a structure called Abstract.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Abstracts are leveraged to measure the topic similarity between a query and their corresponding clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the next step, the search is conducted on the clusters that are most relevant to the query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For further details about creating abstracts and pruning operation, interested readers can refer to our earlier study [17, 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 62 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 Privacy-preserving Clustering Scheme For Dynamic Unstructured datasets 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Overview In the previous section, we explained clustering of static (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', archive) encrypted big datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, many big datasets are dynamic (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', healthcare data, criminal records) [86] and their contents change over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this section, we deal with clustering and subsequently searching over such datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We consider two types of dynamic datasets: First is the semi-dynamic datasets whose contents are updated in batch over time (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', Museum of Modern Art (MoMA) dataset [87]);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Second is fully-dynamic datasets whose contents are constantly updated (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', Twitter streams [88]).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The latest changes on the dataset have to be reflected in the clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Otherwise, altered documents are not retrieved by the search system, even if they include relevant contents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In fact, the updates on the dataset affect the tokens’ co-occurrences and, subsequently, the clustering arrangement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As such, the challenge is to know how the addition or deleting documents change the topics and number of clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Given the size of big datasets, reconstructing clusters (called re-clustering) upon arrival of every single document or a small batch of documents is time-prohibitive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Moreover, the small updates generally cause negligible changes in the co-occurrences of tokens that are unlikely to modify the arrangement of clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Only significant updates can cause decisive changes on the magnitude of 63 co-occurrence and relatedness that entail re-clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Accordingly, the two followup questions are: when to perform re-clustering?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' and how to re-cluster the tokens?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To address these questions, based on the type of dynamic datasets, we propose two clustering schemes in ClusPr: Semi-dynamic data clustering scheme (SD-ClusPr) and Fully-dynamic data clustering scheme (FD-ClusPr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Semi-Dynamic Data Clustering Scheme (SD-ClusPr) In semi-dynamic datasets, topic-based clustering can be initially achieved on the first batch of documents in the dataset according to the method described in the previous section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, the re-clustering decisions are made depending on the changes caused by the new batch of documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is, we need to determine whether the change caused by the extracted tokens of the new batch is significant or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To determine the significance of changes caused by the tokens of the new batch, we utilize χ2 (chi-square) distribution test [89] that can identify significant changes observed in a variable of a given population.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The χ2 test is known as testing goodness of fit and it is represented by Equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10, where Oi is the observed and Ei is the expected value of a particular variable in K trials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' χ2 = k � i=1 [(Oi − Ei)2/Ei] (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10) We consider the number of the extracted tokens in the new batch and the number of tokens in the existing clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Our null hypothesis (H0) is to perform re-clustering and χ2 test is employed to check the validity of H0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' If the difference 64 between the number of new tokens and existing tokens is small, a low value of χ2 is obtained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For one degree of freedom with 95% confidence interval, the value of χ2 = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='841 fails to reject H0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Alternatively, if the number of tokens in the new batch is significantly smaller than the number of existing tokens, χ2 value becomes higher that denotes significant deviation from H0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, the decision is to reject H0 and keep the existing clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Once the re-clustering decision is made, we use the method explained in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 to cluster tokens of the updated dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the event that re-clustering is not achieved, the new tokens are accumulated with the of tokens of the next batches.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As a result, the total number of new tokens becomes significant that leads to a lower χ2 value and subsequently acceptance of H0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Updating Clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Let U1 a new batch of documents that introduces a set of new tokens T = {t1, t2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', tn} that does not exist in the existing clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Assume that based on the re-clustering decision method, mentioned in the previous part, we determine to keep the existing clusters {C1, C2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', Cn} to accommodate T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To distribute ti ∈ T to a cluster, we can measure the relatedness as explained in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Alternatively, we can leverage the set of abstracts {A1, A2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', An}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As they are in the plain-text format, a more accurate relatedness measurement can be conducted using the semantic similarity, as opposed to inferring the relatedness based on token co-occurrences in documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this case, we use Word2Vec [63] model to calculate the relatedness of ti and abstract Aj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, ti is assigned to a 65 cluster that offers the highest relatedness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To avoid poor assignments, we define θ as the relatedness threshold that should be reached to assign ti to Cj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the event that ti cannot join any cluster, a new cluster, called Cnew ∈ C, is formed and ti is considered as its center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The above procedure is repeated for all ti ∈ T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Algorithm 3: Pseudo-code to update clusters in SD-ClusPr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Input : set of abstracts A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' tempIndex ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' θ Output: H,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' map of new tokens to clusters 1 Function SD-ClusPr(A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' tempIndex,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' θ): 2 T ← tempIndex \\ CentralIndex 3 H ← ∅ 4 A ← ∪n i=1Ai 5 Φ ← ∅ 6 //Max-heap to find the abstract with highest similarity 7 foreach token t ∈ T do 8 foreach aij ∈ A do 9 s ← sim (aij,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' t) 10 if s > θ then 11 Add (s,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' i) to Φ 12 end 13 end 14 if Φ ̸= ∅ then 15 //Allocate t to existing cluster 16 (t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' i) ← Extract max pair from Φ 17 Add (t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' i) to H 18 end 19 else 20 //Forming a new abstract and cluster and add it to H 21 An+1 ← {t} 22 A ← ∪n+1 i=1 Ai 23 Add (t,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' n + 1) to H 24 end 25 end 26 Encrypt H and push it to the cloud tier 27 end 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Determining the value of θ Threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We estimate the value of θ threshold by leveraging the abstracts {A1, A2, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='An}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Recall that the elements 66 of abstract Ai are the ones that best represent the topic of its corresponding cluster Ci.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We define coherency of Ai as the average similarity distance across pairs of its elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Let {ai1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', aip} be the set of elements of Ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, coherency of Ai, denoted Ki, is defined based on Equation 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='11 where sim(x, y) shows the similarity distance between (x, y) ∈ Ai × Ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ki = � ∀(x,y)∈Ai×Ai|x̸=y Sim(x, y) �p 2 � (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='11) Then, we define θ as the global minimum across all abstracts (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', θ = min ∀i Ki).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This implies that a new token can join a cluster only if its distance does not worsen the coherency of current clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Otherwise, the new token forms its own cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Algorithm 3 shows the pseudo-code of how to update clusters in SD-ClusPr, in case we choose not to perform re-clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition to the set of abstracts (A) and θ, the algorithm receives the set of tokens for a new document batch, which is stored in form of a temporary index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The algorithm returns the H structure that includes the mapping of new tokens to their respective clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Steps 7 − 9, for each new token, we calculate the similarity distance with respect to all abstract elements aij and check whether the similarity distance exceeds θ or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' If it exceeds θ, we make a pair of similarity distance and corresponding abstract number, denoted as (aij, t) and build max-heap Φ based on the distance (in Step 10 − 12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' If Φ contains any value, we extract from it the pair that has the largest value (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', the abstract that offers the most topic similarity for t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, in Step 17, the pair of 67 (t, i) is added to H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' On the contrary, if Φ is null, it implies that no cluster offers a considerable similarity to t, and so, in Steps 19 − 24, we build a new abstract and cluster using t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Finally, we encrypt the tokens of H and push it to the cloud tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' On the cloud end, cluster manager updates its clusters based on H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Fully-Dynamic Data Clustering Scheme (FD-ClusPr) Unlike SD-ClusPr, for fully-dynamic datasets, clusters have to be formed or updated upon arrival of the documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is, continuous or burst arrival of new documents should trigger FD-ClusPr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Accordingly, in FD-ClusPr, we consider two cases in forming clusters: (A) initial case that occurs when first document arrives and there is no existing cluster and (B) update case, where the existing clusters have to be updated based on the new changes in the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the initial case, the edge tier extracts the set of new tokens from the uploaded document(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We designate the token with the highest frequency to represent the topic and choose it as the cluster center too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, the second most frequent token is clustered based on its similarity distance with the designated cluster center, according to the method discussed in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Also, to determine joining the existing cluster or forming a new one, we initialize the threshold to θ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This procedure continues until all tokens are clustered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the update case, we apply the same method as SD-ClusPr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is, upon uploading a document, the system decides to either perform re-clustering or updating existing clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 68 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8 Security Analysis of the Proposed Clustering Works In this section, we only cover the security analysis of ClusPr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this regard, explaining security analysis of the three-tiered architecture also covers the analysis of two-tiered ClustCrypt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The proposed clustering schemes are applicable in the context of searchable encryption and document retrieval systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' According to the three-tier architecture, described in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2, client- and edge tiers are in the user premises, hence, the activities conducted and the user’s key on these tiers are considered safe and trusted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The Abstract structures are kept on the edge tier in plain-text to enable us to measure the similarity with the search phrase and performing pruning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' On the other hand, activities performed on the cloud-tier are considered as dishonest and prone to different types of attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We are concerned about both internal (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', affiliated parties) and external (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', unaffiliated outside intruders) attackers who desire to learn the encrypted clustered tokens and documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To explain the threats of the attackers, we provide the following preliminaries: View: This term denotes the portion that is visible to the cloud during any given interaction among client, edge, and server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The central index and the set of clusters C1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Cn, the trapdoor of the given encrypted search query Q ′, and the collection of encrypted documents D ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In some models, Q ′ also contains a particular weight for each term.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The search results related to Q ′ are considered as Ic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The view of expanded Q ′ and Ic are symbolized as V (Q ′) and V (Ic) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Trace: This term denotes the information exposed about Ic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Our aim is to 69 allow the attacker to infer the information of Ic as little as possible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The View and Trace enclose all the information that the attacker would gain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To encrypt the document set we use probabilistic encryption model that is considered to be one of the most secure encryption techniques [3, 90].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This does not utilize one-to-one mapping and so, D ′ is not prone to dictionary-based attacks [91].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Each token in a cluster is deterministically encrypted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Thus, each cluster in the View, only shows an encrypted mapping of the tokens and their co-occurrences in the plain-text format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' If any type of attacker can gain access to the cloud, he/she could only understand the importance of a particular encrypted token by observing the co-occurrences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It is technically possible to encrypt co-occurrences using homomorphic encryption [37] and perform computation on the co-occurrences while it is in the encrypted form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1, we discuss that this technique practically falls short on performance [92] and affects the real-time behavior of the search system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As such, in the current implementation, we use co-occurrence information in the plain-text format.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Note that, even when the co-occurrences are not encrypted, the attacker cannot decrypt the token.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' An attacker could obtain a Trace regarding V (Q ′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' From that view, the attacker could only understand the importance of each search term from Q ′ by analyzing the associated weights of the query terms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Similar to the previous consideration, the attacker is not able to reveal the search terms from Q ′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In spite of a minimally trusted computing base, an attacker may still intend to access the 70 system through man-in-the-middle, either honest but compromised or untrusted cloud providers to attack the confidentiality of the user data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' By any means, if the attacker successfully performs a man-in-the-middle attack, he/she can access the document list V (Ic) resulting from searching Q ′ with Trace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' At this point, the attacker may only obtain the documents’ names with encrypted contents that are unreadable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' There are methods (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', [93]) that can be used to tackle frequency attacks when the searches and cluster updates are predictable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Theoretically, an attacker could build a dictionary considering all the clusters’ tokens by performing frequency attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Eventually, the attacker tries to build a clone document set D′ utilizing the dictionary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Although all of the tokens extracted from a particular document are sufficient to learn the topic of the document, it is not possible to unveil the whole document as we do not use all of the keywords of the document set to build the encrypted index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Besides, we encrypt the whole document at once instead of word level encryption before outsourcing it to the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This procedure ensures that even if the document set is compromised on the cloud tier, it is impossible to perform a dictionary attack.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Even if the attacker knows the trace, he/she cannot understand what exactly the retrieved encrypted documents convey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Moreover, attacks can be occurred in the communication between the edge and cloud tiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this case, by monitoring the search process, an attacker could obtain the resultant document list for Q′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, the attacker is not able to decrypt the documents, since they can be 71 decrypted only when they are downloaded on the edge system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' An attacker could also attempt to modify data (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', encrypted tokens and documents) in the clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Such attacks can potentially tamper with the integrity of user data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, this type of attack could be detected, because neither the edge will be able to decrypt the modified tokens to form or update Abstracts, nor the user will be able to decrypt the retrieved documents in the original plain-text form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is because of applying symmetric encryption (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', AES encryption) on the user’s data with keys managed by the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hence, in the event that the encrypted data are altered by an attacker, such data cannot be decrypted by the users’ keys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Actually, protecting the user’s key is crucial to restrain possible attacks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' If the key is compromised, the system cannot detect the attacker and, therefore, both tokens and documents can be exposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 72 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9 Performance Evaluation of Clustering 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Experimental Setup We developed working versions of ClustCrypt and ClusPr and made it available publicly in our Githuba,b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We evaluate the performance of ClusPr using three distinct datasets that have different properties and volumes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We compare and analyze the clustering quality with other approaches that operate in encrypted or unencrypted domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The experiments were conducted on a machine with two 10-core 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8 GHz E5 Intel Xeon processors and 64 GB of memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To evaluate the performance of ClusPr in handling big data, we used a subset of Amazon Common Crawl Corpus (ACCC) dataset [94].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The whole dataset size ≈ 150 terabytes that contains different web-based contents, such as blogs and social media contents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We randomly selected 6, 119 documents that collectively form a ≈ 500 GB document set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The second dataset, named Request For Comments (RFC) [95], is domain- specific and includes documents about the internet and communication networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' RFC includes 2, 000 documents and its total size is ≈ 247 MB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The third dataset is BBC [96] that is not domain-specific and includes news in certain categories such as technology, politics, sports, entertainments, and business.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It contains 2, 225 documents and is ≈ 5 MB.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The reason for choosing this small dataset is that, unlike ACCC and RFC, each document of BBC is short and we can verify clusters’ coherency manually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For each dataset, the documents are passed through Maui keyword extractor [97] to identify keywords semantically represent ahttps://git.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='io/fjDsq bhttps://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/hpcclab/ClustCrypt 73 the document.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Evaluation Metrics and Baselines from Prior Works For performance evaluation of the proposed works, we compare them against four other schemes, where two schemes cluster plain-text data and the other two schemes cluster encrypted data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Among the first two, one of the schemes W2V Kmeans) is based on K-means clustering [98] where feature extraction is done based on Word2Vec [63] embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Another scheme, WordNet [99], is an enhanced version of K-means that generates synonym set based on the input data and then, applies K-means clustering on the sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Token distribution in WordNet is performed based on edge counting method, proposed by Wu and Palmer [99].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Two encrypted clustering schemes that have been used in the comparison are namely, S3BD [3], and HK-means++ [41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We have discussed S3BD and HK-means++ in Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' ClustCrypt is the preliminary version of S-ClusPr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Their difference mainly lies in the way tokens are distributed across the clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In ClustCrypt, the relatedness is simply calculated based on contribution and co-occurrences metrics, whereas in S-ClusPr, the magnitude of both similarity and disparity are considered to measure the relatedness (see Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2for further details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The goodness of clusters set can be quantified by a number of evaluation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, evaluating the performance of a clustering scheme is not as simple as counting errors in classification algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Specifically, instead of 74 considering the absolute values of cluster labels, cluster evaluation metrics either measure the separation of clustered data similar to ground truth set of classes or internal cluster validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Internal cluster validation denotes that members belong to the same class should be more similar than members of other classes and vice versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In practice, class label information is not always available in most of the application scenarios and, therefore, internal validation metrics are the only option for validation in such situation [100, 101].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As there is no ground truth for the considered datasets, we choose evaluation metrics that evaluate the clusters based on statistical analysis of the cluster members.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We evaluate three widely-adopted clustering metrics, namely Silhouette coefficient (SC), Calinski-Harabasz index (CI), and Davies-Bouldin index (DI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Silhouette Coefficient (SC) score interprets and validates intra-cluster consistency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In particular, the metric signifies how similar a cluster member is to its own cluster compared to the other clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The value of the SC score ranges from −1 to +1, where a high value indicates that a given member is well matched to its own cluster and poorly matched to the other ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Calinski-Harabasz Index (CI) denotes how well-defined (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', well-separated) the clusters are.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The CI value of clusters is calculated based on the ratio of the sum of between-clusters dispersion to the sum of inter-cluster dispersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A higher CI value indicates a more topically separated (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', less overlapping) clustering and vice versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Similar to the CI metric, Davies Bouldin Index (DI) is used to measure the goodness of separation across clusters and the reason we consider it in our evaluation is to verify the CI metric 75 evaluation for the clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' DI is calculated based on the ratio of within-cluster distances to the between-cluster distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A lower DI value indicates a more topically-separated clustering and it is preferred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition to these metrics, we measure the clusters’ coherency to evaluate the quality of the topic-based clustering within each cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is a similarity-based evaluation metric to calculate the average of all possible pair-wise token similarity for a given cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In fact, Coherency represents how the tokens in a cluster are related to a certain topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, the average of coherency across all clusters is calculated to represent the overall quality of a certain clustering method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We instrument the pre-trained Google News Word2vec model [63] to determine the similarity between any two given keywords.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The model is a 300-dimension vector representation of three million phrases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The model requires a text dataset as input to build a vocabulary from the input dataset and learns vector representation of the words in the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The model uses cosine similarity and provides the score (−1 ≤ similarity score ≤ 1) for any two given tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We note that, the pre-trained Word2vec model operates only on plain-text tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Subsequently, we do not encrypt the tokens while uploading for evaluation purposes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, the proposed schemes assume tokens to be encrypted and do not use the properties of plain-text tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Evaluation Results 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Evaluating Silhouette Coefficient (SC) Score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 shows the results of SC score evaluation on the three datasets and for varying number of 76 clusters (in the horizontal axis).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We note that, for this experiment, the value of K in W2V Kmeans, WordNet, and HK-means++ is randomly chosen and iteratively evolves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As such, we calculate the SC score for all the considered K values and show them in multiple data points in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, other schemes (namely, S-ClusPr, ClustCrypt, S3BD) are not iterative and provide only one SC score for their determined K values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As the procedure of estimating the number of clusters is similar in ClustCrypt and S-ClusPr schemes, we can see that both of the schemes generate 69, 65, and 133 clusters for the BBC, RFC, and ACCC datasets, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As ACCC is the largest and broadest (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', not domain-specific) dataset, it yields the highest K value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' RFC is not the smallest dataset, however, due to its domain-specific nature, it yields the lowest K value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 represents SC metric outcomes for ClustCrypt, S-ClusPr and the four other compared schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' According to the figure, considering all of the datasets, overall top performers are: WordNet and S-ClusPr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Moreover, S-ClusPr outperforms others in the RFC dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' On the contrary, HK-means++ and S3BD underperform in most of the situation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The experiment indicates that the cluster sets generated by HK-means++ and S3BD contain less intra-cluster similarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' WordNet and S-ClusPr provide the highest intra-cluster similarity and hence, outperform others in all datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Evaluating Calinski-Harabasz Index (CI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 represents CI metric outcomes for S-ClusPr and the four other schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' According to the table, 77 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Silhouette Coefficient (SC) metric for each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The results are obtained from S-ClusPr, HK-means++, ClustCrypt (that are encrypted-based clustering schemes), W2V-Kmeans, and WordNet clustering schemes (that operate on plain-text tokens).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 50 100 150 200 250 Number of clusters 4 6 Davies-Bouldin Index BBC S-ClusPr ClustCrypt WordNet W2V Kmeans S3BD HK-Means++ 50 100 150 200 250 Number of clusters 2 4 6 8 Davies-Bouldin Index RFC 50 100 150 200 250 300 Number of clusters 4 6 Davies-Bouldin Index ACCC 78 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Davies-Bouldin Index (DI) for each dataset using different clustering schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 50 100 150 200 250 Number of clusters 4 6 Davies-Bouldin Index BBC S-ClusPr ClustCrypt WordNet W2V Kmeans S3BD HK-Means++ 50 100 150 200 250 Number of clusters 2 4 6 8 Davies-Bouldin Index RFC 50 100 150 200 250 300 Number of clusters 4 6 Davies-Bouldin Index ACCC 79 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cluster coherency for each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 50 100 150 200 250 Number of clusters 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='15 Coherence BBC S-ClusPr ClustCrypt WordNet W2V Kmeans S3BD HK-Means++ 50 100 150 200 250 Number of clusters 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='20 RFC 50 100 150 200 250 300 Number of clusters 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='15 Coherence ACCC 80 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Calinski-Harabasz Index for the datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' (a) BBC Approaches No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' of Cluster HK- means++ WordNet W2V Kmeans S3BD ClustCrypt S-ClusPr 10 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 50 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='43 277.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='53 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='16 69 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='47 253.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='60 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='22 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='70 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='58 100 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='13 203.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='87 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='37 150 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='05 164.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='43 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='81 200 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='17 122.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='51 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='93 250 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='02 97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='15 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='38 (b) RFC Approaches No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' of Cluster HK- means++ WordNet W2V Kmeans S3BD ClustCrypt S-ClusPr 10 1247.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='20 50 1730.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='26 4320.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='63 60380.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='05 65 1945.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='42 3980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='75 51564.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='61 23760.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='64 29439.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='30 100 1834.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='64 3660.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='78 24374.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='17 150 1684.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='47 3110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='25 18684.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='33 200 846.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='71 2572.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='89 16746.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='74 250 436.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='43 1834.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='58 15139.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='11 the RFC clusters provide large CI values compared to the BBC dataset, regardless of the employed clustering scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It is noteworthy that, we had the same observation for the ACCC dataset, however, we do not show its table due to the shortage of space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The superiority of RFC is because it is a domain-specific dataset with a few topics compared to the other two.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Within Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7b, we can see that although W2V-Kmeans significantly outperforms the other schemes for most of the K values, WordNet, ClustCrypt, and S-ClusPr also provide satisfactory CI values that imply well-partitioned clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 81 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Evaluating Davies Bouldin Index (DI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The DI values for the clusters, obtained by S-ClusPr and the compared schemes are expressed in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In most of the scenarios, we observe that increasing the number of clusters reduces the DI value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is because, typically, configuring clustering schemes to build more clusters on a given dataset leads to a higher coherency within each of the clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' According to the figure, we observe that WordNet scheme outperforms others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The DI value for S-ClusPr is in the acceptable range, which indicates that the scheme can offer a competitive goodness of separation across clusters in compared to the most of other schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' On the other hand, higher DI value yielded by HK-means++ signifies poor cluster separation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Evaluating Cluster Coherency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 shows the clusters’ coherency on the three datasets using various clustering schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Using S-ClusPr, 69, 65, and 133 clusters are created for the BBC, RFC, and ACCC datasets, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As ACCC is the largest and broadest (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', not domain-specific) dataset, it yields the highest K value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' RFC is not the smallest dataset, however, due to its domain-specific nature, it yields the lowest K value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For the same reason, across the three datasets, S-ClusPr offers the highest coherency value (≈ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='16) for the RFC dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In compare to ClustCrypt, we notice that S-ClusPr offers a negligible coherency improvement (≈ 6%) for the BBC and RFC datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, for the ACCC dataset, S-ClusPr improves the coherency by approximately 31%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Analysis of the plain-text-based schemes reveal that, WordNet clusters offer the highest coherency value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is expected, because it is difficult for an encrypted 82 clustering scheme (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', S-ClusPr) to outperform the unencrypted ones, since they do not have access to the semantics of the tokens [99] to build the clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, we observe that the coherency offered by S-ClusPr competes with the one offered by the K-means scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In particular, S-ClusPr provides a higher coherency value than K-means for the RFC and BBC datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To evaluate the suitability of estimated number of clusters (K) by S-ClusPr, we configure both K-means and WordNet to use the estimated K number of clusters for the studied datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' According to the figure, for RFC and BBC, S-ClusPr suggested sets of K clusters offer a higher coherency than K-means and a comparable one to WordNet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the case of ACCC, S-ClusPr even outperforms WordNet in terms of coherency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 83 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Comparing the impact of clustering using S-ClusPr against original clustering of S3BD for the studied datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' BBC RFC ACCC 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='16 Coherence S-ClusPr Original S3BD 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Analyzing the Impact of S-ClusPr on Searchable Encryption Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' One objective of this research is to enhance the performance of S3BD secure search system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As such, we instrumented S-ClusPr in S3BD and compared the coherency of resulting clusters with its original clustering scheme that predetermines a value for k = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Moreover, its center selection only considers the co-occurrences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this experiment, we intend to evaluate the improvement that S-ClusPr achieves within S3BD on the three studied datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this experiment, the estimated values of K for BBC, RFC, and ACCC are 69, 65, and 133, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Impact on the Clustering Coherency of S3BD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 shows that for all the studied datasets, clusters generated by S-ClusPr have remarkably higher coherency than the original clustering scheme of S3BD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This shows determining number of clusters based on dataset characteristics and choosing center tokens 84 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Comparing the relevancy of search results using S-ClusPr vs original S3BD clustering in BBC dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The value of relevancy is calculated based on TSAP@10 scoring metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' News Update Top Movies Recent Attacks Extinct Animal Score Updates Champions League World Health Issue People & Busi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' China Market Europe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Stock Ex 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Relevance Score S-ClusPr Original S3BD based on the centrality concept is effective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Our hypothesis is that, such efficiency improves the accuracy and offers more relevant semantic search results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is because tokens of the clusters are more congruent to the clusters’ topics, hence, more effective pruning is accomplished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For further evaluation of this hypothesis, next experiments concentrate on the impact of S-ClusPr on the search quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Impact on the Search Accuracy of S3BD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The purpose of improving the clusters’ coherency in this study is to ultimately enhance the search accuracy by 85 Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Benchmark queries for each one of the studied datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='ACCC Dataset ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='BBC Dataset ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='RFC Dataset ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Orlando Magic ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='News Update ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Internet ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Samsung Galaxy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Top Movies ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='TCP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Baseball ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='routine ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Recent Attacks ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Fiber Doctor ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Recommendation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Endangered ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Animals ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Wifi ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='North America ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Score Updates ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='IoT ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Tennis ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Tournament ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Champions ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='League ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Radio ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Frequency ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Holy Martyr ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='World Health ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Issue ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='UDP ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Library ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='People and ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Business ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Edge Computing ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Stardock ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='China Market ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Encryption ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Schemes ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Orthodox Church ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='European Stock ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Exchange ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Broadcasting ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='retrieving more relevant documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To evaluate the impact of such improvement, in this part, we compare and analyze how the search accuracy of S3BD system is affected by utilizing S-ClusPr’s clusters against the circumstance where its original clustering method is utilized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='For the evaluation, we generated a set of 10 benchmark search queries that are listed in Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To measure the relevancy of search results for each query, we use TREC-Style Average Precision scoring method [102].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This method works based on the recall-precision concept and the score is calculated by N � i=0 ri/N, where ri denotes the 86 score for ith retrieved document and N is the cutoff number (number of elements in the search results) that we consider as 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, we call it TSAP@10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We measure TSAP@10 score only for the RFC dataset and its benchmark queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The reason is that it is domain-specific and feasible to determine the relevancy of the retrieved documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To compare the relevancy provided by S-ClusPr against the original S3BD clustering, we apply the benchmark queries to the S3BD search system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8, the relevancy score of the results for each query when the two clustering schemes are applied are measured and presented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' According to the Figure, for most of the queries, S-ClusPr clustering offers a higher relevancy score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For the two queries that have identical TSAP@10 score, their retrieved document lists are equivalent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Also, S-ClusPr clusters provide score for News Update and China Market benchmark queries, whereas original S3BD clusters do not retrieve any relevant documents for these queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Impact on the Search Time of S3BD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9 presents the total search time of the benchmark queries for each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The search time is measured as the turnaround time of searching each query—from the time a query is issued until the result set is received.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To eliminate the impact of any randomness in the computing system, we searched each set of benchmarks 10 times and reported the results in form of box plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The figure indicates that when S-ClusPr clustering is utilized, the search time is significantly shorter than the circumstance where the original S3BD clustering is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Longer search time impacts the scalability and real-time quality of the search operation on big data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Analyzing Figures 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9 reveals that 87 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Search time of S3BD when S-ClusPr is used for clustering versus when the original S3BD clustering is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' BBC RFC ACCC 0 5 10 15 20 25 Search Time (ms) S-ClusPr Original S3BD integrating S-ClusPr in the search system, not only makes it more accurate, but makes it faster and more scalable too.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Clusters’ coherency for different updates of the three studied datasets when SD-ClusPr is applied with and without re-clustering option.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Update1 Update2 Update3 Update4 Update5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='16 Coherence Baseline SD-ClusPr (a) BBC Dataset Update1 Update2 Update3 Update4 Update5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='08 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='14 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='16 Coherence Baseline SD-ClusPr (b) RFC Dataset Update1 Update2 Update3 Update4 Update5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='25 Coherence Baseline SD-ClusPr (c) ACCC Dataset 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 Evaluation of Clustering Coherency for Dynamic Schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this part, we analyze the effectiveness of dynamic clustering schemes (SD-ClusPr and FD-ClusPr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We mention in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 that FD-ClusPr is a specific case of SD-ClusPr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hence, we only consider the SD-ClusPr scheme for evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To this end, we leverage the three studied datasets and build subsets that each one serves as a batch update.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Specifically, we consider an existing set of clusters based on 500 88 documents for each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, we sample five times to create a list of five updates that each one includes a set of documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' List U includes the pairs of update names and the size of each update as follows: U =< (U1, 25), (U2, 50), (U3, 100), (U4, 20), (U5, 200) >.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To assure that the results are not biased to any particular sample, we performed the sampling procedure 10 independent times and report the mean and 95% confidence interval of the analysis in the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The reason we designated U3 and U5 to be larger is to examine SD-ClusPr decision in re-clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To evaluate the scheme in terms of the cluster coherency, we build a baseline version from SD-ClusPr that does not consider re-clustering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The baseline only performs clustering based on existing clusters (as explained in Algorithm 3) to accommodate the new updates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figures 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10a, 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10b, and 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10c, respectively, present cluster coherency of five different batch updates of BBC, RFC, and ACCC respectively applying SD-ClusPr scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10a, we observe that the coherency of clusters are decreased in baseline for U3 whereas the coherency obtained for SD-ClusPr beats the previous by around 105%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We observe the similar pattern of coherency variation for U5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For baseline, the lowest coherency is obtained in U5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' On the contrary, in SD-ClusPr, we observe around 115% improvement in coherency for U5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' According to Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6, clusters formed for the RFC dataset shows the highest coherency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Similarly, in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10b, we observe the highest coherency for all updates in compare with other datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' With respect to baseline, we observe that SD-ClusPr causes minor improvements in coherency of both U3 and U5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Since 89 the documents are more domain-specific, clusters do not lose coherency significantly from one update to the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As such, we do not observe significant improvements by SD-ClusPr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Similar to BBC and RFC, in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10c, we observe improvement in the coherency for ACCC dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In particular, the improvement in coherency for U3 and U5 is approximately 45% and 35%, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' From these experiments, we conclude that ClusPr scheme can improve the coherency of clustering even for dynamic datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Specifically, we observed that for sufficiently large batches, such as U3 and U5, SD-ClusPr decides to re-cluster that remarkably improves the clustering coherency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 90 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 Summary In this chapter, we propose two secure clustering solutions, namely ClustCrypt and ClusPr in the form of trusted applications for three forms of unstructured datasets, namely static, semi-dynamic, and dynamic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The proposed clustering functions based on statistical characteristics of the datasets to: (A) determine the suitable number of clusters;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' (B) populate the clusters with topically relevant tokens;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' and (C) adapt the cluster set based on the dynamism of the underlying dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Experimental results, obtained from evaluating ClusPr against other schemes in the literature, on three different test datasets demonstrate between 30% to 60% improvement on the cluster coherency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Moreover, we notice that employing ClusPr within a privacy-preserving enterprise search system can reduce the search time by up to 78%, while improving the search accuracy by up to 35%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the next chapter, we explore how to enable secure enterprise search over unstructured data without jeopardizing its confidentiality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 91 Chapter 4: Edge-Based Intelligence for Privacy-Preserving Enterprise Search on the Cloud 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Overview Cloud-based enterprise search services (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', AWS Kendra) have been entrancing big data owners by offering convenient and real-time search solutions to them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, to offer an intelligent search over the privacy-preserving data, these services have to access the user’s search history that further jeopardizes his/her privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To overcome the privacy problem, the main idea of this research is to separate the intelligence aspect of the search from its pattern matching aspect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' According to this idea, the search intelligence is provided by an on-premises edge tier and the shared cloud tier only serves as an exhaustive pattern matching search utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We propose Smartness at Edge (SAED mechanism) that offers intelligence in the form of semantic and personalized search at the edge tier while maintaining privacy of the search on the cloud tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' At the edge tier, SAED uses a knowledge-based lexical database to expand the query and cover its semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' SAED personalizes the search via an RNN model that can learn the user’s interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A word embedding model is used to retrieve documents based on their semantic relevance to the search query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Problem Statement Ideally, data owners desire a privacy-preserving cloud service that offers semantic and personalized searchability in a real-time manner, without overwhelming their resource-constrained (thin) client devices (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', smartphones).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A 92 large body of research has been undertaken on privacy-preserving enterprise search services in the cloud [55, 57, 103, 53, 3] whose goals are to protect user’s sensitive data from internal and external attackers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, most of these works fall short in retrieving search results that are semantically relevant to the context and user’s interest (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', personalized search) [3, 53].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, these works often rely on the client device and impose significant overhead on it to perform a secure query processing or to encrypt/decrypt user documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To satisfy all of the aforementioned desires of a particular user, our main idea in this research is to separate the intelligence aspect of the enterprise search from its pattern matching aspect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 93 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 SAED: Smart Edge-Leveraged Enterprise Search System 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Architectural Overview In this part, we provide a bird-eye view of the SAED system, that enables intelligent and secure enterprise search on the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The system is structured around three tiers, shown in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2, and explained as follows: Client tier (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', smartphone, tablet) contains a lightweight application that provides a user interface for uploading documents and to search over them in the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Datasets are either uploaded by the user or by the organization that owns the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Edge tier extracts representative keywords of the documents being uploaded to the cloud tier and builds an index on the cloud tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Upon receiving a search query from the client tier, the SAED system on the edge tier offers intelligence by considering the query semantics and the user’s interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The edge tier is located in the client’s premises, hence, deemed as an honest and secure system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To offer a secure enterprise search service, the edge tier encrypts both the uploaded data and the search query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, it decrypts the result set before delivering it back to the client tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cloud tier contains numerous high-end servers that are utilized for storing (encrypted) data and performing the large-scale computation required to exhaustively search against the index [53, 3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The index can be clustered based on the underlying topics of its keywords (please refer to our prior 94 works [3, 1] for further details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Architectural overview of the SAED system within edge tier and as part of the three-tier enterprise search service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' SAED provides semantic search via identifying the query context and combining that with the user’s interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, Query Expansion and Weighting unit of SAED, respectively, incorporate the semantic and assure the relevancy of the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Solid and dashed lines indicate the interactions from user to the cloud tier and from the cloud tier to the user respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Query Handler Interest Detector Weighting Unit Query History Context Identifier Query Expansion Ranking Unit Enterprise Search Service Cloud Tier User Edge Tier SAED ~~ ~~ In Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1, we depict the components of SAED and show the interactions between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' At first, a user-provided search query is received by the Query Handler that keeps track of the user’s search history and initializes the Context Identifier unit whose job is to extract the context and disambiguate the query phrase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, according to the extracted context, the query is proactively expanded by the Query Expansion unit and a query set is constructed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To achieve the personalized search, the Interest Detector unit of SAED leverages the user’s search history to recognize his/her interest and weight each element of the query set (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', expanded queries) based on its relatedness to the user interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Once the pattern matching phase is accomplished on the cloud tier, the resulted documents are returned to SAED on the edge tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Next, the Ranking Unit utilizes the assigned 95 Xweights to order the retrieved documents based on their relevance to the user’s interest and generates a retrieved document list, denoted as Dθ, that is sent to the user’s device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the next parts, we elaborate on each unit of the SAED system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Query Context Identification Identifying the context of a given search phrase is vital to navigate the search to the semantics intended by the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Considering the example of cloud computing as the search query, without a proper context identification the returned document set can potentially include documents about sky and climate, whereas, an efficient context identifier can recognize the right semantic and navigate the search to the topics around distributed, edge, fog, and cloud computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In fact, identifying the context helps the Query Expansion unit to form a query set diversified around relevant keywords that semantically represent the search query and subsequently improve the relevancy of the results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Prior context identification works (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', [104, 105, 62]) have the following shortcomings: first, they often assume each keyword has the same importance in the query and recognize the query context via averaging the embeddings of its keywords.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, not all keywords in a query necessarily help in identifying the context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For example, the keyword various in various cloud providers does not bring any significance to the context and can be eliminated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Second, the embedding methods used by the existing works always provide the same representation for a given keyword, irrespective of the underlying context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is particularly problematic for ambiguous keywords whose meaning vary based on the query 96 context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For instance, the embedding of cloud in the aforementioned example should be different when it is used along with the computing as opposed to when it is used along with the weather in a given query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Third, existing methods only consider the embeddings of the common keywords, while discarding most of the name-entities (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', names and locations) that do not exist in the vocabulary of Word2Vec [64, 106].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For instance, consider best selling books of J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Rowling as the query;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Book and Sell are identified as the query context and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Rowling is discarded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, our analysis suggests that the context of a short query phrase often has contextual association with the discarded name-entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To overcome the shortcomings and identify the actual context of a given query, we propose to take a holistic approach and extract the semantic across query keywords, proportionate to the importance of each keyword.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The main output of the Context Identification unit is a set of keywords, denoted as C, that collectively represent the context of the query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Specifically, to eliminate unimportant keywords that do not contribute to the semantic of query Q, the Context Identification unit utilizes Yake [107], which is a unsupervised keyword extractor that discards unimportant keywords of the query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The remaining keywords (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', the trimmed query, denoted as the Q′ set) are considered for context identification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To learn the true semantic of Q′, the unit leverages the Lesk algorithm [106] of WordNet to disambiguate each keyword q ∈ Q′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Lesk algorithm works based on the fact that keywords in a given sentence (query) tend to imply a certain topic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For keyword q, Lesk can determine its true 97 semantics via comparing the dictionary definitions of q against other keywords in Q′ (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', Q′ − {q}).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Let cq be the set of keywords representing the context of q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, the context of Q is determined as C = ∪∀q∈Q′cq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Lastly, the Context Identifier recognizes name-entities from Q using WordNet and considers them as part of the context, but in a separate set, denoted as N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The reason for considering a separate set is that we apply a different treatment on N and C in the other units of SAED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Algorithm 4: Pseudo-code to detect the context of a given query in the Context Identification unit of SAED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Input : query Q Output: C: set of keywords representing context of Q, N: set of name-entity in Q 1 Function contextIdentification(Q): 2 Q′ ← extract keywords from Q using Yake alg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3 foreach q ∈ Q do 4 if q ∈ Name-entity then 5 N ← N ∪ {q} 6 end 7 else 8 if q ∈ Q′ then 9 Eq ← define q based on Q′ − q using Lesk alg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 10 c ← extract set of keywords of Eq using Yake alg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 11 C ← C ∪ c 12 end 13 end 14 end 15 return C, N 16 end Algorithm 4 provides a pseudo-code for identifying the context of incoming query Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The outputs of the pseudo-code are two sets, namely C and N, that collectively represent the context of Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Step 2 of the pseudo-code, Yake algorithm is used to filter Q by extracting its important keywords and generate the 98 Q′ set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Name-entities of Q are identified by checking against WordNet and form the set N (Steps 4–6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Next, in Steps 8–12, for each keyword q ∈ Q′, the Lesk algorithm is employed to disambiguate q and find its true definition with respect to the rest of keywords in Q′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Important keywords of the definitions form the context set (C) for Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Query Expansion Unit The Query Expansion unit is in charge of proactively expanding the query keywords based on their relevant synonyms that are in line with their identified context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Neglecting the query context and blindly considering all the synonyms, as achieved in [104, 105, 62, 3], leads to finding irrelevant documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Accordingly, the unit leverages the context of Q (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', C and N) to only find the set of synonyms, denoted as P, that are semantically close to the query context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Word2Vec [63] is a shallow neural network model that can be trained to generate vector representation of keywords, such that the cosine similarity of two given keywords indicates the semantic similarity between them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Accordingly, to proactively expand each keyword q ∈ Q, the Query Expansion unit instruments Word2Vec, pre-trained with Google News dataset [108], to form the set of nominated synonyms, denoted as sq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Let si q be a synonym of q (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', si q ∈ sq).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, the similarity of si q and the query context, denoted as sim(si q, C), is defined based on the sum of similarities with each element of C, as shown in Equation 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 99 sim(si q, C) = � ∀Cj∈C sim(si q, Cj) (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1) Then, si q is chosen as an element of P, only if it is semantically close enough to the query context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To determine the sufficient closeness, we consider sim(si q, C) to be greater than the mean of the pair-wise similarity across all members of sq (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', sim(si q, C) > µ∀q∀j(sim(sj q, C))).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We note that because the elements of C and N represent the context of Q, they as well are added to P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Algorithm 5 provides a high level pseudo-code for generating the expanded query set P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Steps 2–7 of the pseudo-code, the synonym set for each q is generated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Next, the similarity between each word si q and C is calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The similarity values are used to calculate the mean similarity of all nominated queries in Step 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Steps 9–15, expanded query set P is formed by including nominated synonyms whose semantic closeness is greater than µ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Lastly, in Step 16, set P is expanded by including context set and name-entities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 User Interest Detection Detecting the user’s search interest is essential to deliver personalized search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In SAED, interest detection is achieved by analyzing two factors: (A) the user’s search history;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' and (B) the user’s reaction to the retrieved results of prior search queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This can be detected based on the results chosen by the user or the time spent for browsing them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Let ∆′ represent the whole resulted documents that are sent to the user and τ represent the documents where the user is interested in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We have τ ⊆ ∆′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 100 Algorithm 5: Pseudo-code to expand query based on the context in the Query Expansion unit of SAED Input : Q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' N Output: P: the expanded query set 1 Function QueryExpansion(Q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' N) 2 foreach q ∈ Q do 3 sq ← use WordNet to obtain synonym set of q 4 foreach si q ∈ sq do 5 sim(si q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' C) ← � ∀Cj∈C sim(si q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cj) 6 end 7 end 8 µ ← calculate mean sim(sj q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' C) across all q ∈ Q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' ∀sj q ∈ sq 9 foreach q ∈ Q do 10 foreach si q ∈ sq do 11 if sim(si q,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' C) > µ then 12 Add si q to set P 13 end 14 end 15 end 16 P ← P ∪ C ∪ N 17 return P 18 end 101 Accordingly,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' the user’s interest can be derived from the topics of τ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The Interest Detector unit uses an existing document classification model [109], operating based on Na¨ıve Biased (NB) method, to determine the topics of τ, denoted as tτ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We also perform majority voting on tτ to find the user’s main interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The process is repeated to store n-prior search interests data of the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The data is characterized as sequential as it is harvested from each successful search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' By analyzing the user’s prior search interests, the edge tier trains a recurrent neural network-based prediction model [110] that can predict the user’s search interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In case of SAED, as the data does not contain long dependency and to keep the model simple and to maintain real-timeliness, instead of a stacked (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', deeper) model, we feed the harvested user-specific historical search data to train a many-to-one vanilla RNN model [111].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Weighting Unit Once SAED learns the user interest, the next step to accomplish a context-aware and personalized enterprise search is to determine the closeness of contextually-expanded queries (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', elements of P) to the user’s interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In fact, not all expanded queries have the same significance in the interpretation of the query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Accordingly, the objective of the Weighting unit is defined as quantifying the closeness of each expanded query to the user’s interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Later, upon completion of the search operation on the cloud tier, the weights are used by the Ranking unit of SAED to prune and sort the result set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Prior weighting schemes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', [53, 3, 62, 59, 105]) often use the word 102 frequency-based approach (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', TF-IDF [3]) and discard the user interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Alternatively, the weighting procedure of SAED quantifies the importance of each expanded query p ∈ P based on two factors: (A) The type of p, which means if it directly belongs to the context (C and N sets) or is derived from them;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' and (B) The semantic similarity of p to the user interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In particular, those elements of P that directly represent the query context or name-entities (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', ∀p|p ∈ P ∩ (C ∪ N)) explicitly indicate the user’s search intention, hence, weighting them should be carried out irrespective of the user interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A deeper analysis indicates that name-entities that potentially exist in a query represent the search intention, thus, biasing the search results to them can lead to a higher user satisfaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As such, the highest weight is assigned to ∀p|p ∈ (P ∩ N).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The highest weight is determined by the domain expert, however, in the experiments we consider it as ηmax = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We define the contribution of q ∈ Q as the ratio of the number of keywords added to C because of q (denoted Cq) to the cardinality of C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Let ηp denote the weight of p ∈ P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, for those elements of P that are in the query context (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', ∀p ∈ (P ∩ C)), ηp is calculated based on the contribution of the query keyword q corresponding to p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Equation 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 formally represents how ηp is calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' ηp = ηmax· |Cq| |C| (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2) The weight assignment for those p that are derived from elements of C, as explained in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 , (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', ∀p|p ∈ P − (C ∪ N)) is carried out via considering semantic similarity of p with the user interest θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is, ηp = sim(p, θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 103 Algorithm 6 provides the high level pseudo-code for distributing weight to the expanded query set P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The algorithm considers P, C, N, and highest weight value η as the inputs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' After assigning weights to ∀p iteratively, it returns the weights mapped with corresponding p as a hash map denoted as ϖ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Step 2 of the pseudo code, θ gets the user’s search interest that is identified by leveraging a pre-trained document classifier and a vanilla RNN model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the following Step, hash map ϖ is initialized to contain the weights that mapped with corresponding p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Overall, in Steps 4–15, weight of each p denoted as ϖp is calculated according to its type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Specifically, in Steps 5–7, ϖp, where p ∈ (P ∩ N) is set by directly assigned η.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Steps 8–11, p, where p ∈ (P ∩ C) is weighted based on its contribution towards context C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' At first, q is determined that generates p and weight ϖp of p is calculated by the ratio between η and total number of keywords added in C for the corresponding q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the following Steps (12–14), ϖp, where p ∈ P − (C ∪ N) is calculated by its semantic similarity with θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Lastly, the algorithm is finished by returning hash map ϖ filled with weights corresponding to their q (Step 16).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 Ranking Unit Once the expanded query set P is formed, the cloud tier performs string matching for each p ∈ P across the index structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We note that, if the user chooses to perform a secure search, the elements of P are encrypted before delivered to the cloud tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, in our prior works [1], we proposed methods for the cloud tier to cluster the index structure and perform the pattern matching only on the clusters that are relevant to the query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 104 Algorithm 6: Pseudo-code to weight expanded query Input : P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' η Output: ϖ 1 Function weighting(P,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' N,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' η) 2 θ ← predict a user’s search interest 3 ϖ ← initialize hash map to store weights mapped with their corresponding keywords 4 foreach p ∈ P do 5 if p ∈ N then 6 ϖp ← η 7 end 8 else if p ∈ C then 9 ϖp ← ηmax· |Cq| |C| 10 end 11 else 12 ϖp ← sim(p,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' θ) /*Compute similarity and store it in hash map */ 13 end 14 end 15 return ϖ 16 end 105 The cloud tier returns the resulted document set,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' denoted as ∆,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' to the edge tier where the Ranking unit of SAED ranks them based on the relevance and the user’s interest and generates a document list,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' called ∆′ to show to the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For a document δi ∈ ∆, the ranking score, denoted as γi, is calculated by aggregating the importance values of each p ∈ P within δi and with respect to its weight (ηp).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The importance of p in δi is conventionally measured based on the TF-IDF score [112].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Accordingly, γi is formally calculated based on Equation 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' γi = � ∀p∈P � ηp · TF-IDF(p, δi) � (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3) The TF-IDF score of p in δi is defined based on the frequency of p in δi versus the inverse document frequency of p across all documents in ∆.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Details of calculating the tf-idf score can be found in [112].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Once the Ranking unit calculates the ranking score for all δi ∈ ∆, then the documents are sorted in the descending order based on their ranks and thus, the document list ∆′ are formed with each δi and displayed to the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 106 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 SAED As a Pluggable Module Enterprise Search Solutions The advantage of SAED is to be independent from the enterprise search service deployed on the cloud tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is, using SAED neither interferes with nor implies any change on the cloud-based enterprise search service.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' SAED can be plugged into any enterprise search solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It provides the search smartness on the on-premises edge tier and leaves the cloud tier only for large-scale pattern matching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The whole SAED solution reforms the enterprise search to be semantic, personalized, and confidential services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this work, we set SAED to work both with AWS Kendra and S3BD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the case of using AWS Kendra, the Query Expansion unit sends the expanded query set P to Kendra to search each keyword p against the dataset on the Amazon cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The resulted documents are received by SAED and ranked before being delivered to the client tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the implementation, we only show top 10 documents from the resulted list to the user.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Similarly, we plugged SAED to S3BD to perform confidential semantic search on the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Because S3BD maintains an encrypted index structure that has to be traversed against each search query, the elements of P had to be encrypted before handing them over to the cloud tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We also verified SAED when it is used along with AWS Kendra where the dataset was encrypted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We noticed that SAED can achieve smart search even when Kendra is set to work with encrypted dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The performance measurement and analysis of using SAED along with AWS Kendra and S3BD are elaborated in the next Section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 107 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Performance Evaluation of SAED 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Experimental Set up We have developed a fully working version of SAED and made it available publicly in our Githuba page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To conduct a comprehensive performance evaluation of SAED on the enterprise search solutions, we developed it to work with both S3BD [3] and AWS Kendra [113].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' S3BD already has the query expansion and weighting mechanisms, but we deactivated them and set it to use the expanded queries generated by SAED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the experiments, the combination of SAED and S3BD is shown as SAED+S3BD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Likewise, the combination of SAED and AWS Kendra is shown as SAED+Kendra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We evaluated SAED using two different datasets, namely Request For Comments (RFC) and BBC that have distinct properties and volume.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The reason we chose the RFC dataset is that it is domain-specific and includes 4, 951 documents about the Internet and wireless communication network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Alternatively, the BBC dataset is more diverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It includes 2, 224 news documents in five distinct categories, including politics, entertainment, business, sports, and technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To conduct a comprehensive evaluation, we used both systematic metrics and human-based feedback as elaborated in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We deployed and experimented SAED on a Virtual Machine (VM) within our local edge computing system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The VM had two 10-core 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8 GHz E5 Xeon processors with 64 GB memory and Ubuntu 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 operating system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' ahttps://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/hpcclab/SAED-Security-At-Edge 108 Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Benchmark search queries developed for the RFC and BBC datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='BBC Dataset ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='RFC Dataset ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='European Commission (EC) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Network Information (NI) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Parliament Archives (PA) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Host Network Configuration (HNC) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Top Camera Phones 2020 (TCP) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Data Transfer (DT) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Credit Card Fraud (CCF) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Service Extension(SE) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Animal Welfare Bill (AWB) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Transport Layer (TL) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Piracy and Copyright Issues (PCI) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Message Authentication (MA) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Car and Property Market (CPM) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Network Access (NA) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Rugby Football League (RFL) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Internet Engineering (IE) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Opera in Vienna (OV) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Fibre Channel (FC) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Windows Operating System (WOS) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Streaming Media Service (SMS) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Benchmark Queries The datasets that we use to carry out the experiments are not featured with any benchmark.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, we required to develop benchmark queries for the datasets before evaluating the performance of SAED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We developed 10 benchmark queries, shown in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1, for each one of the two datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The benchmark queries are proactively designed to explore the breadth and depth of the datasets in question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, some of the queries intentionally contain ambiguous keywords to enable us examining the context detection capability of SAED.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For the sake of brevity, we provide one acronym for each benchmark query (see Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For each benchmark query, we collected at most the top-20 retrieved documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, the quality of the retrieved documents were measured via both automated script and human-based users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Evaluation Metrics We have to measure the search relevancy metric to understand how related 109 the resulted documents are with respect to the user’s query and how they meet the his/her interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For the measurement, we use TREC-Style Average Precision (TSAP) score, described by Mariappan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [102].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' TSAP provides a qualitative score in a relatively fast manner and without the knowledge of the entire dataset [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It works based on the precision-recall concept that is commonly used for judging text retrieval systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The TSAP score is calculated based on N � i=0 ri/N, where ri denotes score for ith retrieved document and N denotes the cutoff number (total number of retrieved documents).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Since we consider N = 10, we call the scoring metric as TSAP@10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To determine ri for retrieved document δ′ i ∈ ∆′, we conducted a human-based evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We engaged five volunteer students to judge the relevancy of each retrieved document.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For every search query, the volunteers labeled each retrieved document as highly relevant, partially relevant, or irrelevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' After performing majority voting based on the provided responses for document i, the value of ri is determined as follows: ri = 1/i if a document is highly relevant ri = 1/2i if a document is partially relevant ri = 0 if a document is irrelevant We report TSAP@10 score to show the relevancy of results for each benchmark query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, mean TSAP score is reported to show the overall relevancy across each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As we set the top 10 documents to be retrieved for 110 each search, the highest possible for TSAP@10 score can be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='292 [102].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition to the TSAP score, we measure Mean F-1 score too to compare the search quality offered by the SAED-plugged enterprise search solutions against the original enterprise search solutions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', without SAED in place).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The F-1 score maintains a balance between the precision and recall metrics, which is useful for unstructured datasets with non-uniform topic distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Evaluating Search Relevancy The purpose of this experiment is to evaluate the search relevancy of enterprise search systems that have SAED plugged into them and compare them against the original (unmodified) systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To evaluate the personalized search, we set (assumed) technology as the user’s interest for both datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We note that, in this part, the enterprise search solutions (S3BD and AWS Kendra) are set to work in the plain-text datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' S3BD vs SAED+S3BD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2a shows the TSAP@10 score for the RFC and BBC datasets for the original S3BD and SAED+S3BD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The horizontal axes in both subfigures show the benchmark queries and the vertical axes show the search relevancy based on the TSAP@10 score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In both Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2a and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2b, we observe that for all queries in both datasets, SAED+S3BD outperforms the S3BD system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, we observe that S3BD produces less relevant results for the BBC dataset compared to the RFC dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is because, unlike the RFC dataset, in several cases, the exact keywords of the benchmark queries do not exist in the BBC dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The worst case 111 Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Comparing TSAP@10 scores of SAED+S3BD and S3BD systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hor- izontal axes show the benchmark queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' EC PA TCP CCF AWB PCI CPM RFL OV WOS 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='30 TSAP@10 Score SEA+S3BD S3BD (a) BBC dataset NI HNC DT SE TL MA NA IE FC SMS 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='30 TSAP@10 Score SEA+S3BD S3BD (b) RFC dataset Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Comparing TSAP@10 scores obtained from SAED+Kendra versus AWS Kendra in searching benchmark queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' EC PA TCP CCF AWB PCI CPM RFL OV WOS 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='30 TSAP@10 Score SAED+Kendra Kendra (a) BBC dataset NI HNC DT SE TL MA NA IE FC SMS 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='30 TSAP@10 Score SAED+Kendra Kendra (b) RFC dataset of these issues has occurred for the PCI query in S3BD, because its query expansion procedure could not capture the complete semantics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In contrast, SAED+S3BD is able to handle the cases where the exact keyword does not exist in the dataset, thus, we see that it yields to a remarkably higher relevancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Even if we consider PCI as an outlier and exclude that from the analysis, in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2a, we still notice that the TSAP@10 score of SAED+S3BD is on average 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2% higher than S3BD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Although the difference between S3BD and SAED+S3BD is less significant for the RFC dataset (in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2b), we still notice some 17% improvement in TSAP@10 score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is because RFC is a domain-specific dataset 112 Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Comparing TSAP@10 scores obtained from SAED+Kendra vs AWS Kendra systems in the encrypted domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' EC PA TCP CCF AWB PCI CPM RFL OV WOS 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='30 TSAP@10 Score SAED+Kendra Kendra (a) Encrypted BBC dataset NI HNC DT SE TL MA NA IE FC SMS 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='05 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='30 TSAP@10 Score SAED+Kendra Kendra (b) Encrypted RFC dataset and the exact keywords of queries can be found in the dataset, hence, making use of smart methods to extract the semantic is not acute to earn relevant results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' From these results, we can conclude that SAED can be specifically effective for generic datasets where numerous topics exist in the documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' AWS Kendra vs SAED+Kendra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Figures 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3a and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3b, we report TSAP@10 score obtained from AWS Kendra versus SAED+Kendra for BBC and RFC datasets, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Specifically, in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3a (BBC dataset), a significant improvement (on average 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5%) is noticed in the TSAP@10 score of SAED+Kendra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, unlike SAED+S3BD, SAED+Kendra does not beat Kendra for all the queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The reason Kendra outperforms SAED+Kendra for AWB and CPM queries is that SAED injects extra keywords and sends the expanded query set to AWS Kendra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, Kendra returns documents that are related to the queries and to the expanded keywords.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We realized that the Ranking unit of SAED occasionally prioritizes documents that include keywords of the expanded queries instead of those with the query keywords.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 113 Similar to the S3BD experiment, we observe that the relevancy resulted from Kendra and SAED+Kendra is less significant for RFC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, we still obtain around 12% improvement in TSAP@10 score according to Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Relevancy of Privacy-Preserving Enterprise Search To examine the efficiency of SAED for privacy-preserving enterprise search systems, we conducted experiments using encrypted BBC and RFC datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The encrypted datasets were uploaded to the cloud tier and the expanded queries were also encrypted and searched on the cloud tier via Kendra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We use the TSAP@10 score, as shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4a and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4b, for the BBC and RFC datasets, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4a indicates that SAED+Kendra substantially outperforms Kendra for all the benchmark queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We can see that for encrypted dataset Kendra cannot do anything except pattern matching and returning documents that exactly include the encrypted query.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, searching for several queries (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', PA,TCP, CPM, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=') does not retrieve any documents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We notice that, in both systems, the highest TSAP@10 score is in searching EC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The reason is the high number of documents in BBC that contain the exact phrase European commission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The reported TSAP@10 scores for the RFC dataset in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4b shows a clear improvement in compared with the BBC dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We observe that seven out of ten queries provide an equal TSAP@10 scores in both systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The reason that makes Kendra competitive to SAED+Kendra is the exact availability of the benchmark queries in RFC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, for HNC and FC, the exact query keywords are 114 not present in the dataset, hence, Kendra fails to find any results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 Discussion of the Relevancy Results In Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2, we report mean F-1 and mean TSAP@10 scores for the SAED-plugged enterprise search systems along with their original versions upon utilizing the datasets both in the plain-text and encrypted forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' From the table, we notice that, regardless of the enterprise search system being employed, a higher search relevancy is consistently achieved for the RFC dataset as opposed to the BBC dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The search relevancy is consistently improved when SAED+Kendra is used and it provides on average of 23% improvement in mean F-1 score and 21% in the mean TSAP@10 score.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Although original S3BD is the underperformer, using SAED+S3BD improves its mean F-1 and mean TSAP@10 scores by on average of 40% and 32%, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Comparing the mean F-1 and the mean TSAP@10 scores obtained from SAED-plugged enterprise search systems versus their original forms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The highest resulted scores are shown in bold font.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' BBC RFC Systems Mean F-1 Mean TSAP@10 Mean F-1 Mean TSAP@10 S3BD 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='17 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='24 SAED+S3BD 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='82 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='92 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='28 Kendra 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='67 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='88 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='26 SAED+Kendra 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='90 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='27 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='93 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='28 Kendra (Encry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=') 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='31 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='09 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='22 SAED+Kendra (Encry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=') 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='73 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='90 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='27 In the encrypted domain, we notice that SAED+Kendra offers a 115 substantially higher (up to 130%) search relevancy for BBC dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As the exact keywords of the given search queries are not present in the encrypted form of BBC dataset, AWS Kendra fails to perform semantic search, rather does only a pattern matching, which makes it an underperformer for this dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' On the other hand, search relevancy is improved for RFC dataset since mean F-1 and mean TSAP@10 scores are improved by at least 20%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is because, most of the queries are present exactly in the dataset and Kendra retrieves most of the relevant documents by relying only on pattern matching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 Evaluating the Search Time Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 presents the total incurred search time of the experimented queries for each dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The search time is calculated as the summation of the elapsed time taken by a query to be processed (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', expansion, weighting) and turnaround time until the result set is received.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To eliminate the impact of any randomness in the computing system, we searched each set of experimented queries 10 times and reported the results in the form of box plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The figure indicates that S3BD system has the highest search time overhead for both datasets which could impact real-time searchability in case of big data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' SAED+S3BD incurs less query processing time overhead compared to the original (unmodified) S3BD system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' On the other hand, AWS Kendra causes the lowest time overhead for both datasets compared to SAED+Kendra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' SAED+Kendra causes around 4 times more time overhead compared to original Kendra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, in the prior set of experiments, we determine that SAED+Kendra achieves a substantially higher 116 search relevancy for most of the queries and, particularly, for datasets with privacy constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Search time comparison among S3BD, Kendra, SAED+S3BD, and SAED+Kendra systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' BBC RFC 0 2 4 6 8 10 Search Time (S) S3BD Kendra SAED+S3BD SAED+Kendra 117 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 Summary A context-aware, personalized, and privacy-preserving enterprise search service is the need of the hour for data owners who wish to use cloud services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Our approach to address this demand was to separate the search intelligence and privacy aspects from the pattern matching aspect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We developed SAED that achieves privacy and intelligence at the edge tier and leaves the large-scale pattern matching for the cloud tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' SAED is pluggable and can work with any enterprise search solution (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', AWS Kendra and S3BD) without dictating any change on them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Utilizing edge computing on the user’s premises preserves the user’s privacy and makes SAED a lightweight solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Leveraging recurrent neural network-based prediction models, WordNet database, and Word2Vec, SAED proactively expands a search query in a proper contextual direction and weights the expanded query set based on the user’s interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, SAED provides the ability to perform semantic search while the data are stored in the encrypted form on the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this case, the existing enterprise search solutions just perform the pattern matching without knowing the underlying data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Evaluation results, verified by human users, show that SAED can improve the relevancy of the retrieved results by on average ≈ 24% for plain-text and ≈ 75% for encrypted generic datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 118 Chapter 5: Multi-Tenancy of Latency-Sensitive Deep Learning Applications on Edge 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Overview In the prior chapter, we propose an enterprise search application, namely SAED in the form of a trusted application for enabling secure search over confidential data in the cloud.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The SAED application spans across edge-to-cloud continuum and consists of several microservices that run on edge to perform the intelligent aspects of searching (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', query processing, personalization, and ranking).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Our investigation indicates that running a number of microservices on the edge consumes a significant percentage of resource, specifically, edge memory is exhausted and service(s) can either be killed or failed to execute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Prior studies quantized the NN models to make them lighter but without model management, the system cannot get actual advantage of multi-tenant processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Edge-MultiAI leverages NN model compression techniques, such as model quantization, and dynamically loads NN models for DL applications to stimulate multi-tenancy on the edge server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We consider the problem and scale it up in order to come across a unified solution of it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Due to the robust uses of smart IoT-based systems, various application requests (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', object detection, face recognition, NLP, and motion capture) incoming from users’ devices execute on edge tier with low-latency constraint on a daily basis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' An exemplar use case of such IoT-based systems is SmartSight [19], illustrated in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1, that aims at providing ambient perception for the blind and visually impaired people.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The system operates based on a smartglass (IoT 119 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Bird-eye view of SmartSight, an IoT-based system that continuously receives various inputs from the smartglass (IoT device) sensors, and processes them via multi-tenant DL applications running on the edge server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' IoT device speech rec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' NLP face rec.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' memory edge system processors multi-tenant DL applications object det.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' video camera voice storage device) and a companion edge server (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', smartphone).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The smartglass continuously captures the inputs via its sensors (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', camera and microphone) and requests the edge server to process DL-based applications, such as object detection to identify obstacles;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' face recognition to identify acquainted people;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' speech recognition, and NLP to understand and react to the user’s commands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To make SmartSight usable, the edge server has to continuously execute multiple (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' multi-tenant) DL application to process incoming requests with low-latency and high accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It is noteworthy that, although cloud datacenters can mitigate the inherent resource limitations of the edge, due to the network latency overhead and data confidentiality [14, 15, 16], offloading the latency-sensitive service requests to the cloud is not a tractable approach in many use cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' DL applications utilize bulky Neural Network (NN) models at their kernel to 120 315Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Load time, inference time, and accuracy of popular NN models individ- ually running on Samsung Galaxy S20+ as the edge server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' NN Models Bit Width Size (MB) Loading Time (ms) Inference Time (ms) Accu- racy (%) InceptionV3 FP32 105 650 100 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='50 INT8 24 380 80 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='20 VGG16 FP32 528 820 52 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='30 INT8 132 185 40 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='18 MobileNetV1 FP32 89 600 15 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='56 INT8 23 192 8 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='70 MobileNetV2 FP32 26 110 10 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='08 INT8 9 65 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='70 MobileNetV3 FP32 14 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='80 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='04 INT8 8 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='45 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='21 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='32 MobileBERT FP32 96 1100 62 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='23 INT8 26 890 40 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='08 infer on the inputs received from the sensors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The NN models have to be kept in memory to enable low-latency (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' warm-start [31]) inference operations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Otherwise, because the NN model size is often huge, loading it into the memory in an on-demand manner (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' cold-start) is counterproductive and affects the latency constraint of the DL applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As the edge servers naturally have a limited memory size (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', 4 GB in the case of Jetson Nano [32]), multi-tenant execution of DL applications on them leads to a memory contention challenge across the processes [14, 33].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Accordingly, the main challenge of this study is to resolve the memory contention across multi-tenant DL applications without compromising their latency and accuracy constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the deep learning context, there are techniques based on the idea of approximate computing, such as quantization [114], that make the model 121 edge-friendly via compressing its NN model, hence, reducing its inference time and accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To understand the impact of such approximations, we conducted a preliminary experiment using a Samsung Galaxy S20+ as the edge server;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' and five popular DNN models, namely InceptionV3, VGG16, MobileNetV1, MobileNetV2, MobileNetV3, MobileBERT, each one at two quantization (precision) levels, namely FP32 and INT8 bit widths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1, we report the average loading time, inference time, and accuracy for their individual executions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We observe that: (A) for all the models, the loading time is 8—17× more than its inference time;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' (B) Loading the high-precision model (FP32 bit width) occupies ≈3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5× more memory than the low-precision (INT8 bit width) one;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' and (C) Loading a low-precision model can reduce the inference accuracy by around 3—6%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' These results demonstrate that the model compression has a considerable potential to mitigate the memory footprint of the DL applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Moreover, the model loading time invariably dominates the inference time [115].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Accordingly, our hypothesis is that the efficient use of model compression and the edge memory can enhance the multi-tenancy and inference time of DL applications without any major loss on their inference accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We propose each DL application to be equipped with multiple NN models with different precision levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The low-precision models have a small memory footprint, hence, allowing for a higher multi-tenancy of DL applications with their models loaded into the memory (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', warm-start inference) that enhances the service latency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, loading overly low-precision (over-quantized) models to maximize multi-tenancy and warm-start inference is not viable, because it reduces 122 the inference accuracy and renders the multi-tenant DL applications to be futile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' On the contrary, loading high-precision (large) NN models on a memory-limited edge system for an indefinite time period unnecessarily occupies an excessive memory space that is detrimental for the multi-tenancy and warm-start inference of other tenants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is, other tenants face a significant slow down (as noted in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1), because they cannot keep their NN model in memory and have to load it from the storage (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', cold-start) to perform the inference operation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, an ideal solution for a multi-tenant edge system should be able to dynamically load a suitable model from the set of models available to the application (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' model zoo), such that it neither interrupts the execution of other applications, nor causes a cold-start inference for them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Problem Statement The research question that we investigate is: how to maximize the number of warm-start inferences for multi-tenant DL applications on edge without compromising the inference accuracy?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The question indicates a trade-off between two objectives: fulfilling the latency constraint of DL applications and maintaining their inference accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The former objective entails having the NN models of DL applications loaded into the memory (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', warm-start inference), whereas, the latter entails retaining high-precision NN models in the memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For application Ai ∈ A with Mi = {mk i | 1 ≤ k ≤ qi} as its model zoo, let ri(t) be a Boolean function that represents an inference request for Ai at time t with value 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Also, let m∗ i ⊆ Mi be an NN model of Ai with size of s∗ i that is currently 123 loaded in the memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This means that, for application Aj that does not have any of its NN models currently in the memory, we have m∗ j = ∅ and s∗ j = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, M ∗ = n� i=1 m∗ i represents the set of currently loaded NN models that occupy S∗ = n � i=1 s∗ i of the memory space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A cold start event for the request arrives at time t for Ai, denoted Ci(M ∗, t) and shown in Equation (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1), occurs when there is no NN model in memory for Ai (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', Mi ∩ M ∗ = ∅).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ci(M ∗, t) = � ri(t) Mi ∩ M ∗ = ∅ 0 otherwise (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1) Assume that utilizing m∗ i ∈ Mi results in an inference accuracy that we denote it as χ∗ i .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, based on Equation (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2), for n multi-tenant DL applications, we can formally state the objective function as minimizing the total number of cold-start inferences, while maximizing the accuracy of the inferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this case, the total memory size available for the NN models (denoted S) serves as the constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' min �� ∞ t n � i=1 Ci(M ∗, t) dt � , max �� ∞ t n � i=1 χ∗ i (t) dt � subject to: ∀t, n � i=1 s∗ i ≤ S (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2) Note that optimal NN model management decisions do not have a greedy nature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is, minimizing the number of cold-start inferences at a given time t does not necessarily lead to the minimum total number of cold-starts with maximum accuracy during the entire applications’ lifetime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In other words, the system may experience a cold-start at time t to prevent multiple ones at a later 124 time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is why, the objective function of Equation 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 includes integrals over t to the ∞ to encompass the impacts of the decisions at t on the future cold-starts and accuracy levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the objectives, the NN models of application Ai are only chosen from its model zoo (Mi), thus, the accuracy (µi(t)) and size functions (si) are discrete functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It is needless to say that minimizing the number of cold-start inferences is equivalent to maximizing the number of warm-start events [116].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the rest of this chapter, we use these two interchangeably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Solution Statement and Contributions To stimulate multi-tenancy on the limited edge memory, we develop a framework, called Edge-MultiAI, that takes advantage of a model zoo for each DL application and can dynamically swap the NN models of the applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To maximize the number of warm-starts with high inference accuracy across multi-tenant DL applications, our approach is to proactively load the high-precision NN models for the applications that are expected to receive inference requests, while loading low-precision models for the others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We utilize the recent memory usage information to predict the memory availability for the next executions while not interrupting other active applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We develop model management heuristic policies that make use of the expected memory availability and the usage pattern of multi-tenant DL applications to choose a suitable NN model for the requester application right before the inference operation, thereby, both the latency and inference accuracy of the application are fulfilled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 125 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Architectural overview of the Edge-MultiAI framework with three tiers: Application, NN Model Manager, and Memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' logic business model loader NN Model Manager N A B model m1 m2 m3 m4 app request C predictor memory predictor Tier Memory multi-tenant DL processes manager memory A B C N memory optimizer memory space of DL processes zoo Application Tier 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Architectural Overview & System Design of Edge-MultiAI Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 illustrates the architectural overview of Edge-MultiAI that facilitates multi-tenancy of DL applications on a resource-limited edge system via enabling the applications to only swap their NN models, instead of the entire application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The framework consists of three tiers: (i) Application tier, (ii) NN model manager, and (iii) Memory tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Application Tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The incoming multi-modal inputs from the connected IoT devices trigger execution of multi-tenant DL applications in the application tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The model zoo for each DL application acts as a repository that contains NN models 126 with different compression levels (sizes) and inference accuracy (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' various precision levels).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The model loader is responsible for loading the chosen NN model from the model zoo into the edge memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' NN Model Manager.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' NN model manager comprises of three components: (i) application request predictor, (ii) memory predictor, and (iii) memory optimizer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' “Application request predictor” collects historical requests to each application and trains a lightweight (edge-friendly) many-to-one vanilla recurrent neural network (RNN) time series prediction model, similar to the one in [110], to periodically foresee the inference request arrivals for each application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Upon arrival of each request, “memory predictor” is in charge of predicting the memory availability based on the recent memory allocations in the entire edge system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We leverage the historical memory allocation data and train another many-to-one vanilla RNN time-series prediction model to predict the available memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Memory optimizer interacts with the application “request predictor” and “memory predictor” to receive: (A) the request arrival time for different applications plus the information of their model zoo;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' and (B) the memory availability information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, the memory optimizer feeds the received information to an NN model management policy that determines the highest possible precision NN model that can be loaded to serve the inference request of a DL application with the minimum impact (in terms of the prediction accuracy or latency) on the execution of other applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Upon facing memory shortage for an arriving inference request, the memory optimizer scavenges the memory allocated to the NN models of 127 other applications via either loading a lower-precision model or forcing them to cold-start.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' After procuring adequate memory, the memory optimizer informs the “model loader” to load the appropriate NN model of the requested application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Memory Tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The tier includes the “memory spaces” allocated to the applications;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' and a “memory manager” that keeps track of the currently loaded models, the available memory spaces, and the current status of the applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The memory manager communicates these information to the NN Model Manager to efficiently allocates them to the arriving requests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Heuristics to Manage Models of Multi-tenant Applications 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Overview Recall that the aim of NN model management policy is to minimize the number of cold-start inferences and maximize the inference accuracy for multi-tenant DL applications on the edge servers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To that end, the memory optimizer strives to maximize the time to retain the loaded models in the edge memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, due to limitations in the available memory space, it is not possible to retain the highest precision NN model of all applications in the memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To resolve this memory contention, the NN models of the applications that are unlikely to be requested in the near future should be assigned a lower priority to remain in the memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Furthermore, Edge-MultiAI makes it possible to dynamically load NN models for the applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This means that, upon predicting time t as the inference request time for a given DL application, Edge-MultiAI can be instructed to load the high-precision NN model of that application immediately 128 before performing the inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Similarly, in the face of a memory shortage, for the application(s) that are unlikely to be requested at time t, Edge-MultiAI can be instructed to unload their NN models or, more interestingly, replace them with a lower precision one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, we know that the request arrivals are inherently uncertain [19] and no prediction model can precisely capture the exact request time for an application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To capture the uncertainty, we consider a request time window, denoted as ∆, around each predicted request time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The value of ∆ is obtained from profiling past request predictions and calculating the mean difference of actual arrival time and the predicted ones across all applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, there is a time overhead, denoted as θi, to load the chosen NN model of an application Ai into the memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In sum, to prevent a cold-start for Ai that is predicted to perform inference at time t, as shown in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3, the NN model has to be loaded at time (ti − ∆ − θi) and kept in memory until (ti + ∆).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Furthermore, there is uncertainty in predictions of “no request” for an application at a given time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is, at time t, there can be an inference request for an application that was predicted not to have an request at that time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To make the system robust against this type of uncertainty and to avoid cold-start inferences in these circumstances, an ideal policy should load low-precision NN models for these applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hence, an unpredicted inference request can be still served as a warm-start by the low-precision model and the latency constraint is maintained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this work, the set of applications whose NN models are retained in 129 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A sample scenario of inference requests for five multi-tenant applications, namely A1 to A5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Each pulse represents the time window within which an inference request is expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Solid lines expresses the event that has already happened and dashed lines after “now” are the request predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' request time window A1 A2 A5 A3 A4 now history window (H) time memory outside of their predicted request time window are called the minimalist set, and denoted as A′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Similarly, the set of applications that are in their request time window and we load a high-precision model for them are called maximalist, and denoted as A∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To resolve the memory contention, the policy can be based on scavenging memory from the minimalist applications to procure the required memory space for the maximalist ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is, in the event that application Ai is predicted to have an inference at time ti, it becomes a member of A∗ set at time ti − ∆ − θi, and then becomes a member of A′ set after ti + ∆;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' thus, its model can be evicted from the memory in the event the memory space is needed for another maximalist application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The NN model eviction is only permitted from A′ set and we aim at retaining a low-precision model for the applications in this set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, 130 due to high inference demand, A′ have to unload their models (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', switch to cold-start) to free space for the model of the applications that are in the maximalist set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In an extreme situation, if A′ is empty, or the scavenged memory from A′ cannot procure sufficient space to load the suitable model for application Ai, the next (smaller) model for Ai is considered, and the aforementioned steps are repeated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ultimately, if the scavenged memory space is inadequate for the lowest precision model of Ai, an inference failure occurs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The memory contention problem can be reduced to the classic binary Knapsack optimization problem [117] where from a collection of items, each one with a weight and a value, we need to select items such that the total value is maximized, while the total weight is bounded to a limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This problem is known to be NP-Complete,hence, we can rely on the heuristic-based solutions for it [118].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the next part, we discuss four NN model management (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' NN model eviction) policies to manage the memory for multi-tenant DL applications such that the number of warm-start inferences is maximized without any major impact on the inference accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Policy 1: Largest-First Model Eviction (LFE) In this policy, to allocate memory for the NN model of a maximalist process, we first evict NN models from set (A′ that occupy the highest memory space, until there is enough space to allocate the high-precision NN model of A∗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For that purpose, members of A′ are sorted based on the size of their currently loaded NN model in the descending order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the event that evicting all the NN models of A′ 131 does not free enough memory space to allocate the NN model of the request, a lower precision NN model (smaller in size) is tried for allocation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This procedure continues until a model from the model zoo can be allocated in the memory;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' otherwise, the edge system is not able to serve that request at that time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Policy 2: Best-Fit Model Eviction (BFE) The limitation of LFE is to evict the largest NN models of the minimalist applications, irrespective of the exact memory requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This means that adopting LFE can free more memory space than the actual requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To tackle the issue, we implement the BFE policy where applications in the minimalist set are sorted based on the difference between their model sizes and the actual memory requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, the NN model with a minimum difference is chosen for eviction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The memory requirement for a maximalist application is first calculated based on its highest precision (largest) NN model to gain the highest inference accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, in the event that evicting the NN models of all the minimalist applications do not free enough memory space to allocate the desired NN model, BFE iteratively selects the next high-precision model from the model zoo of the requested application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Policy 3: Warm-Start-aware Best-Fit Model Eviction (WS-BFE) Let Ai ∈ A∗ an application that is currently in the maximalist set, and Aj ∈ A′ an application that is currently in the minimalist set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It is technically possible that the predicted request time window of Ai overlaps with the one for Aj.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this case, LFE and BFE policies potentially choose to evict the NN model of Aj 132 in favor of the Ai model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is because both of these policies are backward-looking and ignore the fact that Aj can be requested soon after evicting its NN model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Such an eviction decision increases the likelihood of a cold-start inference and to avoid that, we develop WS-BFE that assigns the lowest eviction priority to those applications in A′ that have overlapping time window with Ai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In our early experiments, we realized that another reason for cold-start inferences is due to uncertain nature of request arrivals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is, a minimalist application is unexpectedly requested.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To minimize the likelihood of cold-start inference in these circumstances, we implement WS-BFE to replace the evicted NN model with the lowest-precision (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', smallest) NN model of that application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As such, in the event of an unpredicted request the minimalist applications, there is a low-precision model available to carry out a warm-start inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Policy 4: Intelligent Warm-Start-aware Best-Fit Eviction (iWS-BFE) To make WS-BFE robust against uncertainties in the application request time prediction, we enhance it by applying the Bayesian theory and proposing a new policy, called iWS-BFE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This policy is inspired from the widely-adopted LRU-K cache management policy [119] that considers the least recently used (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', requested) applications are not likely to be requested in the near future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Similarly, iWS-BFE only considers members of A′ as eviction candidates, denoted by E′, that are not recently requested.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3, shows a scenario of predicted request times for A1—A5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To procure memory for A1, we have A′ = {A2, A3, A5}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Because A3 was 133 requested during the “history window” (H), it is likely to be requested in the near future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hence, iWS-BFE, chooses E′ = {A2, A5} for eviction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The value of H is determined based on the mean request inter-arrival time of all applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition to considering LRU, iWS-BFE also makes use of the request prediction, provided by Edge-MultiAI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' That is, it considers the most appropriate application for eviction as the one that has not been recently requested, and is predicted to be requested the latest in future.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, the request time predictions are uncertain, and the system can receive an unexpected request from members of E′ in the current request window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To make iWS-BFE robust against such uncertainty, we calculate the probability of an unexpected request.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For application Aj ∈ E′, let rj denote an unexpected request.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, the probability of rj occurring during the current request window (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', [t, t + ∆]) is defined as P(rj|Ai ∈ A∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The application that is likely to be requested unexpectedly is not an optimal choice for eviction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, in Equation 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3, to calculate the fitness score of Aj for eviction (denoted Score(Aj)), we consider 1 − P(rj|Ai ∈ A∗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To take the predicted request time of Aj into consideration, we calculate the distance between its predicted request time and the current time (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', tj − ti).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To confine the value between [0,1], we normalize the distance based on the latest predicted distance across all k applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Score(Aj) = tj − ti max k∈E′(tk − ti)· � 1 − P(rj|Ai ∈ A∗) � (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3) The pseudo-code of the iWS-BFE policy is provided in Algorithm 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It begins with an initial set of eviction candidates, called τ ⊆ A′, that is formed based 134 on the applications that were not requested during the history window (H).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' From τ, in Step 3, a list of eviction candidates (denoted E) whose elements do not overlap with the request window of active application (Ai) is derived.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Next, in Step 4, we use Equation 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 to calculate the fitness score for each Ek ∈ E and then, build a max-heap tree of E based on the fitness scores (Step 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Steps 6—10, the policy iteratively retrieves the application with the highest fitness score (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', the max-heap root, denoted w) and foresees the amount of memory that can be scavenged upon replacing its loaded model with the lowest-precision one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Once the policy finds enough memory to be scavenged such that the NN model of Ai (denoted mi) can be loaded, in Step 13, it enacts all the NN model replacement decisions and then loads mi in Step 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the event that the scavenged memory is insufficient, the policy switches to the next NN model for Ai that has a lower size and accuracy (Step 17).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In the worst case that even the smallest NN model of Ai cannot fit in the memory, the inference request fails (Step 17) [120].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 135 Algorithm 7: Pseudo-code for iWS-BFE NN model eviction policy 1 Function iWS-BFE(A′, A∗, Ai, H) 2 τ ← Select ∀A′ j ∈ A′ not requested during H 3 E ← Determine ∀A′ j ∈ τ non-overlapping with request window of Ai 4 ∀Ek ∈ E calculate fitness score using Equation 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Build max-heap tree of E based on fitness score ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='while size(mi) > available memory do ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='w ← Extract root of the max-heap tree ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='If w = ∅ then break the loop ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Measure memory scavenged by replacing model of w with its ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='lowest-precision one ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Add scavenged amount to available memory ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='11 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='end ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='12 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='if size(mi) ≤ available memory then ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='13 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Enact NN model replacement(s) decisions ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='14 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Scavenge the leftover memory to load mi ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='15 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='end ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='16 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='else ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='17 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='If there is no model left to check then the inference request fails ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='18 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Repeat Step 6—10 with the next (smaller) model ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='19 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='end ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='20 end ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='136 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Application-specific models with different precision variants that are experimented.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Application NN Model Bit Width Size (MB) Accuracy (%) Face recognition VGG-Face FP32 535.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 FP16 378.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 INT8 144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8 Image classification VIT-base-patch16 FP32 346.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 FP16 242.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 INT8 106.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Speech recognition S2T-librisspeech FP32 285.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 FP16 228.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 INT8 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 Sentence prediction Paraphrase-Mini LM-L12-v2 FP32 471.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 FP16 377.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 INT8 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Text classification Roberta-base FP32 499.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 FP16 392.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 INT8 132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 Performance Evaluation 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Experimental Setup and Evaluation MetricsTo evaluate the efficacy of Edge-MultiAI and its NN model eviction policies, we benchmarked five different DL applications, namely face recognition, speech recognition, image classification, next sentence prediction, and text classification, and recorded their real characteristics, including the model size, and the inference accuracy (shown in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We have developed the E2C simulator that enables modeling the IoT-based systems with different characteristics and configurations, and is available publicly for the community access through our Github pagea.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The simulator has implemented all of the NN model eviction policies, and the user can quickly deploy and examine any one of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The simulator also enables us to generate workload traces that include the aGithub page of the E2C simulator: https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/hpcclab/E2C-Sim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='git 137 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The impact of Edge-MultiAI and its iWS-BFE eviction policy on satis- fying the requested multi-tenancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The large graph represents the summative analysis via increasing the mean of multi-tenancy requested in the horizontal axis, and showing the percentage of requests that were satisfied in the vertical axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For each case, the smaller graph more granularly represents the number of concurrent requests issued and fulfilled during the simulation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='mean requested degree of multi-tenancy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='multi-tenancy satisfication rate (%) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='simulation time ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='degree of multi-tenancy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='#of request ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='iWS-BFE ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='no policy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='simulation time ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='degree of multi-tenancy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='#of request ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='iWS-BFE ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='no policy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='simulation time ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='degree of multi-tenancy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='#of request ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='iWS-BFE ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='no policy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='simulation time ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='degree of multi-tenancy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='#of request ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='iWS-BFE ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='no policy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='simulation time ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='degree of multi-tenancy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='#of request ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='iWS-BFE ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='no policy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='simulation time ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='degree of multi-tenancy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='#of request ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='iWS-BFE ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='no policy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2000 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='request arrival times for each application during the simulation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We configure the actual workload to include an equal number of requests for the five applications, and the inter-arrival times between requests for each application are distributed exponentially within the workload.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To study the uncertainty exists in the inference request predictions, in the evaluations, we generate two sets of workloads, one includes the predicted arrival times for the multi-tenant applications, and the other one includes the actual arrival times of the applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The distribution of request arrivals in the actual workload deviates from the distribution of requests in the predicted workload.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The degree of deviation between the two is measured based on the Kullback-Leibler (KL) [121] divergence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We explore the impact of this deviation in the experiments of next subsections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 138 Our evaluation metrics are: (A) The degree of multi-tenancy under different request arrival intensity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' (B) The inference latency;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' (C) the inference accuracy;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' and (D) The robustness metric to measure the tolerance of different eviction policies against the uncertainty exists in the request predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Impact of Edge-MultiAI on the Degree of Multi-tenancy This experiment is to examine the efficacy of Edge-MultiAI in satisfying the incoming requests to the edge server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To that end, as shown in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4, we increased the workload intensity, via the mean number of concurrent requests issued, and in each case measured the multi-tenancy satisfaction rate, which is the percentage of warm-start inferences out of the total incoming requests during the simulation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We examined two cases: (A) without any solution to stimulate multi-tenancy (called, no policy);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' and (B) with Edge-MultiAI and its iWS-BFE policy in place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The experiment was repeated 10 times and the average rate and 95% confidence intervals for each data point is reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The experiment shows that the degree of multi-tenancy achieved by adopting Edge-MultiAI and its iWS-BFE is remarkably higher than the situation where Edge-MultiAI is not in place.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The smaller graphs show that this superiority occurs consistently during the simulation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We also notice that the impact of employing Edge-MultiAI is more effective for higher degrees of multi-tenancy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In particular, we can see that with the mean degree of multi-tenancy is 5, using Edge-MultiAI and its iWS-BFE policy achieves ≈130% higher satisfaction rate than no policy when mean requested degree of multi-tenancy is larger than 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This 139 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Measuring the percentage of cold-start inferences of multi-tenant appli- cations resulted from the proposed eviction policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The horizontal axis shows the deviation between predicted and actual inference request times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 0% 20% 30% 60% 90% deviation of actual workload from prediction (%) 0 10 20 30 40 50 60 70 cold-start inferences (%) LFE BFE WS-BFE iWS-BFE experiment justifies the efficacy of Edge-MultiAI and the NN model management in stimulating multi-tenancy of DL applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Impact of the Eviction Policies on the Cold-Start Inference The purpose of this experiment is to analyze the impact of different NN model eviction policies on the number of cold-start inferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For that purpose, we measure percentage of cold-start inferences caused by employing different eviction policies, particularly, upon varying the deviation of request prediction from the actual requests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The results, illustrated in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5, show that LFE and BFE perform poorly and cause a remarkable number of cold-start inferences, whereas, WS-BFE and iWS-BFE mitigate the cold-start inferences by at least 65%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is because, in 140 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Measuring the normalized inference accuracy of applications resulted from employing the different eviction policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 0% 20% 30% 60% 90% deviation of actual workload from prediction (%) 0 10 20 30 40 50 60 70 80 normalized inference accuracy (%) LFE BFE WS-BFE iWS-BFE LFE and BFE, upon evicting an NN model, its corresponding application suffers from a cold-start inference in the event of an unpredicted request.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In contrast, in WS-BFE and iWS-BFE, the evicted model is replaced with a low-precision one, hence, unpredicted calls to the corresponding application do not lead to cold-start inferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It is noteworthy that, regardless of the employed policy, the percentage of cold-start inferences rises upon increasing the deviation between predicted and actual request times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Nonetheless, we see that even under 90% deviation, iWS-BFE still substantially outperforms other policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' On average, it yields 102% less cold-start in compare to LFE and BFE, and 40% less than WS-BFE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Impact of the Eviction Policies on the Inference Accuracy In this experiment, we analyze the average inference accuracy caused by employing different model eviction policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Because the accuracy largely varies 141 across different applications, we perform min-max normalization on the accuracy values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Also, for the cold-start inferences, in the accuracy measurements, we consider the accuracy provided by the NN model after it is loaded into the memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 shows the normalized mean inference accuracy obtained from employing different NN model eviction policies upon changing the deviation between predicted and actual request times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' According to the figure, LFE and BFE policies outperform WS-BFE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is because, these two policies do not retain the low-precision models in the memory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Therefore, their inference requests either lead to a cold-start (that was explored in the previous experiment), or they load high-precision models that provide a high inference accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Nonetheless, we observe that iWS-BFE outperforms LFE and BFE in most of the cases, except the one with 90% deviation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The reason for the higher inference accuracy of iWS-BFE is that, it nominates cold-start candidates intelligently, based on their probability of future invocations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This results indicate the importance of the scoring (described in Equation 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3) on efficiently nominating cold-start candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It is noteworthy that the higher inference accuracy of LFE and BFE at 90% deviation comes with the cost of substantially higher cold-start inferences that are detrimental to the “usability” of the IoT-based systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Bi-Objective Analysis of NN Model Eviction Policies Recall that the NN model management for multi-tenant applications in a resource-limited edge system is a bi-objective optimization problem that aims at minimizing the number of cold-start inferences and maximizing the inference 142 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Bi-objective analysis of the different model selection policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' However, these two are generally conflicting objectives and there is not a single optimal solution that can satisfy both objectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Instead, there could be a range of solutions that dominate other solutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To analyze which one of the studied policies dominate others, in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7, we plot the percentage of cold-start inferences versus the model error (defined as 100-accuracy) for different policies and ∆ values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Let D and σ be the mean and standard deviation of residuals of predicted versus actual request times.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Then, ∆ = D ± α· σ ranges by changing the value of 0 ≤ α ≤ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The deviation of actual versus predicted workload in this experiment is 30%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For each policy, the colored area shows the cold-start inferences and model error rate that are dominated by that policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' An ideal policy should approach the graph origin (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', resulting in zero cold-start and zero model error).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7, we observe that Edge-MultiAI dominates other policies and form the Pareto-front, 143 100 cold-start inference (%) 80 60 LFE BFE 40 20 WS-BFE iWS-BFE α= 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='02 0 0 20 40 60 08 100 model error (%)particularly with α = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='02.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We can conclude that the iWS-BFE policy can significantly improve the usability of the systems via causing fewer cold-start inferences and offering a higher inference accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6 Analyzing Robustness against Uncertainties The goal of this experiment is to study how the eviction policies of Edge-MultiAI make the IoT-based system robust against the uncertainty exists between the predicted and actual application request predictor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We define the robustness metric, shown in Equation 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4, to encompass the ratio of warm-start inferences (denoted ϖi) to the total number of requests (denoted γi), and the mean prediction accuracy (ψi) of each application i throughout the simulation period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' R = 1 n· n � i=1 �ϖi γi ψi � (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4) Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8 represents the robustness score achieved by adopting the proposed policies and no policy (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' baseline) against uncertainties in the inference request prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We observe that deploying Edge-MultiAI with any policy provides more robustness than the circumstance where Edge-MultiAI is not in place (no policy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We also notice that the robustness value consistently drops because the rate of inference failure and cold-starts rise for higher deviations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We observe that WS-BFE and iWS-BFE are more robust against deviation than the LFE and BFE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This is because, LFE and BFE do not replace their NN models with a lower-precision one upon eviction, which leads to cold-start inferences for the applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 144 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Robustness of the system against uncertainty in the prediction of infer- ence requests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 0 20% 30% 60% 90% deviation of actual workload from prediction (%) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 robustness LFE BFE WS-BFE iWS-BFE no policy 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 Evaluating the Fairness of NN Model Eviction Policies In this experiment, our goal is to examine whether the achievements of Edge-MultiAI and its policies, explored in the previous experiments, is fairly distributed across all applications, or some applications benefit more than the others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' To that end, we analyze the distribution of cold-start inference and accuracy across different DL applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The name and the NN model characteristics of the examined DL applications are listed in Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Figures 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9 and 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10, respectively, express the percentage of cold-start inferences and inference accuracy for each application upon using various NN model eviction policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' It is noteworthy that in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9, “no policy” indicates the situation where Edge-MultiAI is not in place, and in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10, “maximum” serve as the benchmark, by showing the use of highest-precision NN model for each application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' While Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9 shows that 145 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The percentage of cold-start inferences using different NN model eviction policies versus no policy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' face recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' speech recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' image class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' sent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' pred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' text class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 0 20 40 60 80 cold-start inferences (%) LFE BFE WS-BFE iWS-BFE no policy WS-BFE and iWS-BFE remarkably outperform the other policies across all the applications, Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10 illustrates that, particularly for iWS-BFE, the outperformance does not come with the cost of lower inference accuracy for the applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' More importantly, in both figures, we observe that, for each policy, the percentage of cold-start inferences and accuracy do not fluctuate significantly from one application to the other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This shows that policies are not biased to any particular DL application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Specifically, the rate of cold-start inferences and the accuracy are fairly distributed across different applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 146 Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The inference accuracy obtained from the different policies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The “maximum” is the benchmark, showing the accuracy of the highest-precision model for each application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' face recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' speech recog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' image class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' sent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' pred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' text class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 0 20 40 60 80 normalized inference accuracy (%) maximum LFE BFE WS-BFE iWS-BFE 147 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='7 Summary Smart IoT-based systems often desire continuous execution of multiple latency-sensitive Deep Learning (DL) applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The edge servers serve as the cornerstone of such IoT-based systems, however, their resource limitations hamper the continuous execution of multiple (multi-tenant) DL applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The research aims to stimulate the degree of multi-tenancy of such applications without compromising their latency and accuracy objectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We developed a framework, called Edge-MultiAI, to facilitate multi-tenancy of DL applications via enabling swapping only their NN models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The framework was also equipped with model management policies, particularly iWS-BFE, to choose suitable models for eviction and loading to edge memory, such that the percentage of warm-start inferences is maximized without any major loss in the inference accuracy of the applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Evaluation results indicate that Edge-MultiAI can improve the degree of multi-tenancy by 2×, and iWS-BFE can increase warm-start inferences by 60%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' They also show how different policies are robust against uncertainty in the inference request predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Last but not the least, the experiments show that the policies are not biased to a certain application in their decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 148 Chapter 6: Conclusion and Future Research Directions This chapter summarizes the research and major findings of this dissertation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Additionally, research topics that have surfaced during this research but have not been covered in this dissertation are brought up and discussed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' These potential pathways for the future can be investigated further by other researchers working in this field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Discussion In this dissertation, our main objective was to enable confidential computing across edge-to-cloud continuum by maintaining data integrity and confidentiality during executions that span across the continuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We provide three trusted applications to perform secure clustering and semantic searching over confidential data without revealing any meaningful information to any off-premise tiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In addition, for model management of DL applications, we develop a framework that can effectively facilitate multi-tenancy of DL applications via enabling swapping only their NN models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Chapter 3, we developed solutions for topic-based clustering of both static (ClustCrypt and S-ClusPr) and dynamic unstructured encrypted big datasets (SD-ClusPr and FD-ClusPr).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The proposed solutions approximate the number of clusters for a dataset within a feasible time complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For that purpose, they leverage the tokens’ co-occurrences to measures the tendency of each token to stay with or segregate from other tokens and use that to estimate the number of clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Next, we develop a probabilistic approach to determine the center of each cluster 149 and disseminate encrypted tokens to the most topically related cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Experimental evaluations reveal that for static datasets, S-ClusPr can improve the clustering coherency on average by 65%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Similarly, for semi-dynamic and dynamic datasets, SD-ClusPr and FD-ClusPr can improve the coherency by 55%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' By incorporating ClustCrypt and ClusPr within the context of a secure semantic search system, we learned that the more coherent and accurate topic-based clustering can improve the relevancy of search results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In Chapter 4, we propose an open-source generic pluggable module, namely SAED into existing search services (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', AWS kendra, S3BD) to perform context-aware, personalized, and secure search without dictating any change on them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' SAED can search over the data that is either plain-text or encrypted using client side encryption before outsourcing to the cloud (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', AWS S3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Upon verified by human users, experimental evaluations indicate SAED can improve the relevancy of the retrieved results by on average ≈ 24% for plain-text and ≈ 75% for encrypted datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Our solution in Chapter 4 entailed continuously and simultaneously maintaining multiple DL models that process confidential user data on the trusted edge tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' This was challenging considering the memory limitations on the edge tier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Moreover, such ML models could not be outsourced to Clouds because of the user’s privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' As such in Chapter 5, we propose a framework, namely Edge-MultiAI that that operates based on the idea of approximate computing and ushers the NN models of the DL applications into the edge memory such that the degree of 150 multi-tenancy and the number of warm-starts are maximized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Edge-MultiAI leverages NN model compression techniques, such as model quantization, and dynamically loads NN models for DL applications to stimulate multi-tenancy on the edge server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We also devise a model management heuristic for Edge-MultiAI, called iWS-BFE, that functions based on the Bayesian theory to predict the inference requests for multi-tenant applications, and uses it to choose the appropriate NN models for loading, hence, increasing the number of warm-start inferences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We evaluate the efficacy and robustness of Edge-MultiAI under various configurations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Evaluation results indicate that Edge-MultiAI can improve the degree of multi-tenancy by 2×, and iWS-BFE can increase warm-start inferences by 60%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' They also show how different policies are robust against uncertainty in the inference request predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Last but not the least, the experiments show that the policies are not biased to a certain application in their decisions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Future Research Directions Based on our findings during the exploration of AI-driven confidential computing paradigm across the edge-to-cloud continuum, there are several points where the work could be expanded upon that were not covered in this dissertation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='1 Hierarchical Clustering of unstructured Data We can employ active learning to enable the automatic hierarchical clustering of tokens with similar topics [122, 123, 124].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The active learning paradigm was inspired by situations in which it is simple to collect enormous quantities of unlabeled data (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', pictures and videos downloaded from the internet, 151 speech signals obtained from recordings made with microphones, and so on), but it is difficult or expensive to gain their labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We can exploit the meaning of the deciphered tokens and their distributions in the available clusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' With this information, we incorporate Wikipedia knowledge to formulate hierarchical relationships among the tokens across the confidential dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Later, for new a token, we measure the relatedness between the token and the representation of each topic to propagate the hierarchy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2 Building Classifier from the Encrypted Clusters Clustering is a classic unsupervised learning that groups a massive amount of unlabeled data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We can employ active learning on the clusters to build a classifier that potentially increases the use-cases in trusted computing for unstructured data paradigm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Active learning can leverage the knowledge while querying on cluster to measure the relatedness with the new token to form a decision boundary of a classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' The resultant classifier offers substantially lower cost than traditional supervised learning [122].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='3 Introducing Elasticity in Confidential SearchThe current implementation of SAED framework needs dependency of a connected edge server to facilitate the searching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' One idea is to including flexibility in the framework which will reduce the burden of edge communication with acceptable performance degradation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' For instance, when the user is on the move and does not have access to the edge, SAED should shrink to the bare minimum search intelligence and vice versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 152 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='4 Adding Energy in Model Management Schemes In Edge-MultiAI, NN model management for multi-tenant applications in a resource-limited edge system is a bi-objective optimization problem that aims at minimizing the number of cold-start inferences and maximizing the inference accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Since the edge servers have limited energy, often use battery, considering energy is crucial to assign a job on an edge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Otherwise, due to dead battery, the system could be abruptly switched off that leads to execution failure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Subsequently, we can add the energy as a third objective into the problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this way, we frame the problem as maximizing the warm-starts and total accuracy with memory size and energy budget as constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='5 Cloud Offloading for Latency-tolerant Applications We only consider low-latency applications in Edge-MultiAI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' We can also add offloading option to the cloud tier in the framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' In this way, the system could decide whether processing a task locally (probably with a few cold-starts) is more beneficial (in terms of latency and energy consumption) or offloading it to the cloud server.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 153 Bibliography [1] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zobaed, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ahmad, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Gottumukkala, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Salehi, “Clustcrypt: Privacy-preserving clustering of unstructured big data in the cloud,” in Proceedings of the 21st International Conference on High Performance Computing and Communications (HPCC), 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 609–616.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [2] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Seth, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Dalal, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Jaglan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Le, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Mohan, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Srivastava, “Integrating encryption techniques for secure data storage in the cloud,” Transactions on Emerging Telecommunications Technologies, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 33, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' e4108, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [3] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Jason and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Salehi, “S3BD: secure semantic search over encrypted big data in the cloud,” Journal of Concurrency and Computation:Practice and Experience (CCPE), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 28, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 11, December 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [4] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Sun, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Lou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hou, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Li, “Privacy-preserving keyword search over encrypted data in cloud computing,” in Secure cloud computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Springer, 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 189–212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [5] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhu and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Li, “Privacy-preserving k-means clustering with local synchronization in peer-to-peer networks,” Journal of Peer-to-Peer Networking and Applications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 13, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 6, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [6] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Al-Muhtadi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Shahzad, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Saleem, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Jameel, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Orgun, “Cybersecurity and privacy issues for socially integrated mobile healthcare applications operating in a multi-cloud environment,” Jounral of Health informatics journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 25, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 315–329, May 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [7] “The 15 biggest data breaches of the 21st century,” www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='csoonline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/article/2130877/data-breach/ the-biggest-data-breaches-of-the-21st-century.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='html, November, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [8] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zobaed and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Salehi, “Big data in the cloud,” in Encyclopedia of Big Data, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Schintler and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' McNeely, Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Springer, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [9] “Every Single Yahoo Account Was Hacked,” www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='money.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='cnn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/2017/10/ 03/technology/business/yahoo-breach-3-billion-accounts/index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='html, Accessed May, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [10] “Cloud leak: How a verizon partner exposed millions of customer accounts,” www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='upguard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/breaches/verizon-cloud-leak, Accessed April, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [11] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Shepherd, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Arfaoui, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Gurulian, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Lee, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Markantonakis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Akram, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Sauveron, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Conchon, “Secure and trusted execution: Past, present, and future-a critical review in the context of the internet of things 154 and cyber-physical systems,” in 2016 IEEE Trustcom/BigDataSE/ISPA, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 168–177.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [12] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ning, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Liao, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhang, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Shi, “Preliminary study of trusted execution environments on heterogeneous edge platforms,” in Proceedings of Symposium on Edge Computing (SEC), 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 421–426.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [13] “Confidential computing – the next frontier in data security,” https://confidentialcomputing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='io/wp-content/uploads/sites/85/2021/10/ Everest Group - Confidential Computing - The Next Frontier in Data Security - 2021-10-19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='pdf, Accessed July 5, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [14] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Deng, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhao, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Fang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Yin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Dustdar, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zomaya, “Edge intelligence: The confluence of edge computing and artificial intelligence,” Journal of IEEE Internet of Things, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 7457–7469, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [15] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zobaed, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Salehi, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Buyya, “Saed: Edge-based intelligence for privacy-preserving enterprise search on the cloud,” in 2021 IEEE/ACM 21st International Symposium on Cluster, Cloud and Internet Computing (CCGrid).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' IEEE, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 366–375.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [16] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hussain, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Pakravan, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Salehi, “Analyzing the performance of smart industry 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='0 applications on cloud computing systems,” in proceeginds of 22nd IEEE International Conference on High Performance Computing and Communications (HPCC), 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 11–18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [17] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ahmad, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zobaed, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Gottumukkala, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Salehi, “Edge computing for user-centric secure search on cloud-based encrypted big data,” in Proceedings of the 21st International Conference on High Performance Computing and Communications (HPCC), August 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 662–669.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [18] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Almalki, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Alsamhi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Sahal, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hassan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hawbani, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Rajput, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Saif, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Morgan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Breslin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', “Green iot for eco-friendly and sustainable smart cities: future directions and opportunities,” Mobile Networks and Applications, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1–25, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [19] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Mokhtari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hossen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Jamshidi, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Salehi, “FELARE: fair scheduling of machine learning applications on heterogeneous edge systems,” in Proceedings of International Conference On Cloud Computing, July 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [20] “Protecting data using client-side encryption,” https://docs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='aws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='amazon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/ AmazonS3/latest/userguide/UsingClientSideEncryption.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='html, Accessed November, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [21] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Pham, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Woodworth, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Amini Salehi, “Survey on secure search over encrypted data on the cloud,” Journal of Concurrency and Computation: Practice and Experience, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 31, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 17, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' e5284, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 155 [22] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Long, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Dai, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Liang, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Imran, “Lightweight searchable encryption protocol for industrial internet of things,” Transactions on Industrial Informatics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4248–4259, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chen, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Huang, “Se-ppfm: A searchable encryption scheme supporting privacy-preserving fuzzy multikeyword in cloud systems,” Journal of Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 15, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2980–2988, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [24] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Salehi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Caldwell, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Fernandez, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Mickiewicz, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Rozier, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zonouz, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Redberg, “RESeED: a secure regular-expression search tool for storage clouds,” Journal of Software: Practice and Experience, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 47, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1221–1241, September 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [25] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Valadares, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' da Silva, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Brito, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Salvador, “Achieving data dissemination with security using fiware and intel software guard extensions (sgx),” in Proceedings of IEEE Symposium on Computers and Communications (ISCC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' IEEE, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1–7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [26] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Kehoe, “Mapping security requirements to enterprise search - part 1: Defining specific security requirements,” http://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='ideaeng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/security-eprise-search-p1-0304, 2009, [Online;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' accessed 16-February-2020].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [27] “Announcing amazon kendra: Reinventing enterprise search with machine learning,” https://aws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='amazon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/about-aws/whats-new/2019/12/ announcing-amazon-kendra-reinventing-enterprise-search-with-machine-learning/, 2019, [Online;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' accessed 16-February-2020].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [28] “Azure cognitive services,” https://azure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='microsoft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/en-us/services/cognitive-services, Accessed April, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [29] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Yu, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Liang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' He, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hatcher, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Lu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Lin, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Yang, “A survey on the edge computing for the internet of things,” Journal of IEEE access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 6900–6919, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [30] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Gong, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Lin, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Gong, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Lu, “Intelligent cooperative edge computing in internet of things,” Journal of Internet of Things, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 7, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 9372–9382, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [31] Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='-V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Dang and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ignat, “dtrust: a simple deep learning approach for social recommendation,” in proceedings of 3rd International Conference on Collaboration and Internet Computing (CIC), 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 209–218.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [32] “Jetson nano developer kit,” https://developer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='nvidia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/embedded/jetson-nano-developer-kit, Accessed November, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 156 [33] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Gholami, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Kim, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Dong, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Yao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Mahoney, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Keutzer, “A survey of quantization methods for efficient neural network inference,” in Journal of Low-Power Computer Vision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chapman and Hall/CRC, 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 291–326.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [34] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhu, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Castiglione, “Efficient k-nn query over encrypted data in cloud with limited key-disclosure and offline data owner,” Computers & Security, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 69, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 84–96, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [35] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Tarpey, “Linear transformations and the k-means clustering algorithm: applications to clustering curves,” Journal of the american statistician, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 61, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 34–40, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [36] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Sun, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Li, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Lou, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hou, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Li, “Privacy-preserving multi-keyword text search in the cloud supporting similarity-based ranking,” in Proceedings of the 8th symposium on Information, computer and communications security, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' SIGSAC’13, May 2013, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 71–82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [37] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Gai and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Qiu, “Blend arithmetic operations on tensor-based fully homomorphic encryption over real numbers,” Transactions on Industrial Informatics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 14, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3590–3598, August 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [38] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Xing, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Yu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cheng, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhang, “Mutual privacy preserving k-means clustering in social participatory sensing,” Transactions on Industrial Informatics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 13, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2066–2076, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [39] H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Pang and B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang, “Privacy-preserving association rule mining using homomorphic encryption in a multikey environment,” Systems Journal, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 15, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3131–3141, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [40] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Li, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Li, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Huang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Gao, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chen, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chen, “Privacy-preserving outsourced classification in cloud computing,” Journal of Cluster Computing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 277–286, March 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [41] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Liu, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Xu, “Research on k-means clustering algorithm over encrypted data,” in Proceedings of International Symposium on Cyberspace Safety and Security, December 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 182–191.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [42] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ducas and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Micciancio, “FHEW: Bootstrapping homomorphic encryption in less than a second,” in Advances in Cryptology, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' EUROCRYPT’15, April 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 617–640.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [43] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Vaidya and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Clifton, “Privacy-preserving k-means clustering over vertically partitioned data,” in Proceedings of the 9th international conference on Knowledge discovery and data mining, 2003, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 206–215.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 157 [44] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Song, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wagner, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Perrig, “Practical techniques for searches on encrypted data,” in Proceedings of international symposium on security and privacy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' S&P 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' IEEE, 2000, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 44–55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [45] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Boneh, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Crescenzo, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ostrovsky, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Persiano, “Public key encryption with keyword search,” in Proceedings of international conference on the theory and applications of cryptographic techniques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Springer, 2004, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 506–522.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [46] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cao, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Yang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ren, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Lou, “Privacy-preserving query over encrypted graph-structured data in cloud computing,” in Proceedings of the 31st International Conference on Distributed Computing Systems, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' ICDCS ’11, Washington, DC, USA, 2011, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 393–402.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [47] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Popa, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Redfield, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zeldovich, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Balakrishnan, “Cryptdb: processing queries on an encrypted database,” Journal of Communications of the ACM, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 55, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 103–111, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [48] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Rozier, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zonouz, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Redberg, “Dragonfruit: Cloud provider-agnostic trustworthy cloud data storage and remote processing,” in Proceedings of 19th Pacific Rim International Symposium on Dependable Computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' IEEE, 2013, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 172–177.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [49] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ahmadian, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Plochan, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Roessler, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Marinescu, “Securenosql: An approach for secure search of encrypted nosql databases in the public cloud,” Jounal of International Journal of Information Management, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 37, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 63–74, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [50] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Kettouch, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Luca, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hobbs, “Semild: mediator-based framework for keyword search over semi-structured and linked data,” Journal of Intelligent Information Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 52, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 311–335, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [51] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Naseriparsa, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Islam, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Liu, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chen, “Xsnippets: Exploring semi-structured data via snippets,” Journal of Data & Knowledge Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 124, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 101758, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [52] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Curtmola, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Garay, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Kamara, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ostrovsky, “Searchable symmetric encryption: improved definitions and efficient constructions,” in Proceedings of the 13th ACM conference on Computer and communications security, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' CCS ’06, 2006, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 79–88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [53] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Woodworth, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Salehi, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Raghavan, “S3c: An architecture for space-efficient semantic search over encrypted data in the cloud,” in Proceedings of the 4th International Conference on Big Data, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Big Data’16, December 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3722–3731.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 158 [54] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zobaed and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Amini Salehi, “Privacy-preserving clustering of unstructured big data for cloud-based enterprise search solutions,” Journal of Concurrency and Computation: Practice and Experience, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 34, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 22, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' e7160, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [55] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Li, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cao, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ren, and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Lou, “Fuzzy keyword search over encrypted data in cloud computing,” in Proceedings of the 29th International Conference on Computer Communications, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' INFOCOM ’10, March 2010, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1–5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [56] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Moataz, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Shikfa, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cuppens-Boulahia, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cuppens, “Semantic search over encrypted data,” in Proceedings of International Conference on Telecommunications (ICT), May 2013, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1–5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [57] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Sun, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhu, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Xia, and L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chen, “Privacy preserving keyword based semantic search over encrypted cloud data,” Journal of Security and Its Applications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 8, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3, May 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [58] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Liang, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Qiang, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Yang, “Exploiting real-time information retrieval in the microblogosphere,” in Proceedings of the 12th ACM/IEEE-CS joint conference on Digital Libraries, June 2012, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 267–276.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [59] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Huang, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Feng, “Query expansion with local conceptual word embeddings in microblog retrieval,” IEEE Transactions on Knowledge and Data Engineering, October 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [60] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Deerwester, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Dumais, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Furnas, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Landauer, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Harshman, “Indexing by latent semantic analysis,” Journal of the American society for information science, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 41, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 391–407, September 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [61] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Albishre, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Li, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Xu, “Effective pseudo-relevance for microblog retrieval,” in Proceedings of the Australasian Computer Science Week Multiconference, January 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1–6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [62] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Diaz, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Mitra, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Craswell, “Query expansion with locally-trained word embeddings,” in Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), August 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 367–377.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [63] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Mikolov, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Corrado, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Dean, “Efficient estimation of word representations in vector space,” www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='pub-tools-public-publication-data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' storage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='googleapis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/pdf/41224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='pdf, 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [64] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Miller, “Wordnet: a lexical database for english,” Journal of Communications of the ACM, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 38, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 39–41, 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [65] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Song, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Song, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hu, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Allen, “Integration of association rules and ontologies for semantic query expansion,” Journal of Data & Knowledge Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 63, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 63–75, October 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 159 [66] V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Nakade, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Musaev, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Atkison, “Preliminary research on thesaurus-based query expansion for twitter data extraction,” in Proceedings of the Southeast Regional Conference, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' ACMSE’18, March 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1–4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [67] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Leung, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Li, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Milani, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Franzoni, “Collective evolutionary concept distance based query expansion for effective web document retrieval,” in Proceedings of the International Conference on Computational Science and Its Applications, June 2013, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 657–672.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [68] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chen and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ran, “Deep learning with edge computing: A review,” Proceedings of the IEEE, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 107, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1655–1674, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [69] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Murshed, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Murphy, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hou, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Khan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ananthanarayanan, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hussain, “Machine learning at the network edge: A survey,” Journal of ACM Computing Surveys (CSUR), vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 54, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1–37, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [70] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhou, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chen, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Li, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zeng, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Luo, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhang, “Edge intelligence: Paving the last mile of artificial intelligence with edge computing,” Journal of the IEEE Access, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 107, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1738–1762, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [71] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Han, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Leung, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Niyato, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Yan, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chen, “Convergence of edge computing and deep learning: A comprehensive survey,” IEEE Communications Surveys & Tutorials, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 22, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 869–904, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [72] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Mao, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Nixon, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Krieger, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chen, “Modnn: Local distributed mobile computing system for deep neural network,” in Proceedings of Design, Automation & Test in Europe Conference & Exhibition (DATE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' IEEE, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1396–1401.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [73] K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ko, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Son, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Kim, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Lee, “Disco: A distributed and concurrent offloading framework for mobile edge cloud computing,” in Proceedings of 9th international conference on ubiquitous and future networks (ICUFN), 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 763–766.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [74] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hadidi, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cao, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Woodward, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ryoo, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Kim, “Distributed perception by collaborative robots,” IEEE Robotics and Automation Letters, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3709–3716, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [75] L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Xie, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Markham, and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Trigoni, “Towards monocular vision based obstacle avoidance through deep reinforcement learning,” arXiv preprint arXiv:1706.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='09829, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [76] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Yao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhao, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Su, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Abdelzaher, “DeepIoT: Compressing deep neural network structures for sensing systems with a compressor-critic framework,” in Proceedings of the 15th ACM Conference on Embedded Network Sensor Systems, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1–14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 160 [77] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ma, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Xiang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zheng, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Tian, and X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Liu, “Moving deep learning into web browser: How far can we go?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' in Proceedings of the 19th World Wide Web Conference (WWW), May 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1234–1244.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [78] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Paladhi, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Kumar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Reddy, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Vinayak, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Pusphavathi, “Enhanced possibilistic c-means clustering on big data while ensuring security,” in International Conference on Computer Networks and Communication Technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Springer, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 583–588.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [79] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Samantaray, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Randhawa, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Pati, “An efficient multi-keyword text search over outsourced encrypted cloud data with ranked results,” in Computational Intelligence in Data Mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Springer, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 31–40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [80] W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Diffie and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hellman, “New directions in cryptography,” Transactions on Information Theory, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 22, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 644–654, November 1976.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [81] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Can and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ozkarahan, “Concepts and effectiveness of the cover-coefficient-based clustering methodology for text databases,” Journal of ACM Trans.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Database Syst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 15, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 483–517, December 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [82] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cutting, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Karger, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Pedersen, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Tukey, “Scatter/gather: A cluster-based approach to browsing large document collections,” in ACM SIGIR Forum, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 51, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2, August 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 148–159.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [83] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Aggarwal, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Agarwal, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Jain, “Performance analysis of uncertain k-means clustering algorithm using different distance metrics,” in Computational Intelligence: Theories, Applications and Future Directions-Volume I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Springer, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 237–245.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [84] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Liu and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Croft, “Cluster-based retrieval using language models,” in Proceedings of the 27th International ACM SIGIR Conference on Research and Development in Information Retrieval, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' SIGIR ’04, July 2004, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 186–193.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [85] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Aggarwal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hinneburg, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Keim, “On the surprising behavior of distance metrics in high dimensional space,” in Proceedings of the 8th International conference on database theory, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' ICDT ’01, January 2001, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 420–434.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [86] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Mary and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Kumar, “A density based dynamic data clustering algorithm based on incremental dataset,” Journal of Computer Science, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 8, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 656–664, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [87] “The Museum of Modern Art Data,” tapoueh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='org/blog/2018/07/batch-updates-and-concurrency, Accessed May ,2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 161 [88] “Twitter stream api dataset,” github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/shreybatra/Twitter-Stream-API-Dataset, Accessed March, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [89] “Statistics Solution,” www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='statisticssolutions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/using-chi-square-statistic-in-research/, Accessed July 15, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [90] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Popa, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Redfield, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zeldovich, and H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Balakrishnan, “Cryptdb: Protecting confidentiality with encrypted query processing,” in Proceedings of the 23rd ACM Symposium on Operating Systems Principles, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' SOSP ’11, October 2011, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 85–100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [91] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang, “Offline dictionary attack on password authentication schemes using smart cards,” in Information Security.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Springer International Publishing, 2015, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 221–237.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [92] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Naehrig, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Lauter, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Vaikuntanathan, “Can homomorphic encryption be practical?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' in Proceedings of the 3rd ACM Workshop on Cloud Computing Security Workshop, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' CCSW ’11, October 2011, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 113–124.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [93] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' George, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Kamara, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Moataz, “Structured encryption and dynamic leakage suppression,” in Proceedings of Annual International Conference on the Theory and Applications of Cryptographic Techniques, October 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 370–396.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [94] “Common Crawl on Amazon Web Services (AWS),” https://aws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='amazon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/public-datasets/common-crawl/, Accessed February, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [95] “RFC (request for comments) series,” old.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='datahub.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='io/dataset/rfcs, Accessed March, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [96] “BBC news classification,” www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='kaggle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/c/learn-ai-bbc, Accessed March, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [97] O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Medelyan, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Frank, and I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Witten, “Human-competitive tagging using automatic keyphrase extraction,” in Proceedings of the 14th Conference on Empirical Methods in Natural Language, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' EMNLP ’09, August 2009, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1318–1327.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [98] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Berkhin, “A survey of clustering data mining techniques,” in Grouping multidimensional data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Springer, 2006, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 25–71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [99] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Miller, “Wordnet: a lexical database for english,” Journal of Communications of the ACM, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 38, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 39–41, November 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 162 [100] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Rodriguez, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Comin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Casanova, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Bruno, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Amancio, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Costa, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Rodrigues, “Clustering algorithms: A comparative approach,” Journal of PloS one, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 14, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' e0210236, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [101] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Kwon, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Eysenbach, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Verma, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ng, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' De Filippi, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Stewart, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Perer, “Clustervision: Visual supervision of unsupervised clustering,” IEEE transactions on visualization and computer graphics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 24, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 142–151, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [102] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Mariappan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Suresh, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Bharathi, “A comparative study on the effectiveness of semantic search engine over keyword search engine using tsap measure,” Journal of Computer Applications EGovernance and Cloud Computing Services, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4–6, December 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [103] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Amini Salehi, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Caldwell, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Fernandez, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Mickiewicz, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Redberg, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Rozier, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zonouz, “RESeED: Regular Expression Search over Encrypted Data in the Cloud,” in Proceedings of the 7th International Cloud conference, ser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cloud ’14, June 2014, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 673–680.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [104] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Silva and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Mendoza, “Improving query expansion strategies with word embeddings,” in Proceedings of the ACM Symposium on Document Engineering, September 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [105] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Kuzi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Shtok, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Kurland, “Query expansion using word embeddings,” in Proceedings of the 25th international on conference on information and knowledge management, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [106] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Fellbaum, “Wordnet: An electronic lexical resource,” in The Oxford Handbook of Cognitive Science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Routledge, 2017, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 301–314.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [107] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Campos, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Mangaravite, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Pasquali, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Jorge, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Nunes, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Jatowt, “YAKE!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' collection-independent automatic keyword extractor,” in Proceedings of the 40th European Conference on Information Retrieval, March 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 806–810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [108] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Khatua, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Khatua, and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cambria, “A tale of two epidemics: Contextual word2vec for classifying twitter streams during outbreaks,” Journal of Information Processing & Management, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 56, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 247–257, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [109] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Kastrati, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Imran, and S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Yayilgan, “The impact of deep learning on document classification using semantically rich representations,” Journal of Information Processing & Management, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 56, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1618–1632, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [110] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Pang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhou, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Lin, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chang, “An innovative neural network approach for stock market prediction,” The Journal of Supercomputing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 76, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2098–2118, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 163 [111] “Vanilla recurrent neural network,” http://calvinfeng.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='gitbook.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='io/machine-learning-notebook/supervised-learning/ recurrent-neural-network/recurrent neural networks, Accessed September,2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [112] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Viegas, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Canuto, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Gomes, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Luiz, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Rosa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ribas, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Rocha, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Gon¸calves, “Cluwords: exploiting semantic word clustering representation for enhanced topic modeling,” in Proceedings of the 12th International Conference on Web Search and Data Mining, January 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 753–761.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [113] “Amazon Kendra,” www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='aws.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='amazon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='com/kendra, Accessed April 10, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [114] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhou, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Moosavi-Dezfooli, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Cheung, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Frossard, “Adaptive quantization for deep neural network,” in Proceedings of the AAAI Conference on Artificial Intelligence, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 32, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [115] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Samani and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Salehi, “Exploring the impact of virtualization on the usability of deep learning applications,” in Proceedings of 22nd IEEE International Symposium on Cluster, Cloud and Internet Computing (CCGrid), 2022, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 442–451.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [116] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Manner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Endreß, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Heckel, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wirtz, “Cold start influencing factors in function as a service,” in Proceedings of the 12th IEEE/ACM International Conference on Utility and Cloud Computing Companion (UCC), 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 181–188.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [117] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Chen, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wu, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Han, “Fepim: Contention-free in-memory computing based on ferroelectric field-effect transistors,” in Proceedings of 26th IEEE Asia and South Pacific Design Automation Conference (ASP-DAC), 2021, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 114–119.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [118] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Christensen, “Heuristic algorithms for np-complete problems,” Project report, Institute of Informatics and mathematical Modelling, Technical University of Denmark, 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [119] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' O’neil, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' O’neil, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Weikum, “The LRU-K page replacement algorithm for database disk buffering,” Journal of Acm Sigmod Record, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 22, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 2, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 297–306, 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [120] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Mokhtari, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Denninnart, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Salehi, “Autonomous task dropping mechanism to achieve robustness in heterogeneous computing systems,” in Proceedings of International Parallel and Distributed Processing Symposium Workshops (IPDPSW), 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 17–26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [121] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Van Erven and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Harremos, “R´enyi divergence and kullback-leibler divergence,” IEEE Transactions on Information Theory, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 60, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 7, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 3797–3820, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 164 [122] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Dasgupta and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hsu, “Hierarchical sampling for active learning,” in Proceedings of the 25th international conference on Machine learning, 2008, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 208–215.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [123] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Kumar and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Gupta, “Active learning query strategies for classification, regression, and clustering: a survey,” Journal of Computer Science and Technology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 35, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 913–945, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' [124] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Min, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Zhang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Ciucci, and M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Wang, “Three-way active learning through clustering selection,” International Journal of Machine Learning and Cybernetics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 11, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 1033–1046, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 165 Biographical Sketch Sm Zobaed received his Bachelor of Science in computer science and engineering in the fall of 2015 from Islamic University of Technology (IUT), Bangladesh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' He started his professional career in December of 2015, as a System Engineer in one of the top tech giants named “Huawei Technologies Ltd”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' After around a year and half, he planned to enrich his academic knowledge by pursuing higher education.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Hence, Sm Zobaed started his Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' journey in computer science in the fall of 2017 at the University of Louisiana at Lafayette.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' Sm Zobaed received his M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='Sc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' degree in computer science in the spring of 2019 during his Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' journey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' His research interests are: Natural language processing, Data analytics, and Cloud computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} +page_content=' 166' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/pdAzT4oBgHgl3EQfAfrM/content/2301.00928v1.pdf'} diff --git a/q9AzT4oBgHgl3EQfA_op/content/2301.00934v1.pdf b/q9AzT4oBgHgl3EQfA_op/content/2301.00934v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0803bdbf7120eb1789aece1bf7b4cdf8b1045618 --- /dev/null +++ b/q9AzT4oBgHgl3EQfA_op/content/2301.00934v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d408d9fe9207c4b5b3ad6a2d89d8278d20277771547e5d9378a2aad309d195f7 +size 759421 diff --git a/q9AzT4oBgHgl3EQfA_op/vector_store/index.faiss b/q9AzT4oBgHgl3EQfA_op/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..9f389f0eb97fc060e288f5854a48beb767023659 --- /dev/null +++ b/q9AzT4oBgHgl3EQfA_op/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:75ed2582e6e4db6bf7d162d10bcbb9f899e76c8ad07174307454d0be684c02bd +size 2097197 diff --git a/q9AzT4oBgHgl3EQfA_op/vector_store/index.pkl b/q9AzT4oBgHgl3EQfA_op/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..cf3669afdab0611039908c5ff1f650338744d37e --- /dev/null +++ b/q9AzT4oBgHgl3EQfA_op/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ed222be0d4f4130c924bcecd445bc4c77939e23a9211015e7f8ab7e98d46c120 +size 85366 diff --git a/qdE2T4oBgHgl3EQf0gjz/vector_store/index.pkl b/qdE2T4oBgHgl3EQf0gjz/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..468882944945df4f12455a1288cd3eb4e5d8d4a0 --- /dev/null +++ b/qdE2T4oBgHgl3EQf0gjz/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:89703b3ea84cd98a4b022590eeffaeb6d4b8f1c500a43561d2fa12d829c861a0 +size 58912 diff --git a/qtFRT4oBgHgl3EQfezdF/content/tmp_files/2301.13572v1.pdf.txt b/qtFRT4oBgHgl3EQfezdF/content/tmp_files/2301.13572v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..75424fd456d70fbc7c789b5b7366a831ce86d681 --- /dev/null +++ b/qtFRT4oBgHgl3EQfezdF/content/tmp_files/2301.13572v1.pdf.txt @@ -0,0 +1,2484 @@ +BALANCE: Bayesian Linear Attribution for +Root Cause Localization +Chaoyu Chen† +Ant Group +China +chris.ccy@antgroup.com +Hang Yu† +Ant Group +China +hyu.hugo@antgroup.com +Zhichao Lei +Ant Group +China +leizhichao.lzc@antgroup.com +Jianguo Li∗ +Ant Group +China +lijg.zero@antgroup.com +Shaokang Ren +Ant Group +China +renshaokang.rsk@antgroup.com +Tingkai Zhang +Ant Group +China +tingkai.ztk@antgroup.com +Silin Hu +Ant Group +China +husilin.hsl@antgroup.com +Jianchao Wang +Ant Group +China +luli.wjc@antgroup.com +Wenhui Shi +Ocean Base +China +yushun.swh@oceanbase.com +ABSTRACT +Root Cause Analysis (RCA) plays an indispensable role in dis- +tributed data system maintenance and operations, as it bridges the +gap between fault detection and system recovery. Existing works +mainly study multidimensional localization or graph-based root +cause localization. This paper opens up the possibilities of exploit- +ing the recently developed framework of explainable AI (XAI) for +the purpose of RCA. In particular, we propose BALANCE (BAyesian +Linear AttributioN for root CausE localization), which formulates +the problem of RCA through the lens of attribution in XAI and +seeks to explain the anomalies in the target KPIs by the behavior of +the candidate root causes. BALANCE consists of three innovative +components. First, we propose a Bayesian multicollinear feature +selection (BMFS) model to predict the target KPIs given the can- +didate root causes in a forward manner while promoting sparsity +and concurrently paying attention to the correlation between the +candidate root causes. Second, we introduce attribution analysis +to compute the attribution score for each candidate in a backward +manner. Third, we merge the estimated root causes related to each +KPI if there are multiple KPIs. We extensively evaluate the pro- +posed BALANCE method on one synthesis dataset as well as three +real-world RCA tasks, that is, bad SQL localization, container fault +localization, and fault type diagnosis for Exathlon. Results show +that BALANCE outperforms the state-of-the-art (SOTA) methods +in terms of accuracy with the least amount of running time, and +achieves at least 6% notably higher accuracy than SOTA methods +∗Corresponding author. † Two authors contributed equally to this work. +Permission to make digital or hard copies of all or part of this work for personal or +classroom use is granted without fee provided that copies are not made or distributed +for profit or commercial advantage and that copies bear this notice and the full citation +on the first page. Copyrights for components of this work owned by others than ACM +must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, +to post on servers or to redistribute to lists, requires prior specific permission and/or a +fee. Request permissions from permissions@acm.org. +SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA +© 2023 Association for Computing Machinery. +ACM ISBN 978-1-4503-XXXX-X/18/06...$15.00 +https://doi.org/XXXXXXX.XXXXXXX +for real tasks. BALANCE has been deployed to production to tackle +real-world RCA problems, and the online results further advocate +its usage for real-time diagnosis in distributed data systems. +CCS CONCEPTS +• Software and its engineering; • Information systems → Au- +tonomous database administration; • Computing methodolo- +gies → Feature selection; Regularization; +KEYWORDS +Root Cause Analysis, Bayesian Method, Bad SQLs, Faults Diagnosis, +Distributed System, Attribution Analysis, Explainable AI +ACM Reference Format: +Chaoyu Chen†, Hang Yu†, Zhichao Lei, Jianguo Li, Shaokang Ren, Tingkai +Zhang, Silin Hu, Jianchao Wang, and Wenhui Shi. 2023. BALANCE: Bayesian +Linear Attribution for Root Cause Localization. In Proceedings of In Pro- +ceedings of the 2023 International Conference on Management of Data (SIG- +MOD ’23). ACM, New York, NY, USA, 15 pages. https://doi.org/XXXXXXX. +XXXXXXX +1 +INTRODUCTION +System faults and incidents have a possibly tremendous influence +on distributed data systems which are widely adopted in modern +information technology (IT) and financial companies, since they +may lead to system outrage and further incur astounding financial +loss and jeopardize customer trust [21]. It has been reported by +Forbes that every year IT downtime costs an estimated $26.5 billion +in lost revenue alone, not to mention the indirect expense, including +lost customers and references. Thus, it is imperative to conduct +fast and precise fault diagnosis and recovery before they become +service-impacting. A central task in fault diagnosis and recovery +is root cause analysis (RCA), which bridges the gap between fault +detection and recovery [11, 13]. +Currently, the task of RCA is mainly accomplished by site reliabil- +ity engineers (SREs) with rich operation experience. Unfortunately, +such manual work becomes prohibitively slow due to the increase +arXiv:2301.13572v1 [cs.LG] 31 Jan 2023 + +SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA +Chen et al. +of the scale and complexity of the architecture as well as the dy- +namic and unpredictable nature of the system metrics and events, +thus deviating from the requirement of efficiency. Indeed, as men- +tioned in [19], it can take as long as several hours of manual work to +diagnose the root causes of intermittent slow queries in distributed +database systems. This has sparked considerable research efforts +toward designing automated RCA algorithms based on machine +learning so as to provide aid in saving time and ultimately money. +Literature on RCA algorithms can be broadly divided into two +categories. The first one focuses on multidimensional root cause +localization [5, 32, 47], which seeks to explain the abnormal be- +havior of the additive key performance indicators (KPIs) by iden- +tifying the fault-indicating combinations of their corresponding +multi-dimensional attributes. The success of these algorithms relies +on two assumptions: 1) the value of the KPI in each dimension +equals the sum of the values of its attributes and 2) all the KPIs and +their attributes can be monitored. However, these two assumptions +can be too restrictive in real-world problems, and a more practi- +cal setting is to attribute the anomalies to root cause candidates +without additive assumptions while allowing for missing data. On +the other hand, the second category revolves around graph-based +RCA algorithms [14, 24, 38, 39]. These approaches typically first +construct a causal graph based on tracing service calls or causal +discovery algorithms [46] and then find the root cause node via +rule-based traversing or random walk. A major impediment to the +application of tracing graphs and rule-based traversing is that it is +system invasive and typically incurs arduous work on enumerating +all traces and rules. As an alternative, causal discovery methods are +employed to learn the graph structure as in [39]. Unfortunately, the +causal discovery methods suffer from both high computational and +sample complexity [46], and in consequence, they can be distress- +ingly slow for large graphs and may lead to inaccurate results when +the number of observations for all metrics in the graph is small. +After obtaining the graph, the random walk methods are heuristic +and might fail to converge to the root cause when the number of +random walks is not sufficiently large. +In this paper, we explore alternatives and recast the RCA problem +as a feature attribution problem [16]. To the best of our knowledge, +we are among the first to analyze the root cause through the lens +of attribution. As a commonly used tool in explainable AI (XAI), +attribution methods assign attribution scores to input features, +the absolute value of which represents their importance to the +model prediction or performance [16]. Analogously, we aim to find +the root causes that can best explain the alarmed KPIs in RCA +problems. The attribution scores of the candidate causes represent +their relevance or contribution to the alarmed KPIs. As a motivating +example, in database systems, “bad SQLs” is referred to as SQLs +with deteriorated performance due to indexing errors or changes +in the execution plan. The performance deterioration of these SQLs +typically leads to anomalies in the tenant KPIs and may severely +influence the user experience. In this case, the target (𝒚) are the +tenant KPIs and the candidate causes (𝑿) are SQL metrics. +An attribution task can then be accomplished in two steps: first, +a forward model is constructed that exploits the input features (i.e., +candidate causes) to predict the outputs (i.e., alarmed KPIs), and +next, the significance of the input features are evaluated through +attribution approaches in a backward manner. Particularly in the +bad SQL localization example, the number of candidate SQLs 𝑝 +varies in each case and can be as large as thousands, whereas the +number of observations 𝑛 (the length of the corresponding time +series) is typically small since we only focus on the part around +the anomalies. In other words, the dimension 𝑝 can be larger than +the sample size 𝑛 in the RCA problems. To address this issue and +to automate the feature selection process, we adopt sparse linear +models as the forward model due to their high flexibility, efficiency, +and interpretability. Furthermore, the candidate causes are usually +correlated with each other, and there often exist missing values. To +tackle these problems that plague linear models, we propose a novel +Bayesian multicollinear feature selection (BMFS) model. Afterward, +we provide the attribution score for each candidate cause from +different perspectives, including sensitivity and salience. Finally, +we merge results when there exist multiple alarmed KPIs and each +of them is attributed to a different set of root causes. We name the +overall model BALANCE (BAyesian Linear AttributioN for root +CausE localization). +We would like to point out that both the multidimensional RCA +and the graph-based RCA can be formulated from the perspective +of attribution. Specifically, we can regard the multidimensional +RCA as attributing the anomalies in the KPIs to the combinations +of their attributes. It follows that the additive constraints in the +multidimensional RCA can be removed, and hence, we only need to +consider the abnormal attributes under this scenario. On the other +hand, by regarding all abnormal nodes in the graph as candidate +causes, BALANCE can be used to identify the root cause efficiently +even though the graph structure is not available or cannot be reli- +ably learned, which is often the case in practice. Viewed another +way, BALANCE can also be used as a building block to construct +causal graphs, since linear regression models are frequently used +for causal discovery [49]. Given the graph, BALANCE serves as a +better substitute for random walks as it does not require a large +number of random walks and so is more efficient. +We validate the usefulness of BALANCE on four datasets. First, +we generate synthetic data with a different number of input fea- +tures, different levels of multicollinearity, noise, and sparsity, and +different proportions of missing values, and then compare vari- +ous forward models including the proposed BMFS, Lasso, E-Net +(Elastic net), and ARD (Automatic Relevance Determination). We +find that BMFS typically recovers the underlying true regression +coefficients the best with comparable or even shorter running time, +especially when there exists multicollinearity among the input fea- +tures. Furthermore, we utilize the proposed method to address three +real-world RCA problems. In the first problem, we deal with the +problem of bad SQL localization as mentioned before. Our results +show that the proposed method can identify the human-labeled +root cause SQLs in fewer than 2 seconds per case with accuracy as +high as 83.3%, whereas it takes 3 minutes for SREs on average. The +second application copes with the problem of container fault local- +ization, whose objective is to attribute the abnormal trace failures +in a container to the metrics of the container, such as CPU usage, +memory usage, TCP, etc, and facilitate the self-healing process. The +proposed method can achieve an 𝐹1-score of 0.86, which is at least +20% higher than other baseline methods. Finally, we apply BAL- +ANCE to a public dataset, Exathlon [12], for the purpose of fault +type diagnosis, and the resulting accuracy is again 6% higher than + +BALANCE: Bayesian Linear Attribution for Root Cause Localization +SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA +the SOTA methods. Note that the first application handles KPIs +and candidates that are homogeneous while the latter two tackles +heterogeneous ones. The advantageous performance of BALANCE +in all three scenes shows that attribution-based RCA can be an +effective and efficient tool for general and practical RCA cases. +In summary, our contribution includes: +• To the best of our knowledge, we are among the first to for- +mulate the RCA problem from the perspective of attribution +analysis developed in the field of XAI. To be specific, we explain +the anomaly in the target KPI by attributing it to the behavior +of the candidate’s root causes. +• We propose a novel forward model BMFS that can automatically +select relevant candidates while taking their correlations into +account at the same time. +• We apply the proposed BALANCE approach to three real-world +problems, including bad SQL localization, container fault local- +ization, and fault type diagnosis for Exathlon. All three scenes +demonstrate the effectiveness of BALANCE. We further deploy +BALANCE to production for the former two applications. +2 +RELATED WORKS +Since the proposed model is related to RCA, attribution, and sparse +linear models, we provide a brief review of each of them below. +2.1 +Root Cause Localization +As aforementioned, there are broadly two strategies for root cause +localization. The first one considers the multidimensional root cause +localization methods, such as Adtributor [5], Hotspot [32], and +HALO [47]. More concretely, Adtributor [5] finds the root cause in +each dimension by selecting the most abnormal dimension values. +However, Adtributor assumes that the root cause lies in one dimen- +sion, which can be too restrictive in practice. To extend Adtributor +to the case of multidimensional root causes, Hotspot [32] propa- +gates the anomaly of the KPIs to different dimensions via the ripple +effect and further defines the attribution scores of different dimen- +sion combinations by replacing their real values with the predicted +ones and further computing the differences with and without the re- +placement. Unfortunately, the consequent search space is typically +very large. Although Hotspot employs Monte Carlo tree search and +a hierarchical pruning strategy to reduce the computational cost, +it can still be too slow for large-scale practical problems. Another +drawback of both Adtributor and Hotspot is that they fail to con- +sider the possible dependency among dimensions. As a solution, +HALO [47] learns the hierarchical dependency structure of the +dimensions via conditional entropy and then looks for the root +cause by traversing in this structure. These kinds of methods can +be viewed as a special case of attribution methods since they try +to attribute the anomalies in the KPIs to the combinations of the +associated multidimensional attributes. Note that the target KPIs +in this case is the sum of the attribute values along each dimension. +However, in a more general setting, the target KPIs may be influ- +enced by the root cause candidates in a non-additive manner. The +proposed BALANCE approach provides a recipe for this problem. +The second strategy focuses on the graph-based causal infer- +ence [29]. MonitorRank [14] and Microhecl [17] firstly introduce +service level RCA on known services chain architecture given by +the distributed tracing system. On the other hand, for applications +without known graphs, CauseInfer [10] and CloudRanger [39] build +a causal graph using the PC Algorithm [30]. Once the graph is ob- +tained, statistical root causes are typically inferred via personalized +page rank [40], breadth-first search [10, 17], random walk [14, 39], +etc. To make the graph more reliable, OM Graph [24] considers the +prior knowledge from a knowledge graph with entities represent- +ing all software and hardware in a distributed data system, during +the construction of the causal graph. Furthermore, CloudRCA [48] +optimizes OM Graph by building graphs based on multiple sources +of data, including monitoring metrics, logs, and expert knowledge. +Note that the PC algorithm is still used in both OM graph and +CloudRCA for graph construction. As pointed out in §1, it may be +resource-consuming to construct graphs based on tracing service +calls or other sources of prior knowledge, due to the large-scale and +complicated nature of the entire architecture, while it is unreliable +to build graphs utilizing causal discovery algorithms (e.g., the PC +algorithm) given the limited length of the time series for the metrics +during the anomalies. Such shortcomings hamper the practice use +of graph-based RCA. Another line of research seeks to construct +the causal graph by identifying the lagged temporal dependence +between different metrics [3, 20]. For instance, Granger causality is +adopted in [1, 34] to infer the causal dependencies. However, the +lagged temporal dependence exits only when the granularity of +the monitored metrics is as fine as a millisecond or second in cloud +systems [1], and setting up such a fine-grained monitoring system +is quite costly. By contrast, BALANCE can still be useful when the +graph structure is not available and may in turn assist in graph +construction and the subsequent localization step. +2.2 +Attribution methods +Since we use attribution methods to solve the problem of RCA, we +review some state-of-the-art (SOTA) attribution methods in this sec- +tion. The goal of attribution methods is to understand and explain +why a model makes a certain prediction, thus assisting in winning +user trust and further providing insight into how to enhance the +performance of the model. Generally speaking, attribution methods +can be divided into gradient-based and perturbation-based methods. +Gradient-based methods compute the attribution values by lever- +aging the gradients of the model. The first attempt in this direction +is to compute the absolute gradient of the target output of a model +w.r.t. (with regard to) the input, which is also known as sensitivity +analysis [28]. However, sensitivity analysis is typically quite noisy +and discards the information on the direction of the input change. +One appealing solution is to use the element-wise multiplication of +the gradient and the input (i.e., gradient×input), in order to increase +the sharpness of attribution maps [27]. The major drawback of the +above naive uses of the gradient information on highly non-linear +models is that only the information about the local behavior of the +function in the neighbor of a given input is provided. To address +this problem, many methods are proposed, including Layer-wise +Relevance Propagation (LRP) [4], Integrated Gradients [33], and +DeepLIFT [27]. On the other hand, perturbation-based methods +obtain the attribution of an input feature by removing or altering +it, and then measuring the difference between the output before +and after the perturbation is added. Feature occlusion [44] directly + +SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA +Chen et al. +removes each feature in turn and so requires 𝑝 model evaluations, +where 𝑝 is the number of features. To reduce the heavy compu- +tational burden, Local Interpretable Model-agnostic Explanations +(LIME) [25] resorts to group-wise feature occlusion. These groups +are used to fit a local Lasso regression and the resulting coefficients +are regarded as attributions. Unfortunately, both feature occlusion +and LIME suffer from the pitfall of the high sensitivity to the choice +of hyper-parameters in the model. In other words, these methods +may be influenced by the user-defined parameters in an unpre- +dictable fashion and there is no guarantee that the explanation is +unbiased and faithful. One remedy to this problem is to use SHapley +Additive exPlanations (SHAP) [18], taking advantage of the classi- +cal Shapley values to assign credit to participants in a cooperative +game. Shapley values are proven to be the only consistent attri- +bution approach with several unique axioms in agreement with +human intuition [31]. Nevertheless, it results in a daunting computa- +tional complexity of O(2𝑝). This has sparked recent research efforts +toward reducing the complexity [37]. In BALANCE, we specify the +model between the candidate root causes and the target KPIs to be +linear. As a result, almost all aforementioned attribution methods +can be unified [2], and hence, the proposed model enjoys various +nice properties, as will be discussed in the subsequent sections. +2.3 +Sparse linear models for feature selection +As we employ a sparse linear forward model in BALANCE, we +briefly review the relevant literature in this section. The most pop- +ular sparse linear model is Lasso [35], which intends to find the +coefficients that can best describe the linear relationship between +the observed features and the outputs while enforcing the coeffi- +cients to be sparse via the ℓ1-norm penalty. Three problems stand +in the way of a direct application of Lasso to RCA: First, there often +exist correlations between the candidate causes but Lasso pales in +tackling correlated features due to the nature of the ℓ1 norm [50]. +Second, the tuning parameter in front of the ℓ1 norm, which bal- +ances the trade-off between data fidelity and coefficient sparsity +is unknown in practice and is typically chosen by cross-validated +grid search. As a result, the lasso algorithm has to be run for every +candidate value of the tuning parameter for every partition of the +dataset, leading to a heavy computational burden. Third, missing +values are the rule rather than the exception, but Lasso cannot deal +with them directly. As a remedy to the first problem, E-Net (Elastic +net) is proposed by using the combination of the ℓ1 and the ℓ2 norm +on the coefficients, which introduces the grouping effect to the +correlated coefficients [50]. This merit comes along with an extra +tuning parameter and considerable computational overhead. On +the other hand, the other two issues can be addressed by Bayesian +models, such as ARD (Automatic Relevance Determination) [36]. +The tuning parameter is assumed to be a random variable and its +posterior distribution can be inferred from the data via expectation +maximization. Unfortunately, correlations between features are not +considered in this model. A handful of works are further proposed +to alleviate this deficiency by borrowing the strength from the cor- +related shrinkage priors, such as the group inverse-Gamma Gamma +prior [7] and the correlated spike-and-slab prior [26]. However, +such methods require some prior information that is unavailable in +Merging Module: +Intersection and Union Explanation +Target and Candidates Data +Loader and Organizer +Time Series Database +Forward Module: +BMFS +Backward Module: +Attribution Analysis +Recovery Decision Maker +1 +2 +3 +5 +6 +7 +8 +Collect and aggregate data into time series database +Conduct real-time anomaly detection(AD) on targets +Trigger AD on candidates to reduce its number(optional) +Load abnormal targets +Load (abnormal) candidates corresponding to the targets +Train the forward BMFS model +Compute the attribution of the candidates chosen by BMFS +Merge and rank root causes resulting from multiple targets +Send root causes to recovery decision maker +Root Cause Analysis Service +9 +BALANCE +1 +2 +4 +5 +6 +7 +8 +9 +4 +3 +Data Collection +Target AD +Candidates AD +Figure 1: The overall framework of BALANCE. +practice, such as the grouping information [7] or the prior distribu- +tion for zero coefficients [26]. In this work, we propose BMFS to +overcome the abovementioned issues, which will be discussed in +detail in §4.1. +3 +PROBLEM FORMULATION +In this section, we first introduce the overall framework of BAL- +ANCE. We then delve into in the RCA part, provide some desiderata, +and discuss how such desiderata conceive the proposed method. +The overall framework of BALANCE is depicted in Figure 1. +We first collect the raw data, including both target KPIs and the +candidate root causes, and store them in the time series database. +Concretely, let 𝑿 = [𝒙1, 𝒙2, · · · , 𝒙𝑝] denote the 𝑝 candidate root +causes or the fundamental metrics (e.g., metrics for each SQL) that +are associated with the target KPI or the derived metric 𝒚 (e.g., ten- +ant KPIs). Real-time anomaly detection is only employed to monitor +the target KPI 𝒚 since it is often prohibitively resource-consuming +to monitor all the fundamental metrics (i.e., the candidate root +causes) 𝑿. Although not real-time, the anomaly detection on 𝑿 +can be triggered once an alarm on 𝒚 is raised, since we only need +to focus on the abnormal 𝑿 during RCA. We then collect the data +of the abnormal 𝒚 and 𝑿 before and during the alarm with length +𝑛 from the database, and input the data into the proposed RCA +service, BALANCE, in order to find the root cause. The resulting +estimated root cause serves as an input to the recovery decision +maker, which yields the self-healing plan. +Ideally, we would like an RCA module that satisfies the following +desiderata: +d1. The number of observations (i.e., the length of the time series) +𝑛 is typically small since we only consider the short time +series before and during the anomalies to explain the abnormal +behavior of the targets 𝒚. +d2. The number of candidates 𝑝 is varying, and possibly large in +each case. Therefore, the RCA module should be sufficiently +flexible to deal with the cases where 𝑝 ≤ 𝑛 and 𝑝 > 𝑛. The +latter scenario is more challenging and can be found in practice, + +BALANCE: Bayesian Linear Attribution for Root Cause Localization +SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA +for instance, the number of running SQLs is time-varying in +the bad SQL example, and can be hundreds or even thousands, +whereas 𝑛 = 61. In this case, 𝑝 > 𝑛. +d3. The RCA module should output all possible root causes even +if they are correlated with each other while removing all irrel- +evant candidates at the same time. In practice, it is infeasible +to enumerate and verify all possible causalities between the +candidates, since their interactions are often time-varying and +bi-directional. As such, it is better to list all correlated root +causes and provide the SREs with more information. +d4. The RCA module should be able to deal with missing data that +often exist in the monitor system. +d5. The process of RCA should be efficient. +d6. The results should be interpretable and the importance of the +candidates should be comparable and can be used for further +ranking and decision-making. +On the other hand, attribution methods target producing expla- +nations of the output behavior of a model by assigning a scalar +attribution value 𝑟𝑗, sometimes also called “relevance”, “feature +importance”, or “contribution”, to each input feature 𝑗 of the model. +Formally, given a target output 𝒚, the objective of an attribution +method is to determine the contribution 𝒓 = [𝑟1, · · · ,𝑟𝑝] ∈ R𝑝 of +each input feature 𝒙𝑗 ∈ 𝑿 to the output𝒚. It is therefore straightfor- +ward to exploit attribution methods for RCA. Under the framework +of attribution, first, a forward model 𝒚 = 𝑓 (𝑿) is constructed in +order to predict 𝒚 given 𝑿. Then an attribution method is used to +explain the abnormal behavior of the target KPI 𝒚 by attributing it +to the candidate root causes 𝑿. In this work, we advance to use a +Bayesian sparse linear model as the forward model, with special +attention to the correlation between the candidates. We would like +to motivate the use of the forward model from the following three +perspectives: +• First, the proposed forward model can well capture all the above +desiderata. Specifically, due to the efficiency of linear models, +we fit a different linear model to the data every time the target +KPIs are alarmed, successfully solving the problem of the case- +varying number of candidates (i.e., d2). By leveraging sparsity +in the regression coefficients, sparse linear models can choose +candidates relevant to the target in an automatic way, and can +further handle the large-𝑝-small-𝑛 problem (i.e., d1, d2). After +further considering the multicollinear relationship between the +candidates, d3 can be satisfied. The Bayesian framework in the +proposed model facilitates the processing of the missing data by +inferring their distributions along with the remaining parame- +ters (i.e., d4). By learning the variational posterior distribution +of the tuning parameters rather than estimating them via grid +search, the proposed model is typically more efficient than the +commonly used frequency counterpart (i.e., d5). Finally, linear +models are quite amenable to attribution methods as will be +discussed below (i.e., d6). +• Second, the results (i.e., the estimated root causes) yielded by an +attribution method should be faithful to the underlying process +the SREs are trying to understand. To this end, the methods +reviewed in §2.2 typically adopt a complicated forward model +(i.e., a neural network) to predict𝒚 given 𝑿, in order to maximize +the predictive accuracy. On the other hand, due to the black-box +nature of the forward model, another interpretable model is +further applied to approximate what the forward model has +learned, so as to maximize the descriptive accuracy. For instance, +both LIME [25] and SHAP [18] employ local linear explanation +models, and DeepLIFT [27] linearizes non-linear components of +a neural network. Under the RCA case, it is intractable to train +a neural network as the forward model due to d2, d1, and d5. +Moreover, our objective is not to predict 𝒚 given 𝑿, and hence, +the predictive accuracy is not our main focus. Instead, we are +more concerned with the descriptive error. By specifying the +forward model to be linear, we minimize the descriptive error +to zero. +• Finally, as mentioned in §2.2, Shapley values are justified as the +only possible attribution method that satisfies all axioms that are +consistent with human intuition, and it has been proven in [2] +that almost all aforementioned attribution methods, including +gradient×input, integrated gradients, DeepLIFT, and feature +occlusion generate exact Shapley values when applied to a +linear model and a zero baseline is used. We will discuss how +the proposed linear model fulfills all the axioms in §4.2. +After the forward model is constructed, we then attribute the +anomaly in 𝒚 to the candidates 𝑿 by finding the subset of 𝑿 that +contribute the most to the abnormal behavior of 𝒚. Finally, we rank +the root causes based on the attribution score and merge the results +when there are multiple target KPIs. +4 +METHODOLOGY +In this section, we elaborate the three modules in BALANCE indi- +vidually. +4.1 +Forward Module: Bayesian multicollinear +Features Selection +4.1.1 +Bayesian Formulation. As mentioned in §3, we choose a +sparse linear model as the forward model, that is, 𝒚 = 𝑿𝜷 + 𝝐, +where 𝒚 ∈ R𝑛 denotes the time series of length 𝑛 for a single target +KPI around the anomaly, 𝑿 ∈ R𝑛×𝑝 denotes the time series of +the corresponding 𝑝 candidate root causes, 𝜷 ∈ R𝑝 is the sparse +coefficient vector, and 𝝐 ∼ N (0, 𝛼−1𝑰) represents the independent +Gaussian noise with variance 𝛼−1. Equivalently, we can formulate +the problem from a probabilistic perspective: +𝑝(𝒚|𝜷, 𝑿, 𝛼) = N (𝑿𝜷, 𝛼−1𝑰) +∝ exp +�𝛼 +2 (𝒚 − 𝑿𝜷)𝑇 (𝒚 − 𝑿𝜷) +� +. +(1) +We assume that 𝛼 follows a non-informative Jeffrey’s prior, that is, +𝑝(𝛼) ∝ 1/𝛼. +Now let us focus on the prior distribution on 𝜷. Our objective is to +simultaneously encourage sparsity and handle the multicollinearity +among the features 𝑿. To promote sparsity, one typically resorts +to the Laplace distribution (i.e., the Bayesian counterpart of the +ℓ1-norm) or the student’s T distribution. However, here we choose +the horse-shoe prior [9] due to its advantages over the Laplace and +the student’s T prior. The horse-shoe prior can be expressed as a + +SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA +Chen et al. +2 +0 +2 +j +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +density +student-t +Laplace +horse-shoe +2 +0 +2 +j +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +density +(a) Sparse promoting priors +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +1 / (1 + +2 +j ) +0 +1 +2 +3 +4 +density +(b) Shrinkage weights density +Figure 2: The density of the commonly used sparse promoting pri- +ors, including the Student’s T, Laplace, and horse-shoe prior (a), and +the density of the corresponding shrinkage weights 1/(1 + 𝜎2) (b). +scale mixture of Gaussians: +𝑝(𝛽𝑗 |𝜎𝑗,𝑔) = N (0,𝑔𝜎2 +𝑗 ), +(2) +𝑝(𝜎𝑗) = 𝐶+(0, 1), +(3) +where 𝐶+(0, 1) is a standard half-Cauchy distribution on positive +reals R+, and𝑔 and𝜎𝑗 are respectively the global and local shrinkage +parameters. As 𝑔 becomes small, the global shrinkage parameter 𝑔 +shrinks all the coefficients 𝛽𝑗 in 𝜷 to zero. On the other hand, the +heavy-tailed half-Cauchy priors for the local shrinkage parameters +𝜎𝑗 allow some 𝛽𝑗 to escape from the shrinkage. Therefore, the +resulting 𝜷 would be sparse. In comparison with other commonly- +used sparse promoting priors, such as the Student’s T and Laplace +distribution, we can tell from Figure 2(a) that horse-shoe prior +has a larger density for 0 and for very large 𝛽𝑗. In other words, it +can better separate the zero and non-zero elements in 𝜷. Viewed +another way, given that 𝜎𝑗 follows a half-Cauchy prior on 𝜎𝑗, we +can obtain that [9]: +1 +1 + 𝜎2 +𝑗 +∼ Be +� 1 +2, 1 +2 +� +, +(4) +where Be(0.5, 0.5) denotes a beta distribution with shape param- +eters 0.5, and we refer to 1/(1 + 𝜎2) as the shrinkage weight. As +shown in Figure 2(b), the density function of the shrinkage weight +for the horse-shoe prior (i.e., the orange line) has a U-shape (i.e., +horse-shoe shape); it reaches the lowest value at 0.5 but is un- +bounded at 0 and 1, indicating that this prior prefers 𝜎2 +𝑗 to be either +very small or very large. However, the student’s T and Laplace prior +(see the blue and green lines) do not have this nice property. As +a result, the horse-shoe prior is more robust when dealing with +unknown sparsity and large non-zero elements. +On the other hand, to tackle the multicollinearity, we typically +resort to the g-prior [45]: +𝑝(𝜷|𝑔, 𝜎2, 𝑿) = N +� +0,𝑔𝜎2(𝑿𝑇 𝑿)−1� +, +(5) +where 𝑔 and 𝜎2 are scalars that determine the overall variance of 𝜷, +and the inter-dependencies among different features 𝑿 are charac- +terized empirically by 𝑿𝑇 𝑿. The resulting posterior distribution +on 𝜷 presents a larger correlation among elements in 𝜷 than the +posterior given by other prior distributions, such as the Laplace +(i.e., ℓ1-norm) and the Gaussian with a diagonal covariance (i.e., +!! +" +# +$ +%! +& +Figure 3: Graph representation of BMFS. The box labeled 𝑁 denotes +that the number of repetitions for the subgraph inside is 𝑁. +ℓ2-norm). To bring together the best of both worlds, we propose a +novel prior distribution that seamlessly integrates the horse-shoe +prior and the g-prior: +𝑝(𝜷|𝑔, 𝝈,𝑋) = N +� +0,𝑔 diag(𝝈)𝑿𝑇 𝑿 diag(𝝈) +� +, +(6) +𝑝(𝜎𝑗) = 𝐶+(0, 1), +(7) +where 𝝈 is a 𝑝-dimensional vector. We name the above prior corre- +lated horse-shoe prior. To facilitate the derivation of the variational +inference algorithm, we further reparameterize the above prior +using the canonical exponential family form [22] as: +𝑝(𝜷|𝛾, 𝝀, 𝑿) = N +� +0, +� +𝛾 diag �𝝀 +1 +2 �𝑿𝑇 𝑿 diag �𝝀 +1 +2 ��−1� +∝ exp +�𝑝 +2 log𝛾 + 1 +2 +𝑝 +∑︁ +𝑗=1 +log 𝜆𝑗 +− 𝛾 +2𝝀 +𝑇 +2 �(𝑿𝑇 𝑿) ◦ (𝜷𝜷𝑇 )�𝝀 +1 +2 +� +, +(8) +𝑝(𝜆𝑗) = 1 +𝜋 𝜆− 1 +2 +𝑗 +(𝜆𝑗 + 1)−1, +∀𝜆𝑗 > 0, +(9) +where 𝛾 = 1/𝑔, 𝜆𝑗 = 1/𝜎2 +𝑗 , 𝝀1/2 denotes element-wise square root +of the entries in vector 𝝀, 𝝀𝑇/2 is the transpose of 𝝀1/2, and 𝑝(𝜆𝑗) +can be regarded as a Beta prime distribution or a compound Gamma +distribution. Since we do not have any prior knowledge of the global +shrinkage parameter 𝛾, we employ the non-informative Jeffrey’s +prior, namely, 𝑝(𝛾) ∝ 1/𝛾. +Altogether, the overall Bayesian model can be factorized as: +𝑝(𝒚, 𝜷, 𝝀, 𝛼,𝛾|𝑿) = 𝑝(𝒚|𝑿, 𝜷, 𝛼)𝑝(𝜷|𝛾, 𝝀, 𝑿)𝑝(𝝀)𝑝(𝛾)𝑝(𝛼). +(10) +The corresponding graph representation can be found in Figure 3. +4.1.2 +Variational Inference. Our overarching goal is to infer the +posterior distribution 𝑝(𝜷, 𝝀, 𝛼,𝛾|𝒚, 𝑿). However, it is intractable +to obtain the close-form expression of this posterior distribution, +and thus, we follow the framework of variational inference and +find a tractable variational distribution 𝑞(𝜷, 𝝀, 𝛼,𝛾) that is closest +in Kullback-Leibler (KL) divergence to the exact posterior. For sim- +plicity, we apply the mean-field approximation and factorize the +variational distribution as: +𝑞(𝜷, 𝝀, 𝛼,𝛾) = 𝑞(𝜷) +𝑝 +� +𝑗=1 +𝑞(𝜆𝑗)𝑞(𝛼)𝑞(𝛾). +(11) + +BALANCE: Bayesian Linear Attribution for Root Cause Localization +SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA +One advantage of the mean-field approximation is that the func- +tional form of each factor can be specified by equating the functional +derivatives of the KL divergence w.r.t. the factor to zero [6]. After +obtaining the functional form of the variational distribution, we +then update the parameters of these distributions recursively via +natural gradient descent [15, 43]. It is worthwhile to emphasize that +natural gradients typically result in simpler expressions (i.e., less +computation in each iteration) and faster convergence (i.e., fewer +iteration numbers) than standard gradients [15, 42, 43]. Thus, it is +favored when we are concerned with the efficiency of the algorithm. +In addition, although we assume the variational distributions are +independent in Eq-11, their parameters are dependent on each other +in a straightforward way when optimizing them to minimize the +KL divergence, as demonstrated in the following update rules of +these parameters. In other words, we still capture the interactions +between the variables 𝜷, 𝝀, 𝛼, and 𝛾 to some extent. Now let us +delve into the derivations for each variational distribution. +For 𝑞(𝜷) we can specify it to be a Gaussian distribution when +𝛽𝑗 ∈ R or a log-normal distribution when 𝜷 are constrained to +be non-negative. In the first scenario, 𝑞(𝜷) that minimizes the KL +divergence can be updated as: +𝑞(𝜷; 𝒉𝛽, 𝑱𝛽) ∝ exp +� +−1 +2𝜷𝑇 𝑱𝛽𝜷 + 𝒉𝑇 +𝛽𝜷 +� +, +(12) +where 𝑱𝛽 and 𝒉𝛽 respectively represent the precision matrix (i.e., +the inverse covariance) and the potential vector of 𝛽. Gaussian dis- +tributions parameterized by the precision matrix and the potential +vector are called the canonical form and such form is amenable +to concise update rules as shown below [15, 43]. 𝒉𝛽 and 𝑱𝛽 are +known as the canonical or natural parameters, and the correspond- +ing mean parameters can then be computed as ⟨𝜷⟩ = 𝑱 −1 +𝛽 𝒉𝛽 and +Cov[𝜷] = 𝑱 −1 +𝛽 . Specifically, update rules for 𝑱𝛽 and 𝒉𝛽 can be +derived as: +𝑱 {𝜅 } +𝛽 += (1 − 𝜌)𝑱 {𝜅−1} +𝛽 ++ 𝜌 +� +⟨𝛼⟩𝑿𝑇 𝑿 ++ ⟨𝛾⟩ diag �⟨𝝀 +1 +2 ⟩�𝑿𝑇 𝑿 diag �⟨𝝀 +1 +2 ⟩�� +, +(13) +𝒉{𝜅 } +𝛽 += (1 − 𝜌)𝒉{𝜅−1} +𝛽 ++ 𝜌⟨𝛼⟩𝑿𝑇𝒚, +(14) +where ⟨·⟩ denotes the expectation w.r.t. the corresponding varia- +tional distribution and 𝜌 denotes the step size determined using +the line search method (e.g., the Armijo rule) [43]. To provide more +intuition for the above derivations, we take the update rule for 𝒉𝛽 +as an example. In Eq-14, the natural gradient for 𝒉𝛽 is ⟨𝛼⟩𝑿𝑇𝒚 −𝒉𝛽. +As we update 𝒉𝛽 in the direction of the natural gradient with a step +size 𝜌, we can obtain Eq-14. The update rule for 𝑱𝛽 is derived in the +same fashion, and likewise for the update rules in the sequel. +On the other hand, when we restrict 𝜷 to be non-negative and +use the log-normal distribution as the variational distribution, we +further factorize 𝑞(𝜷) as � +𝑗 𝑞(𝛽𝑗) and 𝑞(𝛽𝑗) can be written as: +𝑞(𝛽𝑗;ℎ𝛽𝑗,𝜁𝛽𝑗 ) ∝ 1 +𝛽𝑗 +√︃ +𝜁𝛽𝑗 exp +� +−1 +2𝜁𝛽𝑗 𝛽2 +𝑗 + ℎ𝛽𝑗 𝛽𝑗 +� +, +(15) +where in each iteration 𝜅 the natural parameters 𝒉𝛽 and 𝜻𝛽 can be +updated as: +𝒉{𝜅 } +𝛽 += (1 − 𝜌)𝒉{𝜅−1} +𝛽 ++ 𝜌 +� +− 𝒄1 ◦ �1 − 2⟨log 𝜷⟩� ++ 𝒄2 ◦ �1 − ⟨log 𝜷⟩� + 1 +� +, +(16) +𝜻 {𝜅 } +𝛽 += (1 − 𝜌)𝜻 {𝜅−1} +𝛽 ++ 𝜌(2𝒄1 − 𝒄2), +(17) +𝒄1 = diag +� +⟨𝛼⟩𝑿𝑇 𝑿 ++ ⟨𝛾⟩ diag �⟨𝝀 +1 +2 ⟩�𝑿𝑇 𝑿 diag �⟨𝝀 +1 +2 ⟩�� +◦ ⟨𝜷2⟩, +(18) +𝒄2 = ⟨𝛼⟩𝑿𝑇𝒚 − off-diag +� +⟨𝛼⟩𝑿𝑇 𝑿 ++ ⟨𝛾⟩ diag �⟨𝝀 +1 +2 ⟩�𝑿𝑇 𝑿 diag �⟨𝝀 +1 +2 ⟩�� +◦ ⟨𝜷⟩, +(19) +where ◦ is the Hadamard (or elementwise) product, 𝜷2 denotes +elementwise square of 𝜷, and off-diag(·) denotes the off-diagonal +part of a matrix by replacing the diagonal with a zero vector. After- +wards, we can compute the mean parameters as ⟨log 𝜷⟩ = 𝒉𝛽 ⊘ 𝜻𝛽, +Var[log 𝜷] = 1 ⊘ 𝜻𝛽, ⟨𝜷⟩ = exp(⟨log 𝜷⟩ + Var[log 𝜷]/2), and +⟨𝜷2⟩ = exp(2⟨log 𝜷⟩ + 2Var[log 𝜷]), where ⊘ denotes elementwise +division. +For 𝑞(𝜆𝑗), we follow [22] and specify its functional form to be: +𝑞(𝜆𝑗;𝑑𝑗) = +1 +𝐸1(𝑑𝑗) (𝜆𝑗 + 1)−1 exp +� +− 𝑑𝑗 +�𝜆𝑗 + 1�� +, +(20) +where 𝐸1(𝑥) = +∫ ∞ +𝑥 +𝑒𝑥𝑝(−𝑡)/𝑡𝑑𝑡 represents the exponential integral +function. It follows that the update rule of 𝒅 is: +𝒅 {𝜅 } = (1 − 𝜌)𝒅 {𝜅−1} ++ 𝜌⟨𝛾⟩ +� +off-diag �𝑿𝑇 𝑿 ◦ ⟨𝜷𝜷𝑇 ⟩�⟨𝝀 +1 +2 ⟩ ◦ 𝒄3 ++ 1 +2 diag �𝑿𝑇 𝑿 ◦ ⟨𝜷𝜷𝑇 ⟩�� +, +(21) +𝒄3 = +� +⟨𝝀 +1 +2 ⟩ ◦ 𝒅 − Γ(1.5) ◦ 𝒅 +1 +2 +� +⊘ �⟨𝝀⟩ ◦ 𝒅 − 1�. +(22) +The mean parameters ⟨𝝀⟩ and ⟨𝝀 +1 +2 ⟩ can be calculated as: +⟨𝝀⟩ = Γ(−1, 𝒅) ⊘ Γ(0, 𝒅), +(23) +⟨𝝀 +1 +2 ⟩ = Γ(1.5)Γ(−0.5, 𝒅) ⊘ Γ(0, 𝒅), +(24) +where Γ represents the gamma function when there is only one +input and the upper incomplete gamma function1 when there are +two inputs, and the step size 𝜌 is again determined by the Armijo +rule. +For𝑞(𝛼) and𝑞(𝛾), we specify them to be the gamma distributions, +and the corresponding update rules are: +𝑞(𝛼;𝑎𝛼,𝑏𝛼) ∝ 𝛼𝑎𝛼−1 exp(−𝑏𝛼𝛼), +(25) +𝑞(𝛾;𝑎𝛾,𝑏𝛾) ∝ 𝛾𝑎𝛾 −1 exp(−𝑏𝛾𝛼), +(26) +1Γ(𝑐,𝑑) = 𝑈 (1 −𝑐, 1 −𝑐,𝑑)/exp(𝑑), where 𝑈 represents Tricomi’s confluent hyper- +geometric function. + +SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA +Chen et al. +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0 +2 +4 +6 +8 +10 +count +nonzero entries +zero entries +GMM fit +threshold +Figure 4: The empirical distribution of 𝜔 for a synthetic dataset: the +orange and blue bars denote the histogram of 𝜔 w.r.t. nonzero and +zero entries in ⟨𝜷 ⟩ respectively, the green line denotes the density +after fitting a GMM to the empirical distribution, and the red line +denotes the chosen threshold ˆ𝜔. +where +𝑎{𝜅 } +𝛼 += (1 − 𝜌)𝑎{𝜅−1} +𝛼 ++ 𝜌𝑛 +2 , +(27) +𝑏 {𝜅 } +𝛼 += (1 − 𝜌)𝑏 {𝜅−1} +𝛼 ++ 𝜌 +2 +�𝒚𝑇𝒚 + tr(⟨𝜷𝜷𝑇 ⟩𝑿𝑇 𝑿) − 2𝒚𝑇 𝑿⟨𝜷⟩�, +(28) +𝑎{𝜅 } +𝛾 += (1 − 𝜌)𝑎{𝜅−1} +𝛾 ++ 𝜌𝑝 +2 , +(29) +𝑏 {𝜅 } +𝛾 += (1 − 𝜌)𝑏 {𝜅−1} +𝛾 ++ 𝜌 +2 +� +⟨𝝀⟩𝑇 diag �𝑿𝑇 𝑿 ◦ ⟨𝜷𝜷𝑇 ⟩� ++ ⟨𝝀 +1 +2 ⟩𝑇 off-diag �𝑿𝑇 𝑿 ◦ ⟨𝜷𝜷𝑇 ⟩�⟨𝝀 +1 +2 ⟩ +� +. +(30) +In practice, entries in 𝒚 and 𝑿 are often missing. In this case, we +generate point estimates for 𝑋𝑖,𝒋 and Bayesian estimates for 𝑦𝑖 by +minimizing the aforementioned KL divergence, that is, +ˆ𝑋𝑖,𝒋 = ⟨𝜷𝒋𝜷𝑇 +𝒋 ⟩−1⟨𝜷𝒋⟩𝑦𝑖, +(31) +𝑞(𝑦𝑖) = N �𝑿𝑖,:⟨𝜷⟩, ⟨𝛼⟩−1�, +(32) +where the vector 𝒋 denotes the indices of the missing values in row +𝑖 in 𝑿, and 𝑿𝑖,: denotes the 𝑖-th row of 𝑿. +4.1.3 +Soft Thresholding. Recall that the half-Cauchy prior on 𝜎𝑗 +leads to the U-shaped prior of the shrinkage weight 1/(1 + 𝜎2 +𝑗 ) (cf. +Eq-4). Since 𝜆𝑗 = 1/𝜎2 +𝑗 , the shrinkage weight can be equivalently +expressed as 𝜆𝑗/(1 + 𝜆𝑗). This U-shaped prior constraints 𝜆𝑗 to +be either very small or very large and can separate the zero and +non-zero entries in 𝜷 in an automatic fashion. Owing to this prior, +we observe that the density of the empirical distribution ˆ𝑝(𝜔) on +𝜔 = ⟨𝜆𝑗⟩/(⟨𝜆𝑗⟩ + 1) for all 𝑗 also follows a U-shape approximately, +where the expectation ⟨𝜆𝑗⟩ is taken over the variational posterior +distribution 𝑞(𝜆𝑗), as shown in Figure 4. As expected, the value of +𝜔 for most true non-zero entries is close to zero and its density +decreases with 𝜔, whereas the value of 𝜔 for most true zero entries +is far away from zero. +To distinguish the non-zero entries from the zero ones, we choose +the threshold to be ˆ𝜔 = arg min ˆ𝑝(𝜔), which is the valley of the +U-shape density and set ⟨𝛽𝑗⟩ = 0 if ⟨𝜆𝑗⟩/(⟨𝜆𝑗⟩+1) > ˆ𝜔. Specifically, +Algorithm 1 Bayesian multicollinear Feature Selection (BMFS) +Input: an alarmed target KPI 𝒚 and candidate root causes 𝑿 associated +with 𝒚; +Output: regression coefficients ⟨𝜷 ⟩; +1: Initialize the parameters for all variatonal distributions; +2: repeat +3: +if 𝜷 can only take positive values then +4: +update 𝑞(𝜷) following Eq-15; +5: +else +6: +update 𝑞(𝜷) following Eq-12; +7: +end if +8: +compute ⟨𝜷 ⟩ and Cov[𝜷 ] given 𝑞(𝜷); +9: +update 𝑞(𝝀) by Eq-20 and compute ⟨𝝀⟩ by Eq-23, ⟨𝝀 +1 +2 ⟩ by Eq-24; +10: +update 𝑞(𝛼) by Eq-25, 𝑞(𝛾) by Eq-26, compute their expectations; +11: +if there exists missing values in 𝑿 and 𝒚 then +12: +impute the missing values following Eq-31 and Eq-32; +13: +end if +14: until convergence; +15: perform soft thresholding as introduced in §4.1.3; +we fit a two-component Gaussian mixture model (GMM) to ˆ𝑝(𝜔): +the means of the two Gaussians are fixed to the smallest and largest +value of 𝜔 across all 𝑗 respectively, while the variances and the +weights are learned from the data. We then find the ˆ𝜔 corresponding +to the minimum of the density of the GMM. +We summarize the entire procedure of BMFS in Algorithm 1. +4.2 +Backward Module: Attribution Analysis +Since our forward model is a linear model, one tempting choice for +attribution score is the regression coefficient, that is, +𝑟𝑗 = |⟨𝛽𝑗⟩|, +(33) +where 𝑟𝑗 denotes the attribution score and | · | denotes the absolute +value. In fact, for linear models, the regression coefficient ⟨𝛽𝑗⟩ +equals the gradient of 𝒚 w.r.t. 𝒙𝑗, thus it describes the sensitivity of +𝒚 to 𝒙𝑗. The value ⟨𝛽𝑗⟩ quantizes the impact of a small change in +𝒙𝑗 to 𝒚. Note that we have a distribution for 𝛽𝑗 instead of a point +estimate. Following the framework of XAI for Bayesian models [8], +we use the mean of 𝛽𝑗 here to compute the attribution score in +this section. Note that other values can also be used, such as the +quantiles, the modes, and the intersection or union of the modes +if there is more than one mode. Since 𝑞(𝛽𝑗) follows a Gaussian +distribution, the mean is the proper choice. +Unfortunately, high sensitivity does not indicate a high con- +tribution to the anomaly in the target KPI. For example, suppose +that the target KPI is a summary or aggregation of the candidate +root causes and that ⟨𝛽𝑗⟩ is non-zero and relatively large, but 𝒙𝑗 is +small. We typically omit 𝒙𝑗 because its scale is small and cannot +contribute much to the overall target. To this end, we resort to the +gradient×input approach, in which the attribution score can be +computed as: +𝑟𝑗 = |⟨𝛽𝑗⟩𝑥𝑗 |. +(34) +This value is known as salience in the literature of attribution [27]. +Now the candidate root causes will be chosen only when both ⟨𝛽𝑗⟩ +and 𝑥𝑗 itself are relatively large. + +BALANCE: Bayesian Linear Attribution for Root Cause Localization +SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA +However, our ultimate objective is to attribute the anomalies in +the target KPIs to the candidate root causes, and hence, our focus +is not on the absolute value of 𝑥𝑗. Instead, we intend to explain the +changes during the anomaly in 𝒚 by the changes in 𝒙𝑗. In other +words, we are interested in the marginal effect of a candidate, and +we are looking for how the target would change after replacing the +abnormal part in the candidates with the normal part. Recall that +in our case, the anomaly or alarm time is given. Hence, we choose +a baseline as the mean or the median of the normal part of the time +series and compute the difference Δ𝑥𝑗 between the anomaly and +the baseline. The resulting attribution score is defined as: +𝑟𝑗 = |⟨𝛽𝑗⟩Δ𝑥𝑗 |. +(35) +To further guarantee the attribution score to be invariant to the +scale of 𝒚, we finally calculate the attribution score as: +𝑟𝑗 = +���� +⟨𝛽𝑗⟩Δ𝑥𝑗 +Δ𝑦 +����. +(36) +It is worthwhile to emphasize that owing to the use of the pro- +posed forward model. The above attribution score satisfies all the +desirable axioms of the Shapley values, including completeness, +null player, symmetry, linearity, and continuity [2]. Here we briefly +go through these axioms in the case of RCA and discuss how the +proposed model copes with them. +• Completeness is satisfied when attributions sum up to the +difference between the value of𝒚 during normal and abnormal +periods. It is obvious that Eq-36 fulfills this requirement. +• Null players: if the target 𝒚 does not depend on some can- +didates 𝒙𝑗, then 𝑟𝑗 = 0. The proposed correlated horse-shoe +prior automatically excludes the irrelevant candidates 𝒙𝑗 and +set the corresponding ⟨𝛽𝑗⟩ = 0. As a result, 𝑟𝑗 = 0. +• Symmetry: if the target 𝒚 depends on two candidates 𝒙𝑗 and +𝒙𝑘 but not on their order, then 𝑟𝑗 = 𝑟𝑘. This axiom is satisfied +by considering multicollinearity in our forward model. +• Linearity: this property is satisfied by linear models naturally. +• Continuity: attributions generated for two nearly identical in- +puts should be nearly identical. This axiom can also be handled +by capturing multicollinearity in our forward model. +Moreover, it is apparent that the above axioms are in agreement +with the desiderata of an ideal RCA mentioned in §3. This again +bolsters our belief that attribution analysis is a natural fit for RCA. +4.3 +Merging Module: Intersection and Union +Explanation +In this subsection, we turn our attention to the case where there +are multiple target KPIs. Under this situation, we first compute the +attribution score𝑟𝑗𝑘 of each candidate root causes 𝒙𝑗 for each target +KPI 𝒚𝑘 following the two steps in the above two subsections. We +then sort the attribution scores 𝑟𝑗𝑘 across 𝑗 in the descending order +for each 𝑘 and refer to this step as ranking. We further retain the top +𝜅 root causes for each target KPI 𝒚𝑘. Note that when 𝜷 is properly +sparse (i.e., the number of non-zero entries in 𝜷 is smaller than +𝜅), the selection step can be omitted. After ranking and selection, +we merge the sets of root causes via the intersection or union of +the sets. The intersection operation indicates that the root cause +is chosen only when it influences all target KPIs, while the union +operation detects all possible root causes that propagate abnormally +to at least one target KPI. +5 +EXPERIMENTS +In this section, we first assess the performance of BALANCE on +synthetic data. We then show the performance of BALANCE on +three real-world applications2, including Bad SQL localization, Con- +tainer fault localization, and Fault Type Diagnosis for Exathon. The +first application mainly focuses on homogeneous pairs of the target +KPIs and the candidate root causes, while the latter two consider +heterogeneous ones. +Implementation Details: We adopt the BALANCE framework, +and for the forward module, we juxtapose our BMFS with other +SOTA methods, including Lasso, E-Net, and ARD in terms of estima- +tion accuracy and run time. The backward module is the same. For a +fair comparison, we replace the correlated horse-shoe prior with the +original horse-shoe prior and regard the resulting method as ARD. +Thus, ARD can be regarded as an ablation study on BMFS by remov- +ing the 𝑔-prior part in BMFS. Note that in the original ARD [36], +the Student’s 𝑇-prior is used instead to encourage sparsity. All +the compared methods have the same computation complexity of +O(𝑝2 max(𝑛, 𝑝)) according to our analysis. All methods are imple- +mented in Python 3.9 except the newly added R package “fsMTS”. +All the experiments are conducted on the same Linux Server with +Intel Xeon E5-2682 v4 @ 2.50GHz processors and 16GB RAM so +that all the execution time could be directly compared. +5.1 +Simulation on Synthetic Data +Here, we generate the synthetic data as follows: +𝒚 = 𝑿𝜷 + 𝝐, +(37) +where 𝑿 ∈ R𝑛×𝑝,𝒚 ∈ R𝑛, 𝜷 ∈ R𝑝, and 𝝐 ∼ N (0, 𝛼−1). To introduce +multicollinearity to 𝑿 and 𝜷, we assume that +𝜷 = 𝑸𝒃, +(38) +𝑿 = 𝒁𝑸−1, +(39) +where 𝒃 ∈ R𝑝𝑧, 𝒁 ∈ R𝑛×𝑝𝑧, and 𝑸 ∈ R𝑝𝑧×𝑝𝑧 denotes the orthogonal +part of the QR decomposition of a certain matrix 𝑾. Note that +𝑝𝑧 ≤ 𝑝. By specifying 𝑾 to be an identity matrix and 𝑝𝑧 = 𝑝, +the resulting features 𝑿 are independent of each other (or absent +of multicollinearity). On the other hand, by specifying 𝑾 to be a +random matrix and 𝑝𝑧 < 𝑝, we introduce some multicollinearity to +𝑿 (a.k.a. partial multicollinearity). Finally, by specifying 𝑾 to be a +selection matrix where each row only has one non-zero element +that can be either 1 or −1 and 𝑝𝑧 < 𝑝, the correlation between two +arbitrary columns in 𝑿 can be 1 or −1. We refer to this case as +“perfect multicollinearity”. +We investigate the impact of the ratio between 𝑝 and 𝑛, the level +of multicollinearity, the level of noise, the level of sparsity, and the +proportion of missing data on the performance of the proposed +BALANCE method. As mentioned before, we compare BMFS with +Lasso, E-Net, and ARD. Specifically for Lasso, the candidate set +2a. The dataset does not contain any Personal Identifiable Information (PII). b. The +dataset is desensitized and encrypted. c. Adequate data protection was carried out +during the experiment to prevent the risk of data copy leakage, and the dataset was +destroyed after the experiment. d. The dataset is only used for academic research, and +it does not represent any real business situation. + +SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA +Chen et al. +0 +200 +400 +600 +800 +1000 +feature dimension: p +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +F1 Score +BMFS +Lasso +E-Net +ARD +0 +200 +400 +600 +800 +1000 +dimension p +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1.0 +F1-score +(a) Absent +0 +200 +400 +600 +800 +1000 +dimension p +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1.0 +F1-score +(b) Partial +0 +200 +400 +600 +800 +1000 +dimension p +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1.0 +F1-score +(c) Perfect +Figure 5: 𝐹1-score as a function of the dimension 𝑝 resulting from all benchmark methods in case of (a) absent of mutlicollinearity, (b) partial +multicollinearity, and (c) perfect multicollinearity. +Table 1: Results of Synthetic Data with different levels of multicollinearity (absent, partial, and perfect) and different dimensions 𝑝 averaged +over 100 trials. Here, 𝑛 = 100, 𝛼−1 = 0.01, and proportion of nonzero coefficients = 0.5%. +𝑝 +Lasso +E-Net +ARD +BMFS +𝐹1-score +MSE +Time (s) +𝐹1-score +MSE +Time (s) +𝐹1-score +MSE +Time (s) +𝐹1-score +MSE +Time (s) +Absent +20 +0.7109 +6.90e-05 +4.70e-01 +0.6623 +7.490e-05 +4.65e-01 +0.9999 +2.60e-05 +2.34e-01 +0.9999 +2.60e-05 +2.35e-01 +50 +0.5148 +4.10e-05 +5.06e-01 +0.4383 +6.60e-05 +5.08e-01 +0.9743 +1.50e-05 +3.10e-01 +0.9887 +1.30e-05 +2.72e-01 +100 +0.4638 +3.00e-05 +5.84e-01 +0.3789 +5.10e-05 +5.88e-01 +0.9137 +1.70e-05 +4.47e-01 +0.9562 +1.20e-05 +4.10e-01 +200 +0.3995 +1.70e-05 +8.59e-01 +0.3943 +3.60e-05 +8.62e-01 +0.9758 +4.00e-06 +3.20e-01 +0.9730 +4.00e-06 +3.51e-01 +500 +0.3221 +9.00e-06 +1.99e+00 +0.3352 +2.60e-05 +2.00e+00 +0.9999 +1.00e-06 +5.32e-01 +0.9943 +1.00e-06 +4.94e-01 +1000 +0.2873 +5.74e-06 +3.01e+00 +0.2894 +1.96e-05 +3.25e+00 +0.9249 +1.87e-05 +2.12e+00 +0.9955 +9.35e-07 +2.00e+00 +Partial +20 +0.6821 +4.16e-02 +4.72e-01 +0.6720 +2.85e-02 +4.77e-01 +0.9724 +2.86e-02 +2.54e-01 +0.9593 +2.87e-02 +4.15e-01 +50 +0.5554 +1.90e-02 +5.50e-01 +0.5445 +1.32e-02 +5.84e-01 +0.9958 +1.30e-02 +2.91e-01 +0.9999 +1.30e-02 +3.70e-01 +100 +0.5221 +9.36e-03 +6.18e-01 +0.4598 +6.48e-03 +6.76e-01 +0.9696 +6.32e-03 +3.82e-01 +0.9999 +6.32e-03 +3.36e-01 +200 +0.4630 +4.56e-03 +8.52e-01 +0.5678 +3.25e-03 +9.52e-01 +0.9271 +3.17e-03 +1.06e+00 +0.9908 +3.16e-03 +4.59e-01 +500 +0.3974 +1.93e-03 +1.87e+00 +0.4843 +1.36e-03 +2.24e+00 +0.8069 +1.32e-03 +1.40e+00 +0.9963 +1.31e-03 +6.55e-01 +1000 +0.3532 +9.19e-04 +2.89e+00 +0.4216 +6.45e-04 +3.83e+00 +0.9431 +6.22e-04 +2.13e+00 +0.9824 +6.18e-04 +2.09e+00 +Perfect +20 +0.7188 +4.24e-02 +4.74e-01 +0.6696 +2.84e-02 +4.82e-01 +0.9474 +2.93e-02 +2.83e-01 +0.9273 +3.02e-02 +4.13e-01 +50 +0.5736 +1.92e-02 +5.11e-01 +0.5257 +1.35e-02 +5.42e-01 +0.9999 +1.33e-02 +2.67e-01 +0.9799 +1.34e-02 +3.61e-01 +100 +0.5301 +9.78e-03 +5.83e-01 +0.4775 +6.82e-03 +6.39e-01 +0.9927 +6.66e-03 +3.15e-01 +0.9944 +6.66e-03 +3.85e-01 +200 +0.4570 +4.36e-03 +7.82e-01 +0.5147 +3.11e-03 +9.04e-01 +0.9693 +3.03e-03 +5.49e-01 +0.9988 +3.03e-03 +4.50e-01 +500 +0.3862 +1.52e-03 +1.81e+00 +0.4705 +1.07e-03 +2.20e+00 +0.8164 +1.03e-03 +1.53e+00 +0.9729 +1.03e-03 +8.11e-01 +1000 +0.3599 +7.62e-04 +2.87e+00 +0.5022 +5.23e-04 +3.69e+00 +0.9205 +5.07e-04 +2.11e+00 +0.9722 +4.99e-04 +2.12e+00 +Table 2: Results of Synthetic Data with different levels of noise standard deviations (noise std) averaged over 100 trials. Here, 𝑛 = 100, 𝑝 = 1000, +and proportion of nonzero coefficients= 0.5%. +noise std +Lasso +E-Net +ARD +BMFS +𝐹1-score +MSE +Time (s) +𝐹1-score +MSE +Time (s) +𝐹1-score +MSE +Time (s) +𝐹1-score +MSE +Time (s) +0.01 +0.8466 +9.07e-04 +2.91e+00 +0.8820 +6.150e-04 +3.84e+00 +0.9250 +6.16e-04 +2.14e+00 +0.9789 +6.10e-04 +2.05e+00 +0.1 +0.3746 +8.81e-04 +2.88e+00 +0.4562 +6.06e-04 +3.71e+00 +0.9231 +5.87e-04 +2.06e+00 +0.9625 +5.80e-04 +2.11e+00 +1.0 +0.3353 +1.07e-03 +3.14e+00 +0.3294 +1.05e-03 +4.57e+00 +0.3596 +1.32e-03 +3.19e+00 +0.4054 +1.39e-03 +3.51e+00 +3.0 +0.1150 +2.19e-03 +3.90e+00 +0.1337 +2.09e-03 +6.19e+00 +0.0863 +1.08e-02 +3.38e+00 +0.0881 +1.16e-02 +3.37e+00 +Table 3: Results of Synthetic Data with different ratios of nonzero coefficients (nonzeros%) averaged over 100 trials. Here, 𝑛 = 100, 𝑝 = 1000, +and 𝛼−1 = 0.01. +nonzeros% +Lasso +E-Net +ARD +BMFS +𝐹1-score +MSE +Time (s) +𝐹1-score +MSE +Time (s) +𝐹1-score +MSE +Time (s) +𝐹1-score +MSE +Time (s) +0.2% +0.4482 +2.16e-04 +2.95e+00 +0.4054 +1.19e-04 +3.53e+00 +0.9766 +1.08e-04 +1.97e+00 +0.9999 +1.07e-04 +1.93e+00 +0.5% +0.3927 +8.20e-04 +2.97e+00 +0.4838 +5.87e-04 +3.96e+00 +0.9296 +5.67e-04 +2.30e+00 +0.9726 +5.63e-04 +1.94e+00 +1% +0.3810 +2.19e-03 +3.02e+00 +0.5448 +1.76e-03 +4.58e+00 +0.8913 +1.75e-03 +2.30e+00 +0.9654 +1.71e-03 +1.97e+00 +2% +0.3687 +6.13e-03 +2.95e+00 +0.5673 +5.47e-03 +5.37e+00 +0.7407 +5.52e-03 +2.51e+00 +0.9238 +5.31e-03 +1.99e+00 +5% +0.3694 +1.61e-02 +3.33e+00 +0.4853 +1.58e-02 +6.71e+00 +0.4409 +1.57e-02 +2.85e+00 +0.5483 +1.56e-02 +2.65e+00 +of the tuning parameter is 30 values spaced evenly in the interval +[−2, 2] in the log scale. For E-Net, the common penalty parameter + +BALANCE: Bayesian Linear Attribution for Root Cause Localization +SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA +Table 4: Results of Synthetic Data with different ratios of missing values in 𝑿 averaged over 100 trials. Here, 𝑛 = 100, 𝑝 = 1000, 𝛼−1 = 0.01, and +the proportion of nonzero coefficients= 0.5%. +missing +values +Lasso +E-Net +ARD +BMFS +𝐹1-score +MSE +Time (s) +𝐹1-score +MSE +Time (s) +𝐹1-score +MSE +Time (s) +𝐹1-score +MSE +Time (s) +10% +0.4306 +6.65e-04 +3.72e+00 +0.3791 +6.87e-04 +3.98e+00 +0.7461 +7.92e-04 +4.23e+00 +0.7494 +7.92e-04 +3.60e+00 +20% +0.4076 +7.46e-04 +3.63e+00 +0.4226 +7.84e-04 +3.98e+00 +0.7074 +8.90e-04 +5.47e+00 +0.7835 +8.04e-04 +4.65e+00 +30% +0.4083 +6.97e-04 +3.45e+00 +0.4381 +7.99e-04 +3.93e+00 +0.6721 +7.90e-04 +6.80e+00 +0.7714 +6.78e-04 +5.94e+00 +40% +0.4103 +8.41e-04 +3.64e+00 +0.3983 +7.69e-04 +4.41e+00 +0.6726 +8.89e-04 +9.81e+00 +0.7670 +7.69e-04 +8.64e+00 +50% +0.3474 +9.73e-04 +4.01e+00 +0.3327 +1.06e-03 +4.97e+00 +0.6170 +9.17e-04 +1.40e+01 +0.6727 +8.68e-04 +1.30e+01 +in front of both the ℓ1 and ℓ2 norm is selected from 10 evenly spaced +values in [−2, 2] in the log scale, and the ℓ1 ratio parameter is chosen +from [0.1, 0.5, 0.9]. The optimal tuning parameters are selected via +cross validation. Since these two methods cannot deal with missing +values explicitly, we replace the missing values with the mean of +the corresponding candidate. We consider three criteria, namely, 𝐹1- +score w.r.t. the zero pattern between the estimated and true 𝜷, mean +squared error (MSE) between estimated and true 𝜷, and running +time. Note that 𝐹1-score is the harmonic mean of precision and +recall, where precision is defined as the ratio between the number +of true root causes identified by the model and the number of all +root causes given by the model, and recall is defined as the ratio +between the number of true root causes identified by the model +and the number of true root causes. The results are summarized +in Tables 1-4. To highlight the merit of BMFS in terms of zero +pattern recovery, we further plot out the 𝐹1-score of all methods as +a function of 𝑝 in Figure 5. +Two major trends can be gleaned from the tables. First, BMFS +typically achieves comparable or better performance than the SOTA +methods in terms of both the estimation accuracy and the running +time, especially when the dimension 𝑝 is high, and the level of +multicollinearity is high. On the other hand, the superiority of BMFS +and ARD over E-Net and Lasso suggests that adaptively learning the +tuning parameters from the data via variational inference is more +advantageous than estimating them via brute-force grid search. +Grid search restricts the tuning parameters to the predefined set of +candidates, and consequently, a carelessly designed set may lead +to unsatisfactory performance. In addition, it can be observed that +the performance of BMFS and E-Net is better than that of ARD and +Lasso respectively, when there exists multicollinearity in the data, +as expected. Indeed, the ℓ1-norm penalized Lasso can only pick at +most 𝑛 candidates when 𝑝 > 𝑛 in theory, even if all candidates are +relevant. More precisely, if there are two or more highly collinear +candidates, Lasso only selects one of them at random. This explains +the deficiency of ARD and Lasso in comparison with BMFS and +E-Net. +Second, the performance of BMFS is robust to the number of di- +mensions, the level of multicollinearity, the noise level, the sparsity +level, and the proportion of missing values. To be specific, we can +see that Bayesian methods constantly outperform the frequency +methods for both 𝑝 ≤ 𝑛 and 𝑝 > 𝑛. Additionally, Bayesian methods +offer a straightforward way to cope with missing values by infer- +ring their distributions from the data at the expense of consuming +more time with the increase of the missing data proportion. In a +contrast, we employ the mean imputation method before applying +the frequentist methods, leading to inaccurate estimation when the +proportion of missing values is large. +Table 5: Different tenant KPIs and the corresponding SQL metrics. +Tenant KPI +SQL Metric +SQL_SELECT_RT +cpu_time +LOGICAL_READS +lr(logical_reads) +SQL_QUEUE_TIME +queue_time +RPC_PACKAGE_IN/OUT +rpc_count +… +direct influence +Tenant KPI: LOGICAL_READS +SQL_1 +SQL_2 +SQL_N +SQL_1 +SQL_2 +SQL_N +Tenant KPI: SQL_SELECT_RT +… +logical reads of SQL +cpu time of SQL +Figure 6: Targets and candidates for bad SQL localization. +5.2 +Bad SQL Localization +Database services are a fundamental infrastructure that is critical +for the everyday business of enterprises. Thus, it is of top priority to +guarantee the high availability of database services. Previous works, +such as iSQUAD [19], concentrate on determining the fault type of +an intermittent slow SQL from typical types given by experts or +from historical data. Different from slow queries, which appear in +massive numbers in the slow query logs, bad SQL localization is +a more comprehensive problem as we consider not only run time +but also logical reads, RPC count, etc. Bad SQLs cannot be always +found in the slow query logs since they may lead to anomalies in the +tenant KPIs via their CPU or memory usage instead of run time. As +mentioned in the introduction, here we aim to find "Bad SQLs" (i.e., +the candidate root causes 𝑿) that are suspicious and responsible +for the anomalies detected in tenant KPIs (i.e., the target KPIs 𝒚). +As shown in Table 5, Tenant KPIs monitor the performance of +tenants, while SQL metrics tell us the performance of each SQL. In +light of expert knowledge and offline data analysis, we find that +almost all bad SQL issues can be reflected by two kinds of tenant +KPIs, that is, SQL_SELECT_RT and LOGIC_READS. As such, the +alarm of these two KPIs is the trigger of our RCA module. Moreover, +we find that the tenant KPIs can be regarded as a summary of the +relevant SQL metrics. For instance, the tenant KPI SQL_SELECT_RT +is influenced by the metric cpu_time of all SQLs, while the other +KPI LOGIC_READS is associated with the metric lr (i.e., logic reads). +Hence, this application of BALANCE considers homogeneous 𝑿 and +𝒚. Figure 6 displays the targets and candidate pairs to be analyzed +by BALANCE in bad SQL localization. + +SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA +Chen et al. +Table 6: Results for bad SQL localization. +Methods +#Hits +#Misses +Accuracy +Time (s) +#Recommend +ARD +68 +24 +0.7556 +1.92e+00 +2.7 +Lasso +64 +24 +0.7111 +3.15e+00 +2.1 +E-Net +64 +26 +0.7222 +2.95e+00 +2.3 +fsMTS +49 +41 +0.5444 +1.20e+01 +5.0 +BMFS +75 +15 +0.8333 +1.78e+00 +2.3 +In addition, on the online monitor platform, the tenant KPIs +are saved as fixed-interval time series, whereas the SQL metrics +are collected by batch sampling: each batch collects the metrics +of all SQLs within 10 seconds before the collection time, and the +next collection starts after the previous one finishes the storage +process and so there are small uneven time gaps between every two +collections that amount to the storage time. To settle this problem, +we aggregate the SQL metrics within every minute and regard them +as time series. As a result, the timestamps of 𝑿 and 𝒚 might not +be aligned. We, therefore, use both 𝑿𝑡 and 𝑿𝑡−1 when aligning +with 𝒚𝑡, and output the SQL 𝑥𝑗 as a possible bad SQL when the +coefficient in front of either 𝒙𝑡 +𝑗 or 𝒙𝑡−1 +𝑗 +is non-zero. +Finally, while there are only two target KPIs, the number of +related SQLs 𝑝 can be very large (e.g., thousands or larger), varying +in each case. The SQLs are often correlated with each other as a +small modification of the WHERE or the LIMIT condition in a SQL +sentence is defined as a new SQL. The proportion of missing data +can also be very large. Furthermore, it is required to find the root +causes within 1 minute, and the results should be interpretable. In a +nutshell, under the problem of bad SQL localization, all 6 desiderata +in §3 should be satisfied. To merge the root causes resulting from +the two KPIs, we retain the top 3 root causes for each KPI (i.e., 𝜅 = 3 +in the merging module), and compute the union of the two sets of +root causes as the final recommendation. +To evaluate the performance of the proposed approach, we collect +90 samples from the SQL diagnosing platform of Ocean Base[41]. +The samples cover over 50 different tenants, and in each sample, +both the tenant KPIs and the SQL metrics are saved as 61-minute +time series (i.e., 𝑛 = 61), including the one-minute abnormal part. +Recall that 𝑝 scales up to hundreds or thousands. Hence, 𝑝 > 𝑛 in +this scenario. Missing data typically exist in the SQL metrics, up +to 50%. To match the requirement of real-time RCA tasks, three +evaluation criteria are selected that is accuracy, number of recom- +mendations, and running time. For each sample, if the true root +causes lie within the set of SQLs recommended by the proposed +method, we count this sample as a “hit”; otherwise, it is a “miss”. +Accuracy is then defined as the proportion of the number of hits +to the overall number of samples. Again, we compare different for- +ward models. As Lasso and E-Net cannot deal with missing data, +we impute the missing values using linear interpolation for ten- +ant KPIs and fill zeros for the SQL metrics. In addition, we further +consider another benchmark method, fsMTS (feature selection for +multivariate time series) [23]. This method considers lagged tempo- +ral dependence and selects features from 𝑿𝑡, · · · , 𝑿𝑡−𝜏, where 𝜏 is +the time lag. It then resorts to an ensemble method to combine the +results from cross-correlation, graphical lasso, random forest, etc. +As fsMTS can only tell us whether a feature is selected, we choose +the tuning parameter such that only 𝜅 = 3 candidates are selected +for each KPI. The results for all methods are presented in Table 6. +It can be observed that the proposed method achieves the highest +accuracy with the lowest number of recommendations and the low- +est amount of computational time. The accuracy is 83.33%, which +is at least 8% higher than the baseline methods. The number of +recommendations is only 2.3, and the running time is only 1.78 +seconds on average. Note that while being complete, the number +of recommendations is supposed to be as small as possible as it +helps the SREs to concentrate on a few root causes so they can +dive in and fix the issue more efficiently. On the other hand, we +can tell from Table 6 that the performance of BMFS and E-Net is +better than that of ARD and Lasso respectively since the former two +methods can cope with the multicollinearity within the data. We +can also find that the Bayesian methods (i.e., BMFS and ARD) out- +perform their frequency counterparts (i.e., E-Net and Lasso) since +they can learn the distribution of the tuning parameters as well as +the missing values adaptively from the data. We have deployed the +proposed method to production, and the online results show that +the accuracy can be as high as 95%, which further demonstrates the +advantages of BALANCE. Finally, fsMTS yields the worst result, +probably because 1) temporal dependence is not the main concern +for time series grouped by the minute; 2) the base learner in the +ensemble, such as graphical lasso, also needs careful tuning of the +penalty parameters but now only the default value is used. +5.3 +Container Fault Localization +In this section, we further apply the proposed approach to another +practical situation, that is, container fault localization. In this situa- +tion, once the number of trace failures associated with a container +is abnormal, the proposed BALANCE method would find the con- +tainer metrics that can best explain the anomaly, and the RCA +results will further lead to self-healing operations such as restart +and traffic throttling. By addressing all trace failures automatically, +the high availability of the cloud-native system can be guaranteed. +In this case, the target KPI 𝒚 is the number of trace failures +associated with a container, and the candidate root causes 𝑿 is the +10 metrics of this container, such as CPU usage, memory usage, +inward and outward traffic, the number of TCP connections, etc. +Note that 𝒚 and 𝑿 are heterogeneous under this setting. Moreover, +there exist strong correlations among the container metrics. For +instance, the metric CPU usage is the sum of another two metrics: +CPU user usage and CPU system usage, and additionally, the metrics +inward traffic in bytes, outward traffic in bytes, inward traffic in +packages, and outward traffic in packages are closely correlated. +Missing data also appears now and then, up to 10%. +To assess the quality of our method, we collect 100 samples in +total from a fault diagnosing platform of Ant Group. For each sam- +ple, we can obtain the alarm time and 30-minute time series for +both 𝑿 and 𝒚 before and during the anomaly. In this case, 𝑛 = 30, +𝑝 = 10, and 𝑝 < 𝑛. We benchmark the proposed forward model +BMFS against Lasso, E-Net, ARD, and fsMTS, and evaluate all mod- +els in terms of precision, recall, 𝐹1-score, and running time. The +results are listed in Table 7. Notice that the deployment of BAL- +ANCE to production yields similar results. BMFS blows out of the +water Lasso, E-Net, ARD, and fsMTS in terms of both 𝐹1-score and +running time. Indeed, the 𝐹1 score resulting from BMFS is above +20% higher than that of the second best method ARD. Concretely, +the precision of BMFS and E-Net is respectively similar to that + +BALANCE: Bayesian Linear Attribution for Root Cause Localization +SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA +0 +20 +60 +80 +40 +time (min) +0 +5 +10 +15 +no. of trace failures +(a) Target KPI 𝒚 +0 +20 +40 +60 +80 +time (min) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +normalized values +CPU_util: 1.25,0.00,1.09,1.58 +CPU_sys: 2.01,5.03,1.75,1.71 +CPU_user: 0.62,0.00,1.33,1.64 +(b) CPU related metrics +0 +20 +40 +60 +80 +time (min) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +normalized values +Mem_util: 0.87,6.25,0.88,1.96 +Mem_used: 1.44,0.00,1.22,1.47 +(c) Memory related metrics +0 +20 +40 +60 +80 +time (min) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +normalized values +Tfc_Pkg_In: 2.88,5.56,1.89,1.93 +Tfc_Pkg_Out: 1.71,0.00,1.67,1.77 +(d) Traffic related metrics +Figure 7: Visualization of the trace failure number 𝒚 and correlated container metrics: the four values associated with each metric in the +legend denote the attribution scores of ARD, Lasso, E-Net, and BMFS sequentially. +Table 7: Results for container fault localization. +Methods +Recall +Precision +𝐹1-score +Time (s) +ARD +0.4784 +0.98804 +0.6266 +3.54e-1 +Lasso +0.5083 +0.5219 +0.4712 +4.96e-1 +E-Net +0.7352 +0.5520 +0.5925 +4.58e-1 +fsMTS +0.4826 +0.5244 +0.4655 +7.01e-1 +BMFS +0.8180 +0.9136 +0.8569 +1.52e-1 +of ARD and Lasso, but the recall of the former two methods is +much higher, indicating that ARD and Lasso mistakenly omit some +relevant metrics and highlighting the appeal of considering multi- +collinearity among candidate root causes. To further elucidate this +point, we depict as an example the target KPI and the correlated +candidate root causes in Figure 7 and show the attribution scores +for ARD, Lasso, E-Net, and BMFS sequentially for each candidate +root cause in the figure. It can be seen that BMFS yields similar +attribution scores for closely correlated root causes (i.e., the axiom +of continuity in §2.2), whereas the attribution scores resulting from +other methods do not always follow this axiom. In addition, we can +observe that the 𝐹1-score of both BMFS and ARD is higher than that +of E-Net and Lasso, implying the merits of learning the distribu- +tions of tuning parameters adaptively from the data. Finally, despite +the heterogeneity between 𝑿 and 𝒚 in this scenario, the proposed +BALANCE still works well, probably due to the model-agnostic +nature of linear attribution methods [18]. On the other hand, we +notice that the relationship between heterogeneous 𝒙𝑗 and𝒚 during +anomalies can be well approximated by a linear model since similar +phenomena (i.e., the waveform anomaly) usually occurs to both +of them during anomalies. For example, an abnormal spike in 𝒙𝑗 +typically leads to a spike in 𝒚, while an abrupt increase in 𝒙𝑗 results +in an increase or decrease in 𝒚. +5.4 +Fault Type Diagnosis for Exathlon Dataset +We further investigate the performance of BALANCE on the pub- +lic benchmark, Exathlon [12], which consists of real data traces +collected from 10 Spark streaming applications in a 4-node clus- +ter over a 2.5-month period. There are 5 types of faults injected +into the traces during executions, including Bursty Input (Type +1), Bursty Input Until Crash (Type 2), Stalled Input (Type 3), CPU +Contention (Type 4), and Process Failure (Type 5). The duration of +the fault injection approximately ranges from 15 to 30 minutes. For +each injection, the time series of 2,283 metrics coming from Spark +are collected. Originally, Exathlon conducts anomaly detection for +multivariate time series and then attributes the anomaly of multi- +variate time series as a whole to individual time series. Here, we +build a new fault-type diagnosis task on top of Exathlon (named +Exathlon-ftd) to evaluate our method. Exathlon-ftd is constructed +in the following way. +First, we define the target KPI 𝒚 and the candidate metrics 𝑿 for +this dataset. The target KPI is supposed to be affected by various +types of faults and can be used to trigger the RCA procedure. To +this end, we conduct anomaly detection using the 3𝜎 rule after +detrending on all metrics for each injection and find the intersec- +tion of the anomalous metrics in all cases. We choose the metric +Processing_Delay from the intersection as our target KPI 𝒚, since +the processing time is influenced by all aforementioned types of +faults both theoretically and empirically. The candidate metrics 𝑿 is +then chosen as the metrics that are abnormal in the same duration +when 𝒚 is abnormal via the candidate AD module in Figure 1. +Second, we establish rules to determine the fault types once the +root causes metrics are selected from 𝑿. For simplicity, we only +focus on the first 4 types of events and define 4 rules (R1-R4) to +determine the fault types given the estimated root cause metrics as: +R1. If the metrics about traffic such as Last_Complete_Batch_Records +and Processed_Records are in the estimated set of root causes, +then it is the problem of the input (i.e., traffic). The fault type +is “Bursty Input” or “Bursty Input Until Crash” if these metrics +are increasing and is “Stalled Input” if decreasing. +R2. If R1 is not satisfied and the estimated set of root causes con- +tains the metrics about CPU that are concentrated on a single +node, then the fault type is “CPU contention”. The rationale +behind is that the traffic problem can lead to anomalies in the +metrics about CPU, but the CPU contention problem cannot +in turn influence the metrics about traffic. +R3. If the above two rules are not satisfied and the estimated set +of root causes contains the metric executor_active_tasks, then +the fault type is “Bursty Input” or “Bursty Input Until Crash”. +We notice that both the traffic increase and the CPU con- +tention problem will cause the abnormal increase in execu- +tor_active_tasks. However, a CPU contention problem typically +results from another program on a single node that consumes +all the CPU cores available on that node, and thus, the root +cause metrics about CPU in the estimated set typically resolve +around a single node (i.e., R2). As this condition does not hold, +we can conclude that the fault type here is “Bursty Input”. +R4. If the above three rules are not satisfied, the fault type is +“Unknown”. +After these two steps, 73 cases are collected in total for the +RCA task. For each case, we aggregate both 𝑿 and 𝒚 by minute, +and we retain 60 minutes and 5 minutes respectively before and + +SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA +Chen et al. +Table 8: Results for Exathlon fault type analysis. +Methods +#Hits +#Misses +Accuracy +Time (s) +#Recommend +ARD +54 +19 +0.7397 +1.29e+00 +3.4 +Lasso +51 +22 +0.6986 +1.58e+00 +4.4 +E-Net +49 +24 +0.6712 +1.67e+00 +4.7 +fsMTS +36 +37 +0.4932 +4.45e+01 +4.9 +BMFS +58 +15 +0.7945 +1.60e+00 +3.2 +after Root_Cause_State time available in the dataset. Thus, 𝑛 = 66. +The number of candidates 𝑿 after anomaly detection scales up +to 𝑝 = 150 approximately. We then compare all methods on the +constructed Exathlon-ftd task. The results are presented in Table 8. +Once again, BMFS outperforms all the compared methods with +the highest accuracy and the fewest number of recommended root +cause metrics. The running time of BMFS is the second best, slightly +longer than that of ARD. +6 +CONCLUSION AND FUTURE WORK +The major contribution of this paper is to shed a different light +on the RCA problem, viewing it from the angle of XAI. In particu- +lar, we assume that the abnormal behavior of the target KPIs can +be explained by the relevant candidate root causes and propose +a novel attribution-based RCA method named BALANCE. Con- +cretely, we first learn a Bayesian sparse multicollinear model that +predicts the target KPIs given the candidate root causes. We then +attribute the abnormal behavior of the target KPIs to the candi- +dates by computing their attribution scores. We empirically show +that the proposed method achieves superior performance for the +synthetic data and three real-world problems, including bad SQL +localization, container fault localization, and fault type diagnosis. +We notice that the target KPIs and the candidate root causes are +homogeneous in the former case and heterogeneous in the latter +two cases, while 𝑝 > 𝑛 in the first and third application and 𝑝 ≤ 𝑛 +in the second one. We have deployed BALANCE to production, +providing real-time root cause diagnosis of bad SQL and container +issues in distributed data systems. Although far from exhaustive, +these applications show that BALANCE has the potential to serve +as a general tool for practical RCA tasks. +In future work, we would like to explore the connections between +attribution-based RCA and graph-based RCA. In addition, we would +like to generalize the linear model in BALANCE to non-linear +forward models, such as the generalized linear models, which can +be more expressive and suitable for describing the relationship +between heterogeneous metrics. +REFERENCES +[1] Pooja Aggarwal, Ajay Gupta, Prateeti Mohapatra, et al. 2020. Localization of +operational faults in cloud applications by mining causal dependencies in logs +using golden signals. In International Conference on Service-Oriented Computing. +137–149. +[2] Marco Ancona, Cengiz Oztireli, and Markus Gross. 2019. Explaining deep neural +networks with a polynomial time algorithm for shapley value approximation. In +International Conference on Machine Learning (ICML). 272–281. +[3] Charles K Assaad, Emilie Devijver, and Eric Gaussier. 2022. Survey and Evaluation +of Causal Discovery Methods for Time Series. Journal of Artificial Intelligence +Research 73 (2022), 767–819. +[4] Sebastian Bach, Alexander Binder, Grégoire Montavon, et al. 2015. On pixel- +wise explanations for non-linear classifier decisions by layer-wise relevance +propagation. PloS One 10, 7 (2015). +[5] Ranjita Bhagwan, Rahul Kumar, Ramachandran Ramjee, et al. 2014. Adtribu- +tor: Revenue debugging in advertising systems. In 11th USENIX Symposium on +Networked Systems Design and Implementation (NSDI). 43–55. +[6] Christopher M Bishop and Nasser M Nasrabadi. 2006. Pattern recognition and +machine learning. Vol. 4. +[7] Jonathan Boss, Jyotishka Datta, Xin Wang, et al. 2021. Group Inverse-Gamma +Gamma Shrinkage for Sparse Regression with Block-Correlated Predictors. arXiv +preprint arXiv:2102.10670 (2021). +[8] Kirill Bykov, Marina M-C Höhne, Adelaida Creosteanu, et al. 2021. Explaining +bayesian neural networks. arXiv preprint arXiv:2108.10346 (2021). +[9] Carlos M Carvalho, Nicholas G Polson, and James G Scott. 2009. Handling sparsity +via the horseshoe. In Artificial Intelligence and Statistics (AIStat). 73–80. +[10] Pengfei Chen, Yong Qi, Pengfei Zheng, et al. 2014. Causeinfer: Automatic and +distributed performance diagnosis with hierarchical causality graph in large +distributed systems. In IEEE Conference on Computer Communications (INFOCOM). +1887–1895. +[11] Yingnong Dang, Qingwei Lin, and Peng Huang. 2019. AIOps: real-world chal- +lenges and research innovations. In IEEE/ACM 41st International Conference on +Software Engineering: Companion Proceedings (ICSE-Companion). 4–5. +[12] Vincent Jacob, Fei Song, Arnaud Stiegler, et al. 2021. Exathlon: A Benchmark +for Explainable Anomaly Detection over Time Series. Proceedings of the VLDB +Endowment (PVLDB) (2021). +[13] Vimalkumar Jeyakumar, Omid Madani, Ali Parandeh, et al. 2019. ExplainIt!–A +declarative root-cause analysis engine for time series data. In Proceedings of the +ACM International Conference on Management of Data (SIGMOD). 333–348. +[14] Myunghwan Kim, Roshan Sumbaly, and Sam Shah. 2013. Root cause detection +in a service-oriented architecture. ACM SIGMETRICS Performance Evaluation +Review 41, 1 (2013), 93–104. +[15] Wu Lin, Mohammad Emtiyaz Khan, and Mark Schmidt. 2019. Fast and simple +natural-gradient variational inference with mixture of exponential-family approx- +imations. In International Conference on Machine Learning (ICML). 3992–4002. +[16] Pantelis Linardatos, Vasilis Papastefanopoulos, and Sotiris Kotsiantis. 2020. Ex- +plainable ai: A review of machine learning interpretability methods. Entropy 23, +1 (2020), 18. +[17] Dewei Liu, Chuan He, Xin Peng, et al. 2021. Microhecl: High-efficient root cause +localization in large-scale microservice systems. In IEEE/ACM 43rd International +Conference on Software Engineering: Software Engineering in Practice (ICSE-SEIP). +338–347. +[18] Scott M Lundberg and Su-In Lee. 2017. A unified approach to interpreting model +predictions. Advances in neural information processing systems (NIPS) 30 (2017). +[19] Minghua Ma, Zheng Yin, Shenglin Zhang, et al. 2020. Diagnosing root causes of +intermittent slow queries in cloud databases. Proceedings of the VLDB Endowment +13, 8 (2020), 1176–1189. +[20] Raha Moraffah, Paras Sheth, Mansooreh Karami, et al. 2021. Causal inference +for time series analysis: Problems, methods and evaluation. Knowledge and +Information Systems (2021), 1–45. +[21] Vinod Nair, Ameya Raul, Shwetabh Khanduja, et al. 2015. Learning a hierarchical +monitoring system for detecting and diagnosing service issues. In Proceedings of +the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data +Mining. 2029–2038. +[22] Sarah E Neville, John T Ormerod, and MP Wand. 2014. Mean field variational +Bayes for continuous sparse signal shrinkage: pitfalls and remedies. Electronic +Journal of Statistics 8, 1 (2014), 1113–1151. +[23] Dmitry Pavlyuk. 2022. fsMTS: Feature Selection for Multivariate Time Series. +[24] Juan Qiu, Qingfeng Du, Kanglin Yin, et al. 2020. A causality mining and knowl- +edge graph based method of root cause diagnosis for performance anomaly in +cloud applications. Applied Sciences 10, 6 (2020), 2166. +[25] Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin. 2016. " Why should i +trust you?" Explaining the predictions of any classifier. In Proceedings of the 22nd +ACM SIGKDD international Conference on Knowledge Discovery & Data mining. +1135–1144. +[26] Veronika Ročková and Edward I George. 2014. Negotiating multicollinearity +with spike-and-slab priors. Metron 72, 2 (2014), 217–229. +[27] Avanti Shrikumar, Peyton Greenside, and Anshul Kundaje. 2017. Learning im- +portant features through propagating activation differences. In International +conference on machine learning (ICML). 3145–3153. +[28] Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman. 2014. Deep inside +convolutional networks: Visualising image classification models and saliency +maps. In ICLR workshop. +[29] Jacopo Soldani and Antonio Brogi. 2022. Anomaly detection and failure root cause +analysis in (micro) service-based cloud applications: A survey. ACM Computing +Surveys (CSUR) 55, 3 (2022), 1–39. +[30] Peter Spirtes and Clark Glymour. 1991. An algorithm for fast recovery of sparse +causal graphs. Social science computer review 9, 1 (1991), 62–72. +[31] Yi Sun and Mukund Sundararajan. 2011. Axiomatic attribution for multilinear +functions. In Proceedings of the 12th ACM conference on Electronic commerce. +177–178. +[32] Yongqian Sun, Youjian Zhao, Ya Su, et al. 2018. Hotspot: Anomaly localization +for additive kpis with multi-dimensional attributes. IEEE Access 6 (2018), 10909– +10923. + +BALANCE: Bayesian Linear Attribution for Root Cause Localization +SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA +[33] Mukund Sundararajan, Ankur Taly, and Qiqi Yan. 2017. Axiomatic attribution +for deep networks. In International conference on machine learning (ICML). 3319– +3328. +[34] Jörg Thalheim, Antonio Rodrigues, Istemi Ekin Akkus, et al. 2017. Sieve: Ac- +tionable insights from monitored metrics in microservices. +arXiv preprint +arXiv:1709.06686 (2017). +[35] Robert Tibshirani. 1996. Regression shrinkage and selection via the lasso. Journal +of the Royal Statistical Society: Series B (Methodological) 58, 1 (1996), 267–288. +[36] Michael E Tipping. 2001. Sparse Bayesian learning and the relevance vector +machine. Journal of machine learning research (JMLR) 1, Jun (2001), 211–244. +[37] Guanchu Wang, Yu-Neng Chuang, Mengnan Du, et al. 2022. Accelerating Shapley +Explanation via Contributive Cooperator Selection. In International Conference +on Machine Learning (ICML). +[38] Hanzhang Wang, Phuong Nguyen, Jun Li, et al. 2019. Grano: Interactive graph- +based root cause analysis for cloud-native distributed data platform. Proceedings +of the VLDB Endowment 12, 12 (2019), 1942–1945. +[39] Ping Wang, Jingmin Xu, Meng Ma, et al. 2018. Cloudranger: Root cause identifi- +cation for cloud native systems. In 18th IEEE/ACM International Symposium on +Cluster, Cloud and Grid Computing (CCGRID). 492–502. +[40] Jianping Weng, Jessie Hui Wang, Jiahai Yang, et al. 2018. Root cause analysis +of anomalies of multitier services in public clouds. IEEE/ACM Transactions on +Networking 26, 4 (2018), 1646–1659. +[41] Zhenkun Yang, Chuanhui Yang, Fusheng Han, Mingqiang Zhuang, Bing Yang, +Zhifeng Yang, Xiaojun Cheng, Yuzhong Zhao, Wenhui Shi, Huafeng Xi, Huang Yu, +Bin Liu, Yi Pan, Boxue Yin, Junquan Chen, and Quanqing Xu. 2022. OceanBase: +A 707 Million tpmC Distributed Relational Database System. Proceedings of the +VLDB Endowment 15, 12 (2022), 3385–3397. +[42] Hang Yu, Songwei Wu, Luyin Xin, et al. 2020. Fast Bayesian Inference of Sparse +Networks with Automatic Sparsity Determination. J. Mach. Learn. Res. 21 (2020), +124–1. +[43] Hang Yu, Luyin Xin, and Justin Dauwels. 2019. Variational wishart approxi- +mation for graphical model selection: Monoscale and multiscale models. IEEE +Transactions on Signal Processing 67, 24 (2019), 6468–6482. +[44] Matthew D Zeiler and Rob Fergus. 2014. Visualizing and understanding convolu- +tional networks. In European conference on computer vision (ECCV). 818–833. +[45] Arnold Zellner. 1986. On assessing prior distributions and Bayesian regression +analysis with g-prior distributions. Bayesian inference and decision techniques +(1986). +[46] Kai Zhang, Chao Tian, Kun Zhang, et al. 2021. A Fast PC Algorithm with Reversed- +order Pruning and A Parallelization Strategy. arXiv preprint arXiv:2109.04626 +(2021). +[47] Xu Zhang, Chao Du, Yifan Li, et al. 2021. HALO: Hierarchy-aware Fault Local- +ization for Cloud Systems. In Proceedings of the 27th ACM SIGKDD Conference on +Knowledge Discovery & Data Mining. 3948–3958. +[48] Yingying Zhang, Zhengxiong Guan, Huajie Qian, et al. 2021. CloudRCA: A Root +Cause Analysis Framework for Cloud Computing Platforms. In Proceedings of +the 30th ACM International Conference on Information & Knowledge Management +(CIKM). 4373–4382. +[49] Xun Zheng, Bryon Aragam, Pradeep K Ravikumar, et al. 2018. Dags with no tears: +Continuous optimization for structure learning. Advances in Neural Information +Processing Systems (NIPS) 31 (2018). +[50] Hui Zou and Trevor Hastie. 2005. Regularization and variable selection via the +elastic net. Journal of the royal statistical society: series B (statistical methodology) +67, 2 (2005), 301–320. + diff --git a/qtFRT4oBgHgl3EQfezdF/content/tmp_files/load_file.txt b/qtFRT4oBgHgl3EQfezdF/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..a4e3043a3e08040128075c23d8ac9d9164982bbb --- /dev/null +++ b/qtFRT4oBgHgl3EQfezdF/content/tmp_files/load_file.txt @@ -0,0 +1,1527 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf,len=1526 +page_content='BALANCE: Bayesian Linear Attribution for Root Cause Localization Chaoyu Chen† Ant Group China chris.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='ccy@antgroup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='com Hang Yu† Ant Group China hyu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='hugo@antgroup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='com Zhichao Lei Ant Group China leizhichao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='lzc@antgroup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='com Jianguo Li∗ Ant Group China lijg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='zero@antgroup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='com Shaokang Ren Ant Group China renshaokang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='rsk@antgroup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='com Tingkai Zhang Ant Group China tingkai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='ztk@antgroup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='com Silin Hu Ant Group China husilin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='hsl@antgroup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='com Jianchao Wang Ant Group China luli.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='wjc@antgroup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='com Wenhui Shi Ocean Base China yushun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='swh@oceanbase.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='com ABSTRACT Root Cause Analysis (RCA) plays an indispensable role in dis- tributed data system maintenance and operations, as it bridges the gap between fault detection and system recovery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Existing works mainly study multidimensional localization or graph-based root cause localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' This paper opens up the possibilities of exploit- ing the recently developed framework of explainable AI (XAI) for the purpose of RCA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In particular, we propose BALANCE (BAyesian Linear AttributioN for root CausE localization), which formulates the problem of RCA through the lens of attribution in XAI and seeks to explain the anomalies in the target KPIs by the behavior of the candidate root causes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' BALANCE consists of three innovative components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' First, we propose a Bayesian multicollinear feature selection (BMFS) model to predict the target KPIs given the can- didate root causes in a forward manner while promoting sparsity and concurrently paying attention to the correlation between the candidate root causes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Second, we introduce attribution analysis to compute the attribution score for each candidate in a backward manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Third, we merge the estimated root causes related to each KPI if there are multiple KPIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We extensively evaluate the pro- posed BALANCE method on one synthesis dataset as well as three real-world RCA tasks, that is, bad SQL localization, container fault localization, and fault type diagnosis for Exathlon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Results show that BALANCE outperforms the state-of-the-art (SOTA) methods in terms of accuracy with the least amount of running time, and achieves at least 6% notably higher accuracy than SOTA methods ∗Corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' † Two authors contributed equally to this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Copyrights for components of this work owned by others than ACM must be honored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Abstracting with credit is permitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Request permissions from permissions@acm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='org.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA © 2023 Association for Computing Machinery.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' ACM ISBN 978-1-4503-XXXX-X/18/06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='$15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='00 https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='org/XXXXXXX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='XXXXXXX for real tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' BALANCE has been deployed to production to tackle real-world RCA problems, and the online results further advocate its usage for real-time diagnosis in distributed data systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' CCS CONCEPTS Software and its engineering;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' • Information systems → Au- tonomous database administration;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' • Computing methodolo- gies → Feature selection;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Regularization;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' KEYWORDS Root Cause Analysis, Bayesian Method, Bad SQLs, Faults Diagnosis, Distributed System, Attribution Analysis, Explainable AI ACM Reference Format: Chaoyu Chen†, Hang Yu†, Zhichao Lei, Jianguo Li, Shaokang Ren, Tingkai Zhang, Silin Hu, Jianchao Wang, and Wenhui Shi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' BALANCE: Bayesian Linear Attribution for Root Cause Localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In Proceedings of In Pro- ceedings of the 2023 International Conference on Management of Data (SIG- MOD ’23).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' ACM, New York, NY, USA, 15 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='org/XXXXXXX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' XXXXXXX 1 INTRODUCTION System faults and incidents have a possibly tremendous influence on distributed data systems which are widely adopted in modern information technology (IT) and financial companies, since they may lead to system outrage and further incur astounding financial loss and jeopardize customer trust [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' It has been reported by Forbes that every year IT downtime costs an estimated $26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5 billion in lost revenue alone, not to mention the indirect expense, including lost customers and references.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Thus, it is imperative to conduct fast and precise fault diagnosis and recovery before they become service-impacting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' A central task in fault diagnosis and recovery is root cause analysis (RCA), which bridges the gap between fault detection and recovery [11, 13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Currently, the task of RCA is mainly accomplished by site reliabil- ity engineers (SREs) with rich operation experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Unfortunately, such manual work becomes prohibitively slow due to the increase arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='13572v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='LG] 31 Jan 2023 SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' of the scale and complexity of the architecture as well as the dy- namic and unpredictable nature of the system metrics and events, thus deviating from the requirement of efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Indeed, as men- tioned in [19], it can take as long as several hours of manual work to diagnose the root causes of intermittent slow queries in distributed database systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' This has sparked considerable research efforts toward designing automated RCA algorithms based on machine learning so as to provide aid in saving time and ultimately money.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Literature on RCA algorithms can be broadly divided into two categories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The first one focuses on multidimensional root cause localization [5, 32, 47], which seeks to explain the abnormal be- havior of the additive key performance indicators (KPIs) by iden- tifying the fault-indicating combinations of their corresponding multi-dimensional attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The success of these algorithms relies on two assumptions: 1) the value of the KPI in each dimension equals the sum of the values of its attributes and 2) all the KPIs and their attributes can be monitored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' However, these two assumptions can be too restrictive in real-world problems, and a more practi- cal setting is to attribute the anomalies to root cause candidates without additive assumptions while allowing for missing data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' On the other hand, the second category revolves around graph-based RCA algorithms [14, 24, 38, 39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' These approaches typically first construct a causal graph based on tracing service calls or causal discovery algorithms [46] and then find the root cause node via rule-based traversing or random walk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' A major impediment to the application of tracing graphs and rule-based traversing is that it is system invasive and typically incurs arduous work on enumerating all traces and rules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As an alternative, causal discovery methods are employed to learn the graph structure as in [39].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Unfortunately, the causal discovery methods suffer from both high computational and sample complexity [46], and in consequence, they can be distress- ingly slow for large graphs and may lead to inaccurate results when the number of observations for all metrics in the graph is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' After obtaining the graph, the random walk methods are heuristic and might fail to converge to the root cause when the number of random walks is not sufficiently large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In this paper, we explore alternatives and recast the RCA problem as a feature attribution problem [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To the best of our knowledge, we are among the first to analyze the root cause through the lens of attribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As a commonly used tool in explainable AI (XAI), attribution methods assign attribution scores to input features, the absolute value of which represents their importance to the model prediction or performance [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Analogously, we aim to find the root causes that can best explain the alarmed KPIs in RCA problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The attribution scores of the candidate causes represent their relevance or contribution to the alarmed KPIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As a motivating example, in database systems, “bad SQLs” is referred to as SQLs with deteriorated performance due to indexing errors or changes in the execution plan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The performance deterioration of these SQLs typically leads to anomalies in the tenant KPIs and may severely influence the user experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In this case, the target (𝒚) are the tenant KPIs and the candidate causes (𝑿) are SQL metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' An attribution task can then be accomplished in two steps: first, a forward model is constructed that exploits the input features (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', candidate causes) to predict the outputs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', alarmed KPIs), and next, the significance of the input features are evaluated through attribution approaches in a backward manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Particularly in the bad SQL localization example, the number of candidate SQLs 𝑝 varies in each case and can be as large as thousands, whereas the number of observations 𝑛 (the length of the corresponding time series) is typically small since we only focus on the part around the anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In other words, the dimension 𝑝 can be larger than the sample size 𝑛 in the RCA problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To address this issue and to automate the feature selection process, we adopt sparse linear models as the forward model due to their high flexibility, efficiency, and interpretability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Furthermore, the candidate causes are usually correlated with each other, and there often exist missing values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To tackle these problems that plague linear models, we propose a novel Bayesian multicollinear feature selection (BMFS) model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Afterward, we provide the attribution score for each candidate cause from different perspectives, including sensitivity and salience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Finally, we merge results when there exist multiple alarmed KPIs and each of them is attributed to a different set of root causes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We name the overall model BALANCE (BAyesian Linear AttributioN for root CausE localization).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We would like to point out that both the multidimensional RCA and the graph-based RCA can be formulated from the perspective of attribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Specifically, we can regard the multidimensional RCA as attributing the anomalies in the KPIs to the combinations of their attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' It follows that the additive constraints in the multidimensional RCA can be removed, and hence, we only need to consider the abnormal attributes under this scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' On the other hand, by regarding all abnormal nodes in the graph as candidate causes, BALANCE can be used to identify the root cause efficiently even though the graph structure is not available or cannot be reli- ably learned, which is often the case in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Viewed another way, BALANCE can also be used as a building block to construct causal graphs, since linear regression models are frequently used for causal discovery [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Given the graph, BALANCE serves as a better substitute for random walks as it does not require a large number of random walks and so is more efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We validate the usefulness of BALANCE on four datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' First, we generate synthetic data with a different number of input fea- tures, different levels of multicollinearity, noise, and sparsity, and different proportions of missing values, and then compare vari- ous forward models including the proposed BMFS, Lasso, E-Net (Elastic net), and ARD (Automatic Relevance Determination).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We find that BMFS typically recovers the underlying true regression coefficients the best with comparable or even shorter running time, especially when there exists multicollinearity among the input fea- tures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Furthermore, we utilize the proposed method to address three real-world RCA problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In the first problem, we deal with the problem of bad SQL localization as mentioned before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Our results show that the proposed method can identify the human-labeled root cause SQLs in fewer than 2 seconds per case with accuracy as high as 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3%, whereas it takes 3 minutes for SREs on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The second application copes with the problem of container fault local- ization, whose objective is to attribute the abnormal trace failures in a container to the metrics of the container, such as CPU usage, memory usage, TCP, etc, and facilitate the self-healing process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The proposed method can achieve an 𝐹1-score of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='86, which is at least 20% higher than other baseline methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Finally, we apply BAL- ANCE to a public dataset, Exathlon [12], for the purpose of fault type diagnosis, and the resulting accuracy is again 6% higher than BALANCE: Bayesian Linear Attribution for Root Cause Localization SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA the SOTA methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Note that the first application handles KPIs and candidates that are homogeneous while the latter two tackles heterogeneous ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The advantageous performance of BALANCE in all three scenes shows that attribution-based RCA can be an effective and efficient tool for general and practical RCA cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In summary, our contribution includes: To the best of our knowledge, we are among the first to for- mulate the RCA problem from the perspective of attribution analysis developed in the field of XAI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To be specific, we explain the anomaly in the target KPI by attributing it to the behavior of the candidate’s root causes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We propose a novel forward model BMFS that can automatically select relevant candidates while taking their correlations into account at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We apply the proposed BALANCE approach to three real-world problems, including bad SQL localization, container fault local- ization, and fault type diagnosis for Exathlon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' All three scenes demonstrate the effectiveness of BALANCE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We further deploy BALANCE to production for the former two applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2 RELATED WORKS Since the proposed model is related to RCA, attribution, and sparse linear models, we provide a brief review of each of them below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1 Root Cause Localization As aforementioned, there are broadly two strategies for root cause localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The first one considers the multidimensional root cause localization methods, such as Adtributor [5], Hotspot [32], and HALO [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' More concretely, Adtributor [5] finds the root cause in each dimension by selecting the most abnormal dimension values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' However, Adtributor assumes that the root cause lies in one dimen- sion, which can be too restrictive in practice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To extend Adtributor to the case of multidimensional root causes, Hotspot [32] propa- gates the anomaly of the KPIs to different dimensions via the ripple effect and further defines the attribution scores of different dimen- sion combinations by replacing their real values with the predicted ones and further computing the differences with and without the re- placement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Unfortunately, the consequent search space is typically very large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Although Hotspot employs Monte Carlo tree search and a hierarchical pruning strategy to reduce the computational cost, it can still be too slow for large-scale practical problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Another drawback of both Adtributor and Hotspot is that they fail to con- sider the possible dependency among dimensions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As a solution, HALO [47] learns the hierarchical dependency structure of the dimensions via conditional entropy and then looks for the root cause by traversing in this structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' These kinds of methods can be viewed as a special case of attribution methods since they try to attribute the anomalies in the KPIs to the combinations of the associated multidimensional attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Note that the target KPIs in this case is the sum of the attribute values along each dimension.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' However, in a more general setting, the target KPIs may be influ- enced by the root cause candidates in a non-additive manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The proposed BALANCE approach provides a recipe for this problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The second strategy focuses on the graph-based causal infer- ence [29].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' MonitorRank [14] and Microhecl [17] firstly introduce service level RCA on known services chain architecture given by the distributed tracing system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' On the other hand, for applications without known graphs, CauseInfer [10] and CloudRanger [39] build a causal graph using the PC Algorithm [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Once the graph is ob- tained, statistical root causes are typically inferred via personalized page rank [40], breadth-first search [10, 17], random walk [14, 39], etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To make the graph more reliable, OM Graph [24] considers the prior knowledge from a knowledge graph with entities represent- ing all software and hardware in a distributed data system, during the construction of the causal graph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Furthermore, CloudRCA [48] optimizes OM Graph by building graphs based on multiple sources of data, including monitoring metrics, logs, and expert knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Note that the PC algorithm is still used in both OM graph and CloudRCA for graph construction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As pointed out in §1, it may be resource-consuming to construct graphs based on tracing service calls or other sources of prior knowledge, due to the large-scale and complicated nature of the entire architecture, while it is unreliable to build graphs utilizing causal discovery algorithms (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', the PC algorithm) given the limited length of the time series for the metrics during the anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Such shortcomings hamper the practice use of graph-based RCA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Another line of research seeks to construct the causal graph by identifying the lagged temporal dependence between different metrics [3, 20].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For instance, Granger causality is adopted in [1, 34] to infer the causal dependencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' However, the lagged temporal dependence exits only when the granularity of the monitored metrics is as fine as a millisecond or second in cloud systems [1], and setting up such a fine-grained monitoring system is quite costly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' By contrast, BALANCE can still be useful when the graph structure is not available and may in turn assist in graph construction and the subsequent localization step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2 Attribution methods Since we use attribution methods to solve the problem of RCA, we review some state-of-the-art (SOTA) attribution methods in this sec- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The goal of attribution methods is to understand and explain why a model makes a certain prediction, thus assisting in winning user trust and further providing insight into how to enhance the performance of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Generally speaking, attribution methods can be divided into gradient-based and perturbation-based methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Gradient-based methods compute the attribution values by lever- aging the gradients of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The first attempt in this direction is to compute the absolute gradient of the target output of a model w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' (with regard to) the input, which is also known as sensitivity analysis [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' However, sensitivity analysis is typically quite noisy and discards the information on the direction of the input change.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' One appealing solution is to use the element-wise multiplication of the gradient and the input (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', gradient×input), in order to increase the sharpness of attribution maps [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The major drawback of the above naive uses of the gradient information on highly non-linear models is that only the information about the local behavior of the function in the neighbor of a given input is provided.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To address this problem, many methods are proposed, including Layer-wise Relevance Propagation (LRP) [4], Integrated Gradients [33], and DeepLIFT [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' On the other hand, perturbation-based methods obtain the attribution of an input feature by removing or altering it, and then measuring the difference between the output before and after the perturbation is added.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Feature occlusion [44] directly SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' removes each feature in turn and so requires 𝑝 model evaluations, where 𝑝 is the number of features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To reduce the heavy compu- tational burden, Local Interpretable Model-agnostic Explanations (LIME) [25] resorts to group-wise feature occlusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' These groups are used to fit a local Lasso regression and the resulting coefficients are regarded as attributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Unfortunately, both feature occlusion and LIME suffer from the pitfall of the high sensitivity to the choice of hyper-parameters in the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In other words, these methods may be influenced by the user-defined parameters in an unpre- dictable fashion and there is no guarantee that the explanation is unbiased and faithful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' One remedy to this problem is to use SHapley Additive exPlanations (SHAP) [18], taking advantage of the classi- cal Shapley values to assign credit to participants in a cooperative game.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Shapley values are proven to be the only consistent attri- bution approach with several unique axioms in agreement with human intuition [31].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Nevertheless, it results in a daunting computa- tional complexity of O(2𝑝).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' This has sparked recent research efforts toward reducing the complexity [37].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In BALANCE, we specify the model between the candidate root causes and the target KPIs to be linear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As a result, almost all aforementioned attribution methods can be unified [2], and hence, the proposed model enjoys various nice properties, as will be discussed in the subsequent sections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3 Sparse linear models for feature selection As we employ a sparse linear forward model in BALANCE, we briefly review the relevant literature in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The most pop- ular sparse linear model is Lasso [35], which intends to find the coefficients that can best describe the linear relationship between the observed features and the outputs while enforcing the coeffi- cients to be sparse via the ℓ1-norm penalty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Three problems stand in the way of a direct application of Lasso to RCA: First, there often exist correlations between the candidate causes but Lasso pales in tackling correlated features due to the nature of the ℓ1 norm [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Second, the tuning parameter in front of the ℓ1 norm, which bal- ances the trade-off between data fidelity and coefficient sparsity is unknown in practice and is typically chosen by cross-validated grid search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As a result, the lasso algorithm has to be run for every candidate value of the tuning parameter for every partition of the dataset, leading to a heavy computational burden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Third, missing values are the rule rather than the exception, but Lasso cannot deal with them directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As a remedy to the first problem, E-Net (Elastic net) is proposed by using the combination of the ℓ1 and the ℓ2 norm on the coefficients, which introduces the grouping effect to the correlated coefficients [50].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' This merit comes along with an extra tuning parameter and considerable computational overhead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' On the other hand, the other two issues can be addressed by Bayesian models, such as ARD (Automatic Relevance Determination) [36].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The tuning parameter is assumed to be a random variable and its posterior distribution can be inferred from the data via expectation maximization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Unfortunately, correlations between features are not considered in this model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' A handful of works are further proposed to alleviate this deficiency by borrowing the strength from the cor- related shrinkage priors, such as the group inverse-Gamma Gamma prior [7] and the correlated spike-and-slab prior [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' However,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='such methods require some prior information that is unavailable in ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Merging Module: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Intersection and Union Explanation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Target and Candidates Data ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Loader and Organizer ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Time Series Database ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Forward Module: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='BMFS ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Backward Module: ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Attribution Analysis ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Recovery Decision Maker ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Collect and aggregate data into time series database ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Conduct real-time anomaly detection(AD) on targets ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Trigger AD on candidates to reduce its number(optional) ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Load abnormal targets ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Load (abnormal) candidates corresponding to the targets ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Train the forward BMFS model ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Compute the attribution of the candidates chosen by BMFS ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Merge and rank root causes resulting from multiple targets ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Send root causes to recovery decision maker ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Root Cause Analysis Service ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='BALANCE ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Data Collection ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Target AD ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Candidates AD ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='Figure 1: The overall framework of BALANCE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' practice, such as the grouping information [7] or the prior distribu- tion for zero coefficients [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In this work, we propose BMFS to overcome the abovementioned issues, which will be discussed in detail in §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 3 PROBLEM FORMULATION In this section, we first introduce the overall framework of BAL- ANCE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We then delve into in the RCA part, provide some desiderata, and discuss how such desiderata conceive the proposed method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The overall framework of BALANCE is depicted in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We first collect the raw data, including both target KPIs and the candidate root causes, and store them in the time series database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Concretely, let 𝑿 = [𝒙1, 𝒙2, · · · , 𝒙𝑝] denote the 𝑝 candidate root causes or the fundamental metrics (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', metrics for each SQL) that are associated with the target KPI or the derived metric 𝒚 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', ten- ant KPIs).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Real-time anomaly detection is only employed to monitor the target KPI 𝒚 since it is often prohibitively resource-consuming to monitor all the fundamental metrics (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', the candidate root causes) 𝑿.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Although not real-time, the anomaly detection on 𝑿 can be triggered once an alarm on 𝒚 is raised, since we only need to focus on the abnormal 𝑿 during RCA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We then collect the data of the abnormal 𝒚 and 𝑿 before and during the alarm with length 𝑛 from the database, and input the data into the proposed RCA service, BALANCE, in order to find the root cause.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The resulting estimated root cause serves as an input to the recovery decision maker, which yields the self-healing plan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Ideally, we would like an RCA module that satisfies the following desiderata: d1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The number of observations (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', the length of the time series) 𝑛 is typically small since we only consider the short time series before and during the anomalies to explain the abnormal behavior of the targets 𝒚.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' d2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The number of candidates 𝑝 is varying, and possibly large in each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Therefore, the RCA module should be sufficiently flexible to deal with the cases where 𝑝 ≤ 𝑛 and 𝑝 > 𝑛.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The latter scenario is more challenging and can be found in practice, BALANCE: Bayesian Linear Attribution for Root Cause Localization SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA for instance, the number of running SQLs is time-varying in the bad SQL example, and can be hundreds or even thousands, whereas 𝑛 = 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In this case, 𝑝 > 𝑛.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' d3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The RCA module should output all possible root causes even if they are correlated with each other while removing all irrel- evant candidates at the same time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In practice, it is infeasible to enumerate and verify all possible causalities between the candidates, since their interactions are often time-varying and bi-directional.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As such, it is better to list all correlated root causes and provide the SREs with more information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' d4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The RCA module should be able to deal with missing data that often exist in the monitor system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' d5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The process of RCA should be efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' d6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The results should be interpretable and the importance of the candidates should be comparable and can be used for further ranking and decision-making.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' On the other hand, attribution methods target producing expla- nations of the output behavior of a model by assigning a scalar attribution value 𝑟𝑗, sometimes also called “relevance”, “feature importance”, or “contribution”, to each input feature 𝑗 of the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Formally, given a target output 𝒚, the objective of an attribution method is to determine the contribution 𝒓 = [𝑟1, · · · ,𝑟𝑝] ∈ R𝑝 of each input feature 𝒙𝑗 ∈ 𝑿 to the output𝒚.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' It is therefore straightfor- ward to exploit attribution methods for RCA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Under the framework of attribution, first, a forward model 𝒚 = 𝑓 (𝑿) is constructed in order to predict 𝒚 given 𝑿.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Then an attribution method is used to explain the abnormal behavior of the target KPI 𝒚 by attributing it to the candidate root causes 𝑿.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In this work, we advance to use a Bayesian sparse linear model as the forward model, with special attention to the correlation between the candidates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We would like to motivate the use of the forward model from the following three perspectives: First, the proposed forward model can well capture all the above desiderata.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Specifically, due to the efficiency of linear models, we fit a different linear model to the data every time the target KPIs are alarmed, successfully solving the problem of the case- varying number of candidates (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', d2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' By leveraging sparsity in the regression coefficients, sparse linear models can choose candidates relevant to the target in an automatic way, and can further handle the large-𝑝-small-𝑛 problem (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', d1, d2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' After further considering the multicollinear relationship between the candidates, d3 can be satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The Bayesian framework in the proposed model facilitates the processing of the missing data by inferring their distributions along with the remaining parame- ters (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', d4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' By learning the variational posterior distribution of the tuning parameters rather than estimating them via grid search, the proposed model is typically more efficient than the commonly used frequency counterpart (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', d5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Finally, linear models are quite amenable to attribution methods as will be discussed below (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', d6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Second, the results (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', the estimated root causes) yielded by an attribution method should be faithful to the underlying process the SREs are trying to understand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To this end, the methods reviewed in §2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2 typically adopt a complicated forward model (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', a neural network) to predict𝒚 given 𝑿, in order to maximize the predictive accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' On the other hand, due to the black-box nature of the forward model, another interpretable model is further applied to approximate what the forward model has learned, so as to maximize the descriptive accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For instance, both LIME [25] and SHAP [18] employ local linear explanation models, and DeepLIFT [27] linearizes non-linear components of a neural network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Under the RCA case, it is intractable to train a neural network as the forward model due to d2, d1, and d5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Moreover, our objective is not to predict 𝒚 given 𝑿, and hence, the predictive accuracy is not our main focus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Instead, we are more concerned with the descriptive error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' By specifying the forward model to be linear, we minimize the descriptive error to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Finally, as mentioned in §2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2, Shapley values are justified as the only possible attribution method that satisfies all axioms that are consistent with human intuition, and it has been proven in [2] that almost all aforementioned attribution methods, including gradient×input, integrated gradients, DeepLIFT, and feature occlusion generate exact Shapley values when applied to a linear model and a zero baseline is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We will discuss how the proposed linear model fulfills all the axioms in §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' After the forward model is constructed, we then attribute the anomaly in 𝒚 to the candidates 𝑿 by finding the subset of 𝑿 that contribute the most to the abnormal behavior of 𝒚.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Finally, we rank the root causes based on the attribution score and merge the results when there are multiple target KPIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 4 METHODOLOGY In this section, we elaborate the three modules in BALANCE indi- vidually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1 Forward Module: Bayesian multicollinear Features Selection 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1 Bayesian Formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As mentioned in §3, we choose a sparse linear model as the forward model, that is, 𝒚 = 𝑿𝜷 + 𝝐, where 𝒚 ∈ R𝑛 denotes the time series of length 𝑛 for a single target KPI around the anomaly, 𝑿 ∈ R𝑛×𝑝 denotes the time series of the corresponding 𝑝 candidate root causes, 𝜷 ∈ R𝑝 is the sparse coefficient vector, and 𝝐 ∼ N (0, 𝛼−1𝑰) represents the independent Gaussian noise with variance 𝛼−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Equivalently, we can formulate the problem from a probabilistic perspective: 𝑝(𝒚|𝜷, 𝑿, 𝛼) = N (𝑿𝜷, 𝛼−1𝑰) ∝ exp �𝛼 2 (𝒚 − 𝑿𝜷)𝑇 (𝒚 − 𝑿𝜷) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' (1) We assume that 𝛼 follows a non-informative Jeffrey’s prior, that is, 𝑝(𝛼) ∝ 1/𝛼.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Now let us focus on the prior distribution on 𝜷.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Our objective is to simultaneously encourage sparsity and handle the multicollinearity among the features 𝑿.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To promote sparsity, one typically resorts to the Laplace distribution (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', the Bayesian counterpart of the ℓ1-norm) or the student’s T distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' However, here we choose the horse-shoe prior [9] due to its advantages over the Laplace and the student’s T prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The horse-shoe prior can be expressed as a SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2 0 2 j 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7 density student-t Laplace horse-shoe 2 0 2 j 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7 density (a) Sparse promoting priors 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 1 / (1 + 2 j ) 0 1 2 3 4 density (b) Shrinkage weights density Figure 2: The density of the commonly used sparse promoting pri- ors, including the Student’s T, Laplace, and horse-shoe prior (a), and the density of the corresponding shrinkage weights 1/(1 + 𝜎2) (b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' scale mixture of Gaussians: 𝑝(𝛽𝑗 |𝜎𝑗,𝑔) = N (0,𝑔𝜎2 𝑗 ), (2) 𝑝(𝜎𝑗) = 𝐶+(0, 1), (3) where 𝐶+(0, 1) is a standard half-Cauchy distribution on positive reals R+, and𝑔 and𝜎𝑗 are respectively the global and local shrinkage parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As 𝑔 becomes small, the global shrinkage parameter 𝑔 shrinks all the coefficients 𝛽𝑗 in 𝜷 to zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' On the other hand, the heavy-tailed half-Cauchy priors for the local shrinkage parameters 𝜎𝑗 allow some 𝛽𝑗 to escape from the shrinkage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Therefore, the resulting 𝜷 would be sparse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In comparison with other commonly- used sparse promoting priors, such as the Student’s T and Laplace distribution, we can tell from Figure 2(a) that horse-shoe prior has a larger density for 0 and for very large 𝛽𝑗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In other words, it can better separate the zero and non-zero elements in 𝜷.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Viewed another way, given that 𝜎𝑗 follows a half-Cauchy prior on 𝜎𝑗, we can obtain that [9]: 1 1 + 𝜎2 𝑗 ∼ Be � 1 2, 1 2 � , (4) where Be(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5) denotes a beta distribution with shape param- eters 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5, and we refer to 1/(1 + 𝜎2) as the shrinkage weight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As shown in Figure 2(b), the density function of the shrinkage weight for the horse-shoe prior (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', the orange line) has a U-shape (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', horse-shoe shape);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' it reaches the lowest value at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5 but is un- bounded at 0 and 1, indicating that this prior prefers 𝜎2 𝑗 to be either very small or very large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' However, the student’s T and Laplace prior (see the blue and green lines) do not have this nice property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As a result, the horse-shoe prior is more robust when dealing with unknown sparsity and large non-zero elements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' On the other hand, to tackle the multicollinearity, we typically resort to the g-prior [45]: 𝑝(𝜷|𝑔, 𝜎2, 𝑿) = N � 0,𝑔𝜎2(𝑿𝑇 𝑿)−1� , (5) where 𝑔 and 𝜎2 are scalars that determine the overall variance of 𝜷, and the inter-dependencies among different features 𝑿 are charac- terized empirically by 𝑿𝑇 𝑿.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The resulting posterior distribution on 𝜷 presents a larger correlation among elements in 𝜷 than the posterior given by other prior distributions, such as the Laplace (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', ℓ1-norm) and the Gaussian with a diagonal covariance (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' !' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' " # $ %!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' & Figure 3: Graph representation of BMFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The box labeled 𝑁 denotes that the number of repetitions for the subgraph inside is 𝑁.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' ℓ2-norm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To bring together the best of both worlds, we propose a novel prior distribution that seamlessly integrates the horse-shoe prior and the g-prior: 𝑝(𝜷|𝑔, 𝝈,𝑋) = N � 0,𝑔 diag(𝝈)𝑿𝑇 𝑿 diag(𝝈) � , (6) 𝑝(𝜎𝑗) = 𝐶+(0, 1), (7) where 𝝈 is a 𝑝-dimensional vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We name the above prior corre- lated horse-shoe prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To facilitate the derivation of the variational inference algorithm,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' we further reparameterize the above prior using the canonical exponential family form [22] as: 𝑝(𝜷|𝛾,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 𝝀,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 𝑿) = N � 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' � 𝛾 diag �𝝀 1 2 �𝑿𝑇 𝑿 diag �𝝀 1 2 ��−1� ∝ exp �𝑝 2 log𝛾 + 1 2 𝑝 ∑︁ 𝑗=1 log 𝜆𝑗 − 𝛾 2𝝀 𝑇 2 �(𝑿𝑇 𝑿) ◦ (𝜷𝜷𝑇 )�𝝀 1 2 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' (8) 𝑝(𝜆𝑗) = 1 𝜋 𝜆− 1 2 𝑗 (𝜆𝑗 + 1)−1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' ∀𝜆𝑗 > 0,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' (9) where 𝛾 = 1/𝑔,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 𝜆𝑗 = 1/𝜎2 𝑗 ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 𝝀1/2 denotes element-wise square root of the entries in vector 𝝀,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 𝝀𝑇/2 is the transpose of 𝝀1/2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' and 𝑝(𝜆𝑗) can be regarded as a Beta prime distribution or a compound Gamma distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Since we do not have any prior knowledge of the global shrinkage parameter 𝛾, we employ the non-informative Jeffrey’s prior, namely, 𝑝(𝛾) ∝ 1/𝛾.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Altogether, the overall Bayesian model can be factorized as: 𝑝(𝒚, 𝜷, 𝝀, 𝛼,𝛾|𝑿) = 𝑝(𝒚|𝑿, 𝜷, 𝛼)𝑝(𝜷|𝛾, 𝝀, 𝑿)𝑝(𝝀)𝑝(𝛾)𝑝(𝛼).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' (10) The corresponding graph representation can be found in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2 Variational Inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Our overarching goal is to infer the posterior distribution 𝑝(𝜷, 𝝀, 𝛼,𝛾|𝒚, 𝑿).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' However, it is intractable to obtain the close-form expression of this posterior distribution, and thus, we follow the framework of variational inference and find a tractable variational distribution 𝑞(𝜷, 𝝀, 𝛼,𝛾) that is closest in Kullback-Leibler (KL) divergence to the exact posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For sim- plicity, we apply the mean-field approximation and factorize the variational distribution as: 𝑞(𝜷, 𝝀, 𝛼,𝛾) = 𝑞(𝜷) 𝑝 � 𝑗=1 𝑞(𝜆𝑗)𝑞(𝛼)𝑞(𝛾).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' (11) BALANCE: Bayesian Linear Attribution for Root Cause Localization SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA One advantage of the mean-field approximation is that the func- tional form of each factor can be specified by equating the functional derivatives of the KL divergence w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' the factor to zero [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' After obtaining the functional form of the variational distribution, we then update the parameters of these distributions recursively via natural gradient descent [15, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' It is worthwhile to emphasize that natural gradients typically result in simpler expressions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', less computation in each iteration) and faster convergence (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', fewer iteration numbers) than standard gradients [15, 42, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Thus, it is favored when we are concerned with the efficiency of the algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In addition, although we assume the variational distributions are independent in Eq-11, their parameters are dependent on each other in a straightforward way when optimizing them to minimize the KL divergence, as demonstrated in the following update rules of these parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In other words, we still capture the interactions between the variables 𝜷, 𝝀, 𝛼, and 𝛾 to some extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Now let us delve into the derivations for each variational distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For 𝑞(𝜷) we can specify it to be a Gaussian distribution when 𝛽𝑗 ∈ R or a log-normal distribution when 𝜷 are constrained to be non-negative.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In the first scenario, 𝑞(𝜷) that minimizes the KL divergence can be updated as: 𝑞(𝜷;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 𝒉𝛽, 𝑱𝛽) ∝ exp � −1 2𝜷𝑇 𝑱𝛽𝜷 + 𝒉𝑇 𝛽𝜷 � , (12) where 𝑱𝛽 and 𝒉𝛽 respectively represent the precision matrix (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', the inverse covariance) and the potential vector of 𝛽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Gaussian dis- tributions parameterized by the precision matrix and the potential vector are called the canonical form and such form is amenable to concise update rules as shown below [15, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 𝒉𝛽 and 𝑱𝛽 are known as the canonical or natural parameters, and the correspond- ing mean parameters can then be computed as ⟨𝜷⟩ = 𝑱 −1 𝛽 𝒉𝛽 and Cov[𝜷] = 𝑱 −1 𝛽 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Specifically, update rules for 𝑱𝛽 and 𝒉𝛽 can be derived as: 𝑱 {𝜅 } 𝛽 = (1 − 𝜌)𝑱 {𝜅−1} 𝛽 + 𝜌 � ⟨𝛼⟩𝑿𝑇 𝑿 + ⟨𝛾⟩ diag �⟨𝝀 1 2 ⟩�𝑿𝑇 𝑿 diag �⟨𝝀 1 2 ⟩�� , (13) 𝒉{𝜅 } 𝛽 = (1 − 𝜌)𝒉{𝜅−1} 𝛽 + 𝜌⟨𝛼⟩𝑿𝑇𝒚, (14) where ⟨·⟩ denotes the expectation w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' the corresponding varia- tional distribution and 𝜌 denotes the step size determined using the line search method (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', the Armijo rule) [43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To provide more intuition for the above derivations, we take the update rule for 𝒉𝛽 as an example.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In Eq-14, the natural gradient for 𝒉𝛽 is ⟨𝛼⟩𝑿𝑇𝒚 −𝒉𝛽.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As we update 𝒉𝛽 in the direction of the natural gradient with a step size 𝜌, we can obtain Eq-14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The update rule for 𝑱𝛽 is derived in the same fashion, and likewise for the update rules in the sequel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' On the other hand, when we restrict 𝜷 to be non-negative and use the log-normal distribution as the variational distribution, we further factorize 𝑞(𝜷) as � 𝑗 𝑞(𝛽𝑗) and 𝑞(𝛽𝑗) can be written as: 𝑞(𝛽𝑗;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='ℎ𝛽𝑗,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='𝜁𝛽𝑗 ) ∝ 1 𝛽𝑗 √︃ 𝜁𝛽𝑗 exp � −1 2𝜁𝛽𝑗 𝛽2 𝑗 + ℎ𝛽𝑗 𝛽𝑗 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' (15) where in each iteration 𝜅 the natural parameters 𝒉𝛽 and 𝜻𝛽 can be updated as: 𝒉{𝜅 } 𝛽 = (1 − 𝜌)𝒉{𝜅−1} 𝛽 + 𝜌 � − 𝒄1 ◦ �1 − 2⟨log 𝜷⟩� + 𝒄2 ◦ �1 − ⟨log 𝜷⟩� + 1 � ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' (16) 𝜻 {𝜅 } 𝛽 = (1 − 𝜌)𝜻 {𝜅−1} 𝛽 + 𝜌(2𝒄1 − 𝒄2),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' (17) 𝒄1 = diag � ⟨𝛼⟩𝑿𝑇 𝑿 + ⟨𝛾⟩ diag �⟨𝝀 1 2 ⟩�𝑿𝑇 𝑿 diag �⟨𝝀 1 2 ⟩�� ⟨𝜷2⟩,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' (18) 𝒄2 = ⟨𝛼⟩𝑿𝑇𝒚 − off-diag � ⟨𝛼⟩𝑿𝑇 𝑿 + ⟨𝛾⟩ diag �⟨𝝀 1 2 ⟩�𝑿𝑇 𝑿 diag �⟨𝝀 1 2 ⟩�� ⟨𝜷⟩,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' (19) where ◦ is the Hadamard (or elementwise) product,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 𝜷2 denotes elementwise square of 𝜷,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' and off-diag(·) denotes the off-diagonal part of a matrix by replacing the diagonal with a zero vector.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' After- wards, we can compute the mean parameters as ⟨log 𝜷⟩ = 𝒉𝛽 ⊘ 𝜻𝛽, Var[log 𝜷] = 1 ⊘ 𝜻𝛽, ⟨𝜷⟩ = exp(⟨log 𝜷⟩ + Var[log 𝜷]/2), and ⟨𝜷2⟩ = exp(2⟨log 𝜷⟩ + 2Var[log 𝜷]), where ⊘ denotes elementwise division.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For 𝑞(𝜆𝑗), we follow [22] and specify its functional form to be: 𝑞(𝜆𝑗;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='𝑑𝑗) = 1 𝐸1(𝑑𝑗) (𝜆𝑗 + 1)−1 exp � − 𝑑𝑗 �𝜆𝑗 + 1�� , (20) where 𝐸1(𝑥) = ∫ ∞ 𝑥 𝑒𝑥𝑝(−𝑡)/𝑡𝑑𝑡 represents the exponential integral function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' It follows that the update rule of 𝒅 is: 𝒅 {𝜅 } = (1 − 𝜌)𝒅 {𝜅−1} + 𝜌⟨𝛾⟩ � off-diag �𝑿𝑇 𝑿 ◦ ⟨𝜷𝜷𝑇 ⟩�⟨𝝀 1 2 ⟩ ◦ 𝒄3 + 1 2 diag �𝑿𝑇 𝑿 ◦ ⟨𝜷𝜷𝑇 ⟩�� , (21) 𝒄3 = � ⟨𝝀 1 2 ⟩ ◦ 𝒅 − Γ(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5) ◦ 𝒅 1 2 � ⊘ �⟨𝝀⟩ ◦ 𝒅 − 1�.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' (22) The mean parameters ⟨𝝀⟩ and ⟨𝝀 1 2 ⟩ can be calculated as: ⟨𝝀⟩ = Γ(−1, 𝒅) ⊘ Γ(0, 𝒅), (23) ⟨𝝀 1 2 ⟩ = Γ(1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5)Γ(−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5, 𝒅) ⊘ Γ(0, 𝒅), (24) where Γ represents the gamma function when there is only one input and the upper incomplete gamma function1 when there are two inputs, and the step size 𝜌 is again determined by the Armijo rule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For𝑞(𝛼) and𝑞(𝛾), we specify them to be the gamma distributions, and the corresponding update rules are: 𝑞(𝛼;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='𝑎𝛼,𝑏𝛼) ∝ 𝛼𝑎𝛼−1 exp(−𝑏𝛼𝛼), (25) 𝑞(𝛾;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='𝑎𝛾,𝑏𝛾) ∝ 𝛾𝑎𝛾 −1 exp(−𝑏𝛾𝛼), (26) 1Γ(𝑐,𝑑) = 𝑈 (1 −𝑐, 1 −𝑐,𝑑)/exp(𝑑), where 𝑈 represents Tricomi’s confluent hyper- geometric function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7 0 2 4 6 8 10 count nonzero entries zero entries GMM fit threshold Figure 4: The empirical distribution of 𝜔 for a synthetic dataset: the orange and blue bars denote the histogram of 𝜔 w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' nonzero and zero entries in ⟨𝜷 ⟩ respectively, the green line denotes the density after fitting a GMM to the empirical distribution, and the red line denotes the chosen threshold ˆ𝜔.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' where 𝑎{𝜅 } 𝛼 = (1 − 𝜌)𝑎{𝜅−1} 𝛼 + 𝜌𝑛 2 , (27) 𝑏 {𝜅 } 𝛼 = (1 − 𝜌)𝑏 {𝜅−1} 𝛼 + 𝜌 2 �𝒚𝑇𝒚 + tr(⟨𝜷𝜷𝑇 ⟩𝑿𝑇 𝑿) − 2𝒚𝑇 𝑿⟨𝜷⟩�, (28) 𝑎{𝜅 } 𝛾 = (1 − 𝜌)𝑎{𝜅−1} 𝛾 + 𝜌𝑝 2 , (29) 𝑏 {𝜅 } 𝛾 = (1 − 𝜌)𝑏 {𝜅−1} 𝛾 + 𝜌 2 � ⟨𝝀⟩𝑇 diag �𝑿𝑇 𝑿 ◦ ⟨𝜷𝜷𝑇 ⟩� + ⟨𝝀 1 2 ⟩𝑇 off-diag �𝑿𝑇 𝑿 ◦ ⟨𝜷𝜷𝑇 ⟩�⟨𝝀 1 2 ⟩ � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' (30) In practice, entries in 𝒚 and 𝑿 are often missing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In this case, we generate point estimates for 𝑋𝑖,𝒋 and Bayesian estimates for 𝑦𝑖 by minimizing the aforementioned KL divergence, that is, ˆ𝑋𝑖,𝒋 = ⟨𝜷𝒋𝜷𝑇 𝒋 ⟩−1⟨𝜷𝒋⟩𝑦𝑖, (31) 𝑞(𝑦𝑖) = N �𝑿𝑖,:⟨𝜷⟩, ⟨𝛼⟩−1�, (32) where the vector 𝒋 denotes the indices of the missing values in row 𝑖 in 𝑿, and 𝑿𝑖,: denotes the 𝑖-th row of 𝑿.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3 Soft Thresholding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Recall that the half-Cauchy prior on 𝜎𝑗 leads to the U-shaped prior of the shrinkage weight 1/(1 + 𝜎2 𝑗 ) (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Eq-4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Since 𝜆𝑗 = 1/𝜎2 𝑗 , the shrinkage weight can be equivalently expressed as 𝜆𝑗/(1 + 𝜆𝑗).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' This U-shaped prior constraints 𝜆𝑗 to be either very small or very large and can separate the zero and non-zero entries in 𝜷 in an automatic fashion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Owing to this prior, we observe that the density of the empirical distribution ˆ𝑝(𝜔) on 𝜔 = ⟨𝜆𝑗⟩/(⟨𝜆𝑗⟩ + 1) for all 𝑗 also follows a U-shape approximately, where the expectation ⟨𝜆𝑗⟩ is taken over the variational posterior distribution 𝑞(𝜆𝑗), as shown in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As expected, the value of 𝜔 for most true non-zero entries is close to zero and its density decreases with 𝜔, whereas the value of 𝜔 for most true zero entries is far away from zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To distinguish the non-zero entries from the zero ones, we choose the threshold to be ˆ𝜔 = arg min ˆ𝑝(𝜔), which is the valley of the U-shape density and set ⟨𝛽𝑗⟩ = 0 if ⟨𝜆𝑗⟩/(⟨𝜆𝑗⟩+1) > ˆ𝜔.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Specifically, Algorithm 1 Bayesian multicollinear Feature Selection (BMFS) Input: an alarmed target KPI 𝒚 and candidate root causes 𝑿 associated with 𝒚;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Output: regression coefficients ⟨𝜷 ⟩;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 1: Initialize the parameters for all variatonal distributions;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2: repeat 3: if 𝜷 can only take positive values then 4: update 𝑞(𝜷) following Eq-15;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 5: else 6: update 𝑞(𝜷) following Eq-12;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 7: end if 8: compute ⟨𝜷 ⟩ and Cov[𝜷 ] given 𝑞(𝜷);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 9: update 𝑞(𝝀) by Eq-20 and compute ⟨𝝀⟩ by Eq-23, ⟨𝝀 1 2 ⟩ by Eq-24;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 10: update 𝑞(𝛼) by Eq-25, 𝑞(𝛾) by Eq-26, compute their expectations;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 11: if there exists missing values in 𝑿 and 𝒚 then 12: impute the missing values following Eq-31 and Eq-32;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 13: end if 14: until convergence;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 15: perform soft thresholding as introduced in §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' we fit a two-component Gaussian mixture model (GMM) to ˆ𝑝(𝜔): the means of the two Gaussians are fixed to the smallest and largest value of 𝜔 across all 𝑗 respectively, while the variances and the weights are learned from the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We then find the ˆ𝜔 corresponding to the minimum of the density of the GMM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We summarize the entire procedure of BMFS in Algorithm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2 Backward Module: Attribution Analysis Since our forward model is a linear model, one tempting choice for attribution score is the regression coefficient, that is, 𝑟𝑗 = |⟨𝛽𝑗⟩|, (33) where 𝑟𝑗 denotes the attribution score and | · | denotes the absolute value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In fact, for linear models, the regression coefficient ⟨𝛽𝑗⟩ equals the gradient of 𝒚 w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 𝒙𝑗, thus it describes the sensitivity of 𝒚 to 𝒙𝑗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The value ⟨𝛽𝑗⟩ quantizes the impact of a small change in 𝒙𝑗 to 𝒚.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Note that we have a distribution for 𝛽𝑗 instead of a point estimate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Following the framework of XAI for Bayesian models [8], we use the mean of 𝛽𝑗 here to compute the attribution score in this section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Note that other values can also be used, such as the quantiles, the modes, and the intersection or union of the modes if there is more than one mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Since 𝑞(𝛽𝑗) follows a Gaussian distribution, the mean is the proper choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Unfortunately, high sensitivity does not indicate a high con- tribution to the anomaly in the target KPI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For example, suppose that the target KPI is a summary or aggregation of the candidate root causes and that ⟨𝛽𝑗⟩ is non-zero and relatively large, but 𝒙𝑗 is small.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We typically omit 𝒙𝑗 because its scale is small and cannot contribute much to the overall target.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To this end, we resort to the gradient×input approach, in which the attribution score can be computed as: 𝑟𝑗 = |⟨𝛽𝑗⟩𝑥𝑗 |.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' (34) This value is known as salience in the literature of attribution [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Now the candidate root causes will be chosen only when both ⟨𝛽𝑗⟩ and 𝑥𝑗 itself are relatively large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' BALANCE: Bayesian Linear Attribution for Root Cause Localization SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA However, our ultimate objective is to attribute the anomalies in the target KPIs to the candidate root causes, and hence, our focus is not on the absolute value of 𝑥𝑗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Instead, we intend to explain the changes during the anomaly in 𝒚 by the changes in 𝒙𝑗.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In other words, we are interested in the marginal effect of a candidate, and we are looking for how the target would change after replacing the abnormal part in the candidates with the normal part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Recall that in our case, the anomaly or alarm time is given.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Hence, we choose a baseline as the mean or the median of the normal part of the time series and compute the difference Δ𝑥𝑗 between the anomaly and the baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The resulting attribution score is defined as: 𝑟𝑗 = |⟨𝛽𝑗⟩Δ𝑥𝑗 |.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' (35) To further guarantee the attribution score to be invariant to the scale of 𝒚, we finally calculate the attribution score as: 𝑟𝑗 = ���� ⟨𝛽𝑗⟩Δ𝑥𝑗 Δ𝑦 ����.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' (36) It is worthwhile to emphasize that owing to the use of the pro- posed forward model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The above attribution score satisfies all the desirable axioms of the Shapley values, including completeness, null player, symmetry, linearity, and continuity [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Here we briefly go through these axioms in the case of RCA and discuss how the proposed model copes with them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Completeness is satisfied when attributions sum up to the difference between the value of𝒚 during normal and abnormal periods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' It is obvious that Eq-36 fulfills this requirement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Null players: if the target 𝒚 does not depend on some can- didates 𝒙𝑗, then 𝑟𝑗 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The proposed correlated horse-shoe prior automatically excludes the irrelevant candidates 𝒙𝑗 and set the corresponding ⟨𝛽𝑗⟩ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As a result, 𝑟𝑗 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Symmetry: if the target 𝒚 depends on two candidates 𝒙𝑗 and 𝒙𝑘 but not on their order, then 𝑟𝑗 = 𝑟𝑘.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' This axiom is satisfied by considering multicollinearity in our forward model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Linearity: this property is satisfied by linear models naturally.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Continuity: attributions generated for two nearly identical in- puts should be nearly identical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' This axiom can also be handled by capturing multicollinearity in our forward model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Moreover, it is apparent that the above axioms are in agreement with the desiderata of an ideal RCA mentioned in §3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' This again bolsters our belief that attribution analysis is a natural fit for RCA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3 Merging Module: Intersection and Union Explanation In this subsection, we turn our attention to the case where there are multiple target KPIs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Under this situation, we first compute the attribution score𝑟𝑗𝑘 of each candidate root causes 𝒙𝑗 for each target KPI 𝒚𝑘 following the two steps in the above two subsections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We then sort the attribution scores 𝑟𝑗𝑘 across 𝑗 in the descending order for each 𝑘 and refer to this step as ranking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We further retain the top 𝜅 root causes for each target KPI 𝒚𝑘.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Note that when 𝜷 is properly sparse (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', the number of non-zero entries in 𝜷 is smaller than 𝜅), the selection step can be omitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' After ranking and selection, we merge the sets of root causes via the intersection or union of the sets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The intersection operation indicates that the root cause is chosen only when it influences all target KPIs, while the union operation detects all possible root causes that propagate abnormally to at least one target KPI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 5 EXPERIMENTS In this section, we first assess the performance of BALANCE on synthetic data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We then show the performance of BALANCE on three real-world applications2, including Bad SQL localization, Con- tainer fault localization, and Fault Type Diagnosis for Exathon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The first application mainly focuses on homogeneous pairs of the target KPIs and the candidate root causes, while the latter two consider heterogeneous ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Implementation Details: We adopt the BALANCE framework, and for the forward module, we juxtapose our BMFS with other SOTA methods, including Lasso, E-Net, and ARD in terms of estima- tion accuracy and run time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The backward module is the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For a fair comparison, we replace the correlated horse-shoe prior with the original horse-shoe prior and regard the resulting method as ARD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Thus, ARD can be regarded as an ablation study on BMFS by remov- ing the 𝑔-prior part in BMFS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Note that in the original ARD [36], the Student’s 𝑇-prior is used instead to encourage sparsity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' All the compared methods have the same computation complexity of O(𝑝2 max(𝑛, 𝑝)) according to our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' All methods are imple- mented in Python 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9 except the newly added R package “fsMTS”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' All the experiments are conducted on the same Linux Server with Intel Xeon E5-2682 v4 @ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='50GHz processors and 16GB RAM so that all the execution time could be directly compared.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1 Simulation on Synthetic Data Here, we generate the synthetic data as follows: 𝒚 = 𝑿𝜷 + 𝝐, (37) where 𝑿 ∈ R𝑛×𝑝,𝒚 ∈ R𝑛, 𝜷 ∈ R𝑝, and 𝝐 ∼ N (0, 𝛼−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To introduce multicollinearity to 𝑿 and 𝜷, we assume that 𝜷 = 𝑸𝒃, (38) 𝑿 = 𝒁𝑸−1, (39) where 𝒃 ∈ R𝑝𝑧, 𝒁 ∈ R𝑛×𝑝𝑧, and 𝑸 ∈ R𝑝𝑧×𝑝𝑧 denotes the orthogonal part of the QR decomposition of a certain matrix 𝑾.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Note that 𝑝𝑧 ≤ 𝑝.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' By specifying 𝑾 to be an identity matrix and 𝑝𝑧 = 𝑝, the resulting features 𝑿 are independent of each other (or absent of multicollinearity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' On the other hand, by specifying 𝑾 to be a random matrix and 𝑝𝑧 < 𝑝, we introduce some multicollinearity to 𝑿 (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' partial multicollinearity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Finally, by specifying 𝑾 to be a selection matrix where each row only has one non-zero element that can be either 1 or −1 and 𝑝𝑧 < 𝑝, the correlation between two arbitrary columns in 𝑿 can be 1 or −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We refer to this case as “perfect multicollinearity”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We investigate the impact of the ratio between 𝑝 and 𝑛, the level of multicollinearity, the level of noise, the level of sparsity, and the proportion of missing data on the performance of the proposed BALANCE method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As mentioned before, we compare BMFS with Lasso, E-Net, and ARD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Specifically for Lasso, the candidate set 2a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The dataset does not contain any Personal Identifiable Information (PII).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The dataset is desensitized and encrypted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' c.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Adequate data protection was carried out during the experiment to prevent the risk of data copy leakage, and the dataset was destroyed after the experiment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The dataset is only used for academic research, and it does not represent any real business situation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 0 200 400 600 800 1000 feature dimension: p 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 F1 Score BMFS Lasso E-Net ARD 0 200 400 600 800 1000 dimension p 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 F1-score (a) Absent 0 200 400 600 800 1000 dimension p 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 F1-score (b) Partial 0 200 400 600 800 1000 dimension p 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 F1-score (c) Perfect Figure 5: 𝐹1-score as a function of the dimension 𝑝 resulting from all benchmark methods in case of (a) absent of mutlicollinearity, (b) partial multicollinearity, and (c) perfect multicollinearity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Table 1: Results of Synthetic Data with different levels of multicollinearity (absent, partial, and perfect) and different dimensions 𝑝 averaged over 100 trials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Here, 𝑛 = 100, 𝛼−1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='01, and proportion of nonzero coefficients = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 𝑝 Lasso E-Net ARD BMFS 𝐹1-score MSE Time (s) 𝐹1-score MSE Time (s) 𝐹1-score MSE Time (s) 𝐹1-score MSE Time (s) Absent 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7109 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='90e-05 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='70e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6623 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='490e-05 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='65e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9999 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='60e-05 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='34e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9999 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='60e-05 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='35e-01 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5148 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='10e-05 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='06e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4383 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='60e-05 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='08e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9743 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='50e-05 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='10e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9887 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='30e-05 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='72e-01 100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4638 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='00e-05 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='84e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3789 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='10e-05 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='88e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9137 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='70e-05 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='47e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9562 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='20e-05 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='10e-01 200 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3995 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='70e-05 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='59e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3943 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='60e-05 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='62e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9758 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='00e-06 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='20e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9730 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='00e-06 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='51e-01 500 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3221 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='00e-06 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='99e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3352 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='60e-05 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='00e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9999 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='00e-06 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='32e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9943 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='00e-06 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='94e-01 1000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2873 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='74e-06 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='01e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2894 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='96e-05 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='25e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9249 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='87e-05 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='12e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9955 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='35e-07 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='00e+00 Partial 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6821 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='16e-02 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='72e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6720 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='85e-02 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='77e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9724 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='86e-02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='54e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9593 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='87e-02 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='15e-01 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5554 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='90e-02 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='50e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5445 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='32e-02 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='84e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9958 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='30e-02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='91e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9999 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='30e-02 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='70e-01 100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5221 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='36e-03 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='18e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4598 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='48e-03 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='76e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9696 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='32e-03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='82e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9999 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='32e-03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='36e-01 200 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4630 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='56e-03 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='52e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5678 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='25e-03 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='52e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9271 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='17e-03 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='06e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9908 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='16e-03 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='59e-01 500 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3974 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='93e-03 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='87e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4843 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='36e-03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='24e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8069 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='32e-03 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='40e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9963 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='31e-03 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='55e-01 1000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3532 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='19e-04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='89e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4216 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='45e-04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='83e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9431 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='22e-04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='13e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9824 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='18e-04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='09e+00 Perfect 20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7188 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='24e-02 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='74e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6696 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='84e-02 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='82e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9474 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='93e-02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='83e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9273 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='02e-02 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='13e-01 50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5736 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='92e-02 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='11e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5257 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='35e-02 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='42e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9999 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='33e-02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='67e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9799 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='34e-02 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='61e-01 100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5301 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='78e-03 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='83e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4775 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='82e-03 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='39e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9927 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='66e-03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='15e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9944 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='66e-03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='85e-01 200 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4570 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='36e-03 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='82e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5147 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='11e-03 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='04e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9693 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='03e-03 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='49e-01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9988 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='03e-03 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='50e-01 500 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3862 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='52e-03 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='81e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4705 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='07e-03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='20e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8164 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='03e-03 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='53e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9729 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='03e-03 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='11e-01 1000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3599 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='62e-04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='87e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5022 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='23e-04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='69e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9205 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='07e-04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='11e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9722 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='99e-04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='12e+00 Table 2: Results of Synthetic Data with different levels of noise standard deviations (noise std) averaged over 100 trials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Here, 𝑛 = 100, 𝑝 = 1000, and proportion of nonzero coefficients= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' noise std Lasso E-Net ARD BMFS 𝐹1-score MSE Time (s) 𝐹1-score MSE Time (s) 𝐹1-score MSE Time (s) 𝐹1-score MSE Time (s) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8466 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='07e-04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='91e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8820 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='150e-04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='84e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9250 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='16e-04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='14e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9789 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='10e-04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='05e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3746 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='81e-04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='88e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4562 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='06e-04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='71e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9231 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='87e-04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='06e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9625 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='80e-04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='11e+00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3353 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='07e-03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='14e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3294 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='05e-03 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='57e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3596 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='32e-03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='19e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4054 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='39e-03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='51e+00 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1150 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='19e-03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='90e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1337 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='09e-03 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='19e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0863 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='08e-02 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='38e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0881 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='16e-02 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='37e+00 Table 3: Results of Synthetic Data with different ratios of nonzero coefficients (nonzeros%) averaged over 100 trials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Here, 𝑛 = 100, 𝑝 = 1000, and 𝛼−1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' nonzeros% Lasso E-Net ARD BMFS 𝐹1-score MSE Time (s) 𝐹1-score MSE Time (s) 𝐹1-score MSE Time (s) 𝐹1-score MSE Time (s) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2% 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4482 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='16e-04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='95e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4054 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='19e-04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='53e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9766 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='08e-04 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='97e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9999 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='07e-04 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='93e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5% 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3927 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='20e-04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='97e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4838 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='87e-04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='96e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9296 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='67e-04 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='30e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9726 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='63e-04 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='94e+00 1% 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3810 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='19e-03 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='02e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5448 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='76e-03 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='58e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8913 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='75e-03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='30e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9654 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='71e-03 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='97e+00 2% 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3687 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='13e-03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='95e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5673 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='47e-03 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='37e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7407 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='52e-03 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='51e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9238 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='31e-03 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='99e+00 5% 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3694 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='61e-02 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='33e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4853 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='58e-02 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='71e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4409 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='57e-02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='85e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5483 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='56e-02 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='65e+00 of the tuning parameter is 30 values spaced evenly in the interval [−2, 2] in the log scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For E-Net, the common penalty parameter BALANCE: Bayesian Linear Attribution for Root Cause Localization SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA Table 4: Results of Synthetic Data with different ratios of missing values in 𝑿 averaged over 100 trials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Here, 𝑛 = 100, 𝑝 = 1000, 𝛼−1 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='01, and the proportion of nonzero coefficients= 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' missing values Lasso E-Net ARD BMFS 𝐹1-score MSE Time (s) 𝐹1-score MSE Time (s) 𝐹1-score MSE Time (s) 𝐹1-score MSE Time (s) 10% 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4306 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='65e-04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='72e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3791 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='87e-04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='98e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7461 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='92e-04 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='23e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7494 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='92e-04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='60e+00 20% 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4076 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='46e-04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='63e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4226 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='84e-04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='98e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7074 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='90e-04 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='47e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7835 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='04e-04 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='65e+00 30% 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4083 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='97e-04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='45e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4381 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='99e-04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='93e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6721 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='90e-04 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='80e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7714 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='78e-04 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='94e+00 40% 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4103 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='41e-04 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='64e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3983 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='69e-04 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='41e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6726 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='89e-04 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='81e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7670 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='69e-04 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='64e+00 50% 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3474 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='73e-04 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='01e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3327 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='06e-03 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='97e+00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6170 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='17e-04 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='40e+01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6727 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='68e-04 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='30e+01 in front of both the ℓ1 and ℓ2 norm is selected from 10 evenly spaced values in [−2, 2] in the log scale, and the ℓ1 ratio parameter is chosen from [0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The optimal tuning parameters are selected via cross validation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Since these two methods cannot deal with missing values explicitly, we replace the missing values with the mean of the corresponding candidate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We consider three criteria, namely, 𝐹1- score w.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='r.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' the zero pattern between the estimated and true 𝜷, mean squared error (MSE) between estimated and true 𝜷, and running time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Note that 𝐹1-score is the harmonic mean of precision and recall, where precision is defined as the ratio between the number of true root causes identified by the model and the number of all root causes given by the model, and recall is defined as the ratio between the number of true root causes identified by the model and the number of true root causes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The results are summarized in Tables 1-4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To highlight the merit of BMFS in terms of zero pattern recovery, we further plot out the 𝐹1-score of all methods as a function of 𝑝 in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Two major trends can be gleaned from the tables.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' First, BMFS typically achieves comparable or better performance than the SOTA methods in terms of both the estimation accuracy and the running time, especially when the dimension 𝑝 is high, and the level of multicollinearity is high.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' On the other hand, the superiority of BMFS and ARD over E-Net and Lasso suggests that adaptively learning the tuning parameters from the data via variational inference is more advantageous than estimating them via brute-force grid search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Grid search restricts the tuning parameters to the predefined set of candidates, and consequently, a carelessly designed set may lead to unsatisfactory performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In addition, it can be observed that the performance of BMFS and E-Net is better than that of ARD and Lasso respectively, when there exists multicollinearity in the data, as expected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Indeed, the ℓ1-norm penalized Lasso can only pick at most 𝑛 candidates when 𝑝 > 𝑛 in theory, even if all candidates are relevant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' More precisely, if there are two or more highly collinear candidates, Lasso only selects one of them at random.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' This explains the deficiency of ARD and Lasso in comparison with BMFS and E-Net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Second, the performance of BMFS is robust to the number of di- mensions, the level of multicollinearity, the noise level, the sparsity level, and the proportion of missing values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To be specific, we can see that Bayesian methods constantly outperform the frequency methods for both 𝑝 ≤ 𝑛 and 𝑝 > 𝑛.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Additionally, Bayesian methods offer a straightforward way to cope with missing values by infer- ring their distributions from the data at the expense of consuming more time with the increase of the missing data proportion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In a contrast, we employ the mean imputation method before applying the frequentist methods, leading to inaccurate estimation when the proportion of missing values is large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Table 5: Different tenant KPIs and the corresponding SQL metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Tenant KPI SQL Metric SQL_SELECT_RT cpu_time LOGICAL_READS lr(logical_reads) SQL_QUEUE_TIME queue_time RPC_PACKAGE_IN/OUT rpc_count … direct influence Tenant KPI: LOGICAL_READS SQL_1 SQL_2 SQL_N SQL_1 SQL_2 SQL_N Tenant KPI: SQL_SELECT_RT … logical reads of SQL cpu time of SQL Figure 6: Targets and candidates for bad SQL localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2 Bad SQL Localization Database services are a fundamental infrastructure that is critical for the everyday business of enterprises.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Thus, it is of top priority to guarantee the high availability of database services.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Previous works, such as iSQUAD [19], concentrate on determining the fault type of an intermittent slow SQL from typical types given by experts or from historical data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Different from slow queries, which appear in massive numbers in the slow query logs, bad SQL localization is a more comprehensive problem as we consider not only run time but also logical reads, RPC count, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Bad SQLs cannot be always found in the slow query logs since they may lead to anomalies in the tenant KPIs via their CPU or memory usage instead of run time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As mentioned in the introduction, here we aim to find "Bad SQLs" (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', the candidate root causes 𝑿) that are suspicious and responsible for the anomalies detected in tenant KPIs (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', the target KPIs 𝒚).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As shown in Table 5, Tenant KPIs monitor the performance of tenants, while SQL metrics tell us the performance of each SQL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In light of expert knowledge and offline data analysis, we find that almost all bad SQL issues can be reflected by two kinds of tenant KPIs, that is, SQL_SELECT_RT and LOGIC_READS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As such, the alarm of these two KPIs is the trigger of our RCA module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Moreover, we find that the tenant KPIs can be regarded as a summary of the relevant SQL metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For instance, the tenant KPI SQL_SELECT_RT is influenced by the metric cpu_time of all SQLs, while the other KPI LOGIC_READS is associated with the metric lr (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', logic reads).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Hence, this application of BALANCE considers homogeneous 𝑿 and 𝒚.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Figure 6 displays the targets and candidate pairs to be analyzed by BALANCE in bad SQL localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Table 6: Results for bad SQL localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Methods #Hits #Misses Accuracy Time (s) #Recommend ARD 68 24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7556 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='92e+00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7 Lasso 64 24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7111 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='15e+00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='1 E-Net 64 26 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7222 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='95e+00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3 fsMTS 49 41 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5444 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='20e+01 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 BMFS 75 15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8333 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='78e+00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3 In addition, on the online monitor platform, the tenant KPIs are saved as fixed-interval time series, whereas the SQL metrics are collected by batch sampling: each batch collects the metrics of all SQLs within 10 seconds before the collection time, and the next collection starts after the previous one finishes the storage process and so there are small uneven time gaps between every two collections that amount to the storage time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To settle this problem, we aggregate the SQL metrics within every minute and regard them as time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As a result, the timestamps of 𝑿 and 𝒚 might not be aligned.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We, therefore, use both 𝑿𝑡 and 𝑿𝑡−1 when aligning with 𝒚𝑡, and output the SQL 𝑥𝑗 as a possible bad SQL when the coefficient in front of either 𝒙𝑡 𝑗 or 𝒙𝑡−1 𝑗 is non-zero.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Finally, while there are only two target KPIs, the number of related SQLs 𝑝 can be very large (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', thousands or larger), varying in each case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The SQLs are often correlated with each other as a small modification of the WHERE or the LIMIT condition in a SQL sentence is defined as a new SQL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The proportion of missing data can also be very large.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Furthermore, it is required to find the root causes within 1 minute, and the results should be interpretable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In a nutshell, under the problem of bad SQL localization, all 6 desiderata in §3 should be satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To merge the root causes resulting from the two KPIs, we retain the top 3 root causes for each KPI (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', 𝜅 = 3 in the merging module), and compute the union of the two sets of root causes as the final recommendation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To evaluate the performance of the proposed approach, we collect 90 samples from the SQL diagnosing platform of Ocean Base[41].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The samples cover over 50 different tenants, and in each sample, both the tenant KPIs and the SQL metrics are saved as 61-minute time series (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', 𝑛 = 61), including the one-minute abnormal part.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Recall that 𝑝 scales up to hundreds or thousands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Hence, 𝑝 > 𝑛 in this scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Missing data typically exist in the SQL metrics, up to 50%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To match the requirement of real-time RCA tasks, three evaluation criteria are selected that is accuracy, number of recom- mendations, and running time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For each sample, if the true root causes lie within the set of SQLs recommended by the proposed method, we count this sample as a “hit”;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' otherwise, it is a “miss”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Accuracy is then defined as the proportion of the number of hits to the overall number of samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Again, we compare different for- ward models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As Lasso and E-Net cannot deal with missing data, we impute the missing values using linear interpolation for ten- ant KPIs and fill zeros for the SQL metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In addition, we further consider another benchmark method, fsMTS (feature selection for multivariate time series) [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' This method considers lagged tempo- ral dependence and selects features from 𝑿𝑡, · · · , 𝑿𝑡−𝜏, where 𝜏 is the time lag.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' It then resorts to an ensemble method to combine the results from cross-correlation, graphical lasso, random forest, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As fsMTS can only tell us whether a feature is selected, we choose the tuning parameter such that only 𝜅 = 3 candidates are selected for each KPI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The results for all methods are presented in Table 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' It can be observed that the proposed method achieves the highest accuracy with the lowest number of recommendations and the low- est amount of computational time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The accuracy is 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='33%, which is at least 8% higher than the baseline methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The number of recommendations is only 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3, and the running time is only 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='78 seconds on average.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Note that while being complete, the number of recommendations is supposed to be as small as possible as it helps the SREs to concentrate on a few root causes so they can dive in and fix the issue more efficiently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' On the other hand, we can tell from Table 6 that the performance of BMFS and E-Net is better than that of ARD and Lasso respectively since the former two methods can cope with the multicollinearity within the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We can also find that the Bayesian methods (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', BMFS and ARD) out- perform their frequency counterparts (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', E-Net and Lasso) since they can learn the distribution of the tuning parameters as well as the missing values adaptively from the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We have deployed the proposed method to production, and the online results show that the accuracy can be as high as 95%, which further demonstrates the advantages of BALANCE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Finally, fsMTS yields the worst result, probably because 1) temporal dependence is not the main concern for time series grouped by the minute;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2) the base learner in the ensemble, such as graphical lasso, also needs careful tuning of the penalty parameters but now only the default value is used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='3 Container Fault Localization In this section, we further apply the proposed approach to another practical situation, that is, container fault localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In this situa- tion, once the number of trace failures associated with a container is abnormal, the proposed BALANCE method would find the con- tainer metrics that can best explain the anomaly, and the RCA results will further lead to self-healing operations such as restart and traffic throttling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' By addressing all trace failures automatically, the high availability of the cloud-native system can be guaranteed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In this case, the target KPI 𝒚 is the number of trace failures associated with a container, and the candidate root causes 𝑿 is the 10 metrics of this container, such as CPU usage, memory usage, inward and outward traffic, the number of TCP connections, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Note that 𝒚 and 𝑿 are heterogeneous under this setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Moreover, there exist strong correlations among the container metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For instance, the metric CPU usage is the sum of another two metrics: CPU user usage and CPU system usage, and additionally, the metrics inward traffic in bytes, outward traffic in bytes, inward traffic in packages, and outward traffic in packages are closely correlated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Missing data also appears now and then, up to 10%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To assess the quality of our method, we collect 100 samples in total from a fault diagnosing platform of Ant Group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For each sam- ple, we can obtain the alarm time and 30-minute time series for both 𝑿 and 𝒚 before and during the anomaly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In this case, 𝑛 = 30, 𝑝 = 10, and 𝑝 < 𝑛.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We benchmark the proposed forward model BMFS against Lasso, E-Net, ARD, and fsMTS, and evaluate all mod- els in terms of precision, recall, 𝐹1-score, and running time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The results are listed in Table 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Notice that the deployment of BAL- ANCE to production yields similar results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' BMFS blows out of the water Lasso, E-Net, ARD, and fsMTS in terms of both 𝐹1-score and running time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Indeed, the 𝐹1 score resulting from BMFS is above 20% higher than that of the second best method ARD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Concretely, the precision of BMFS and E-Net is respectively similar to that BALANCE: Bayesian Linear Attribution for Root Cause Localization SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA 0 20 60 80 40 time (min) 0 5 10 15 no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' of trace failures (a) Target KPI 𝒚 0 20 40 60 80 time (min) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 normalized values CPU_util: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='25,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='00,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='09,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='58 CPU_sys: 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='01,5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='03,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='75,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='71 CPU_user: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='62,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='00,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='33,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='64 (b) CPU related metrics 0 20 40 60 80 time (min) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 normalized values Mem_util: 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='87,6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='25,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='88,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='96 Mem_used: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='44,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='00,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='22,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='47 (c) Memory related metrics 0 20 40 60 80 time (min) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='0 normalized values Tfc_Pkg_In: 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='88,5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='56,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='89,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='93 Tfc_Pkg_Out: 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='71,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='00,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='67,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='77 (d) Traffic related metrics Figure 7: Visualization of the trace failure number 𝒚 and correlated container metrics: the four values associated with each metric in the legend denote the attribution scores of ARD, Lasso, E-Net, and BMFS sequentially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Table 7: Results for container fault localization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Methods Recall Precision 𝐹1-score Time (s) ARD 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4784 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='98804 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6266 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='54e-1 Lasso 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5083 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5219 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4712 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='96e-1 E-Net 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7352 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5520 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5925 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='58e-1 fsMTS 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4826 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5244 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4655 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='01e-1 BMFS 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8180 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9136 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='8569 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='52e-1 of ARD and Lasso, but the recall of the former two methods is much higher, indicating that ARD and Lasso mistakenly omit some relevant metrics and highlighting the appeal of considering multi- collinearity among candidate root causes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To further elucidate this point, we depict as an example the target KPI and the correlated candidate root causes in Figure 7 and show the attribution scores for ARD, Lasso, E-Net, and BMFS sequentially for each candidate root cause in the figure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' It can be seen that BMFS yields similar attribution scores for closely correlated root causes (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', the axiom of continuity in §2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2), whereas the attribution scores resulting from other methods do not always follow this axiom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In addition, we can observe that the 𝐹1-score of both BMFS and ARD is higher than that of E-Net and Lasso, implying the merits of learning the distribu- tions of tuning parameters adaptively from the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Finally, despite the heterogeneity between 𝑿 and 𝒚 in this scenario, the proposed BALANCE still works well, probably due to the model-agnostic nature of linear attribution methods [18].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' On the other hand, we notice that the relationship between heterogeneous 𝒙𝑗 and𝒚 during anomalies can be well approximated by a linear model since similar phenomena (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', the waveform anomaly) usually occurs to both of them during anomalies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For example, an abnormal spike in 𝒙𝑗 typically leads to a spike in 𝒚, while an abrupt increase in 𝒙𝑗 results in an increase or decrease in 𝒚.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4 Fault Type Diagnosis for Exathlon Dataset We further investigate the performance of BALANCE on the pub- lic benchmark, Exathlon [12], which consists of real data traces collected from 10 Spark streaming applications in a 4-node clus- ter over a 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='5-month period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' There are 5 types of faults injected into the traces during executions, including Bursty Input (Type 1), Bursty Input Until Crash (Type 2), Stalled Input (Type 3), CPU Contention (Type 4), and Process Failure (Type 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The duration of the fault injection approximately ranges from 15 to 30 minutes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For each injection, the time series of 2,283 metrics coming from Spark are collected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Originally, Exathlon conducts anomaly detection for multivariate time series and then attributes the anomaly of multi- variate time series as a whole to individual time series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Here, we build a new fault-type diagnosis task on top of Exathlon (named Exathlon-ftd) to evaluate our method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Exathlon-ftd is constructed in the following way.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' First, we define the target KPI 𝒚 and the candidate metrics 𝑿 for this dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The target KPI is supposed to be affected by various types of faults and can be used to trigger the RCA procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' To this end, we conduct anomaly detection using the 3𝜎 rule after detrending on all metrics for each injection and find the intersec- tion of the anomalous metrics in all cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We choose the metric Processing_Delay from the intersection as our target KPI 𝒚, since the processing time is influenced by all aforementioned types of faults both theoretically and empirically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The candidate metrics 𝑿 is then chosen as the metrics that are abnormal in the same duration when 𝒚 is abnormal via the candidate AD module in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Second, we establish rules to determine the fault types once the root causes metrics are selected from 𝑿.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For simplicity, we only focus on the first 4 types of events and define 4 rules (R1-R4) to determine the fault types given the estimated root cause metrics as: R1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' If the metrics about traffic such as Last_Complete_Batch_Records and Processed_Records are in the estimated set of root causes, then it is the problem of the input (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', traffic).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The fault type is “Bursty Input” or “Bursty Input Until Crash” if these metrics are increasing and is “Stalled Input” if decreasing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' R2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' If R1 is not satisfied and the estimated set of root causes con- tains the metrics about CPU that are concentrated on a single node, then the fault type is “CPU contention”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The rationale behind is that the traffic problem can lead to anomalies in the metrics about CPU, but the CPU contention problem cannot in turn influence the metrics about traffic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' R3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' If the above two rules are not satisfied and the estimated set of root causes contains the metric executor_active_tasks, then the fault type is “Bursty Input” or “Bursty Input Until Crash”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We notice that both the traffic increase and the CPU con- tention problem will cause the abnormal increase in execu- tor_active_tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' However, a CPU contention problem typically results from another program on a single node that consumes all the CPU cores available on that node, and thus, the root cause metrics about CPU in the estimated set typically resolve around a single node (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=', R2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' As this condition does not hold, we can conclude that the fault type here is “Bursty Input”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' R4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' If the above three rules are not satisfied, the fault type is “Unknown”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' After these two steps, 73 cases are collected in total for the RCA task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' For each case, we aggregate both 𝑿 and 𝒚 by minute, and we retain 60 minutes and 5 minutes respectively before and SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Table 8: Results for Exathlon fault type analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Methods #Hits #Misses Accuracy Time (s) #Recommend ARD 54 19 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7397 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='29e+00 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4 Lasso 51 22 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6986 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='58e+00 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4 E-Net 49 24 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='6712 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='67e+00 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7 fsMTS 36 37 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='4932 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='45e+01 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='9 BMFS 58 15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='7945 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='60e+00 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='2 after Root_Cause_State time available in the dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Thus, 𝑛 = 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The number of candidates 𝑿 after anomaly detection scales up to 𝑝 = 150 approximately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We then compare all methods on the constructed Exathlon-ftd task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The results are presented in Table 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Once again, BMFS outperforms all the compared methods with the highest accuracy and the fewest number of recommended root cause metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' The running time of BMFS is the second best, slightly longer than that of ARD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 6 CONCLUSION AND FUTURE WORK The major contribution of this paper is to shed a different light on the RCA problem, viewing it from the angle of XAI.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In particu- lar, we assume that the abnormal behavior of the target KPIs can be explained by the relevant candidate root causes and propose a novel attribution-based RCA method named BALANCE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Con- cretely, we first learn a Bayesian sparse multicollinear model that predicts the target KPIs given the candidate root causes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We then attribute the abnormal behavior of the target KPIs to the candi- dates by computing their attribution scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We empirically show that the proposed method achieves superior performance for the synthetic data and three real-world problems, including bad SQL localization, container fault localization, and fault type diagnosis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We notice that the target KPIs and the candidate root causes are homogeneous in the former case and heterogeneous in the latter two cases, while 𝑝 > 𝑛 in the first and third application and 𝑝 ≤ 𝑛 in the second one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' We have deployed BALANCE to production, providing real-time root cause diagnosis of bad SQL and container issues in distributed data systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Although far from exhaustive, these applications show that BALANCE has the potential to serve as a general tool for practical RCA tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In future work, we would like to explore the connections between attribution-based RCA and graph-based RCA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In addition, we would like to generalize the linear model in BALANCE to non-linear forward models, such as the generalized linear models, which can be more expressive and suitable for describing the relationship between heterogeneous metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' REFERENCES [1] Pooja Aggarwal, Ajay Gupta, Prateeti Mohapatra, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Localization of operational faults in cloud applications by mining causal dependencies in logs using golden signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In International Conference on Service-Oriented Computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 137–149.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [2] Marco Ancona, Cengiz Oztireli, and Markus Gross.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Explaining deep neural networks with a polynomial time algorithm for shapley value approximation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In International Conference on Machine Learning (ICML).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 272–281.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [3] Charles K Assaad, Emilie Devijver, and Eric Gaussier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Survey and Evaluation of Causal Discovery Methods for Time Series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Journal of Artificial Intelligence Research 73 (2022), 767–819.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [4] Sebastian Bach, Alexander Binder, Grégoire Montavon, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' On pixel- wise explanations for non-linear classifier decisions by layer-wise relevance propagation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' PloS One 10, 7 (2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [5] Ranjita Bhagwan, Rahul Kumar, Ramachandran Ramjee, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Adtribu- tor: Revenue debugging in advertising systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In 11th USENIX Symposium on Networked Systems Design and Implementation (NSDI).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 43–55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [6] Christopher M Bishop and Nasser M Nasrabadi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Pattern recognition and machine learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [7] Jonathan Boss, Jyotishka Datta, Xin Wang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Group Inverse-Gamma Gamma Shrinkage for Sparse Regression with Block-Correlated Predictors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' arXiv preprint arXiv:2102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='10670 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [8] Kirill Bykov, Marina M-C Höhne, Adelaida Creosteanu, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Explaining bayesian neural networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' arXiv preprint arXiv:2108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='10346 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [9] Carlos M Carvalho, Nicholas G Polson, and James G Scott.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Handling sparsity via the horseshoe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In Artificial Intelligence and Statistics (AIStat).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 73–80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [10] Pengfei Chen, Yong Qi, Pengfei Zheng, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Causeinfer: Automatic and distributed performance diagnosis with hierarchical causality graph in large distributed systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In IEEE Conference on Computer Communications (INFOCOM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 1887–1895.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [11] Yingnong Dang, Qingwei Lin, and Peng Huang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' AIOps: real-world chal- lenges and research innovations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In IEEE/ACM 41st International Conference on Software Engineering: Companion Proceedings (ICSE-Companion).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 4–5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [12] Vincent Jacob, Fei Song, Arnaud Stiegler, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Exathlon: A Benchmark for Explainable Anomaly Detection over Time Series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Proceedings of the VLDB Endowment (PVLDB) (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [13] Vimalkumar Jeyakumar, Omid Madani, Ali Parandeh, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' ExplainIt!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='–A declarative root-cause analysis engine for time series data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In Proceedings of the ACM International Conference on Management of Data (SIGMOD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 333–348.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [14] Myunghwan Kim, Roshan Sumbaly, and Sam Shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Root cause detection in a service-oriented architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' ACM SIGMETRICS Performance Evaluation Review 41, 1 (2013), 93–104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [15] Wu Lin, Mohammad Emtiyaz Khan, and Mark Schmidt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Fast and simple natural-gradient variational inference with mixture of exponential-family approx- imations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In International Conference on Machine Learning (ICML).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 3992–4002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [16] Pantelis Linardatos, Vasilis Papastefanopoulos, and Sotiris Kotsiantis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Ex- plainable ai: A review of machine learning interpretability methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Entropy 23, 1 (2020), 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [17] Dewei Liu, Chuan He, Xin Peng, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Microhecl: High-efficient root cause localization in large-scale microservice systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In IEEE/ACM 43rd International Conference on Software Engineering: Software Engineering in Practice (ICSE-SEIP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 338–347.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [18] Scott M Lundberg and Su-In Lee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' A unified approach to interpreting model predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Advances in neural information processing systems (NIPS) 30 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [19] Minghua Ma, Zheng Yin, Shenglin Zhang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Diagnosing root causes of intermittent slow queries in cloud databases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Proceedings of the VLDB Endowment 13, 8 (2020), 1176–1189.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [20] Raha Moraffah, Paras Sheth, Mansooreh Karami, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Causal inference for time series analysis: Problems, methods and evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Knowledge and Information Systems (2021), 1–45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [21] Vinod Nair, Ameya Raul, Shwetabh Khanduja, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Learning a hierarchical monitoring system for detecting and diagnosing service issues.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2029–2038.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [22] Sarah E Neville, John T Ormerod, and MP Wand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Mean field variational Bayes for continuous sparse signal shrinkage: pitfalls and remedies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Electronic Journal of Statistics 8, 1 (2014), 1113–1151.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [23] Dmitry Pavlyuk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' fsMTS: Feature Selection for Multivariate Time Series.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [24] Juan Qiu, Qingfeng Du, Kanglin Yin, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' A causality mining and knowl- edge graph based method of root cause diagnosis for performance anomaly in cloud applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Applied Sciences 10, 6 (2020), 2166.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [25] Marco Tulio Ribeiro, Sameer Singh, and Carlos Guestrin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' " Why should i trust you?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='" Explaining the predictions of any classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In Proceedings of the 22nd ACM SIGKDD international Conference on Knowledge Discovery & Data mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 1135–1144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [26] Veronika Ročková and Edward I George.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Negotiating multicollinearity with spike-and-slab priors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Metron 72, 2 (2014), 217–229.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [27] Avanti Shrikumar, Peyton Greenside, and Anshul Kundaje.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Learning im- portant features through propagating activation differences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In International conference on machine learning (ICML).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 3145–3153.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [28] Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Deep inside convolutional networks: Visualising image classification models and saliency maps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In ICLR workshop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [29] Jacopo Soldani and Antonio Brogi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Anomaly detection and failure root cause analysis in (micro) service-based cloud applications: A survey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' ACM Computing Surveys (CSUR) 55, 3 (2022), 1–39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [30] Peter Spirtes and Clark Glymour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 1991.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' An algorithm for fast recovery of sparse causal graphs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Social science computer review 9, 1 (1991), 62–72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [31] Yi Sun and Mukund Sundararajan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Axiomatic attribution for multilinear functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In Proceedings of the 12th ACM conference on Electronic commerce.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 177–178.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [32] Yongqian Sun, Youjian Zhao, Ya Su, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Hotspot: Anomaly localization for additive kpis with multi-dimensional attributes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' IEEE Access 6 (2018), 10909– 10923.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' BALANCE: Bayesian Linear Attribution for Root Cause Localization SIGMOD ’23, June 18–23, 2023, Seattle, WA, USA [33] Mukund Sundararajan, Ankur Taly, and Qiqi Yan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Axiomatic attribution for deep networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In International conference on machine learning (ICML).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 3319– 3328.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [34] Jörg Thalheim, Antonio Rodrigues, Istemi Ekin Akkus, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Sieve: Ac- tionable insights from monitored metrics in microservices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' arXiv preprint arXiv:1709.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='06686 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [35] Robert Tibshirani.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Regression shrinkage and selection via the lasso.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Journal of the Royal Statistical Society: Series B (Methodological) 58, 1 (1996), 267–288.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [36] Michael E Tipping.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Sparse Bayesian learning and the relevance vector machine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Journal of machine learning research (JMLR) 1, Jun (2001), 211–244.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [37] Guanchu Wang, Yu-Neng Chuang, Mengnan Du, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Accelerating Shapley Explanation via Contributive Cooperator Selection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In International Conference on Machine Learning (ICML).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [38] Hanzhang Wang, Phuong Nguyen, Jun Li, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Grano: Interactive graph- based root cause analysis for cloud-native distributed data platform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Proceedings of the VLDB Endowment 12, 12 (2019), 1942–1945.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [39] Ping Wang, Jingmin Xu, Meng Ma, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Cloudranger: Root cause identifi- cation for cloud native systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In 18th IEEE/ACM International Symposium on Cluster, Cloud and Grid Computing (CCGRID).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 492–502.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [40] Jianping Weng, Jessie Hui Wang, Jiahai Yang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Root cause analysis of anomalies of multitier services in public clouds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' IEEE/ACM Transactions on Networking 26, 4 (2018), 1646–1659.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [41] Zhenkun Yang, Chuanhui Yang, Fusheng Han, Mingqiang Zhuang, Bing Yang, Zhifeng Yang, Xiaojun Cheng, Yuzhong Zhao, Wenhui Shi, Huafeng Xi, Huang Yu, Bin Liu, Yi Pan, Boxue Yin, Junquan Chen, and Quanqing Xu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' OceanBase: A 707 Million tpmC Distributed Relational Database System.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Proceedings of the VLDB Endowment 15, 12 (2022), 3385–3397.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [42] Hang Yu, Songwei Wu, Luyin Xin, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Fast Bayesian Inference of Sparse Networks with Automatic Sparsity Determination.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 21 (2020), 124–1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [43] Hang Yu, Luyin Xin, and Justin Dauwels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Variational wishart approxi- mation for graphical model selection: Monoscale and multiscale models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' IEEE Transactions on Signal Processing 67, 24 (2019), 6468–6482.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [44] Matthew D Zeiler and Rob Fergus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Visualizing and understanding convolu- tional networks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In European conference on computer vision (ECCV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 818–833.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [45] Arnold Zellner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 1986.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' On assessing prior distributions and Bayesian regression analysis with g-prior distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Bayesian inference and decision techniques (1986).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [46] Kai Zhang, Chao Tian, Kun Zhang, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' A Fast PC Algorithm with Reversed- order Pruning and A Parallelization Strategy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' arXiv preprint arXiv:2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content='04626 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [47] Xu Zhang, Chao Du, Yifan Li, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' HALO: Hierarchy-aware Fault Local- ization for Cloud Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In Proceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 3948–3958.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [48] Yingying Zhang, Zhengxiong Guan, Huajie Qian, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' CloudRCA: A Root Cause Analysis Framework for Cloud Computing Platforms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' In Proceedings of the 30th ACM International Conference on Information & Knowledge Management (CIKM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 4373–4382.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [49] Xun Zheng, Bryon Aragam, Pradeep K Ravikumar, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Dags with no tears: Continuous optimization for structure learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Advances in Neural Information Processing Systems (NIPS) 31 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' [50] Hui Zou and Trevor Hastie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Regularization and variable selection via the elastic net.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} +page_content=' Journal of the royal statistical society: series B (statistical methodology) 67, 2 (2005), 301–320.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/qtFRT4oBgHgl3EQfezdF/content/2301.13572v1.pdf'} diff --git a/r9E2T4oBgHgl3EQfLQZF/content/2301.03711v1.pdf b/r9E2T4oBgHgl3EQfLQZF/content/2301.03711v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..fc0d05e482221c4d596089f288f6abb9a09fdf11 --- /dev/null +++ b/r9E2T4oBgHgl3EQfLQZF/content/2301.03711v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:75bed03f182c1f866fe86cbeb094cab09143705ae83139ae4e2da411f45ae2f7 +size 9565811 diff --git a/rtE0T4oBgHgl3EQfrQGn/content/tmp_files/2301.02564v1.pdf.txt b/rtE0T4oBgHgl3EQfrQGn/content/tmp_files/2301.02564v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..7869dc9b265e8c9c4bacacf1584294983388fa4d --- /dev/null +++ b/rtE0T4oBgHgl3EQfrQGn/content/tmp_files/2301.02564v1.pdf.txt @@ -0,0 +1,1757 @@ +Draft version January 9, 2023 +Typeset using LATEX twocolumn style in AASTeX631 +Early Insights for Atmospheric Retrievals of Exoplanets using JWST Transit Spectroscopy +Savvas Constantinou,1 Nikku Madhusudhan,1 and Siddharth Gandhi2, 3, 4 +1Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK +2Leiden Observatory, Leiden University, Postbus 9513 2300 RA, Leiden, The Netherlands +3Department of Physics, University of Warwick, Coventry CV4 7AL, UK +4Centre for Exoplanets and Habitability, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK +(Accepted 24 December 2022, The Astrophysical Journal Letters) +Abstract +We have entered the era of the James Webb Space Telescope (JWST). We use the first JWST +transmission spectrum of the hot Saturn-mass exoplanet, WASP-39 b, obtained with the NIRSpec +instrument in the 3-5 µm range to investigate (a) what atmospheric constraints are possible with +JWST-quality data in this spectral range, (b) requirements for atmospheric models used in retrievals, +(c) effect of differences between data reduction pipelines on retrieved atmospheric properties, and (d) +complementarity between JWST data in the 3-5 µm range and HST observations at shorter wave- +lengths. JWST spectra in the 3-5 µm range provide a promising avenue for chemical detections while +encompassing a window in cloud opacity for several prominent aerosols. We confirm recent inferences +of CO2, SO2, H2O, and CO in WASP-39 b, report tentative evidence for H2S, and retrieve elemental +abundances consistent with Saturn’s metallicity. We retrieve molecular abundances with ∼0.3-0.6 dex +precision with this relatively limited spectral range. When considering the 3-5 µm data alone, reported +differences in spectra with different reduction pipelines can affect abundance estimates by up to ∼1 dex +and the detectability of less prominent species. Complementing with data at shorter wavelengths, e.g. +with other JWST instruments or HST WFC3 (∼0.8-1.7 µm), can significantly improve the accuracy +and precision of the abundance estimates. The high data quality enables constraints on aerosol prop- +erties, including their composition, modal size and extent, motivating their consideration in retrievals. +Our results highlight the promise of JWST exoplanet spectroscopy, while underscoring the importance +of robust data reduction and atmospheric retrieval approaches in the JWST era. +Keywords: James Webb Space Telescope (2291) — Exoplanet Atmospheres (487) — Radiative Transfer +(1335) — Transmission Spectroscopy (2133) — Infrared Spectroscopy (2285) +1. INTRODUCTION +The first observations with the James Webb Space +Telescope (JWST) are now available, heralding the +dawn of a new era in our understanding of exoplan- +etary atmospheres. +With a virtually complete cover- +age of the near-mid infrared, transmission spectroscopy +with JWST enables simultaneous constraints on multi- +ple chemical species and other physical properties in ex- +oplanetary atmospheres (Beichman et al. 2014; Steven- +son et al. 2016; Batalha & Line 2017; Kalirai 2018; Bean +et al. 2018; Sarkar et al. 2020). The generational leap in +Corresponding author: S. Constantinou, N. Madhusudhan +sc938@cam.ac.uk, nmadhu@ast.cam.ac.uk +our understanding of chemical and physical processes in +exoplanets is already underway. +Exoplanet transmission spectroscopy with the Hubble +Space Telescope (HST), along with ground-based ob- +servations with facilities like the Very Large Telescope +(VLT), have over the last 20 years been a key driver of +the field’s remarkable growth (Seager & Sasselov 2000; +Charbonneau et al. 2002; Vidal-Madjar et al. 2003; Dem- +ing et al. 2013; Ehrenreich et al. 2015; Sing et al. 2016; +Nikolov et al. 2016; Kreidberg 2018). Paired with the- +oretical developments in atmospheric modelling and re- +trievals, HST transmission spectra in the optical and +near-infrared (NIR) have led to important constraints +on the abundances of chemical species including H2O, +arXiv:2301.02564v1 [astro-ph.EP] 6 Jan 2023 + +2 +Na and K, as well as the properties of clouds and hazes +in several exoplanetary atmospheres (Madhusudhan & +Seager 2009; Madhusudhan et al. 2014; Kreidberg et al. +2014; Wakeford et al. 2018; Barstow et al. 2017; Pinhas +et al. 2019; Welbanks et al. 2019; Madhusudhan 2018). +Most of these atmospheric detections were made for ir- +radiated gas giants, whose relative rarity (Howard et al. +2010; Mayor et al. 2011; Wang et al. 2015; Fulton et al. +2021) is offset by their comparative observability. This +is largely due to their extended, hydrogen-dominated +atmospheres giving rise to large spectral signatures and +hence high signal-to-noise observations. +Our goal in this work is to obtain a first glimpse into +atmospheric properties of exoplanets that can be re- +trieved with JWST-quality transmission spectra. While +observations with HST have been limited to wavelengths +below 1.7 µm, JWST promises a substantial increase +in both sensitivity and spectral range. +In particular, +the ∼3-5 µm range accessible with the NIRSpec instru- +ment (Ferruit et al. 2012) opens uncharted territory in +chemical discovery space, as evidenced by recent infer- +ences of CO2 and SO2 in the atmosphere of an exoplanet +(The JWST Transiting Exoplanet Community Early Re- +lease Science Team et al. 2022; Rustamkulov et al. 2022; +Alderson et al. 2022). Here we assess atmospheric con- +straints that are possible with JWST transmission spec- +tra in the ∼3-5µm range and modeling requirements for +retrieval frameworks in the JWST-era. We further in- +vestigate the sensitivity of retrievals to differences in +spectra obtained using different data reduction pipelines +as well as complementarity with NIR spectra with the +HST/WFC3 instrument (0.8-1.7 µm). +We focus on WASP-39 b, which is one of the first exo- +planets whose transmission spectrum has been observed +with JWST. The planet has a mass of 0.28 ± 0.03 MJ, +a radius of 1.28 ± 0.04 RJ and a zero-albedo equilib- +rium temperature of 1170 K (Faedi et al. 2011; Mancini +et al. 2018). It orbits a G8-type host star with an in- +termediate brightness of J = 10.7 and V = 12.1 (Faedi +et al. 2011). +WASP-39 b is therefore an example of +the immense diversity in the known exoplanet popula- +tion. While its closest solar system analogue by mass +is Saturn (M = 0.3 MJ), it is significantly larger, with +a radius greater than Jupiter’s and significantly more +strongly irradiated than any solar system gas giant. The +notably low gravity of WASP-39 b makes its atmosphere +highly conducive to transmission spectroscopy observa- +tions and has already led to detections of H2O, Na and +K with prior HST and ground-based facilities (Fischer +et al. 2016; Nikolov et al. 2016; Sing et al. 2016; Tsiaras +et al. 2018; Wakeford et al. 2018; Pinhas et al. 2019; +Kirk et al. 2019; Welbanks et al. 2019; Kawashima & +Min 2021). +As a result, WASP-39 b is the target of +choice for the JWST Early Release Science (ERS) pro- +gram, which has already led to novel inferences of CO2 +and SO2 in its atmosphere (The JWST Transiting Ex- +oplanet Community Early Release Science Team et al. +2022; Alderson et al. 2022; Rustamkulov et al. 2022). +We consider the JWST observations of WASP-39 b +over the 3-5 µm range, obtained with the NIRSpec +PRISM spectrograph(The JWST Transiting Exoplanet +Community Early Release Science Team et al. 2022). +Beyond its high data quality, this spectral range is rep- +resentative of the majority of observations JWST is set +to make over Cycle 1. Specifically, most Cycle 1 observa- +tions are set to be made with the NIRSpec spectrograph +using the G395 grating over a similar ∼3-5 µm range. +As such, our work is also a feasibility study, with the +present observations of WASP-39 b constituting a near- +best case scenario. +We also consider how minor variations in the JWST +observations, particularly those arising from differences +between reduction pipelines, can affect the retrieved at- +mospheric constraints. We do this by retrieving on two +different reduction of the same observations, obtained +with the Tiberius and Eureka pipelines, which have been +reported to give slightly different results, particularly +over the 3.6 µm Spitzer band (The JWST Transiting Ex- +oplanet Community Early Release Science Team et al. +2022). +Besides analysing the JWST data alone, we also +consider their complementarity with prior observa- +tions. +For this work, we consider pairing the 3-5 µm +JWST observations with those obtained previously with +HST/WFC3 (0.8-1.7 µm), examining how this affects +the precision and accuracy of atmospheric constraints. +This pairing is particularly important, as several of the +Cycle 1 targets have or are set to be also observed with +HST/WFC3. In doing so, we seek to assess the com- +plementarity between JWST 3-5 µm observations and +HST. +In what follows, we discuss the observations in section +2 and our retrieval methodology in section 3. The results +of our investigation are presented in section 4, followed +by our summary and discussion in section 5. +2. PRIOR AND CURRENT OBSERVATIONS +The atmosphere of WASP-39 b has been extensively +probed in transmission spectroscopy from both ground +and space. +The first space-based observations were +carried out in 2013, using the HST/STIS G430L and +G750L gratings (GO 12473, PI: D Sing) (Fischer et al. +2016; Sing et al. 2016), covering the 0.29-1.0 µm wave- +length range. +Paired with photometric observations + +3 +1 +2 +3 +4 +5 +Wavelength (µm) +2.00 +2.05 +2.10 +2.15 +2.20 +2.25 +2.30 +Transit Depth (%) +WASP-39 b +2°3 Hsc +6°8 Hsc +HST/WFC3 +JWST/NIRSpec PRISM +Best Fit Model +Without Aerosols +°2 +0 +2 +4 +6 +8 +Scale Heights +H2O +H2O +H2O +H2S +SO2 +CO2 +CO +H2O +Figure 1. +A transmission spectrum of WASP-39 b. The circles with error bars show the JWST NIRSpec PRISM spectrum +in the 3-5 µm range reduced with the Tiberius pipeline (The JWST Transiting Exoplanet Community Early Release Science +Team et al. 2022) along with prior HST/WFC3 observations in the 0.8-1.7 µm range (Wakeford et al. 2018). The solid curve in +brown shows our retrieved best fit spectrum, and the same spectrum but without opacity contributions from aerosols is shown +in blue for reference (see section 4.2.1). The heights of the prominent spectral features in the JWST and HST bands in terms of +a characteristic atmospheric scale height are denoted by arrows; a nominal slant photospheric temperature of 800 K is assumed +motivated by the retrieved constraints. The contributions of individual molecules are shown in figure 6 in the Appendix. +with Spitzer (90092, PI: J.-M. D´esert), these observa- +tions were used to infer a cloud-free atmosphere, with +prominent spectral features arising from Na and K. This +is in agreement with conclusions drawn from ground- +based VLT observations by Nikolov et al. (2016), span- +ning the 0.4-0.8 µm range using the Focal Reducer/Low +Dispersion Spectrograph 2 (FORS2) (096.C-0765, PI: N. +Nikolov). +Further spectroscopic observations were carried out +in the NIR using the the HST Wide Field Camera 3 +(WFC3) G102 and G141 grisms (GO 14169, PI: H. +Wakeford; GO 14260, PI: D. Deming), which together +cover a wavelength range of 0.8-1.7 µm. +These ob- +servations revealed prominent H2O absorption features. +Combining the new HST/WFC3 observations with prior +ones with VLT, HST/STIS and Spitzer, Wakeford et al. +(2018) report an enriched atmospheric metallicity con- +straint of 151+48 +−46× solar using a retrieval framework as- +suming chemical equilibrium. +The median value cor- +responds to log-mixing ratios of ∼ −1.3, ∼ −3.6 and +∼ −4.8 for H2O, Na and K, respectively. By contrast, +Tsiaras et al. (2018), using an alternative reduction of +the same HST/WFC3 G141 observations, find a signifi- +cantly lower H2O log-mixing ratio of −5.94 ± 0.61. +This disparity in the inferred atmospheric composi- +tion of WASP-39 b persisted through subsequent anal- +yses. Retrievals carried out by Pinhas et al. (2019) us- +ing the WFC3 G141 observations reduced by Tsiaras +et al. (2018) along with HST/STIS and Spitzer data +found an H2O log-mixing ratio corresponding to a sub- +solar metallicity, at −4.07+0.72 +−0.78, but Na and K log- +mixing ratios corresponding to a super-solar metallic- +ity, at −3.86+1.31 +−1.36 and −4.22+1.25 +−1.12. +Kirk et al. (2019) +presented a combined transmission spectrum consisting +of the HST/WFC3 observations presented by Wakeford +et al. (2018) and Spitzer photometry in the NIR, while +combining HST/STIS and VLT observations with new +observations using the William Herschel Telescope in the +optical. Using a retrieval framework assuming equilib- +rium chemistry, they obtain an atmospheric metallicity +constraint of 282+65 +−58× solar, at its median corresponding +to H2O, Na and K log-mixing ratios of -0.9, -3.3 and -4.5, +respectively. Using this same combined dataset, Wel- +banks et al. (2019) find that composition constraints are +dependent on the choice of prior, obtaining log-mixing +ratio estimates of −0.65+0.14 +−1.83, −3.62+1.14 +−2.69 and −5.62+2.30 +−2.05 +for H2O, Na and K with their canonical retrieval, and +−2.43+0.27 +−0.24, −6.17+0.50 +−0.51 and −7.24+0.71 +−1.06 for a more con- +strained prior. More recently, Kawashima & Min (2021) +analysing the combined HST/STIS, WFC3 and Spitzer +observations presented by Sing et al. (2016), Fischer +et al. (2016) and Wakeford et al. (2018), constrain an at- +mospheric metallicity consistent with solar to within 1- +σ when considering disequilibrium chemistry. They also +report a moderately super-solar metallicity constraint, +corresponding to an H2O log-mixing ratio of ∼-2.6. +The JWST observations of WASP-39 b used in the +present study have been obtained with the Near Infrared +Spectrograph (NIRSpec) PRISM (Ferruit et al. 2012; +Birkmann et al. 2014) over a single transit in July 2022 +as part of the JWST Early Release Science (ERS) (The +JWST Transiting Exoplanet Community Early Release +Science Team et al. 2022). Spanning a subset of the full +NIRSpec PRISM ∼0.6-5 µm range, the new data shows + +4 +absorption peaks that are significantly larger in size than +those observed previously in the HST/WFC3 bandpass, +corresponding to 6-8 vs 2-3 atmospheric scale heights. +Several reductions of the same observations were pre- +sented, which are reported to be largely comparable but +with small deviations, especially in the 3-4 µm range. +For the sake of robustness, we consider two reductions, +based on their level of agreement over the Spitzer 3.6 µm +bandpass, in order to assess the effect different reduc- +tion pipelines may have on the retrieved atmospheric +properties. +Specifically, we use the data obtained us- +ing the Eureka and Tiberius pipelines. Both the Eureka +and Tiberius pipelines give rise to observations which, +when binned to the Spitzer 3.6 µm bandpass, are at a +higher transit depth than that observed by Spitzer it- +self. The Tiberius pipeline value is consistent with the +Spitzer point to within 1-σ, while the Eureka value lies +at ∼2-σ of the Spitzer point and between those of the +tshirt and FIREFLy pipelines. The 3-5 µm JWST data +obtained with the Tiberius pipeline that are used in the +present study are shown in figure 1, along with prior +observations with HST/WFC3. +3. METHODS +We retrieve the atmospheric properties of WASP-39 b +from the spectroscopic observations described in section +2 using a variant of the AURA retrieval framework (Pin- +has et al. 2018). The forward model computes radiative +transfer in a plane-parallel atmosphere in transmission +geometry. The model assumes hydrostatic equilibrium +and local thermodynamic equilibrium in a H2-rich at- +mosphere. The pressure-temperature (P-T) profile and +uniformly-distributed volume mixing ratios of the chem- +ical absorbers are free parameters in the model. In this +work, we additionally retrieve the properties of Mie scat- +tering aerosols, as discussed below. +We also consider +the conventional parametric cloud/haze prescription in +AURA, for reference, as well as the effect of stellar het- +erogeneities. The parametric atmospheric model is cou- +pled to a Bayesian inference and parametric estimation +routine based on the Nested Sampling algorithm, im- +plemented via the PyMultiNest package (Feroz et al. +2009; Buchner et al. 2014; Feroz et al. 2019). +In order to consider the spectral contributions of +aerosols the model includes extinction from Mie scat- +tering particles in the planetary atmosphere. Using the +approach in Pinhas & Madhusudhan (2017) we explore +a range of possible condensate species that can be preva- +lent in irradiated giant exoplanets, e.g., MgSiO3, Na2S, +MnS, ZnS, SiO2, Al2O3, FeO, Fe2O3, TiO2, NaCl and +Mg2SiO4, based on data from Wakeford & Sing (2015); +Pinhas & Madhusudhan (2017). The extinction cross +sections are computed following Mie theory (Bohren +et al. 1983). +We assume a modified gamma distribu- +tion for the aerosol particle sizes Deirmendjian (1969), +with the modal particle size, rc, of the distribution, be- +ing a free parameter in the model. We additionally con- +sider the vertical extent of the aerosol layer, described +by the relative scale height of the aerosols, hc = +Hc +H , +where Hc is the aerosol scale height and H is the atmo- +spheric scale height. hc is another free parameter in the +model with values ranging from 0 to 1. An hc value of 1 +implies that aerosols have a constant mixing ratio with +altitude, while a value of 0 corresponds to no aerosols +being present in the observable atmosphere. We incor- +porate this in our model as an exponential decrease in +the aerosol mixing ratio with altitude: +Xi(z) = Xi,0 exp +� +−(n − 1)z +H(z) +� +, +(1) +where Xi denotes the mixing ratio of the ith aerosol +species, H(z) is the local atmospheric scale height kBT +µg +at an altitude z, and n = +1 +hc . Our model also accounts +for an inhomogeneous coverage of the terminator atmo- +sphere by aerosols, whose coverage fraction, fc, is a third +free parameter. +Our aerosol model can include an arbitrary number of +aerosol species. The mixing ratio of each of the aerosol +species is a separate free parameter. For the retrievals +we consider in this work, the modal particle size, vertical +extent and fractional coverage parameters are universal, +applying to all aerosol species in the model. +In light of the JWST observations probing a novel +part of the spectrum and the high precision of obser- +vations, we carry out a staged retrieval approach. We +begin by considering a maximal set of gaseous and Mie +scattering aerosol species. This maximal model consid- +ers opacity contributions from a large number of gaseous +chemical species. It also includes Mie scattering arising +from inhomogeneous coverage of the terminator atmo- +sphere by aerosols of MgSiO3, Na2S, MnS, ZnS, SiO2, +Al2O3, FeO, Fe2O3, TiO2, NaCl and Mg2SiO4 (Wake- +ford & Sing 2015; Pinhas & Madhusudhan 2017). +We then consider a reduced canonical set of param- +eters, based on initial indications by our maximal re- +trieval and chemical expectations, which we use for all +retrieval cases presented in this work. The final set of +gaseous chemical species included in the present canoni- +cal model comprises of H2O, CO, CO2, H2S, SO2, CH4, +NH3, HCN, C2H2. +We additionally include opacity +contributions arising from H2-H2 and H2-He collision- +induced absorption (Richard et al. 2012), as well as +ZnS (Querry 1987) and MgSiO3 (Dorschner et al. 1995) +aerosols. +Our choice for these two aerosol species is + +5 +driven by both thermochemical expectations for the con- +densates based on the terminator temperature (Morley +et al. 2013) and indicative constraints obtained with our +maximal model retrievals. The absorption cross-sections +for the gaseous species are derived following Gandhi & +Madhusudhan (2017), using line lists of H2O, CO and +CO2 from Rothman et al. (2010) and Li et al. (2015), +CH4 from Yurchenko & Tennyson (2014), NH3 from +Yurchenko et al. (2011), HCN from Harris et al. (2006) +and Barber et al. (2014), C2H2 from Chubb et al. (2020) +SO2 from Underwood et al. (2016) and H2S from Azzam +et al. (2016) and Chubb et al. (2018). +Our canonical atmospheric model has a total of 21 +free parameters. The first 9 correspond to the individual +log-mixing ratios of the gaseous chemical species listed +above. Another two free parameters describe the log- +mixing ratios of ZnS and MgSiO3 aerosols and another +3 describe their fractional coverage, modal particle size +and vertical extent, as described above. The terminator +temperature profile is modelled by 6 parameters using +the parametrisation of Madhusudhan & Seager (2009). +The last free parameter for our canonical model is the +planet radius, RP, defined at a nominal reference pres- +sure of 0.1 bar. For retrievals on combined JWST and +HST/WFC3 observations, we additionally retrieved for +a linear offset between the two datasets. +We use log-uniform priors between 10−12-10−0.3 for +the mixing ratios of gaseous species, and between 10−30- +10−6 for the mixing ratios of MgSiO3 and ZnS aerosols. +We set the prior for the modal particle size, rc to a log- +uniform distribution ranging between 1 nm and 1µm and +both the fc and hc priors are uniform between 0-1. The +prior for the temperature at the top of the atmosphere, +T0, is also uniformly distributed between 300-1600 K. +For completeness, we also explore retrievals including +the effects of stellar heterogeneities as well as a more +traditional parametric approach to model clouds/hazes, +instead of Mie scattering by aerosols, as pursued by de- +fault in AURA. For the parametric clouds/hazes, we +use a four-parameter combination of inhomogeneous +grey opacity clouds and modified Rayleigh-like hazes +(MacDonald & Madhusudhan 2017; Pinhas et al. 2018). +We incorporate stellar heterogeneities in the model fol- +lowing (Rackham et al. 2017) as described in Pinhas +et al. (2018). This model involves three free parame- +ters, describing the fractional surface coverage of het- +erogeneities, their overall effective temperature, and the +temperature of the pristine photosphere. +4. RESULTS +We now proceed to investigate the performance of at- +mospheric retrievals on a JWST spectrum of WASP- +39 b. +We first consider the JWST/NIRSpec PRISM +observations on their own, examining the constraints +such observations can lead to. +We also assess how +the retrieved atmospheric constraints vary due to minor +differences between reduction pipelines, by considering +JWST observations reduced by both Tiberius and Eu- +reka. We then present our findings from joint retrievals +on both the JWST observations over the 3-5 µm range +and prior HST/WFC3 data. In doing so we establish the +complementarity between JWST and HST/WFC3. We +once again carry this out for data obtained with both +the Tiberius and Eureka reduction pipelines, examin- +ing the differences between the resulting atmospheric +constraints and how they vary with differences in our +retrieved atmospheric model. Our retrieved constraints +are summarised in table 1. +4.1. Retrievals with JWST Data +We first focus on the recently-released JWST observa- +tions of WASP-39 b. As discussed in section 3, we anal- +yse the observations with a staged retrieval approach. +We begin by considering a maximal set of chemical +species, including gases and Mie scattering aerosols. We +then consider a reduced set of chemical absorbers, based +on physical plausibility and their initial constraints ob- +tained by our maximal retrieval. +Our reduced set of +chemical species comprising our canonical model con- +sists of H2O, CO, CH4, HCN, H2S and SO2, as well as +ZnS and MgSiO3 aerosols. 1 +We consider data obtained with the Tiberius and Eu- +reka pipelines presented by The JWST Transiting Ex- +oplanet Community Early Release Science Team et al. +(2022), which produce somewhat different transit depths +when binned over the Spitzer 3.6 µm photometric band. +Specifically, the Tiberius pipeline produces data that are +the closest to the Spitzer 3.6 µm transit depth measure- +ment, with all other pipelines including Eureka which +yields transit depths that are more than 1-σ higher than +the Spitzer value. +The retrieved spectral fit to the JWST observations +with our canonical model is shown in figure 2. The ob- +servations display a highly prominent absorption peak +at 4.3 µm that has been previously attributed to CO2 +(The JWST Transiting Exoplanet Community Early Re- +lease Science Team et al. 2022), as well as a smaller +absorption feature at 4.0 µm. Moreover, the spectrum +trends upwards at shorter wavelengths. For both reduc- +tion pipelines, our retrievals produce good fits to the +data. +1 During the preparation of this work, we learned about the in- +dependent inference of SO2 using the same data (Rustamkulov +et al. 2022). + +6 +3.0 +3.5 +4.0 +4.5 +5.0 +2.05 +2.10 +2.15 +2.20 +2.25 +2.30 +Transit Depth (%) +JWST +0.8 +0.9 +1.0 +1.1 +1.2 +1.3 +1.4 +1.5 +1.6 +1.7 +2.05 +2.10 +2.15 +2.20 +Transit Depth (%) +JWST + HST/WFC3 +3.0 +3.5 +4.0 +4.5 +5.0 +Wavelength (µm) +2.05 +2.10 +2.15 +2.20 +2.25 +2.30 +Transit Depth (%) +Median +1σ +2σ +Tiberius +Eureka +HST/WFC3 +JWST (Tiberius) +JWST (Tiberius) +Figure 2. +Retrieved spectral fits obtained for two of the retrievals considered in this work, using our canonical model described +in section 3. The top panel shows the retrieved spectral fit for JWST NIRSpec PRISM 3-5 µm observations reduced with the +Tiberius pipeline (data shown in black errorbars with yellow circles). Also shown are the same observations reduced with the +Eureka pipeline (in green). The lower two panels show different wavelength regions of the retrieved spectral fit to the combination +of HST/WFC3 observations (0.8-1.7 µm) and JWST/NIRSpec PRISM observations reduced with Tiberius; see section 2. In +all three panels, the darkest orange line denotes the median retrieved spectrum while the two lighter orange regions denote the +corresponding 1- and 2-σ contours. +4.1.1. Tiberius Reduction +We begin by considering the data obtained via the +Tiberius reduction pipeline. As shown in figure 2, our +retrieval obtains a good fit to the two significant ab- +sorption features at 4.0 and 4.3 µm, as well as the trend +of increasing transit depth towards lower wavelengths. +Moreover, the retrieval also fits smaller features within +that trend. We confirm that the larger peak at 4.3 µm +is due to CO2 and the smaller peak at 4.0 µm due to +SO2, as reported previously (The JWST Transiting Ex- +oplanet Community Early Release Science Team et al. +2022; Rustamkulov et al. 2022). +Our retrievals obtain constraints for the log-mixing +ratios of CO2, SO2, H2O, H2S and CO. Driven by the +very prominent CO2 absorption peak at 4.3 µm, we +constrain the log-mixing ratio of CO2 to −6.28+0.38 +−0.31. +Additionally, our retrieval attributes the smaller ab- +sorption peak seen at 4.0 µm to SO2, constraining its +log-mixing ratio to −7.01+0.23 +−0.20. +CO is invoked to ex- +plain the data redward of the CO2 feature, with a log- +mixing ratio of −4.25+0.39 +−0.35. Additionally, H2O and H2S +are constrained to log-mixing ratios of −4.85+0.38 +−0.35 and +−5.32+0.36 +−0.42, respectively, and are used to fit the spec- +trum below 4.0 µm. +The posterior distributions re- +trieved for each of these molecules are shown in figure +3. + +7 +Table 1. Retrieved atmospheric parameters for WASP-39 b. +Case +log(XH2O) +log(XCO2) +log(XSO2) +log(XCO) +log(XH2S) +T0/K +Canonical Retrieval Model +JWST Tiberius +−4.85+0.38 +−0.35 +−6.28+0.38 +−0.31 +−7.01+0.23 +−0.20 +−4.25+0.39 +−0.35 +−5.32+0.36 +−0.42 +862+64 +−63 +JWST Eureka +−3.29+0.59 +−0.56 +−5.11+0.63 +−0.54 +−6.40+0.39 +−0.35 +−4.17+0.61 +−0.61 +−4.11+0.49 +−0.46 +738+54 +−55 +Tiberius + HST/WFC3 +−3.27+0.26 +−0.24 +−4.52+0.36 +−0.30 +−5.94+0.22 +−0.19 +−2.58+0.51 +−0.50 +−4.01+0.27 +−0.24 +757+40 +−43 +Eureka + HST/WFC3 +−3.28+0.33 +−0.27 +−4.57+0.51 +−0.38 +−6.31+0.25 +−0.24 +−3.61+0.37 +−0.40 +−4.17+0.29 +−0.26 +666+53 +−72 +Other Retrieval Models +Tiberius + HST/WFC3, Parametric Cl./Hz. +−3.69+0.31 +−0.25 +−4.75+0.41 +−0.39 +−6.21+0.24 +−0.23 +−2.40+0.47 +−0.45 +−4.49+0.31 +−0.25 +758+63 +−61 +Eureka + HST/WFC3, Parametric Cl./Hz. +−3.14+0.34 +−0.31 +−4.49+0.41 +−0.41 +−6.32+0.30 +−0.29 +−3.62+0.48 +−0.62 +−4.49+0.41 +−0.41 +683+52 +−44 +Tiberius + HST/WFC3, Stellar Het. +−3.44+0.27 +−0.26 +−4.65+0.34 +−0.33 +−6.05+0.22 +−0.21 +−2.85+0.42 +−0.44 +−4.19+0.26 +−0.25 +763+49 +−51 +Eureka + HST/WFC3, Stellar Het. +−3.34+0.31 +−0.27 +−4.58+0.41 +−0.34 +−6.29+0.24 +−0.24 +−3.58+0.35 +−0.36 +−4.09+0.24 +−0.26 +656+53 +−48 +Note—The table shows the retrieved log-mixing ratios of molecules with notable detection significances along with the temperature at the top +of the model atmosphere. The top four rows show the retrievals using our canonical model, with the top two obtained with JWST NIRSpec +3-5 µm data alone and the remaining two with a combination of JWST and HST data. We consider JWST data reported using two pipelines, +Tiberius and Eureka, as discussed in section 4. The bottom four rows show constraints on the JWST+HST data obtained with two other +retrieval considerations: (a) replacing the Mie scattering aerosols with a conventional parametric cloud/haze prescription, and (b) including +stellar heterogeneities, as described in section 3. +In addition to the above mixing ratio constraints, our +retrieval obtains a P-T profile that is consistent with an +isotherm to within 1-σ, constraining T0, the tempera- +ture at the top of the model atmosphere to 862+64 +−63 K. +Additionally, this retrieval does not obtain any con- +straints for the properties of Mie scattering aerosols. +The posterior distributions for the log-mixing ratios of +MgSiO3 and ZnS which are largely unconstrained, with +that of MgSiO3 displaying a somewhat prominent peak +at ∼-10. The posterior distributions for the modal par- +ticle size, fractional terminator coverage and vertical ex- +tent are also unconstrained. +We carry out additional retrievals to assess the detec- +tion significance for each of the constrained molecules +presented above. We do this by performing a Bayesian +model comparison between our canonical retrieval model +and one without the molecule in question (Pinhas et al. +2018). We find that both SO2 and, particularly, CO2 +are confidently detected. In the case of CO2, the model +including it is preferred at a ∼16-σ level, while the +inclusion of SO2 in the model is favoured at a ∼4- +σ level. +This is consistent with the fact that both +molecules present significant absorption features in the +observed wavelength range, and their exclusion therefore +significantly deteriorates the achievable fit. +All other +molecules are retrieved with a lower detection signifi- +cance. We find that H2O, which was previously detected +with HST/WFC3 observations, and CO, which was un- +detected before the advent of JWST, are both preferred +at a ∼3-σ level. Additionally, H2S is marginally pre- +ferred at a ∼2-σ level. +We therefore find that while the detection significance +of each molecule varies significantly, they are all re- +trieved with roughly similar precision, e.g. both CO2 +and H2S are constrained with a precision of 0.4 dex, +despite CO2 having an extremely high detection signif- +icance while the H2S is only marginally preferred. As +such, the precision with which the abundance of a chem- +ical species is estimated is not necessarily indicative of +how robustly it is detected. +4.1.2. Eureka Reduction +We now consider retrievals carried out on the 3- +5 µm JWST data obtained with the Eureka reduction +pipeline. This dataset is more deviant from the Spitzer +3.6 µm channel datapoint than that from the Tiberius +pipeline, with the resulting averaged transit depth lying +∼2 σ higher than the Spitzer point. It is representa- +tive of multiple data reductions presented by The JWST +Transiting Exoplanet Community Early Release Science +Team et al. (2022). +With this dataset, our retrievals once again provide +abundance constraints for several molecules. These in- +clude CO2, at a log-mixing ratio of −5.11+0.63 +−0.54, as well as +SO2 at −6.40+0.39 +−0.35, which the retrieval invokes to explain +the feature at 4.0 µm, similarly to our findings with the +Tiberius reduction data. The retrieval also constrains +the mixing ratios of H2O, CO and H2S to −3.29+0.59 +−0.56, +−4.17+0.61 +−0.61 and −4.11+0.49 +−0.46, respectively. The retrieval + +8 +−7 −6 −5 −4 −3 −2 +log(XH2O) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Probability density +−7 −6 −5 −4 −3 −2 +log(XCO2) +−7 −6 −5 −4 −3 −2 +log(XSO2) +−7 −6 −5 −4 −3 −2 +log(XCO) +−7 −6 −5 −4 −3 −2 +log(XH2S) +−7 −6 −5 −4 −3 −2 +log(XH2O) +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +Probability density +−7 −6 −5 −4 −3 −2 +log(XCO2) +−7 −6 −5 −4 −3 −2 +log(XSO2) +−7 −6 −5 −4 −3 −2 +log(XCO) +−7 −6 −5 −4 −3 −2 +log(XH2S) +JWST +JWST + HST/WFC3 +JWST Tiberius +JWST Eureka +Tiberius + HST/WFC3 +Eureka + HST/WFC3 +Figure 3. Posterior distributions of retrieved molecular abundances. Top: Posteriors obtained with JWST NIRSpec PRISM +3-5 µm data reduced by the Tiberius and Eureka pipelines (The JWST Transiting Exoplanet Community Early Release Science +Team et al. 2022). Bottom: Posteriors with the same two JWST spectra combined with HST/WFC3 data (Wakeford et al. +2018). From left to right, the panels show the posteriors for log-mixing ratios of H2O, CO2, SO2, CO and H2S. Horizontal +errorbars denote the retrieved median and 1-σ interval for the posterior of corresponding colour. +additionally obtains posterior distributions for CH4 and +HCN which are notably peaked at log-mixing ratio val- +ues of ∼-7 and ∼-6, respectively, but have significant +probability density extending to the lower end of the +prior range. +As such neither constitutes a precise or +robust constraint. +The retrieval does not obtain any constraints for the +properties of our included ZnS and MgSiO3 aerosols. +The mixing ratios for both aerosol species remain un- +constrained, as were the posteriors for the fractional +cloud coverage, particle size and vertical extent. Higher +aerosol mixing ratios coincide with smaller particle sizes, +which together result in negligible spectral contribu- +tions. +We also once again retrieve a P-T profile that +is consistent with an isotherm to within 1-σ. Our re- +trieval constrains T0, the temperature at the top of the +atmosphere, to 738+54 +−55 K. +As before, we perform Bayesian model comparisons +to assess the degree of model preference for including +each molecule with abundance constraints. We find a +very significant model preference towards the inclusion +of CO2 at ≳20-σ, while SO2 and H2O are preferred at a +∼4-σ level. The detection significances for CO and H2S +are once again not as high as those obtained for CO2 +and SO2, both of which are preferred ∼3-σ level. +The inclusion of CO in the model is favoured at a +∼3-σ level. Lastly, the inclusion of H2S is preferred at +a ∼4-σ level. As with our prior retrieval on data from +the Tiberius pipeline, we find that the precision with +which the mixing ratio of each species is constrained is +not indicative of how confidently it is detected. +4.1.3. Comparison of Retrieved Constraints +Both reduction pipelines lead to mixing ratio con- +straints with precisions below one dex. +Additionally, +both lead to extremely confident detection significances +for CO2 as well as a slightly less confident but still ro- +bust detection of SO2. They also both result in moder- +ate model preferences in favour of H2O and CO. +Despite the above, we find significant differences in at- +mospheric parameters retrieved with the two datasets. +Most notably, despite their precision, the retrieved +abundance constraints for CO2, SO2, H2O and CO from + +9 +the two datasets are not consistent to within 1-σ, in +some cases differing by 1 dex or more. This indicates +that each dataset leads retrievals to a different spectral +baseline. As a result, retrievals then invoke different am- +plitudes of spectral features in order to explain the data. +Another significant difference is in the detection signifi- +cance of H2S, with Eureka leading to a relatively robust +detection of 4-σ while Tiberius leads to only a tentative +indication of its presence, with a 2-σ detection signifi- +cance. We additionally find other pipeline-specific fea- +tures, in the form of peaked, but largely unconstrained +posterior distributions for HCN and CH4 obtained with +the Eureka pipeline data but not with the Tiberius data. +We also find differences between the retrieved temper- +ature profiles. While both retrievals obtain P-T profiles +that are consistent with an isotherm, they lie more than +2-σ away from each other. This is likely another conse- +quence of the two datasets leading retrievals to different +spectral baselines. +Thanks to the extreme precision of the JWST obser- +vations, we therefore find that pipeline-specific features +can lead to significant differences in retrieved quanti- +ties. As such, we find that while both retrievals lead to +molecular detections of key species, they can lead to sig- +nificantly different mixing ratio estimates. As such, the +significance with which a chemical species is detected +may not always indicate an accurate abundance esti- +mate, when considering spectra in the ∼3-5 µm range +alone. +4.2. Retrievals on Combined JWST and HST +Observations +We now examine how atmospheric constraints re- +trieved from JWST observations in the ∼3-5 µm are +affected when we additionally include observations at +shorter wavelengths obtained with HST/WFC3. This +allows us to assess the complementarity of JWST obser- +vations over the 3-5 µm range, which form a substan- +tial part of JWST Cycle 1 programs, with HST spec- +tra at shorter wavelengths (0.8-1.7 µm). As before, we +consider JWST spectra obtained with the Tiberius and +Eureka pipelines and in both cases combine them with +HST/WFC3 G102 and G141 observations in the ∼0.8- +1.7µm range presented by Wakeford et al. (2018). We +retrieve with the same canonical atmospheric model as +in prior sections, which is described in detail in section +3. As noted there, we additionally retrieve for a ver- +tical linear offset between the JWST and HST/WFC3 +datasets. +4.2.1. Tiberius Reduction and HST/WFC3 +We first consider adding HST/WFC3 observations to +∼3-5 µm JWST/NIRSpec PRISM data reduced with the +Tiberius pipeline. Our retrieval once again achieves a +good fit to the JWST/NIRSpec observations, while also +finding a good fit to the HST/WFC3 data. The best-fit +spectrum, along with the corresponding scale heights of +different features is shown in figure 1. The individual +molecular opacity contributions to the best-fit spectrum +are shown in figure 6 in the Appendix. Additionally, the +retrieved median spectral fit and corresponding 1- and +2-σ contours are shown in figure 2. The retrieval invokes +H2O to explain the HST/WFC3 data as expected, while +the JWST observations are explained with CO2, SO2 +H2S and CO. Notably, the size of the CO2 feature is +significantly larger (∼8 scale heights) than that of H2O +in the HST/WFC3 band (∼2-3 scale heights). +The retrieved atmospheric constraints from this com- +bined dataset retrieval are notably different to those ob- +tained from the JWST data alone, with the increased +spectral coverage at shorter wavelengths leading the re- +trieval to better constrain the spectral baseline. Specif- +ically, the retrieved log-mixing ratios for CO2 and SO2 +are now −4.52+0.36 +−0.30 and −5.94+0.22 +−0.19, while that of H2O +is constrained to −3.27+0.26 +−0.24. Additionally, CO and H2S +are constrained to log-mixing ratios of −2.58+0.51 +−0.50 and +−4.01+0.27 +−0.24. Compared to the estimates obtained from +our retrieval on Tiberius-derived data alone, the present +constraints are all higher by ∼1 dex or more. The com- +plete posterior distribution is shown in figure 4. +The increase in wavelength coverage also allows our +retrieval to constrain the broad wavelength contribu- +tions from Mie scattering MgSiO3 aerosols. Specifically, +we obtain a log-mixing ratio constraint of −6.99+0.55 +−0.65 +for MgSiO3 particles, with a modal particle size of +log(rc/µm) = −2.71+0.20 +−0.17. These particles are found to +be extended up to high altitudes, with a relative scale +height, hc of 0.85+0.08 +−0.9 and occupying roughly half of the +terminator atmosphere, with a coverage fraction con- +strained to 51+7 +−7%. Meanwhile, we also find an upper +limit for the mixing ratio of ZnS particles of -9.81 at +99% confidence. This indicates that the data are best +fit by spectral features specific to MgSiO3. +The retrieved spectral contributions from the MgSiO3 +aerosol particles are such that there is significant opacity +contributions over the HST/WFC3 wavelength range, +while the 3-5 µm range covered by the NIRSpec PRISM +observations lie mostly within an opacity window. As +such, it is likely that retrievals on these JWST observa- +tions alone are unable to distinguish between a cloud- +free case and one with most of the observations lying +within an opacity window of a partially cloudy atmo- +sphere. + +10 +Figure 4. Full posterior distribution from the retrieval using the JWST/NIRSpec PRISM 3-5 µm spectrum, reduced with the +Tiberius pipeline, combined with HST/WFC3 data (0.8-1.7 µm). The model parameters correspond to the canonical atmospheric +model described in section 3. Horizontal errorbars denote the median and 1-σ interval for each retrieved parameter. Also shown +is the retrieved P-T profile, with the black line denoting the median retrieved profile, while darker and lighter orange contours +indicate the 1- and 2-σ intervals. + +3.5 +0g(XH20 +log(Xco2)1 +log(XH2s) i +log(Xs02) 1. +1og(Xc2H2 )1. +log(XcH4) 1. +log(XNH, )1. +log(XHCN)1. +g(XMasio) +og(Xzns) +10- +Median +10-5 +1g +2g +log(Pi) +10-4 +Je +0g(P2) +10- +0g(P3) +P +10-2 +log(rc/m): +10-1 +100 +Offset (ppmo) +800 +1000 +1200 +TK +Rp(R)11 +Our retrieval also finds a P-T profile that is not consis- +tent with an isotherm to within 1-σ, as shown in figure +4. Specifically, our retrieval constrains T0, the temper- +ature at the top of the atmosphere to 757+40 +−43 K. The +constrained P-T profile then increases in temperature +at higher pressures, with the median profile reaching a +temperature of ∼900 K at a pressure of 1 bar. +We once again carry out a Bayesian model compari- +son to assess the detection significance for each molecule. +We find that the inclusion of CO2 is again very strongly +preferred, at a ∼20 σ level. H2O is now also strongly +preferred, at a ∼ 13 σ level, thanks to the addition of +HST/WFC3 observations which encompass strong H2O +absorption features. +SO2 meanwhile is preferred at a +∼4 σ level while now the inclusion of H2S is also pre- +ferred at a ∼4 σ level. Lastly, the inclusion of CO is +preferred at ∼3 σ level. H2S in particular is now more +strongly preferred than when retrieving on JWST data +alone in section 4.1.1. +We therefore find that the inclusion of HST/WFC3 +observations are highly informative to retrievals on +JWST observations in the ∼3-5 µm range. +This is +evident in the significantly higher retrieved abundance +constraints relative to those obtained with the same +JWST data alone in section 4.1.1, as well as their in- +creased precision and detection significances. Moreover, +we find that combined HST/WFC3 and JWST obser- +vations over the 3-5 µm range can, in principle, lead +to constraints for the physical properties of atmospheric +aerosols, as well as the terminator’s temperature struc- +ture. +4.2.2. Eureka Reduction and HST/WFC3 +We now consider pairing the JWST/NIRSpec 3- +5 µm data obtained with the Eureka pipeline with +HST/WFC3 G141 and G102 observations. Unlike the +retrievals on data from the Tiberius pipeline described +above, we find that combining HST/WFC3 data with +observations reduced with Eureka does not lead to sig- +nificant changes in the retrieved atmospheric properties. +Specifically, our retrieval constrains the log-mixing ra- +tio of CO2 to −4.57+0.51 +−0.38, SO2 to −6.31+0.25 +−0.24, H2O to +−3.28+0.33 +−0.27, CO to −3.61+0.37 +−0.40 and H2S to −4.17+0.29 +−0.26. +These constraints are generally more precise than those +obtained with the corresponding JWST/NIRSpec data +alone. +We find tentative indications of spectral contributions +from Mie-scattering aerosols using this dataset. Specifi- +cally, we find an upper limit for the mixing ratio of ZnS +of -6.65 at 99% confidence, which corresponds to signif- +icant spectral contributions. The same is true for the +constraints obtained for log(rc/µm), fc and Hc, which +have 99% confidence upper limits of 0.96, -6.15 and 0.97. +This indicates that the data do not preclude significant +spectral contributions from aerosols. +Meanwhile, the +posterior for the mixing ratio of MgSiO3 aerosols is un- +constrained. +The retrieval finds an atmospheric P-T profile that +is consistent with an isotherm to within 1-σ. Specifi- +cally, it constrains the T0, the temperature at the top +of the atmosphere to 666+53 +−72 K. Notably, this temper- +ature is more than 1-σ away from that obtained with +only JWST/NIRSpec data. +As with other retrievals, we find that the inclusion of +CO2 in our retrieved atmospheric model is very strongly +preferred, with a detection significance of ∼25 σ. H2O is +also preferred at a lower but still highly confident ∼12 σ +level. Meanwhile, SO2, H2S and CO are all preferred at +a ∼3 σ level. +We therefore find that the addition of HST/WFC3 ob- +servations to the Eureka pipeline data once again affects +the retrieved atmospheric properties. In addition to im- +proving the precision of all abundance constraints, in- +cluding those with no features in the HST/WFC3 band, +it also leads to different results for aerosol parameters. +4.2.3. Comparison of Retrieved Constraints +We find that the retrieved mixing ratio values for H2O, +CO2, SO2 and H2S all now agree to within 1-σ between +the two JWST pipelines. This is a notable difference +with our prior retrievals on JWST data alone, which +differed by 1 dex or more. On combining HST/WFC3 +data with JWST data from the Tiberius pipeline, we +find that there is a significant change in the retrieved +abundance constraints, in some cases increasing by more +than 1 dex relative to those obtained from JWST obser- +vations alone. Meanwhile, adding HST/WFC3 observa- +tions to data from the Eureka pipeline does not result +in as significant a shift in retrieved mixing ratios. +Despite the general agreement between the retrieved +mixing ratio values, differences still persist between the +two JWST datasets. Most notably, the retrieved mixing +ratios of CO differ by more than 1-σ. +Such pipeline- +specific constraints persist when we consider an ex- +panded retrieval model, such as one including KOH and +NaOH, which may be present based on prior Na and K +constraints. In this case, we find that the HST/WFC3 ++ Eureka dataset leads to a preference for KOH rather +then H2S, while retrieving on HST/WFC3 + Tiberius +still leads to a preference for H2S over KOH. +Secondly, we find different reduction pipelines also +lead to different constraints for aerosols present in +the atmosphere. +In the case of our retrievals on +the HST/WFC3 + Tiberius dataset, we obtain pre- +cise constraints on sub-micron MgSiO3 aerosols covering +roughly half the terminator atmosphere with an effec- + +12 +tively full vertical atmospheric extent. The retrieval also +specifically invoked MgSiO3 as opposed to ZnS, which +is also a part of our canonical model. Meanwhile, the +retrieval on HST/WFC3 + Eureka data instead leads to +only tentative constraints for ZnS aerosols and none for +MgSiO3. +Lastly, we also find different retrieved temperature +profiles. +Retrieving on HST/WFC3 + Tiberius data, +we find a non-isothermal P-T profile, which may also +be consistent with that obtained with Tiberius pipeline +data alone, depending on the specific altitude probed +by the retrieval. Meanwhile, the HST/WFC3 + Eureka +dataset leads to a P-T profile that is consistent with +an isotherm. It is also inconsistent with the tempera- +ture obtained with Eureka pipeline data alone, as well as +the temperature obtained with HST/WFC3 + Tiberius. +The temperature constraint is relevant for interpreting +the retrieved atmospheric composition and understand- +ing the physical and chemical processes giving rise to +them. +We also conclude that while precise transmis- +sion spectra over a wide wavelength range can in princi- +ple lead to constraints for the terminator’s temperature +structure, such constraints are sensitive to minor varia- +tions in the data, such as those introduced by differences +in reduction pipelines. +We also consider how our findings are affected by +changes to our model, described in section 3, the re- +sults of which are summarised in table 1. +On in- +cluding the effects of stellar heterogeneities in our +model, we find that our retrieved abundance constraints +are consistent with those obtained with our canonical +model. +We also consider the impact of using a para- +metric cloud/haze prescription rather than physically- +motivated Mie-scattering aerosols. In this case, we find +that our retrieved abundances are different by up to +∼0.5 dex, underscoring the need for a physically mo- +tivated aerosol model in order to obtain accurate abun- +dance constraints in the JWST era. +5. SUMMARY AND DISCUSSION +We use the first JWST observations of an exoplanet +transmission spectrum in the 3-5 µm range to obtain +early insights into atmospheric retrievals that are possi- +ble in the JWST era. This spectral range is particularly +important to investigate, considering the large alloca- +tion of JWST time in Cycle 1 for exoplanet spectroscopy +using NIRSpec observations in the ∼3-5µm range. We +focus on the JWST NIRSpec PRISM observations of the +hot Saturn WASP-39b, observed as part of the JWST +ERS program (The JWST Transiting Exoplanet Com- +munity Early Release Science Team et al. 2022), ar- +guably one of the most promising exoplanets for trans- +mission spectroscopy. Our goal is to investigate (a) the +nature of atmospheric constraints that are possible with +high-precision JWST data in the ∼3-5 µm range, (b) +modeling requirements for atmospheric retrievals with +such data, (c) how sensitive the retrieved atmospheric +properties are to differences in spectra from different re- +duction pipelines, and (d) how such data may be com- +plemented with observations at shorter wavelengths. +5.1. Key Lessons +We identify the following key lessons for atmospheric +retrievals of transiting exoplanets using JWST transmis- +sion spectra, particularly in the 3-5 µm range. +• The ∼3-5 µm range provides an important av- +enue for molecular detections, as it encompasses +windows in extinction cross section for several +aerosols. Consequently, molecular opacity within +this range can give rise to highly prominent spec- +tral features. +JWST observations over the ∼3- +5 µm may therefore lead to confident molecular +detections even for potentially cloudy atmospheres +with low-amplitude (≲2-3 scale height) spectral +features in the HST/WFC3 hand (∼0.8-1.7 µm) +(e.g. Stevenson 2016; Fu et al. 2017; Crossfield & +Kreidberg 2017). Our results add to studies using +simulated JWST observations (Wakeford & Sing +2015; Pinhas & Madhusudhan 2017; Mai & Line +2019; Lacy & Burrows 2020). +• In order for retrievals to obtain accurate abun- +dance estimates with JWST observations in the +∼3-5 µm range, complementary observations may +be needed at shorter wavelengths. This allows re- +trievals to constrain the spectral baseline needed +for accurate and precise estimates of molecular +abundances. Specifically, we find that complemen- +tary observations with HST/WFC3 can be highly +effective for this goal, resulting in changes in the +retrieved abundances by up to one dex in some +cases, compared to retrievals using ∼3-5 µm spec- +tra alone. +• JWST +observations +over +a +wide +wavelength +range can in principle constrain the presence of +clouds/hazes, as well as their specific nature, e.g. +particle composition and size. This has been pre- +viously considered with simulated JWST observa- +tions (e.g. Benneke & Seager 2013; Wakeford & +Sing 2015; Pinhas & Madhusudhan 2017; Mai & +Line 2019; Lacy & Burrows 2020) and with HST- +era observations (Benneke et al. 2019). It is there- +fore important that atmospheric retrievals have + +13 +the capability to properly treat the complex spec- +tral signatures that aerosols can contribute to a +planet’s transmission spectrum. +• As expected from prior theoretical works, JWST +transmission spectra in the near-infrared can +provide precise abundance constraints for sev- +eral prominent molecules in exoplanetary atmo- +spheres(e.g. Beichman et al. 2014; Greene et al. +2016; Howe et al. 2017; Kalirai 2018; Bean et al. +2018). +For the present case, we retrieve abun- +dance constraints with a precision of ∼0.3-0.5 dex +for prominent molecules, even with the relatively +limited spectral range considered. Combining this +data with other JWST observations can lead to +even more precise abundance constraints. +• Small differences in JWST spectra, such as those +arising due to different reduction pipelines, can +have a notable impact on the retrieved con- +straints and detections, particularly forless promi- +nent species. This is thanks to the high precision +that JWST observations can have, especially for +giant exoplanets. For the case of the WASP-39 b +observations we consider, which are for a single +transit, we find that differences in spectra aris- +ing from differences between reduction pipelines +can affect which species are detected at a 2-3σ +level. Therefore, robust data reduction pipelines +are needed in order to converge on accurate chem- +ical detections. +• A high detection significance for a particular chem- +ical species does not indicate that its abundance +is constrained accurately. +For instance, retriev- +ing on JWST/NIRSpec PRISM observations ob- +tained with the Tiberius pipeline leads to a ∼25σ +detection significance. However, on supplement- +ing these observations with HST/WFC3 G141 and +G102 data, the retrieved mixing ratio estimate is +1 dex higher, as the retrieval finds a different spec- +tral baseline. +• The precision with which the abundance of a +chemical species is constrained is not indicative +of how confidently it is detected. For instance, us- +ing JWST NIRSpec PRISM observations reduced +with the Tiberius pipeline, we constrain the mix- +ing ratios of CO2 and H2S with a precision of +≲0.4 dex. While CO2 is detected with extremely +high confidence, however, H2S is not, with our re- +trievals finding only a tentative 2-σ model prefer- +ence for its inclusion. It is therefore essential that +10−1 +100 +Mass (MJ) +100 +101 +102 +Elemental Abundance (×Solar) +J +S +UN +WASP-39 b +�O +H +� �C +H +� � S +H +� +Figure 5. Initial constraints on the elemental abundances +in the atmosphere of WASP-39 b. +The O/H (blue), C/H +(red) and S/H (yellow) ratios are derived from the molecular +abundances retrieved from JWST data in the 3-5 µm range +combined with HST/WFC3 data (0.8-1.7 µm). The elemen- +tal abundances are shown relative to solar values (Asplund +et al. 2021). +The dashed vertical line denotes the planet +mass (0.28 MJ). +Closed and open circles within the gray +shaded region refer to retrievals using JWST data from the +Tiberius and Eureka pipelines, respectively, offset horizon- +tally for clarity. The C/H abundances for solar system giant +planets (Atreya et al. 2022) along with a linear fit (in brown) +and the O/H in Jupiter from Juno (Li et al. 2020) are shown +for reference. +future studies assess the robustness of their find- +ings by carrying out a full Bayesian model com- +parison for each chemical species that may be de- +tected. +• The spectral ranges of JWST instruments allow +for the detection of chemical species that have not +been hitherto considered in exoplanet retrievals, +and potentially chemical processes that may have +not been anticipated. In the present example of +WASP-39 b, we independently confirm the pres- +ence of SO2 reported by Rustamkulov et al. (2022) +and Alderson et al. (2022), while also finding +tentative indications of H2S. We therefore find +that retrieval frameworks must be open to diverse +chemistry if they are to be capable of fully taking +advantage of JWST observations. +5.2. +The Atmosphere of WASP-39 b +In light of the above considerations, we present ini- +tial constraints on the atmospheric properties of WASP- +39 b. We confirm the presence of CO2, CO and SO2 +reported by The JWST Transiting Exoplanet Commu- +nity Early Release Science Team et al. (2022) and Rus- + +14 +tamkulov et al. (2022); Alderson et al. (2022). We ad- +ditionally find tentative indications for the presence of +H2S, with detection sigificances between ∼2-4 σ across +our retrievals. Our abundance estimate of SO2 supports +prior findings of disequilibrium chemistry at work in the +atmosphere of WASP-39 b (Tsai et al. 2022). +Addi- +tionally, the presence of H2S suggested by our retrievals +further supports this, as H2S is expected to be the pri- +mary sulfur reservoir under chemical equilibrium deeper +in the atmosphere (Zahnle et al. 2009; Wang et al. 2017; +Hobbs et al. 2021; Polman et al. 2022), which photo- +chemically reacts with H2O in the upper atmosphere to +form SO2. +As our retrievals obtain abundance constraints for a +range of oxygen-, carbon- and sulfur-bearing species, we +can begin to probe the relative enrichment of each ele- +ment in the atmosphere of WASP-39 b, as shown in fig- +ure 5. Considering the constraints obtained with JWST +observations reduced by the Tiberius pipeline combined +with HST/WFC3 data, we find that the inferred O/H, +C/H and S/H values correspond to 15+30 +−10×, 21+46 +−14× and +17+15 +−7 × solar enrichments, respectively (Asplund et al. +2021). Such enhancements are consistent with the at- +mospheric metallicity of Saturn based on CH4 measure- +ments, at 8.67±0.35× solar, and with recent suggestions +for WASP-39 b(Alderson et al. 2022; Rustamkulov et al. +2022; Feinstein et al. 2022). Meanwhile, the equivalent +O/H, C/H and S/H inferences using JWST observa- +tions reduced with the Eureka pipeline and HST/WFC3 +data correspond to 4+6 +−2×, 2+4 +−1× and 11+11 +−7 × solar en- +richments. In this case, the oxygen and sulfur enrich- +ments are still consistent with the metallicity of Saturn, +while carbon is somewhat less enriched. We note that +the uncertainties in our O/H and C/H estimates are +primarily driven by the CO mixing ratio constraints, +which are retrieved with precisions of ∼0.4-0.5 dex. Re- +trievals combining the present JWST/NIRSpec PRISM +data with recently-published NIRSpec G395H obser- +vations(Alderson et al. 2022) that also encompass the +∼4.8 µm CO feature may further refine the present es- +timates. +Beyond constraints for gaseous species, we also obtain +tentative indications of non-gray opacity contributions +from Mie-scattering aerosols. Specifically, our retrieval +on JWST data reduced with the Tiberius pipeline and +HST/WFC3 observations infers the presence of MgSiO3 +aerosols. These aerosols are found to have a modal par- +ticle size of ∼2 nm and cover ∼50% of the planet’s ter- +minator. Meanwhile, retrieving on JWST data from Eu- +reka and HST/WFC3 observations, we find tentative in- +dications of ZnS aerosols instead. These compositional +constraints are consistent with thermochemical expec- +tations for condensing species (Morley et al. 2013). Our +findings are also in agreement with preferences for non- +grey spectral contributions from aerosols obtained with +a forward model analysis of NIRISS observations (Fein- +stein et al. 2022). +Our retrievals also lead to constraints for the planet’s +terminator temperature. Using the Tiberius reduction +of the JWST data along with HST/WFC3 data, we find +tentative indications of a non-isothermal temperature, +with a temperature of 757+40 +−43 K at the top of the at- +mosphere. +Meanwhile, JWST data from Eureka and +HST/WFC3 observations instead lead to a P-T profile +that is consistent with an isotherm, with a temperature +of 666+53 +−72 K. +WASP-39 b and its ERS observations are set to allow +an in-depth comparison between a solar-system planet +and an extrasolar planet. Our results contribute an early +step towards a next-generation comparative study be- +tween Saturn and an exoplanet that is a near-Saturn +analogue in both mass and metallicity. +The results presented above are only initial constraints +for the atmospheric properties of WASP-39 b, obtained +with a relatively limited spectral range of JWST obser- +vations (∼3-5 µm). Future retrievals with all available +data (∼0.6-5 µm) can significantly improve upon the +constraints presented in this work. However, our study +highlights the need for rigorous data reduction and re- +trieval considerations as well as a robust exploration of +the available parameter space. +The retrievals in this +work involved ∼109 model evaluations to achieve that +goal. +In addition to physically motivated aerosol consid- +erations, future retrievals may also consider the effect +of inhomogeneous temperature (Nixon & Madhusudhan +2022) and chemical (Rocchetto et al. 2016) structures, +as well as the impact of stellar heterogeneity aided by +optical data (Rackham et al. 2017; Pinhas et al. 2018) +and other molecular opacity sources. While such model +sophistication may not be applicable in all cases, es- +pecially for moderately irradiated planets like WASP- +39 b, a holistic approach is recommended for accurate +retrievals of atmospheric properties in the JWST era. +Our results provide a glimpse into the richness of at- +mospheric science that JWST is set to enable, thanks to +its unprecedented sensitivity and wide spectral cover- +age that includes hitherto unexplored wavelengths. Our +results also highlight the sophistication demanded of at- +mospheric models and retrievals, as well as the robust- +ness required of reduction pipelines, if we are to rise to +the challenge and make full use of the discovery oppor- +tunities that JWST presents. + +15 +This work was performed using resources provided +by the Cambridge Service for Data Driven Discovery +(CSD3) operated by the University of Cambridge Re- +search Computing Service (www.csd3.cam.ac.uk), pro- +vided by Dell EMC and Intel using Tier-2 funding from +the Engineering and Physical Sciences Research Coun- +cil (capital grant EP/P020259/1), and DiRAC fund- +ing from the Science and Technology Facilities Council +(www.dirac.ac.uk). This work uses data reduced from +observations made with the NASA/ESA/CSA JWST, +as part of The Transiting Exoplanet Community Early +Release Science (ERS) Program (PI: N. Batalha). We +thank NASA, ESA, CSA, STScI, the ERS team, and +everyone whose efforts have contributed to JWST and +exoplanet science with JWST. +We thank the anonymous referee for their valuable +comments. SC thanks Anjali Piette for helpful discus- +sion on Mie scattering. NM acknowledges support from +the MERAC Foundation, Switzerland, and the UK Sci- +ence and Technology Facilities Council (STFC). SG is +grateful to Leiden Observatory at Leiden University for +the award of the Oort Fellowship. +APPENDIX +Figure 6 shows the spectral contributions from gaseous species in our retrieved best fit spectrum, obtained for +JWST/NIRSpec PRISM observations reduced with Tiberius and HST/WFC3 data. We note that this figure does not +include spectral contributions from MgSiO3 aerosols, for visual clarity. As such, the combined spectral contributions +correspond to the blue curve in figure 1. +1 +2 +3 +4 +5 +Wavelength (µm) +2.0 +2.1 +2.2 +2.3 +Transit Depth (%) +Combined +H2O +CO +CO2 +H2S +SO2 +Figure 6. The spectral contributions from H2O, CO, CO2, SO2 and H2S to the best fit spectrum obtained from the retrieval +on JWST observations reduced by the Tiberius pipeline combined with HST/WFC3 data. Also shown is the resulting spectrum +from all molecular spectral contributions, corresponding to the aerosol-free model shown in figure 1. Spectral contributions from +MgSiO3 aerosols as shown in figure 1 are not included here, for visual clarity. +REFERENCES +Alderson, L., Wakeford, H. R., Alam, M. K., et al. 2022, +arXiv e-prints, arXiv:2211.10488. +https://arxiv.org/abs/2211.10488 +Asplund, M., Amarsi, A. M., & Grevesse, N. 2021, A&A, +653, A141, doi: 10.1051/0004-6361/202140445 +Atreya, S. K., Crida, A., Guillot, T., et al. 2022, arXiv +e-prints, arXiv:2205.06914. +https://arxiv.org/abs/2205.06914 +Azzam, A. A. A., Tennyson, J., Yurchenko, S. N., & +Naumenko, O. V. 2016, MNRAS, 460, 4063, +doi: 10.1093/mnras/stw1133 +Barber, R. J., Strange, J. K., Hill, C., et al. 2014, MNRAS, +437, 1828, doi: 10.1093/mnras/stt2011 +Barstow, J. K., Aigrain, S., Irwin, P. G. J., & Sing, D. K. +2017, ApJ, 834, 50, doi: 10.3847/1538-4357/834/1/50 + +16 +Batalha, N. E., & Line, M. R. 2017, AJ, 153, 151, +doi: 10.3847/1538-3881/aa5faa +Bean, J. L., Stevenson, K. B., Batalha, N. M., et al. 2018, +PASP, 130, 114402, doi: 10.1088/1538-3873/aadbf3 +Beichman, C., Benneke, B., Knutson, H., et al. 2014, PASP, +126, 1134, doi: 10.1086/679566 +Benneke, B., & Seager, S. 2013, ApJ, 778, 153, +doi: 10.1088/0004-637X/778/2/153 +Benneke, B., Knutson, H. A., Lothringer, J., et al. 2019, +Nature Astronomy, 3, 813, +doi: 10.1038/s41550-019-0800-5 +Birkmann, S. M., Ferruit, P., Alves de Oliveira, C., et al. +2014, in Society of Photo-Optical Instrumentation +Engineers (SPIE) Conference Series, Vol. 9143, Space +Telescopes and Instrumentation 2014: Optical, Infrared, +and Millimeter Wave, ed. J. Oschmann, Jacobus M., +M. Clampin, G. G. Fazio, & H. A. MacEwen, 914308, +doi: 10.1117/12.2054642 +Bohren, C. F., Huffman, D. R., & Kam, Z. 1983, Nature, +306, 625 +Buchner, J., Georgakakis, A., Nandra, K., et al. 2014, +A&A, 564, A125, doi: 10.1051/0004-6361/201322971 +Charbonneau, D., Brown, T. M., Noyes, R. W., & Gilliland, +R. L. 2002, ApJ, 568, 377, doi: 10.1086/338770 +Chubb, K. L., Tennyson, J., & Yurchenko, S. N. 2020, +Monthly Notices of the Royal Astronomical Society, 493, +1531, doi: 10.1093/mnras/staa229 +Chubb, K. L., Naumenko, O., Keely, S., et al. 2018, +JQSRT, 218, 178, doi: 10.1016/j.jqsrt.2018.07.012 +Crossfield, I. J. M., & Kreidberg, L. 2017, AJ, 154, 261, +doi: 10.3847/1538-3881/aa9279 +Deirmendjian, D. 1969, Electromagnetic scattering on +spherical polydispersions. +Deming, D., Wilkins, A., McCullough, P., et al. 2013, ApJ, +774, 95, doi: 10.1088/0004-637X/774/2/95 +Dorschner, J., Begemann, B., Henning, T., Jaeger, C., & +Mutschke, H. 1995, A&A, 300, 503 +Ehrenreich, D., Bourrier, V., Wheatley, P. J., et al. 2015, +Nature, 522, 459, doi: 10.1038/nature14501 +Faedi, F., Barros, S. C. C., Anderson, D. R., et al. 2011, +A&A, 531, A40, doi: 10.1051/0004-6361/201116671 +Feinstein, A. D., Radica, M., Welbanks, L., et al. 2022, +arXiv e-prints, arXiv:2211.10493. +https://arxiv.org/abs/2211.10493 +Feroz, F., Hobson, M. P., & Bridges, M. 2009, MNRAS, +398, 1601, doi: 10.1111/j.1365-2966.2009.14548.x +Feroz, F., Hobson, M. P., Cameron, E., & Pettitt, A. N. +2019, The Open Journal of Astrophysics, 2, 10, +doi: 10.21105/astro.1306.2144 +Ferruit, P., Bagnasco, G., Barho, R., et al. 2012, in Society +of Photo-Optical Instrumentation Engineers (SPIE) +Conference Series, Vol. 8442, Space Telescopes and +Instrumentation 2012: Optical, Infrared, and Millimeter +Wave, ed. M. C. Clampin, G. G. Fazio, H. A. MacEwen, +& J. Oschmann, Jacobus M., 84422O, +doi: 10.1117/12.925810 +Fischer, P. D., Knutson, H. A., Sing, D. K., et al. 2016, +ApJ, 827, 19, doi: 10.3847/0004-637X/827/1/19 +Fu, G., Deming, D., Knutson, H., et al. 2017, ApJL, 847, +L22, doi: 10.3847/2041-8213/aa8e40 +Fulton, B. J., Rosenthal, L. J., Hirsch, L. A., et al. 2021, +ApJS, 255, 14, doi: 10.3847/1538-4365/abfcc1 +Gandhi, S., & Madhusudhan, N. 2017, MNRAS, 472, 2334, +doi: 10.1093/mnras/stx1601 +Greene, T. P., Line, M. R., Montero, C., et al. 2016, ApJ, +817, 17, doi: 10.3847/0004-637X/817/1/17 +Harris, G. J., Tennyson, J., Kaminsky, B. M., Pavlenko, +Y. V., & Jones, H. R. A. 2006, MNRAS, 367, 400, +doi: 10.1111/j.1365-2966.2005.09960.x +Hobbs, R., Rimmer, P. B., Shorttle, O., & Madhusudhan, +N. 2021, MNRAS, 506, 3186, +doi: 10.1093/mnras/stab1839 +Howard, A. W., Marcy, G. W., Johnson, J. A., et al. 2010, +Science, 330, 653, doi: 10.1126/science.1194854 +Howe, A. R., Burrows, A., & Deming, D. 2017, ApJ, 835, +96, doi: 10.3847/1538-4357/835/1/96 +Kalirai, J. 2018, Contemporary Physics, 59, 251, +doi: 10.1080/00107514.2018.1467648 +Kawashima, Y., & Min, M. 2021, A&A, 656, A90, +doi: 10.1051/0004-6361/202141548 +Kirk, J., L´opez-Morales, M., Wheatley, P. J., et al. 2019, +AJ, 158, 144, doi: 10.3847/1538-3881/ab397d +Kreidberg, L. 2018, in Handbook of Exoplanets, ed. H. J. +Deeg & J. A. Belmonte, 100, +doi: 10.1007/978-3-319-55333-7 100 +Kreidberg, L., Bean, J. L., D´esert, J.-M., et al. 2014, ApJL, +793, L27, doi: 10.1088/2041-8205/793/2/L27 +Lacy, B. I., & Burrows, A. 2020, ApJ, 904, 25, +doi: 10.3847/1538-4357/abbc6c +Li, C., Ingersoll, A., Bolton, S., et al. 2020, Nature +Astronomy, 4, 609, doi: 10.1038/s41550-020-1009-3 +Li, G., Gordon, I. E., Rothman, L. S., et al. 2015, ApJS, +216, 15, doi: 10.1088/0067-0049/216/1/15 +MacDonald, R. J., & Madhusudhan, N. 2017, MNRAS, 469, +1979, doi: 10.1093/mnras/stx804 +Madhusudhan, N. 2018, in Handbook of Exoplanets, ed. +H. J. Deeg & J. A. Belmonte, 104, +doi: 10.1007/978-3-319-55333-7 104 + +17 +Madhusudhan, N., Crouzet, N., McCullough, P. R., +Deming, D., & Hedges, C. 2014, ApJL, 791, L9, +doi: 10.1088/2041-8205/791/1/L9 +Madhusudhan, N., & Seager, S. 2009, ApJ, 707, 24, +doi: 10.1088/0004-637X/707/1/24 +Mai, C., & Line, M. R. 2019, ApJ, 883, 144, +doi: 10.3847/1538-4357/ab3e6d +Mancini, L., Esposito, M., Covino, E., et al. 2018, A&A, +613, A41, doi: 10.1051/0004-6361/201732234 +Mayor, M., Marmier, M., Lovis, C., et al. 2011, arXiv +e-prints, arXiv:1109.2497. +https://arxiv.org/abs/1109.2497 +Morley, C. V., Fortney, J. J., Kempton, E. M. R., et al. +2013, ApJ, 775, 33, doi: 10.1088/0004-637X/775/1/33 +Nikolov, N., Sing, D. K., Gibson, N. P., et al. 2016, ApJ, +832, 191, doi: 10.3847/0004-637X/832/2/191 +Nixon, M. C., & Madhusudhan, N. 2022, ApJ, 935, 73, +doi: 10.3847/1538-4357/ac7c09 +Pinhas, A., & Madhusudhan, N. 2017, MNRAS, 471, 4355, +doi: 10.1093/mnras/stx1849 +Pinhas, A., Madhusudhan, N., Gandhi, S., & MacDonald, +R. 2019, MNRAS, 482, 1485, doi: 10.1093/mnras/sty2544 +Pinhas, A., Rackham, B. V., Madhusudhan, N., & Apai, D. +2018, MNRAS, 480, 5314, doi: 10.1093/mnras/sty2209 +Polman, J., Waters, L. B. F. M., Min, M., Miguel, Y., & +Khorshid, N. 2022, arXiv e-prints, arXiv:2208.00469. +https://arxiv.org/abs/2208.00469 +Querry, M. 1987, Chemical Research, Development and +Engineering Center, U.S. Army Armament Munitions +Chemical Command +Rackham, B., Espinoza, N., Apai, D., et al. 2017, ApJ, 834, +151, doi: 10.3847/1538-4357/aa4f6c +Richard, C., Gordon, I., Rothman, L., et al. 2012, JQSRT, +113, 1276 , +doi: https://doi.org/10.1016/j.jqsrt.2011.11.004 +Rocchetto, M., Waldmann, I. P., Venot, O., Lagage, P. O., +& Tinetti, G. 2016, ApJ, 833, 120, +doi: 10.3847/1538-4357/833/1/120 +Rothman, L., Gordon, I., Barber, R., et al. 2010, JQSRT, +111, 2139 , +doi: https://doi.org/10.1016/j.jqsrt.2010.05.001 +Rustamkulov, Z., Sing, D. K., Mukherjee, S., et al. 2022, +arXiv e-prints, arXiv:2211.10487. +https://arxiv.org/abs/2211.10487 +Sarkar, S., Madhusudhan, N., & Papageorgiou, A. 2020, +MNRAS, 491, 378, doi: 10.1093/mnras/stz2958 +Seager, S., & Sasselov, D. D. 2000, ApJ, 537, 916, +doi: 10.1086/309088 +Sing, D. K., Fortney, J. J., Nikolov, N., et al. 2016, Nature, +529, 59, doi: 10.1038/nature16068 +Stevenson, K. B. 2016, ApJL, 817, L16, +doi: 10.3847/2041-8205/817/2/L16 +Stevenson, K. B., Lewis, N. K., Bean, J. L., et al. 2016, +PASP, 128, 094401, +doi: 10.1088/1538-3873/128/967/094401 +The JWST Transiting Exoplanet Community Early Release +Science Team, Ahrer, E.-M., Alderson, L., et al. 2022, +arXiv e-prints, arXiv:2208.11692. +https://arxiv.org/abs/2208.11692 +Tsai, S.-M., Lee, E. K. H., Powell, D., et al. 2022, arXiv +e-prints, arXiv:2211.10490. +https://arxiv.org/abs/2211.10490 +Tsiaras, A., Waldmann, I. P., Zingales, T., et al. 2018, AJ, +155, 156, doi: 10.3847/1538-3881/aaaf75 +Underwood, D. S., Tennyson, J., Yurchenko, S. N., et al. +2016, MNRAS, 459, 3890, doi: 10.1093/mnras/stw849 +Vidal-Madjar, A., Lecavelier des Etangs, A., D´esert, J. M., +et al. 2003, Nature, 422, 143, doi: 10.1038/nature01448 +Wakeford, H. R., & Sing, D. K. 2015, A&A, 573, A122, +doi: 10.1051/0004-6361/201424207 +Wakeford, H. R., Sing, D. K., Deming, D., et al. 2018, AJ, +155, 29, doi: 10.3847/1538-3881/aa9e4e +Wang, D., Miguel, Y., & Lunine, J. 2017, ApJ, 850, 199, +doi: 10.3847/1538-4357/aa978e +Wang, J., Fischer, D. A., Horch, E. P., & Huang, X. 2015, +ApJ, 799, 229, doi: 10.1088/0004-637X/799/2/229 +Welbanks, L., Madhusudhan, N., Allard, N. F., et al. 2019, +ApJLett, 887, L20, doi: 10.3847/2041-8213/ab5a89 +Yurchenko, S. N., Barber, R. J., & Tennyson, J. 2011, +MNRAS, 413, 1828, +doi: 10.1111/j.1365-2966.2011.18261.x +Yurchenko, S. N., & Tennyson, J. 2014, MNRAS, 440, 1649, +doi: 10.1093/mnras/stu326 +Zahnle, K., Marley, M. S., Freedman, R. S., Lodders, K., & +Fortney, J. J. 2009, ApJL, 701, L20, +doi: 10.1088/0004-637X/701/1/L20 + diff --git a/rtE0T4oBgHgl3EQfrQGn/content/tmp_files/load_file.txt b/rtE0T4oBgHgl3EQfrQGn/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..eb272246a00372767a4ff05a9d8e71a7f15ed966 --- /dev/null +++ b/rtE0T4oBgHgl3EQfrQGn/content/tmp_files/load_file.txt @@ -0,0 +1,1578 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf,len=1577 +page_content='Draft version January 9,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2023 Typeset using LATEX twocolumn style in AASTeX631 Early Insights for Atmospheric Retrievals of Exoplanets using JWST Transit Spectroscopy Savvas Constantinou,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1 Nikku Madhusudhan,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1 and Siddharth Gandhi2,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 3,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 4 1Institute of Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' University of Cambridge,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Madingley Road,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Cambridge CB3 0HA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' UK 2Leiden Observatory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Leiden University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Postbus 9513 2300 RA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Leiden,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The Netherlands 3Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' University of Warwick,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Coventry CV4 7AL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' UK 4Centre for Exoplanets and Habitability,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' University of Warwick,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Gibbet Hill Road,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Coventry CV4 7AL,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' UK (Accepted 24 December 2022,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The Astrophysical Journal Letters) Abstract We have entered the era of the James Webb Space Telescope (JWST).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We use the first JWST transmission spectrum of the hot Saturn-mass exoplanet,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' WASP-39 b,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' obtained with the NIRSpec instrument in the 3-5 µm range to investigate (a) what atmospheric constraints are possible with JWST-quality data in this spectral range,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (b) requirements for atmospheric models used in retrievals,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (c) effect of differences between data reduction pipelines on retrieved atmospheric properties,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' and (d) complementarity between JWST data in the 3-5 µm range and HST observations at shorter wave- lengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' JWST spectra in the 3-5 µm range provide a promising avenue for chemical detections while encompassing a window in cloud opacity for several prominent aerosols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We confirm recent inferences of CO2, SO2, H2O, and CO in WASP-39 b, report tentative evidence for H2S, and retrieve elemental abundances consistent with Saturn’s metallicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We retrieve molecular abundances with ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='6 dex precision with this relatively limited spectral range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' When considering the 3-5 µm data alone, reported differences in spectra with different reduction pipelines can affect abundance estimates by up to ∼1 dex and the detectability of less prominent species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Complementing with data at shorter wavelengths, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' with other JWST instruments or HST WFC3 (∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='7 µm), can significantly improve the accuracy and precision of the abundance estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The high data quality enables constraints on aerosol prop- erties, including their composition, modal size and extent, motivating their consideration in retrievals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our results highlight the promise of JWST exoplanet spectroscopy, while underscoring the importance of robust data reduction and atmospheric retrieval approaches in the JWST era.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Keywords: James Webb Space Telescope (2291) — Exoplanet Atmospheres (487) — Radiative Transfer (1335) — Transmission Spectroscopy (2133) — Infrared Spectroscopy (2285) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' INTRODUCTION The first observations with the James Webb Space Telescope (JWST) are now available, heralding the dawn of a new era in our understanding of exoplan- etary atmospheres.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' With a virtually complete cover- age of the near-mid infrared, transmission spectroscopy with JWST enables simultaneous constraints on multi- ple chemical species and other physical properties in ex- oplanetary atmospheres (Beichman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Steven- son et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Batalha & Line 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Kalirai 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Bean et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Sarkar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The generational leap in Corresponding author: S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Constantinou, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Madhusudhan sc938@cam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='uk, nmadhu@ast.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='cam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='uk our understanding of chemical and physical processes in exoplanets is already underway.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Exoplanet transmission spectroscopy with the Hubble Space Telescope (HST), along with ground-based ob- servations with facilities like the Very Large Telescope (VLT), have over the last 20 years been a key driver of the field’s remarkable growth (Seager & Sasselov 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Charbonneau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Vidal-Madjar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Dem- ing et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Ehrenreich et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Sing et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Nikolov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Kreidberg 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Paired with the- oretical developments in atmospheric modelling and re- trievals, HST transmission spectra in the optical and near-infrared (NIR) have led to important constraints on the abundances of chemical species including H2O, arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='02564v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='EP] 6 Jan 2023 2 Na and K, as well as the properties of clouds and hazes in several exoplanetary atmospheres (Madhusudhan & Seager 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Madhusudhan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Kreidberg et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Wakeford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Barstow et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Pinhas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Welbanks et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Madhusudhan 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Most of these atmospheric detections were made for ir- radiated gas giants, whose relative rarity (Howard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Mayor et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Fulton et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2021) is offset by their comparative observability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This is largely due to their extended, hydrogen-dominated atmospheres giving rise to large spectral signatures and hence high signal-to-noise observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our goal in this work is to obtain a first glimpse into atmospheric properties of exoplanets that can be re- trieved with JWST-quality transmission spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' While observations with HST have been limited to wavelengths below 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='7 µm, JWST promises a substantial increase in both sensitivity and spectral range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In particular, the ∼3-5 µm range accessible with the NIRSpec instru- ment (Ferruit et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2012) opens uncharted territory in chemical discovery space, as evidenced by recent infer- ences of CO2 and SO2 in the atmosphere of an exoplanet (The JWST Transiting Exoplanet Community Early Re- lease Science Team et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Rustamkulov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Alderson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Here we assess atmospheric con- straints that are possible with JWST transmission spec- tra in the ∼3-5µm range and modeling requirements for retrieval frameworks in the JWST-era.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We further in- vestigate the sensitivity of retrievals to differences in spectra obtained using different data reduction pipelines as well as complementarity with NIR spectra with the HST/WFC3 instrument (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='7 µm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We focus on WASP-39 b, which is one of the first exo- planets whose transmission spectrum has been observed with JWST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The planet has a mass of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='28 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='03 MJ, a radius of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='28 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='04 RJ and a zero-albedo equilib- rium temperature of 1170 K (Faedi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Mancini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' It orbits a G8-type host star with an in- termediate brightness of J = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='7 and V = 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1 (Faedi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' WASP-39 b is therefore an example of the immense diversity in the known exoplanet popula- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' While its closest solar system analogue by mass is Saturn (M = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3 MJ), it is significantly larger, with a radius greater than Jupiter’s and significantly more strongly irradiated than any solar system gas giant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The notably low gravity of WASP-39 b makes its atmosphere highly conducive to transmission spectroscopy observa- tions and has already led to detections of H2O, Na and K with prior HST and ground-based facilities (Fischer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Nikolov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Sing et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Tsiaras et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Wakeford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Pinhas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Kirk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Welbanks et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Kawashima & Min 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As a result, WASP-39 b is the target of choice for the JWST Early Release Science (ERS) pro- gram, which has already led to novel inferences of CO2 and SO2 in its atmosphere (The JWST Transiting Ex- oplanet Community Early Release Science Team et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Alderson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Rustamkulov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We consider the JWST observations of WASP-39 b over the 3-5 µm range, obtained with the NIRSpec PRISM spectrograph(The JWST Transiting Exoplanet Community Early Release Science Team et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Beyond its high data quality, this spectral range is rep- resentative of the majority of observations JWST is set to make over Cycle 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Specifically, most Cycle 1 observa- tions are set to be made with the NIRSpec spectrograph using the G395 grating over a similar ∼3-5 µm range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As such, our work is also a feasibility study, with the present observations of WASP-39 b constituting a near- best case scenario.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We also consider how minor variations in the JWST observations, particularly those arising from differences between reduction pipelines, can affect the retrieved at- mospheric constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We do this by retrieving on two different reduction of the same observations, obtained with the Tiberius and Eureka pipelines, which have been reported to give slightly different results, particularly over the 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='6 µm Spitzer band (The JWST Transiting Ex- oplanet Community Early Release Science Team et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Besides analysing the JWST data alone, we also consider their complementarity with prior observa- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' For this work, we consider pairing the 3-5 µm JWST observations with those obtained previously with HST/WFC3 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='7 µm), examining how this affects the precision and accuracy of atmospheric constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This pairing is particularly important, as several of the Cycle 1 targets have or are set to be also observed with HST/WFC3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In doing so, we seek to assess the com- plementarity between JWST 3-5 µm observations and HST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In what follows, we discuss the observations in section 2 and our retrieval methodology in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The results of our investigation are presented in section 4, followed by our summary and discussion in section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' PRIOR AND CURRENT OBSERVATIONS The atmosphere of WASP-39 b has been extensively probed in transmission spectroscopy from both ground and space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The first space-based observations were carried out in 2013, using the HST/STIS G430L and G750L gratings (GO 12473, PI: D Sing) (Fischer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Sing et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016), covering the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='29-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 µm wave- length range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Paired with photometric observations 3 1 2 3 4 5 Wavelength (µm) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='00 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='05 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='10 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='15 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='20 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='25 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='30 Transit Depth (%) WASP-39 b 2°3 Hsc 6°8 Hsc HST/WFC3 JWST/NIRSpec PRISM Best Fit Model Without Aerosols °2 0 2 4 6 8 Scale Heights H2O H2O H2O H2S SO2 CO2 CO H2O Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' A transmission spectrum of WASP-39 b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The circles with error bars show the JWST NIRSpec PRISM spectrum in the 3-5 µm range reduced with the Tiberius pipeline (The JWST Transiting Exoplanet Community Early Release Science Team et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022) along with prior HST/WFC3 observations in the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='7 µm range (Wakeford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The solid curve in brown shows our retrieved best fit spectrum, and the same spectrum but without opacity contributions from aerosols is shown in blue for reference (see section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The heights of the prominent spectral features in the JWST and HST bands in terms of a characteristic atmospheric scale height are denoted by arrows;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' a nominal slant photospheric temperature of 800 K is assumed motivated by the retrieved constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The contributions of individual molecules are shown in figure 6 in the Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' with Spitzer (90092, PI: J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' D´esert), these observa- tions were used to infer a cloud-free atmosphere, with prominent spectral features arising from Na and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This is in agreement with conclusions drawn from ground- based VLT observations by Nikolov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2016), span- ning the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='4-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8 µm range using the Focal Reducer/Low Dispersion Spectrograph 2 (FORS2) (096.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='C-0765, PI: N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Nikolov).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Further spectroscopic observations were carried out in the NIR using the the HST Wide Field Camera 3 (WFC3) G102 and G141 grisms (GO 14169, PI: H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Wakeford;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' GO 14260, PI: D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Deming), which together cover a wavelength range of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='7 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' These ob- servations revealed prominent H2O absorption features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Combining the new HST/WFC3 observations with prior ones with VLT, HST/STIS and Spitzer, Wakeford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2018) report an enriched atmospheric metallicity con- straint of 151+48 −46× solar using a retrieval framework as- suming chemical equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The median value cor- responds to log-mixing ratios of ∼ −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3, ∼ −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='6 and ∼ −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8 for H2O, Na and K, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' By contrast, Tsiaras et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2018), using an alternative reduction of the same HST/WFC3 G141 observations, find a signifi- cantly lower H2O log-mixing ratio of −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='94 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This disparity in the inferred atmospheric composi- tion of WASP-39 b persisted through subsequent anal- yses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Retrievals carried out by Pinhas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2019) us- ing the WFC3 G141 observations reduced by Tsiaras et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2018) along with HST/STIS and Spitzer data found an H2O log-mixing ratio corresponding to a sub- solar metallicity, at −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='07+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='72 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='78, but Na and K log- mixing ratios corresponding to a super-solar metallic- ity, at −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='86+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='31 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='36 and −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='22+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='25 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Kirk et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2019) presented a combined transmission spectrum consisting of the HST/WFC3 observations presented by Wakeford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2018) and Spitzer photometry in the NIR, while combining HST/STIS and VLT observations with new observations using the William Herschel Telescope in the optical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Using a retrieval framework assuming equilib- rium chemistry, they obtain an atmospheric metallicity constraint of 282+65 −58× solar, at its median corresponding to H2O, Na and K log-mixing ratios of -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='9, -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3 and -4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='5, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Using this same combined dataset, Wel- banks et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2019) find that composition constraints are dependent on the choice of prior, obtaining log-mixing ratio estimates of −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='65+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='14 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='83, −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='62+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='14 −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='69 and −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='62+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='30 −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='05 for H2O, Na and K with their canonical retrieval, and −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='43+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='27 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='24, −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='17+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='50 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='51 and −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='24+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='71 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='06 for a more con- strained prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' More recently, Kawashima & Min (2021) analysing the combined HST/STIS, WFC3 and Spitzer observations presented by Sing et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2016), Fischer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2016) and Wakeford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2018), constrain an at- mospheric metallicity consistent with solar to within 1- σ when considering disequilibrium chemistry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' They also report a moderately super-solar metallicity constraint, corresponding to an H2O log-mixing ratio of ∼-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The JWST observations of WASP-39 b used in the present study have been obtained with the Near Infrared Spectrograph (NIRSpec) PRISM (Ferruit et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Birkmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2014) over a single transit in July 2022 as part of the JWST Early Release Science (ERS) (The JWST Transiting Exoplanet Community Early Release Science Team et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Spanning a subset of the full NIRSpec PRISM ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='6-5 µm range, the new data shows 4 absorption peaks that are significantly larger in size than those observed previously in the HST/WFC3 bandpass, corresponding to 6-8 vs 2-3 atmospheric scale heights.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Several reductions of the same observations were pre- sented, which are reported to be largely comparable but with small deviations, especially in the 3-4 µm range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' For the sake of robustness, we consider two reductions, based on their level of agreement over the Spitzer 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='6 µm bandpass, in order to assess the effect different reduc- tion pipelines may have on the retrieved atmospheric properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Specifically, we use the data obtained us- ing the Eureka and Tiberius pipelines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Both the Eureka and Tiberius pipelines give rise to observations which, when binned to the Spitzer 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='6 µm bandpass, are at a higher transit depth than that observed by Spitzer it- self.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The Tiberius pipeline value is consistent with the Spitzer point to within 1-σ, while the Eureka value lies at ∼2-σ of the Spitzer point and between those of the tshirt and FIREFLy pipelines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The 3-5 µm JWST data obtained with the Tiberius pipeline that are used in the present study are shown in figure 1, along with prior observations with HST/WFC3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' METHODS We retrieve the atmospheric properties of WASP-39 b from the spectroscopic observations described in section 2 using a variant of the AURA retrieval framework (Pin- has et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The forward model computes radiative transfer in a plane-parallel atmosphere in transmission geometry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The model assumes hydrostatic equilibrium and local thermodynamic equilibrium in a H2-rich at- mosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The pressure-temperature (P-T) profile and uniformly-distributed volume mixing ratios of the chem- ical absorbers are free parameters in the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In this work, we additionally retrieve the properties of Mie scat- tering aerosols, as discussed below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We also consider the conventional parametric cloud/haze prescription in AURA, for reference, as well as the effect of stellar het- erogeneities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The parametric atmospheric model is cou- pled to a Bayesian inference and parametric estimation routine based on the Nested Sampling algorithm, im- plemented via the PyMultiNest package (Feroz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Buchner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Feroz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In order to consider the spectral contributions of aerosols the model includes extinction from Mie scat- tering particles in the planetary atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Using the approach in Pinhas & Madhusudhan (2017) we explore a range of possible condensate species that can be preva- lent in irradiated giant exoplanets, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', MgSiO3, Na2S, MnS, ZnS, SiO2, Al2O3, FeO, Fe2O3, TiO2, NaCl and Mg2SiO4, based on data from Wakeford & Sing (2015);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Pinhas & Madhusudhan (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The extinction cross sections are computed following Mie theory (Bohren et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 1983).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We assume a modified gamma distribu- tion for the aerosol particle sizes Deirmendjian (1969), with the modal particle size, rc, of the distribution, be- ing a free parameter in the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We additionally con- sider the vertical extent of the aerosol layer, described by the relative scale height of the aerosols, hc = Hc H , where Hc is the aerosol scale height and H is the atmo- spheric scale height.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' hc is another free parameter in the model with values ranging from 0 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' An hc value of 1 implies that aerosols have a constant mixing ratio with altitude, while a value of 0 corresponds to no aerosols being present in the observable atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We incor- porate this in our model as an exponential decrease in the aerosol mixing ratio with altitude: Xi(z) = Xi,0 exp � −(n − 1)z H(z) � , (1) where Xi denotes the mixing ratio of the ith aerosol species, H(z) is the local atmospheric scale height kBT µg at an altitude z, and n = 1 hc .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our model also accounts for an inhomogeneous coverage of the terminator atmo- sphere by aerosols, whose coverage fraction, fc, is a third free parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our aerosol model can include an arbitrary number of aerosol species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The mixing ratio of each of the aerosol species is a separate free parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' For the retrievals we consider in this work, the modal particle size, vertical extent and fractional coverage parameters are universal, applying to all aerosol species in the model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In light of the JWST observations probing a novel part of the spectrum and the high precision of obser- vations, we carry out a staged retrieval approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We begin by considering a maximal set of gaseous and Mie scattering aerosol species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This maximal model consid- ers opacity contributions from a large number of gaseous chemical species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' It also includes Mie scattering arising from inhomogeneous coverage of the terminator atmo- sphere by aerosols of MgSiO3, Na2S, MnS, ZnS, SiO2, Al2O3, FeO, Fe2O3, TiO2, NaCl and Mg2SiO4 (Wake- ford & Sing 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Pinhas & Madhusudhan 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We then consider a reduced canonical set of param- eters, based on initial indications by our maximal re- trieval and chemical expectations, which we use for all retrieval cases presented in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The final set of gaseous chemical species included in the present canoni- cal model comprises of H2O, CO, CO2, H2S, SO2, CH4, NH3, HCN, C2H2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We additionally include opacity contributions arising from H2-H2 and H2-He collision- induced absorption (Richard et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2012), as well as ZnS (Querry 1987) and MgSiO3 (Dorschner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 1995) aerosols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our choice for these two aerosol species is 5 driven by both thermochemical expectations for the con- densates based on the terminator temperature (Morley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2013) and indicative constraints obtained with our maximal model retrievals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The absorption cross-sections for the gaseous species are derived following Gandhi & Madhusudhan (2017), using line lists of H2O, CO and CO2 from Rothman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2010) and Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2015), CH4 from Yurchenko & Tennyson (2014), NH3 from Yurchenko et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2011), HCN from Harris et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2006) and Barber et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2014), C2H2 from Chubb et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2020) SO2 from Underwood et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2016) and H2S from Azzam et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2016) and Chubb et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our canonical atmospheric model has a total of 21 free parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The first 9 correspond to the individual log-mixing ratios of the gaseous chemical species listed above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Another two free parameters describe the log- mixing ratios of ZnS and MgSiO3 aerosols and another 3 describe their fractional coverage, modal particle size and vertical extent, as described above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The terminator temperature profile is modelled by 6 parameters using the parametrisation of Madhusudhan & Seager (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The last free parameter for our canonical model is the planet radius, RP, defined at a nominal reference pres- sure of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1 bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' For retrievals on combined JWST and HST/WFC3 observations, we additionally retrieved for a linear offset between the two datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We use log-uniform priors between 10−12-10−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3 for the mixing ratios of gaseous species, and between 10−30- 10−6 for the mixing ratios of MgSiO3 and ZnS aerosols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We set the prior for the modal particle size, rc to a log- uniform distribution ranging between 1 nm and 1µm and both the fc and hc priors are uniform between 0-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The prior for the temperature at the top of the atmosphere, T0, is also uniformly distributed between 300-1600 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' For completeness, we also explore retrievals including the effects of stellar heterogeneities as well as a more traditional parametric approach to model clouds/hazes, instead of Mie scattering by aerosols, as pursued by de- fault in AURA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' For the parametric clouds/hazes, we use a four-parameter combination of inhomogeneous grey opacity clouds and modified Rayleigh-like hazes (MacDonald & Madhusudhan 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Pinhas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We incorporate stellar heterogeneities in the model fol- lowing (Rackham et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2017) as described in Pinhas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This model involves three free parame- ters, describing the fractional surface coverage of het- erogeneities, their overall effective temperature, and the temperature of the pristine photosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' RESULTS We now proceed to investigate the performance of at- mospheric retrievals on a JWST spectrum of WASP- 39 b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We first consider the JWST/NIRSpec PRISM observations on their own, examining the constraints such observations can lead to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We also assess how the retrieved atmospheric constraints vary due to minor differences between reduction pipelines, by considering JWST observations reduced by both Tiberius and Eu- reka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We then present our findings from joint retrievals on both the JWST observations over the 3-5 µm range and prior HST/WFC3 data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In doing so we establish the complementarity between JWST and HST/WFC3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We once again carry this out for data obtained with both the Tiberius and Eureka reduction pipelines, examin- ing the differences between the resulting atmospheric constraints and how they vary with differences in our retrieved atmospheric model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our retrieved constraints are summarised in table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Retrievals with JWST Data We first focus on the recently-released JWST observa- tions of WASP-39 b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As discussed in section 3, we anal- yse the observations with a staged retrieval approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We begin by considering a maximal set of chemical species, including gases and Mie scattering aerosols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We then consider a reduced set of chemical absorbers, based on physical plausibility and their initial constraints ob- tained by our maximal retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our reduced set of chemical species comprising our canonical model con- sists of H2O, CO, CH4, HCN, H2S and SO2, as well as ZnS and MgSiO3 aerosols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 1 We consider data obtained with the Tiberius and Eu- reka pipelines presented by The JWST Transiting Ex- oplanet Community Early Release Science Team et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2022), which produce somewhat different transit depths when binned over the Spitzer 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='6 µm photometric band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Specifically, the Tiberius pipeline produces data that are the closest to the Spitzer 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='6 µm transit depth measure- ment, with all other pipelines including Eureka which yields transit depths that are more than 1-σ higher than the Spitzer value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The retrieved spectral fit to the JWST observations with our canonical model is shown in figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The ob- servations display a highly prominent absorption peak at 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3 µm that has been previously attributed to CO2 (The JWST Transiting Exoplanet Community Early Re- lease Science Team et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022), as well as a smaller absorption feature at 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Moreover, the spectrum trends upwards at shorter wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' For both reduc- tion pipelines, our retrievals produce good fits to the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 1 During the preparation of this work, we learned about the in- dependent inference of SO2 using the same data (Rustamkulov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 6 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='05 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='10 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='15 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='20 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='25 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='30 Transit Depth (%) JWST 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='4 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='7 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='05 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='10 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='15 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='20 Transit Depth (%) JWST + HST/WFC3 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='5 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='5 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 Wavelength (µm) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='05 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='10 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='15 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='20 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='25 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='30 Transit Depth (%) Median 1σ 2σ Tiberius Eureka HST/WFC3 JWST (Tiberius) JWST (Tiberius) Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Retrieved spectral fits obtained for two of the retrievals considered in this work, using our canonical model described in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The top panel shows the retrieved spectral fit for JWST NIRSpec PRISM 3-5 µm observations reduced with the Tiberius pipeline (data shown in black errorbars with yellow circles).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Also shown are the same observations reduced with the Eureka pipeline (in green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The lower two panels show different wavelength regions of the retrieved spectral fit to the combination of HST/WFC3 observations (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='7 µm) and JWST/NIRSpec PRISM observations reduced with Tiberius;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' see section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In all three panels, the darkest orange line denotes the median retrieved spectrum while the two lighter orange regions denote the corresponding 1- and 2-σ contours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Tiberius Reduction We begin by considering the data obtained via the Tiberius reduction pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As shown in figure 2, our retrieval obtains a good fit to the two significant ab- sorption features at 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3 µm, as well as the trend of increasing transit depth towards lower wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Moreover, the retrieval also fits smaller features within that trend.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We confirm that the larger peak at 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3 µm is due to CO2 and the smaller peak at 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 µm due to SO2, as reported previously (The JWST Transiting Ex- oplanet Community Early Release Science Team et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Rustamkulov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our retrievals obtain constraints for the log-mixing ratios of CO2, SO2, H2O, H2S and CO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Driven by the very prominent CO2 absorption peak at 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3 µm, we constrain the log-mixing ratio of CO2 to −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='28+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='38 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Additionally, our retrieval attributes the smaller ab- sorption peak seen at 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 µm to SO2, constraining its log-mixing ratio to −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='01+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='23 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' CO is invoked to ex- plain the data redward of the CO2 feature, with a log- mixing ratio of −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='25+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='39 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Additionally, H2O and H2S are constrained to log-mixing ratios of −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='85+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='38 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='35 and −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='32+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='36 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='42, respectively, and are used to fit the spec- trum below 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 µm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The posterior distributions re- trieved for each of these molecules are shown in figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 7 Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Retrieved atmospheric parameters for WASP-39 b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Case log(XH2O) log(XCO2) log(XSO2) log(XCO) log(XH2S) T0/K Canonical Retrieval Model JWST Tiberius −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='85+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='38 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='35 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='28+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='38 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='31 −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='01+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='23 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='20 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='25+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='39 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='35 −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='32+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='36 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='42 862+64 −63 JWST Eureka −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='29+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='59 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='56 −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='11+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='63 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='54 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='40+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='39 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='35 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='17+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='61 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='61 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='11+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='49 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='46 738+54 −55 Tiberius + HST/WFC3 −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='27+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='26 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='24 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='52+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='36 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='30 −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='94+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='22 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='19 −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='58+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='51 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='50 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='01+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='27 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='24 757+40 −43 Eureka + HST/WFC3 −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='28+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='33 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='27 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='57+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='51 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='38 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='31+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='25 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='24 −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='61+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='37 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='40 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='17+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='29 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='26 666+53 −72 Other Retrieval Models Tiberius + HST/WFC3, Parametric Cl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='/Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='69+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='31 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='25 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='75+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='41 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='39 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='21+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='24 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='23 −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='40+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='47 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='45 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='49+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='31 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='25 758+63 −61 Eureka + HST/WFC3, Parametric Cl.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='/Hz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='14+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='34 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='31 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='49+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='41 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='41 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='32+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='30 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='29 −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='62+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='48 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='62 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='49+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='41 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='41 683+52 −44 Tiberius + HST/WFC3, Stellar Het.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='44+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='27 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='26 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='65+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='34 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='33 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='05+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='22 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='21 −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='85+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='42 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='44 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='19+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='26 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='25 763+49 −51 Eureka + HST/WFC3, Stellar Het.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='34+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='31 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='27 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='58+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='41 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='34 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='29+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='24 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='24 −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='58+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='35 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='36 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='09+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='24 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='26 656+53 −48 Note—The table shows the retrieved log-mixing ratios of molecules with notable detection significances along with the temperature at the top of the model atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The top four rows show the retrievals using our canonical model, with the top two obtained with JWST NIRSpec 3-5 µm data alone and the remaining two with a combination of JWST and HST data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We consider JWST data reported using two pipelines, Tiberius and Eureka, as discussed in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The bottom four rows show constraints on the JWST+HST data obtained with two other retrieval considerations: (a) replacing the Mie scattering aerosols with a conventional parametric cloud/haze prescription, and (b) including stellar heterogeneities, as described in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In addition to the above mixing ratio constraints, our retrieval obtains a P-T profile that is consistent with an isotherm to within 1-σ, constraining T0, the tempera- ture at the top of the model atmosphere to 862+64 −63 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Additionally, this retrieval does not obtain any con- straints for the properties of Mie scattering aerosols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The posterior distributions for the log-mixing ratios of MgSiO3 and ZnS which are largely unconstrained, with that of MgSiO3 displaying a somewhat prominent peak at ∼-10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The posterior distributions for the modal par- ticle size, fractional terminator coverage and vertical ex- tent are also unconstrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We carry out additional retrievals to assess the detec- tion significance for each of the constrained molecules presented above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We do this by performing a Bayesian model comparison between our canonical retrieval model and one without the molecule in question (Pinhas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We find that both SO2 and, particularly, CO2 are confidently detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In the case of CO2, the model including it is preferred at a ∼16-σ level, while the inclusion of SO2 in the model is favoured at a ∼4- σ level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This is consistent with the fact that both molecules present significant absorption features in the observed wavelength range, and their exclusion therefore significantly deteriorates the achievable fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' All other molecules are retrieved with a lower detection signifi- cance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We find that H2O, which was previously detected with HST/WFC3 observations, and CO, which was un- detected before the advent of JWST, are both preferred at a ∼3-σ level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Additionally, H2S is marginally pre- ferred at a ∼2-σ level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We therefore find that while the detection significance of each molecule varies significantly, they are all re- trieved with roughly similar precision, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' both CO2 and H2S are constrained with a precision of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='4 dex, despite CO2 having an extremely high detection signif- icance while the H2S is only marginally preferred.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As such, the precision with which the abundance of a chem- ical species is estimated is not necessarily indicative of how robustly it is detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Eureka Reduction We now consider retrievals carried out on the 3- 5 µm JWST data obtained with the Eureka reduction pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This dataset is more deviant from the Spitzer 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='6 µm channel datapoint than that from the Tiberius pipeline, with the resulting averaged transit depth lying ∼2 σ higher than the Spitzer point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' It is representa- tive of multiple data reductions presented by The JWST Transiting Exoplanet Community Early Release Science Team et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' With this dataset, our retrievals once again provide abundance constraints for several molecules.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' These in- clude CO2, at a log-mixing ratio of −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='11+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='63 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='54, as well as SO2 at −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='40+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='39 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='35, which the retrieval invokes to explain the feature at 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 µm, similarly to our findings with the Tiberius reduction data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The retrieval also constrains the mixing ratios of H2O, CO and H2S to −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='29+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='59 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='56, −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='17+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='61 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='61 and −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='11+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='49 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='46, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The retrieval 8 −7 −6 −5 −4 −3 −2 log(XH2O) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 Probability density −7 −6 −5 −4 −3 −2 log(XCO2) −7 −6 −5 −4 −3 −2 log(XSO2) −7 −6 −5 −4 −3 −2 log(XCO) −7 −6 −5 −4 −3 −2 log(XH2S) −7 −6 −5 −4 −3 −2 log(XH2O) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 Probability density −7 −6 −5 −4 −3 −2 log(XCO2) −7 −6 −5 −4 −3 −2 log(XSO2) −7 −6 −5 −4 −3 −2 log(XCO) −7 −6 −5 −4 −3 −2 log(XH2S) JWST JWST + HST/WFC3 JWST Tiberius JWST Eureka Tiberius + HST/WFC3 Eureka + HST/WFC3 Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Posterior distributions of retrieved molecular abundances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Top: Posteriors obtained with JWST NIRSpec PRISM 3-5 µm data reduced by the Tiberius and Eureka pipelines (The JWST Transiting Exoplanet Community Early Release Science Team et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Bottom: Posteriors with the same two JWST spectra combined with HST/WFC3 data (Wakeford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' From left to right, the panels show the posteriors for log-mixing ratios of H2O, CO2, SO2, CO and H2S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Horizontal errorbars denote the retrieved median and 1-σ interval for the posterior of corresponding colour.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' additionally obtains posterior distributions for CH4 and HCN which are notably peaked at log-mixing ratio val- ues of ∼-7 and ∼-6, respectively, but have significant probability density extending to the lower end of the prior range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As such neither constitutes a precise or robust constraint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The retrieval does not obtain any constraints for the properties of our included ZnS and MgSiO3 aerosols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The mixing ratios for both aerosol species remain un- constrained, as were the posteriors for the fractional cloud coverage, particle size and vertical extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Higher aerosol mixing ratios coincide with smaller particle sizes, which together result in negligible spectral contribu- tions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We also once again retrieve a P-T profile that is consistent with an isotherm to within 1-σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our re- trieval constrains T0, the temperature at the top of the atmosphere, to 738+54 −55 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As before, we perform Bayesian model comparisons to assess the degree of model preference for including each molecule with abundance constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We find a very significant model preference towards the inclusion of CO2 at ≳20-σ, while SO2 and H2O are preferred at a ∼4-σ level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The detection significances for CO and H2S are once again not as high as those obtained for CO2 and SO2, both of which are preferred ∼3-σ level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The inclusion of CO in the model is favoured at a ∼3-σ level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Lastly, the inclusion of H2S is preferred at a ∼4-σ level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As with our prior retrieval on data from the Tiberius pipeline, we find that the precision with which the mixing ratio of each species is constrained is not indicative of how confidently it is detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Comparison of Retrieved Constraints Both reduction pipelines lead to mixing ratio con- straints with precisions below one dex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Additionally, both lead to extremely confident detection significances for CO2 as well as a slightly less confident but still ro- bust detection of SO2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' They also both result in moder- ate model preferences in favour of H2O and CO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Despite the above, we find significant differences in at- mospheric parameters retrieved with the two datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Most notably, despite their precision, the retrieved abundance constraints for CO2, SO2, H2O and CO from 9 the two datasets are not consistent to within 1-σ, in some cases differing by 1 dex or more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This indicates that each dataset leads retrievals to a different spectral baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As a result, retrievals then invoke different am- plitudes of spectral features in order to explain the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Another significant difference is in the detection signifi- cance of H2S, with Eureka leading to a relatively robust detection of 4-σ while Tiberius leads to only a tentative indication of its presence, with a 2-σ detection signifi- cance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We additionally find other pipeline-specific fea- tures, in the form of peaked, but largely unconstrained posterior distributions for HCN and CH4 obtained with the Eureka pipeline data but not with the Tiberius data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We also find differences between the retrieved temper- ature profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' While both retrievals obtain P-T profiles that are consistent with an isotherm, they lie more than 2-σ away from each other.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This is likely another conse- quence of the two datasets leading retrievals to different spectral baselines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Thanks to the extreme precision of the JWST obser- vations, we therefore find that pipeline-specific features can lead to significant differences in retrieved quanti- ties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As such, we find that while both retrievals lead to molecular detections of key species, they can lead to sig- nificantly different mixing ratio estimates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As such, the significance with which a chemical species is detected may not always indicate an accurate abundance esti- mate, when considering spectra in the ∼3-5 µm range alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Retrievals on Combined JWST and HST Observations We now examine how atmospheric constraints re- trieved from JWST observations in the ∼3-5 µm are affected when we additionally include observations at shorter wavelengths obtained with HST/WFC3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This allows us to assess the complementarity of JWST obser- vations over the 3-5 µm range, which form a substan- tial part of JWST Cycle 1 programs, with HST spec- tra at shorter wavelengths (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='7 µm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As before, we consider JWST spectra obtained with the Tiberius and Eureka pipelines and in both cases combine them with HST/WFC3 G102 and G141 observations in the ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8- 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='7µm range presented by Wakeford et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We retrieve with the same canonical atmospheric model as in prior sections, which is described in detail in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As noted there, we additionally retrieve for a ver- tical linear offset between the JWST and HST/WFC3 datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Tiberius Reduction and HST/WFC3 We first consider adding HST/WFC3 observations to ∼3-5 µm JWST/NIRSpec PRISM data reduced with the Tiberius pipeline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our retrieval once again achieves a good fit to the JWST/NIRSpec observations, while also finding a good fit to the HST/WFC3 data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The best-fit spectrum, along with the corresponding scale heights of different features is shown in figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The individual molecular opacity contributions to the best-fit spectrum are shown in figure 6 in the Appendix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Additionally, the retrieved median spectral fit and corresponding 1- and 2-σ contours are shown in figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The retrieval invokes H2O to explain the HST/WFC3 data as expected, while the JWST observations are explained with CO2, SO2 H2S and CO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Notably, the size of the CO2 feature is significantly larger (∼8 scale heights) than that of H2O in the HST/WFC3 band (∼2-3 scale heights).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The retrieved atmospheric constraints from this com- bined dataset retrieval are notably different to those ob- tained from the JWST data alone, with the increased spectral coverage at shorter wavelengths leading the re- trieval to better constrain the spectral baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Specif- ically, the retrieved log-mixing ratios for CO2 and SO2 are now −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='52+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='36 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='30 and −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='94+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='22 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='19, while that of H2O is constrained to −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='27+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='26 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Additionally, CO and H2S are constrained to log-mixing ratios of −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='58+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='51 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='50 and −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='01+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='27 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Compared to the estimates obtained from our retrieval on Tiberius-derived data alone, the present constraints are all higher by ∼1 dex or more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The com- plete posterior distribution is shown in figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The increase in wavelength coverage also allows our retrieval to constrain the broad wavelength contribu- tions from Mie scattering MgSiO3 aerosols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Specifically, we obtain a log-mixing ratio constraint of −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='99+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='55 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='65 for MgSiO3 particles, with a modal particle size of log(rc/µm) = −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='71+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='20 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' These particles are found to be extended up to high altitudes, with a relative scale height, hc of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='85+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='08 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='9 and occupying roughly half of the terminator atmosphere, with a coverage fraction con- strained to 51+7 −7%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Meanwhile, we also find an upper limit for the mixing ratio of ZnS particles of -9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='81 at 99% confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This indicates that the data are best fit by spectral features specific to MgSiO3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The retrieved spectral contributions from the MgSiO3 aerosol particles are such that there is significant opacity contributions over the HST/WFC3 wavelength range, while the 3-5 µm range covered by the NIRSpec PRISM observations lie mostly within an opacity window.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As such, it is likely that retrievals on these JWST observa- tions alone are unable to distinguish between a cloud- free case and one with most of the observations lying within an opacity window of a partially cloudy atmo- sphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 10 Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Full posterior distribution from the retrieval using the JWST/NIRSpec PRISM 3-5 µm spectrum, reduced with the Tiberius pipeline, combined with HST/WFC3 data (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='7 µm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The model parameters correspond to the canonical atmospheric model described in section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Horizontal errorbars denote the median and 1-σ interval for each retrieved parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Also shown is the retrieved P-T profile, with the black line denoting the median retrieved profile, while darker and lighter orange contours indicate the 1- and 2-σ intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='5 0g(XH20 log(Xco2)1 log(XH2s) i log(Xs02) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 1og(Xc2H2 )1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' log(XcH4) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' log(XNH, )1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' log(XHCN)1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' g(XMasio) og(Xzns) 10- Median 10-5 1g 2g log(Pi) 10-4 Je 0g(P2) 10- 0g(P3) P 10-2 log(rc/m): 10-1 100 Offset (ppmo) 800 1000 1200 TK Rp(R)11 Our retrieval also finds a P-T profile that is not consis- tent with an isotherm to within 1-σ, as shown in figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Specifically, our retrieval constrains T0, the temper- ature at the top of the atmosphere to 757+40 −43 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The constrained P-T profile then increases in temperature at higher pressures, with the median profile reaching a temperature of ∼900 K at a pressure of 1 bar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We once again carry out a Bayesian model compari- son to assess the detection significance for each molecule.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We find that the inclusion of CO2 is again very strongly preferred, at a ∼20 σ level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' H2O is now also strongly preferred, at a ∼ 13 σ level, thanks to the addition of HST/WFC3 observations which encompass strong H2O absorption features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' SO2 meanwhile is preferred at a ∼4 σ level while now the inclusion of H2S is also pre- ferred at a ∼4 σ level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Lastly, the inclusion of CO is preferred at ∼3 σ level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' H2S in particular is now more strongly preferred than when retrieving on JWST data alone in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We therefore find that the inclusion of HST/WFC3 observations are highly informative to retrievals on JWST observations in the ∼3-5 µm range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This is evident in the significantly higher retrieved abundance constraints relative to those obtained with the same JWST data alone in section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1, as well as their in- creased precision and detection significances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Moreover, we find that combined HST/WFC3 and JWST obser- vations over the 3-5 µm range can, in principle, lead to constraints for the physical properties of atmospheric aerosols, as well as the terminator’s temperature struc- ture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Eureka Reduction and HST/WFC3 We now consider pairing the JWST/NIRSpec 3- 5 µm data obtained with the Eureka pipeline with HST/WFC3 G141 and G102 observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Unlike the retrievals on data from the Tiberius pipeline described above, we find that combining HST/WFC3 data with observations reduced with Eureka does not lead to sig- nificant changes in the retrieved atmospheric properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Specifically, our retrieval constrains the log-mixing ra- tio of CO2 to −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='57+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='51 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='38, SO2 to −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='31+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='25 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='24, H2O to −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='28+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='33 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='27, CO to −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='61+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='37 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='40 and H2S to −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='17+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='29 −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' These constraints are generally more precise than those obtained with the corresponding JWST/NIRSpec data alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We find tentative indications of spectral contributions from Mie-scattering aerosols using this dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Specifi- cally, we find an upper limit for the mixing ratio of ZnS of -6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='65 at 99% confidence, which corresponds to signif- icant spectral contributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The same is true for the constraints obtained for log(rc/µm), fc and Hc, which have 99% confidence upper limits of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='96, -6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='15 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='97.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This indicates that the data do not preclude significant spectral contributions from aerosols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Meanwhile, the posterior for the mixing ratio of MgSiO3 aerosols is un- constrained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The retrieval finds an atmospheric P-T profile that is consistent with an isotherm to within 1-σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Specifi- cally, it constrains the T0, the temperature at the top of the atmosphere to 666+53 −72 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Notably, this temper- ature is more than 1-σ away from that obtained with only JWST/NIRSpec data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As with other retrievals, we find that the inclusion of CO2 in our retrieved atmospheric model is very strongly preferred, with a detection significance of ∼25 σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' H2O is also preferred at a lower but still highly confident ∼12 σ level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Meanwhile, SO2, H2S and CO are all preferred at a ∼3 σ level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We therefore find that the addition of HST/WFC3 ob- servations to the Eureka pipeline data once again affects the retrieved atmospheric properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In addition to im- proving the precision of all abundance constraints, in- cluding those with no features in the HST/WFC3 band, it also leads to different results for aerosol parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Comparison of Retrieved Constraints We find that the retrieved mixing ratio values for H2O, CO2, SO2 and H2S all now agree to within 1-σ between the two JWST pipelines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This is a notable difference with our prior retrievals on JWST data alone, which differed by 1 dex or more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' On combining HST/WFC3 data with JWST data from the Tiberius pipeline, we find that there is a significant change in the retrieved abundance constraints, in some cases increasing by more than 1 dex relative to those obtained from JWST obser- vations alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Meanwhile, adding HST/WFC3 observa- tions to data from the Eureka pipeline does not result in as significant a shift in retrieved mixing ratios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Despite the general agreement between the retrieved mixing ratio values, differences still persist between the two JWST datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Most notably, the retrieved mixing ratios of CO differ by more than 1-σ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Such pipeline- specific constraints persist when we consider an ex- panded retrieval model, such as one including KOH and NaOH, which may be present based on prior Na and K constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In this case, we find that the HST/WFC3 + Eureka dataset leads to a preference for KOH rather then H2S, while retrieving on HST/WFC3 + Tiberius still leads to a preference for H2S over KOH.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Secondly, we find different reduction pipelines also lead to different constraints for aerosols present in the atmosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In the case of our retrievals on the HST/WFC3 + Tiberius dataset, we obtain pre- cise constraints on sub-micron MgSiO3 aerosols covering roughly half the terminator atmosphere with an effec- 12 tively full vertical atmospheric extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The retrieval also specifically invoked MgSiO3 as opposed to ZnS, which is also a part of our canonical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Meanwhile, the retrieval on HST/WFC3 + Eureka data instead leads to only tentative constraints for ZnS aerosols and none for MgSiO3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Lastly, we also find different retrieved temperature profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Retrieving on HST/WFC3 + Tiberius data, we find a non-isothermal P-T profile, which may also be consistent with that obtained with Tiberius pipeline data alone, depending on the specific altitude probed by the retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Meanwhile, the HST/WFC3 + Eureka dataset leads to a P-T profile that is consistent with an isotherm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' It is also inconsistent with the tempera- ture obtained with Eureka pipeline data alone, as well as the temperature obtained with HST/WFC3 + Tiberius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The temperature constraint is relevant for interpreting the retrieved atmospheric composition and understand- ing the physical and chemical processes giving rise to them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We also conclude that while precise transmis- sion spectra over a wide wavelength range can in princi- ple lead to constraints for the terminator’s temperature structure, such constraints are sensitive to minor varia- tions in the data, such as those introduced by differences in reduction pipelines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We also consider how our findings are affected by changes to our model, described in section 3, the re- sults of which are summarised in table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' On in- cluding the effects of stellar heterogeneities in our model, we find that our retrieved abundance constraints are consistent with those obtained with our canonical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We also consider the impact of using a para- metric cloud/haze prescription rather than physically- motivated Mie-scattering aerosols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In this case, we find that our retrieved abundances are different by up to ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='5 dex, underscoring the need for a physically mo- tivated aerosol model in order to obtain accurate abun- dance constraints in the JWST era.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' SUMMARY AND DISCUSSION We use the first JWST observations of an exoplanet transmission spectrum in the 3-5 µm range to obtain early insights into atmospheric retrievals that are possi- ble in the JWST era.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This spectral range is particularly important to investigate, considering the large alloca- tion of JWST time in Cycle 1 for exoplanet spectroscopy using NIRSpec observations in the ∼3-5µm range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We focus on the JWST NIRSpec PRISM observations of the hot Saturn WASP-39b, observed as part of the JWST ERS program (The JWST Transiting Exoplanet Com- munity Early Release Science Team et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022), ar- guably one of the most promising exoplanets for trans- mission spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our goal is to investigate (a) the nature of atmospheric constraints that are possible with high-precision JWST data in the ∼3-5 µm range, (b) modeling requirements for atmospheric retrievals with such data, (c) how sensitive the retrieved atmospheric properties are to differences in spectra from different re- duction pipelines, and (d) how such data may be com- plemented with observations at shorter wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Key Lessons We identify the following key lessons for atmospheric retrievals of transiting exoplanets using JWST transmis- sion spectra, particularly in the 3-5 µm range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The ∼3-5 µm range provides an important av- enue for molecular detections, as it encompasses windows in extinction cross section for several aerosols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Consequently, molecular opacity within this range can give rise to highly prominent spec- tral features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' JWST observations over the ∼3- 5 µm may therefore lead to confident molecular detections even for potentially cloudy atmospheres with low-amplitude (≲2-3 scale height) spectral features in the HST/WFC3 hand (∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='7 µm) (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Stevenson 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Fu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Crossfield & Kreidberg 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our results add to studies using simulated JWST observations (Wakeford & Sing 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Pinhas & Madhusudhan 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Mai & Line 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Lacy & Burrows 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In order for retrievals to obtain accurate abun- dance estimates with JWST observations in the ∼3-5 µm range, complementary observations may be needed at shorter wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This allows re- trievals to constrain the spectral baseline needed for accurate and precise estimates of molecular abundances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Specifically, we find that complemen- tary observations with HST/WFC3 can be highly effective for this goal, resulting in changes in the retrieved abundances by up to one dex in some cases, compared to retrievals using ∼3-5 µm spec- tra alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' JWST observations over a wide wavelength range can in principle constrain the presence of clouds/hazes, as well as their specific nature, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' particle composition and size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This has been pre- viously considered with simulated JWST observa- tions (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Benneke & Seager 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Wakeford & Sing 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Pinhas & Madhusudhan 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Mai & Line 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Lacy & Burrows 2020) and with HST- era observations (Benneke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' It is there- fore important that atmospheric retrievals have 13 the capability to properly treat the complex spec- tral signatures that aerosols can contribute to a planet’s transmission spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As expected from prior theoretical works, JWST transmission spectra in the near-infrared can provide precise abundance constraints for sev- eral prominent molecules in exoplanetary atmo- spheres(e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Beichman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Greene et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Howe et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Kalirai 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Bean et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' For the present case, we retrieve abun- dance constraints with a precision of ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='5 dex for prominent molecules, even with the relatively limited spectral range considered.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Combining this data with other JWST observations can lead to even more precise abundance constraints.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Small differences in JWST spectra, such as those arising due to different reduction pipelines, can have a notable impact on the retrieved con- straints and detections, particularly forless promi- nent species.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This is thanks to the high precision that JWST observations can have, especially for giant exoplanets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' For the case of the WASP-39 b observations we consider, which are for a single transit, we find that differences in spectra aris- ing from differences between reduction pipelines can affect which species are detected at a 2-3σ level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Therefore, robust data reduction pipelines are needed in order to converge on accurate chem- ical detections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' A high detection significance for a particular chem- ical species does not indicate that its abundance is constrained accurately.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' For instance, retriev- ing on JWST/NIRSpec PRISM observations ob- tained with the Tiberius pipeline leads to a ∼25σ detection significance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' However, on supplement- ing these observations with HST/WFC3 G141 and G102 data, the retrieved mixing ratio estimate is 1 dex higher, as the retrieval finds a different spec- tral baseline.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The precision with which the abundance of a chemical species is constrained is not indicative of how confidently it is detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' For instance, us- ing JWST NIRSpec PRISM observations reduced with the Tiberius pipeline, we constrain the mix- ing ratios of CO2 and H2S with a precision of ≲0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='4 dex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' While CO2 is detected with extremely high confidence, however, H2S is not, with our re- trievals finding only a tentative 2-σ model prefer- ence for its inclusion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' It is therefore essential that 10−1 100 Mass (MJ) 100 101 102 Elemental Abundance (×Solar) J S UN WASP-39 b �O H � �C H � � S H � Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Initial constraints on the elemental abundances in the atmosphere of WASP-39 b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The O/H (blue), C/H (red) and S/H (yellow) ratios are derived from the molecular abundances retrieved from JWST data in the 3-5 µm range combined with HST/WFC3 data (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='7 µm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The elemen- tal abundances are shown relative to solar values (Asplund et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The dashed vertical line denotes the planet mass (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='28 MJ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Closed and open circles within the gray shaded region refer to retrievals using JWST data from the Tiberius and Eureka pipelines, respectively, offset horizon- tally for clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The C/H abundances for solar system giant planets (Atreya et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022) along with a linear fit (in brown) and the O/H in Jupiter from Juno (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2020) are shown for reference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' future studies assess the robustness of their find- ings by carrying out a full Bayesian model com- parison for each chemical species that may be de- tected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The spectral ranges of JWST instruments allow for the detection of chemical species that have not been hitherto considered in exoplanet retrievals, and potentially chemical processes that may have not been anticipated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In the present example of WASP-39 b, we independently confirm the pres- ence of SO2 reported by Rustamkulov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2022) and Alderson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2022), while also finding tentative indications of H2S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We therefore find that retrieval frameworks must be open to diverse chemistry if they are to be capable of fully taking advantage of JWST observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The Atmosphere of WASP-39 b In light of the above considerations, we present ini- tial constraints on the atmospheric properties of WASP- 39 b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We confirm the presence of CO2, CO and SO2 reported by The JWST Transiting Exoplanet Commu- nity Early Release Science Team et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2022) and Rus- 14 tamkulov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2022);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Alderson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We ad- ditionally find tentative indications for the presence of H2S, with detection sigificances between ∼2-4 σ across our retrievals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our abundance estimate of SO2 supports prior findings of disequilibrium chemistry at work in the atmosphere of WASP-39 b (Tsai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Addi- tionally, the presence of H2S suggested by our retrievals further supports this, as H2S is expected to be the pri- mary sulfur reservoir under chemical equilibrium deeper in the atmosphere (Zahnle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Hobbs et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Polman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022), which photo- chemically reacts with H2O in the upper atmosphere to form SO2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As our retrievals obtain abundance constraints for a range of oxygen-, carbon- and sulfur-bearing species, we can begin to probe the relative enrichment of each ele- ment in the atmosphere of WASP-39 b, as shown in fig- ure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Considering the constraints obtained with JWST observations reduced by the Tiberius pipeline combined with HST/WFC3 data, we find that the inferred O/H, C/H and S/H values correspond to 15+30 −10×, 21+46 −14× and 17+15 −7 × solar enrichments, respectively (Asplund et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Such enhancements are consistent with the at- mospheric metallicity of Saturn based on CH4 measure- ments, at 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='67±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='35× solar, and with recent suggestions for WASP-39 b(Alderson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Rustamkulov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Feinstein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Meanwhile, the equivalent O/H, C/H and S/H inferences using JWST observa- tions reduced with the Eureka pipeline and HST/WFC3 data correspond to 4+6 −2×, 2+4 −1× and 11+11 −7 × solar en- richments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In this case, the oxygen and sulfur enrich- ments are still consistent with the metallicity of Saturn, while carbon is somewhat less enriched.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We note that the uncertainties in our O/H and C/H estimates are primarily driven by the CO mixing ratio constraints, which are retrieved with precisions of ∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='4-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='5 dex.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Re- trievals combining the present JWST/NIRSpec PRISM data with recently-published NIRSpec G395H obser- vations(Alderson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022) that also encompass the ∼4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='8 µm CO feature may further refine the present es- timates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Beyond constraints for gaseous species, we also obtain tentative indications of non-gray opacity contributions from Mie-scattering aerosols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Specifically, our retrieval on JWST data reduced with the Tiberius pipeline and HST/WFC3 observations infers the presence of MgSiO3 aerosols.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' These aerosols are found to have a modal par- ticle size of ∼2 nm and cover ∼50% of the planet’s ter- minator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Meanwhile, retrieving on JWST data from Eu- reka and HST/WFC3 observations, we find tentative in- dications of ZnS aerosols instead.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' These compositional constraints are consistent with thermochemical expec- tations for condensing species (Morley et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our findings are also in agreement with preferences for non- grey spectral contributions from aerosols obtained with a forward model analysis of NIRISS observations (Fein- stein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our retrievals also lead to constraints for the planet’s terminator temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Using the Tiberius reduction of the JWST data along with HST/WFC3 data, we find tentative indications of a non-isothermal temperature, with a temperature of 757+40 −43 K at the top of the at- mosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Meanwhile, JWST data from Eureka and HST/WFC3 observations instead lead to a P-T profile that is consistent with an isotherm, with a temperature of 666+53 −72 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' WASP-39 b and its ERS observations are set to allow an in-depth comparison between a solar-system planet and an extrasolar planet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our results contribute an early step towards a next-generation comparative study be- tween Saturn and an exoplanet that is a near-Saturn analogue in both mass and metallicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The results presented above are only initial constraints for the atmospheric properties of WASP-39 b, obtained with a relatively limited spectral range of JWST obser- vations (∼3-5 µm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Future retrievals with all available data (∼0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='6-5 µm) can significantly improve upon the constraints presented in this work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' However, our study highlights the need for rigorous data reduction and re- trieval considerations as well as a robust exploration of the available parameter space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The retrievals in this work involved ∼109 model evaluations to achieve that goal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' In addition to physically motivated aerosol consid- erations, future retrievals may also consider the effect of inhomogeneous temperature (Nixon & Madhusudhan 2022) and chemical (Rocchetto et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016) structures, as well as the impact of stellar heterogeneity aided by optical data (Rackham et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Pinhas et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018) and other molecular opacity sources.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' While such model sophistication may not be applicable in all cases, es- pecially for moderately irradiated planets like WASP- 39 b, a holistic approach is recommended for accurate retrievals of atmospheric properties in the JWST era.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our results provide a glimpse into the richness of at- mospheric science that JWST is set to enable, thanks to its unprecedented sensitivity and wide spectral cover- age that includes hitherto unexplored wavelengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Our results also highlight the sophistication demanded of at- mospheric models and retrievals, as well as the robust- ness required of reduction pipelines, if we are to rise to the challenge and make full use of the discovery oppor- tunities that JWST presents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 15 This work was performed using resources provided by the Cambridge Service for Data Driven Discovery (CSD3) operated by the University of Cambridge Re- search Computing Service (www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='csd3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='cam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='uk), pro- vided by Dell EMC and Intel using Tier-2 funding from the Engineering and Physical Sciences Research Coun- cil (capital grant EP/P020259/1), and DiRAC fund- ing from the Science and Technology Facilities Council (www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='dirac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='uk).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' This work uses data reduced from observations made with the NASA/ESA/CSA JWST, as part of The Transiting Exoplanet Community Early Release Science (ERS) Program (PI: N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Batalha).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We thank NASA, ESA, CSA, STScI, the ERS team, and everyone whose efforts have contributed to JWST and exoplanet science with JWST.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We thank the anonymous referee for their valuable comments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' SC thanks Anjali Piette for helpful discus- sion on Mie scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' NM acknowledges support from the MERAC Foundation, Switzerland, and the UK Sci- ence and Technology Facilities Council (STFC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' SG is grateful to Leiden Observatory at Leiden University for the award of the Oort Fellowship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' APPENDIX Figure 6 shows the spectral contributions from gaseous species in our retrieved best fit spectrum, obtained for JWST/NIRSpec PRISM observations reduced with Tiberius and HST/WFC3 data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' We note that this figure does not include spectral contributions from MgSiO3 aerosols, for visual clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' As such, the combined spectral contributions correspond to the blue curve in figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 1 2 3 4 5 Wavelength (µm) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3 Transit Depth (%) Combined H2O CO CO2 H2S SO2 Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' The spectral contributions from H2O, CO, CO2, SO2 and H2S to the best fit spectrum obtained from the retrieval on JWST observations reduced by the Tiberius pipeline combined with HST/WFC3 data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Also shown is the resulting spectrum from all molecular spectral contributions, corresponding to the aerosol-free model shown in figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Spectral contributions from MgSiO3 aerosols as shown in figure 1 are not included here, for visual clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' REFERENCES Alderson, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Wakeford, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Alam, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022, arXiv e-prints, arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='10488.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='org/abs/2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='10488 Asplund, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Amarsi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Grevesse, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2021, A&A, 653, A141, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1051/0004-6361/202140445 Atreya, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Crida, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Guillot, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022, arXiv e-prints, arXiv:2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='06914.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='org/abs/2205.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='06914 Azzam, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Tennyson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Yurchenko, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Naumenko, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016, MNRAS, 460, 4063, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1093/mnras/stw1133 Barber, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Strange, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Hill, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2014, MNRAS, 437, 1828, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1093/mnras/stt2011 Barstow, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Aigrain, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Irwin, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Sing, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2017, ApJ, 834, 50, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/1538-4357/834/1/50 16 Batalha, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Line, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2017, AJ, 153, 151, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/1538-3881/aa5faa Bean, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Stevenson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Batalha, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018, PASP, 130, 114402, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1088/1538-3873/aadbf3 Beichman, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Benneke, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Knutson, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2014, PASP, 126, 1134, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1086/679566 Benneke, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Seager, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2013, ApJ, 778, 153, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1088/0004-637X/778/2/153 Benneke, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Knutson, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Lothringer, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2019, Nature Astronomy, 3, 813, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1038/s41550-019-0800-5 Birkmann, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Ferruit, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Alves de Oliveira, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2014, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 9143, Space Telescopes and Instrumentation 2014: Optical, Infrared, and Millimeter Wave, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Oschmann, Jacobus M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Clampin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Fazio, & H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' MacEwen, 914308, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1117/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2054642 Bohren, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Huffman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Kam, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 1983, Nature, 306, 625 Buchner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Georgakakis, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Nandra, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2014, A&A, 564, A125, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1051/0004-6361/201322971 Charbonneau, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Brown, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Noyes, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Gilliland, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2002, ApJ, 568, 377, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1086/338770 Chubb, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Tennyson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Yurchenko, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2020, Monthly Notices of the Royal Astronomical Society, 493, 1531, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1093/mnras/staa229 Chubb, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Naumenko, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Keely, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018, JQSRT, 218, 178, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='jqsrt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='012 Crossfield, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Kreidberg, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2017, AJ, 154, 261, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/1538-3881/aa9279 Deirmendjian, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 1969, Electromagnetic scattering on spherical polydispersions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Deming, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Wilkins, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', McCullough, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2013, ApJ, 774, 95, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1088/0004-637X/774/2/95 Dorschner, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Begemann, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Henning, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Jaeger, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Mutschke, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 1995, A&A, 300, 503 Ehrenreich, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Bourrier, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Wheatley, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2015, Nature, 522, 459, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1038/nature14501 Faedi, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Barros, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Anderson, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2011, A&A, 531, A40, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1051/0004-6361/201116671 Feinstein, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Radica, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Welbanks, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022, arXiv e-prints, arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='10493.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='org/abs/2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='10493 Feroz, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Hobson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Bridges, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2009, MNRAS, 398, 1601, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='14548.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='x Feroz, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Hobson, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Cameron, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Pettitt, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2019, The Open Journal of Astrophysics, 2, 10, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='21105/astro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2144 Ferruit, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Bagnasco, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Barho, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2012, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 8442, Space Telescopes and Instrumentation 2012: Optical, Infrared, and Millimeter Wave, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Clampin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Fazio, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' MacEwen, & J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Oschmann, Jacobus M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', 84422O, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1117/12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='925810 Fischer, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Knutson, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Sing, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016, ApJ, 827, 19, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/0004-637X/827/1/19 Fu, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Deming, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Knutson, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2017, ApJL, 847, L22, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/2041-8213/aa8e40 Fulton, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Rosenthal, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Hirsch, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2021, ApJS, 255, 14, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/1538-4365/abfcc1 Gandhi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Madhusudhan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2017, MNRAS, 472, 2334, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1093/mnras/stx1601 Greene, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Line, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Montero, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016, ApJ, 817, 17, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/0004-637X/817/1/17 Harris, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Tennyson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Kaminsky, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Pavlenko, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Jones, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2006, MNRAS, 367, 400, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='09960.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='x Hobbs, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Rimmer, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Shorttle, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Madhusudhan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2021, MNRAS, 506, 3186, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1093/mnras/stab1839 Howard, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Marcy, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Johnson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2010, Science, 330, 653, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1126/science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1194854 Howe, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Burrows, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Deming, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2017, ApJ, 835, 96, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/1538-4357/835/1/96 Kalirai, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018, Contemporary Physics, 59, 251, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1080/00107514.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1467648 Kawashima, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Min, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2021, A&A, 656, A90, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1051/0004-6361/202141548 Kirk, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', L´opez-Morales, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Wheatley, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2019, AJ, 158, 144, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/1538-3881/ab397d Kreidberg, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018, in Handbook of Exoplanets, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Deeg & J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Belmonte, 100, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1007/978-3-319-55333-7 100 Kreidberg, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Bean, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', D´esert, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2014, ApJL, 793, L27, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1088/2041-8205/793/2/L27 Lacy, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Burrows, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2020, ApJ, 904, 25, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/1538-4357/abbc6c Li, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Ingersoll, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Bolton, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2020, Nature Astronomy, 4, 609, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1038/s41550-020-1009-3 Li, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Gordon, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Rothman, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2015, ApJS, 216, 15, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1088/0067-0049/216/1/15 MacDonald, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Madhusudhan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2017, MNRAS, 469, 1979, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1093/mnras/stx804 Madhusudhan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018, in Handbook of Exoplanets, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Deeg & J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Belmonte, 104, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1007/978-3-319-55333-7 104 17 Madhusudhan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Crouzet, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', McCullough, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Deming, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Hedges, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2014, ApJL, 791, L9, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1088/2041-8205/791/1/L9 Madhusudhan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Seager, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2009, ApJ, 707, 24, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1088/0004-637X/707/1/24 Mai, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Line, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2019, ApJ, 883, 144, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/1538-4357/ab3e6d Mancini, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Esposito, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Covino, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018, A&A, 613, A41, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1051/0004-6361/201732234 Mayor, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Marmier, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Lovis, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2011, arXiv e-prints, arXiv:1109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2497.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='org/abs/1109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2497 Morley, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Fortney, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Kempton, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2013, ApJ, 775, 33, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1088/0004-637X/775/1/33 Nikolov, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Sing, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Gibson, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016, ApJ, 832, 191, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/0004-637X/832/2/191 Nixon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Madhusudhan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022, ApJ, 935, 73, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/1538-4357/ac7c09 Pinhas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Madhusudhan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2017, MNRAS, 471, 4355, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1093/mnras/stx1849 Pinhas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Madhusudhan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Gandhi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & MacDonald, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2019, MNRAS, 482, 1485, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1093/mnras/sty2544 Pinhas, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Rackham, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Madhusudhan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Apai, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018, MNRAS, 480, 5314, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1093/mnras/sty2209 Polman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Waters, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Min, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Miguel, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Khorshid, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022, arXiv e-prints, arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='00469.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='org/abs/2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='00469 Querry, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 1987, Chemical Research, Development and Engineering Center, U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' Army Armament Munitions Chemical Command Rackham, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Espinoza, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Apai, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2017, ApJ, 834, 151, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/1538-4357/aa4f6c Richard, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Gordon, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Rothman, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2012, JQSRT, 113, 1276 , doi: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='jqsrt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='004 Rocchetto, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Waldmann, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Venot, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Lagage, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Tinetti, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016, ApJ, 833, 120, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/1538-4357/833/1/120 Rothman, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Gordon, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Barber, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2010, JQSRT, 111, 2139 , doi: https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1016/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='jqsrt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='05.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='001 Rustamkulov, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Sing, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Mukherjee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022, arXiv e-prints, arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='10487.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='org/abs/2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='10487 Sarkar, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Madhusudhan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Papageorgiou, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2020, MNRAS, 491, 378, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1093/mnras/stz2958 Seager, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Sasselov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2000, ApJ, 537, 916, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1086/309088 Sing, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Fortney, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Nikolov, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016, Nature, 529, 59, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1038/nature16068 Stevenson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016, ApJL, 817, L16, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/2041-8205/817/2/L16 Stevenson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Lewis, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Bean, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016, PASP, 128, 094401, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1088/1538-3873/128/967/094401 The JWST Transiting Exoplanet Community Early Release Science Team, Ahrer, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Alderson, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022, arXiv e-prints, arXiv:2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='11692.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='org/abs/2208.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='11692 Tsai, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Lee, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Powell, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2022, arXiv e-prints, arXiv:2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='10490.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' https://arxiv.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='org/abs/2211.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='10490 Tsiaras, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Waldmann, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Zingales, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018, AJ, 155, 156, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/1538-3881/aaaf75 Underwood, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Tennyson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Yurchenko, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2016, MNRAS, 459, 3890, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1093/mnras/stw849 Vidal-Madjar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Lecavelier des Etangs, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', D´esert, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2003, Nature, 422, 143, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1038/nature01448 Wakeford, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Sing, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2015, A&A, 573, A122, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1051/0004-6361/201424207 Wakeford, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Sing, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Deming, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2018, AJ, 155, 29, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/1538-3881/aa9e4e Wang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Miguel, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Lunine, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2017, ApJ, 850, 199, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/1538-4357/aa978e Wang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Fischer, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Horch, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Huang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2015, ApJ, 799, 229, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1088/0004-637X/799/2/229 Welbanks, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Madhusudhan, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Allard, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2019, ApJLett, 887, L20, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='3847/2041-8213/ab5a89 Yurchenko, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Barber, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Tennyson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2011, MNRAS, 413, 1828, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1111/j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1365-2966.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='18261.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='x Yurchenko, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Tennyson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2014, MNRAS, 440, 1649, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1093/mnras/stu326 Zahnle, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Marley, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Freedman, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', Lodders, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=', & Fortney, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content=' 2009, ApJL, 701, L20, doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} +page_content='1088/0004-637X/701/1/L20' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/rtE0T4oBgHgl3EQfrQGn/content/2301.02564v1.pdf'} diff --git a/stAzT4oBgHgl3EQfPPv2/content/tmp_files/2301.01182v1.pdf.txt b/stAzT4oBgHgl3EQfPPv2/content/tmp_files/2301.01182v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..a7b940f600065aff943cbe3479660b293191e488 --- /dev/null +++ b/stAzT4oBgHgl3EQfPPv2/content/tmp_files/2301.01182v1.pdf.txt @@ -0,0 +1,708 @@ +PMT-IQA: PROGRESSIVE MULTI-TASK LEARNING FOR BLIND IMAGE QUALITY +ASSESSMENT +Qingyi Pan1,2,3 +Ning Guo1 +Letu Qingge4 +Jingyi Zhang2 +Pei Yang1,† +1 Tsinghua University, Department of Computer Technology and Application, China +2 Tsinghua University, Center for Statistical Science & Department of Industrial Engineering, China +3 Tsinghua University, Dept. of Computer Science & Technology, China +4 North Carolina A&T State University, Department of Computer Science, USA +ABSTRACT +Blind image quality assessment (BIQA) remains challenging +due to the diversity of distortion and image content variation, +which complicate the distortion patterns crossing different +scales and aggravate the difficulty of the regression problem +for BIQA. However, existing BIQA methods often fail to con- +sider multi-scale distortion patterns and image content, and +little research has been done on learning strategies to make +the regression model produce better performance. +In this +paper, we propose a simple yet effective Progressive Multi- +Task Image Quality Assessment (PMT-IQA) model, which +contains a multi-scale feature extraction module (MS) and a +progressive multi-task learning module (PMT), to help the +model learn complex distortion patterns and better optimize +the regression issue to align with the law of human learning +process from easy to hard. +To verify the effectiveness of +the proposed PMT-IQA model, we conduct experiments on +four widely used public datasets, and the experimental re- +sults indicate that the performance of PMT-IQA is superior to +the comparison approaches, and both MS and PMT modules +improve the model’s performance. +Index Terms— Blind image quality assessment, no- +reference image quality assessment, multi-scale feature, pro- +gressive multi-task learning +1. INTRODUCTION +With the popularity of smartphones and other camera devices +in recent years, a vast amount of images have been produced +and play an increasingly important role in people’s informa- +tion interaction. However, these images could be distorted by +various factors, including the professional level of the pho- +tographer, equipment performance, transmission and device +storage, etc. Therefore, it is of great need to assess the quality +of images. Although people can subjectively evaluate the im- +age quality accurately and reliably, it is very limited in prac- +tical applications due to time-consuming and laborious [1]. +This work is supported by the National Natural Science Foundation of +China under Grant 61866031. † Corresponding author. +Fig. 1. The motivation of PMT-IQA. Image quality assess- +ment can be divided into two steps: multi-scale vision system +and human learning procedure. +Consequently, objective image quality assessment (IQA) [2], +which aims to explore models for automatically evaluating the +image quality in line with the human vision system (HVS), +has attracted much attention in the past few years [1, 3, 4, 5]. +Among all the objective IQA methods, blind IQA (BIQA) ap- +proaches, which are also called no-reference IQA (NR-IQA) +methods, are the most challenging ones as they use no extra +reference information. Yet much progress has been made on +this topic, it is still an open and challenging issue, and in this +study, we are committed to exploring the BIQA problem. +The diversity of distortion and image content variation are +the main reasons why BIQA is full of challenges. On the one +hand, they complicate the distortion patterns, covering multi- +ple scales, from local to global. On the other hand, the com- +plex input space aggravates the difficulty of the regression +problem for BIQA. However, existing works often fail to con- +sider multi-scale distortion patterns and image content. Some +attempts have been made to design end-to-end architectures +for IQA. For example, Li et al. [6] extract global features us- +ing a pre-trained deep convolutional neural network (DCNN). +However, most real-world image data distortion patterns exist +in local areas. Therefore, the global features are not enough to +capture the complex distortions. In addition, human learning +process follows the law from easy to hard, which is known +as the easy-to-hard effect proposed by Pavlov [7] in 1927. +However, existing BIQA methods tend to solve the complex +regression problem directly. +arXiv:2301.01182v1 [eess.IV] 3 Jan 2023 + +Easy +Hard +hink +Score +Multi-Scale +Image +Learning +Assessment +Vision systemConcat + +Prediction +6.42 +Score +Loss +Loss +Total +Loss +Assessment +Rating +Multi-Scale Feature Extraction +Progressive Multi-Task learning +Image Dataset +Flow of Feature map +Prediction Label +Epoch +Epoch +Fig. 2. Progressive Multi-Task learning Image Quality Assessment architecture. It divides the task of IQA into two steps: +Multi-Scale Semantic Feature Extraction and Progressive Multi-Task learning. +In this paper, we proposed a simple yet effective image +quality assessment architecture inspired by the multi-scale +characteristics of HVS and the from easy to hard law of hu- +man learning shown in Fig. 1. We name the proposed network +as Progressive Multi-Task Image Quality Assessment (PMT- +IQA), since it is designed to capture distortion related patterns +using a task transfer strategy simulating the from easy to hard +human learning law. The idea behind the proposed model +is as below. Firstly, we extract global-to-local distortions by +designing a multi-scale semantic feature extraction module. +Secondly, inspired by the the from easy to hard learning law, +we build a progressive multi-task learning scheme, which can +gradually shift from an easy task (i.e. quality level classifi- +cation) to a hard one (quality score regression). At last, we +evaluate the performance of the proposed PMT-IQA on sev- +eral widely used public IQA datasets, and the experimental +results validate the effectiveness of the PMT-IQA model. +2. METHODS +2.1. Overview of the Proposed Model +The architecture of the proposed Progressive Mult-Task Im- +age Quality Assessment (PMT-IQA) model is presented in +Fig. 2. +It contains a multi-scale feature extraction mod- +ule (MS) and a progressive multi-task learning module (PMT) +to explore the diversity of distortion and image content varia- +tion as Eq. (1). +fθ(·) = gφ ◦ hψ(·) +(1) +where fθ(·) represents the complete model with paramters θ, +hψ is the MS module, which obtains local-to-global distor- +tions, and PMT module gφ learns complex regression prob- +lems. The definition of the parameters θ = {φ, ψ} will be +declared in the next section. +2.2. Multi-Scale Semantic Feature Extraction +To characterize various distortions, we utilize convolutions +to extract multi-scale features (from local to global), each of +which corresponding to a feature map si. Then we concate- +nate all features, as shown in Eq. (2). +hψ(xi) = concat(s1, · · · sj, · · · , sn) +(2) +More specifically, we use a pretrained ResNet50 [8] as the +backbone architecture in PMT-IQA, and collect feature maps +from four stages of ResNet50. Then we use 1 × 1 convo- +lution and global average pooling for dimension alignment. +The output of MS module h(·) is fed into the PMT module +for prediction. +2.3. Progressive Multi-Task Image Quality Assessment +As introduced in section 1, the diversity of distortion and im- +age content variation make the input space of quality scalar +score regression issue complicated and increase the difficulty +of model learning. Inspired by the law of the human learn- +ing process, we introduce a quality level classification task +simplified from the complex quality regression task aiming to +help optimize the regression task. Specifically, we divide the +range of scalar quality score into discrete sub-intervals, and +let each sub-interval be a quality category, which represents +a specific quality level, for the quality classification task. Let +w be the interval length, [ymin, ymax] be the range of quality +score, then we can obtain K categories as: +K = ⌊|ymax − ymin| +w +⌋ +(3) +For sample xi with scalar quality score yi, we can get the cor- +responding quality category label yc +i ∈ Y = {1, · · · , K} by +mapping yi into the corresponding discrete quality interval. +As shown in Fig. 2, the PMT gφ contains two parts: +scalar image quality score assessment module gφ1 : Rh → R + +0 +0 +0 +0l1l2X1.0 +0.8 +0.6 +0.4. +0.2 +0 +25 +50 +75 +100 +125 +150 +175 +200 +Epoch1.0 +21 +0.8 +0.6 +0.4. +0.2 +0 +25 +50 +75 +100 125 +150 +175 +200 +Epochand image quality level classification module gφ2 : Rh → +[0, 1]K. +Both gφ1 and gφ2 are implemented using a sim- +ple Multilayer Perception (MLP), where gφ1 is composed +of three fully connected layers and gφ2 contains three fully +connected layers and one softmax layer. +Suppose φ1 = +{W (φ1) +1 +, W (φ1) +2 +, W (φ1) +3 +} and φ2 = {W (φ2) +1 +, W (φ2) +2 +, W (φ2) +3 +}, +where W (φ1) +i +, W (φ2) +i +are the parameters of the i-th layer of +gφ1 and gφ2 respectively, then for an input X (note that X is +actually [ ˆX; 1] corresponding to real input ˆX as W φj +i +repre- +sents weight and bias), gφ1 and gφ2 are defined as follows: +gφ1(X) = W (φ1) +3 +(W (φ1) +2 +(W (φ1) +1 +X)) +(4) +gφ2(X) = ( +exp(o1) +�K +i=1 exp(oi) +, · · · , +exp(oK) +�K +i=1 exp(oi) +) +(5) +where oi is the i-th component of W (φ2) +3 +(W (φ2) +2 +(W (φ2) +1 +X)). +Given the definition of gφ1 and gφ2, the objective loss +function in PMT-IQA can be defined in Eq. (6). +λ1 +n +� +i=1 +ℓ1(gφ1(h(xi)), yi) + λ2 +n +� +i=1 +ℓ2(gφ2(h(xi)), yc +i ) +(6) +where ℓ1 and ℓ2 denote L1 loss and cross-entropy loss respec- +tively. Parameters λ1, λ2 > 0 are dynamic hyperparameters +in the training procedure. +To simulate the from easy to hard learning law [7], we +make the model focusing on learning the classification task +in the early stage of training, and gradually concentrates on +scalar quality score assessment with the progress of training +by dynamically adjusting the weights of the classification and +regression tasks as: +λ1(t) = +t +T + 1ω, λ2(t) = 1 − λ1(t) +(7) +where t represents the t-th epoch, T denotes the maxi- +mum epochs. ω is a trade-off to balance the two losses’ scale +difference. We adopt the Adam optimizer [9] to optimize the +PMT-IQA parameters φ and ψ jointly. +3. EXPERIMENT +3.1. Experimental Setup +3.1.1. Datasets +We use four publicly available IQA datasets, including +LIVE Challenge (LIVE-C) [10], BID [11], LIVE [12], and +CSIQ [13], to evaluate each IQA method. +In these four +datasets, BID and LIVE-C are authentic distortion datasets, +where BID contains 586 figures with realistic blurry dis- +tortions, and LIVE-C includes 1162 real-world images col- +lected by various cameras. In addition to authentic distortion +Table 1. The hyperparameters obtained by Optuna on the four +test datasets. +Dataset +LR +Batch +ω +Optimizer +BID +1.09e-4 +12 +0.9419 +Adam +LIVE-C +4.72e-4 +12 +0.9841 +Adam +LIVE +3.23e-4 +12 +0.9941 +Adam +CSIQ +4.72e-4 +12 +0.8931 +Adam +Fig. 3. SRCC and PLCC values of PMT-IQA on BID dataset +in the training procedure. +datasets, we also evaluate PMT-IQA on two synthetic image +datasets LIVE and CSIQ, which contain 779 and 866 images +with 5 and 6 individual distortions, respectively. +3.1.2. Evaluation Metrics +We select two commonly-used evaluation metrics, Spear- +man’s rank-order correlation coefficient (SRCC) [14] and +Pearson’s linear correlation coefficient (PLCC) [14], to eval- +uate the performances of IQA algorithms. Both SRCC and +PLCC range from -1 to 1, and a larger value indicates a better +performance. +3.1.3. Implementation Details +Each dataset is divided into training set and test set accord- +ing to 4:1. The quality scores are scaled into [0,1] to improve +stability, as shown in Fig. 3. During training, we augment +each training image by randomly cropping and horizontally +flipping ten times for LIVE-C and five times for the other +three datasets. A recently proposed hyperparameter search- +ing framework optuna [22] is employed to optimize hyperpa- +rameters and the values of hyperparameters of PMT-IQA on +four datasets are reported in Table 1. In addition, dropout and +weight-decay strategies are used to avoid overfitting. + +0.90 +0.85 +0.80 +0.75 +0.70 +0.65 +SRCC +0.60 +PLCC +5 +10 +15 +20 +25 +30 +EpochTable 2. The SRCC and PLCC values of various methods on BID, LIVE-C, LIVE and CSIQ datasets and the average rank of +SRCC and PLCC for each method. Best performance in boldface and numbers in parentheses indicate corresponding ranks. +We report the median SRCC and PLCC in ten runs. +BID +LIVE-C +LIVE +CSIQ +Average Rank of +Methods +SRCC +PLCC +SRCC +PLCC +SRCC +PLCC +SRCC +PLCC +SRCC +PLCC +BRISQUE [15] +0.562(8) +0.593(8) +0.608(9) +0.629(9) +0.939(8) +0.935(7) +0.746(10) +0.829(6) +8.75(10) +7.50(8) +AlexNet [16] +- +- +0.766(7) +0.807(7) +0.932(9) +0.841(11) +0.766(9) +0.811(9) +8.33(9) +9.00(10) +ResNet50 [8] +0.583(7) +0.599(7) +0.824(5) +0.868(5) +0.947(6) +0.913(8) +0.823(5) +0.876(5) +5.75(5) +6.25(5) +ILNIQE [17] +0.516(10) +0.554(10) +0.432(11) +0.508(11) +0.903(10) +0.865(10) +0.806(7) +0.808(10) +9.50(11) +10.25(11) +HOSA [18] +0.721(6) +0.736(6) +0.640(8) +0.678(8) +0.946(7) +0.947(6) +0.741(11) +0.823(7) +8.00(8) +6.75(6) +BIECON [19] +0.539(9) +0.576(9) +0.595(10) +0.613(10) +0.961(5) +0.962(4) +0.815(6) +0.803(11) +7.50(7) +8.50(9) +SFA [6] +0.826(4) +0.840(4) +0.812(6) +0.833(6) +0.883(11) +0.895(9) +0.796(8) +0.818(8) +7.25(6) +6.75(6) +PQR [20] +0.775(5) +0.794(5) +0.857(2) +0.872(3) +0.965(3) +0.951(5) +0.873(4) +0.901(4) +3.50(4) +4.25(4) +DB-CNN [21] +0.845(3) +0.859(3) +0.851(4) +0.869(4) +0.968(2) +0.971(1) +0.946(1) +0.959(1) +2.50(2) +2.25(2) +HyperIQA [4] +0.869(2) +0.878(2) +0.859(1) +0.882(2) +0.962(4) +0.966(3) +0.923(3) +0.942(3) +2.50(2) +2.50(3) +Ours +0.874(1) +0.883(1) +0.856(3) +0.893(1) +0.969(1) +0.971(1) +0.929(2) +0.951(2) +1.75(1) +1.25(1) +3.2. Performance Evaluation +We select ten BIQA methods as strong baselines, including +BRISQUE [15], ILNIQUE [17], AlexNet [16], ResNet50 [8], +HOSA [18], BIECON [19], SFA [6], PQR [20], DB-CNN +[21] and HyperIQA [4], to evaluate the performance of our +proposed PMT-IQA. The SRCC and PLCC values of each +method on the four test datasets are listed in Table 2. From +Table 2, we can find that the PMT-IQA approach outper- +forms all the comparison methods on BID, and LIVE for +both SRCC and PLCC evaluation. For the CSIQ dataset, both +SRCC and PLCC of PMT-IQA are only weaker than those of +DB-CNN. On the more challenging LIVE-C dataset, PMT- +IQA also achieved competitive results, with the largest PLCC +value (0.893) and SRCC value (0.856), which are very close +to the best result (0.859) obtained by HyperIQA. In order to +compare the performance of each method more intuitively, +we also provide the ranks of all methods (i.e. the numbers +in parentheses in Table 2) and the average ranks of SRCC +and PLCC of each method (i.e. the last two columns of Ta- +ble 2), and our proposed PMT-IQA obtains the best overall +performance according to the average rank metric. +3.3. Ablation Study +To further verify the effectiveness of MS and PMT modules, +we conduct several subtle ablation studies on BID and LIVE. +The variants include (1) ResNet: Pre-trained ResNet50 ar- +chitecture on ImageNet, adding fully-connected layer for pre- +diction (i.e., without MS and PMT). (2) Type1: The entire +architecture in Fig. 2 with only MS (i.e., without PMT). (3) +Type2: The entire architecture in Fig. 2 with MS and PMT +using fixed λ1 and λ2, and we use λ1 = λ2 = 0.5 in our +implementation based on test experiments. (4) PMT-IQA: +The entire architecture PMT-IQA in Fig. 2 with MS and PMT +using dynamic task weights as Eq. 7. +We tune the hidden dimension to ensure variants have +(a) BID +(b) LIVE +Fig. 4. The ablation study on the BID and LIVE datasets. +similar numbers of parameters to the completed PMT-IQA by +removing the performance gain induced by model complex- +ity for fairness. Fig. 4 shows the ablation study results. As +shown in Fig. 4, we can see that PMT-IQA achieves the best +performance on both BID and LIVE-C datasets. In addition, +both the MS and PMT modules improve the image quality +assessment results. Compared with MS, PMT improves the +overall performance more significantly for SRCC evaluation +on both BID and LIVE. Moreover, the comparison between +the results of Type2 and PMT-IQA shows that the strategy +of dynamically adjusting the task weights to make the net- +work learn from an easy task to a complex task is effective. +The novel progressive shift of tasks in PMT-IQA is essential +in the prediction/training strategies. Therefore, the ablation +study results again verify the effectiveness of the proposed +PMT-IQA approach. +4. CONCLUSION +In this paper, we propose a simple yet effective progressive +multi-task learning model for blind image quality assessment. +Our model contains a multi-scale feature extraction module +and a progressive multi-task learning module to help the +model learn complex distortion patterns and better optimize + +1.2 +ResNet +Typel +1.0 +Type2 +PMT-IQA +0.8 +0.6 +0.4 +0.2 +SRCC +PLCC1.00 +ResNet +Typel +0.98 +Type2 +PMT-IQA +0.96 +0.94 +0.92 +0.90 +SRCC +PLCCthe regression problem by simulating the from easy to hard +human learning law. +Extensive experimental results show +that although the proposed PMT-IQA method has a simple +architecture, it can still achieve superior performance than +various baselines on the four test datasets. +5. REFERENCES +[1] Guangtao Zhai and Xiongkuo Min, “Perceptual image +quality assessment: a survey,” Science China Informa- +tion Sciences, vol. 63, no. 11, pp. 1–52, 2020. +[2] Jongyoo Kim, Hui Zeng, Deepti Ghadiyaram, Sanghoon +Lee, Lei Zhang, and Alan C Bovik, “Deep convolutional +neural models for picture-quality prediction: Challenges +and solutions to data-driven image quality assessment,” +IEEE Signal processing magazine, vol. 34, no. 6, pp. +130–141, 2017. +[3] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P +Simoncelli, “Image quality assessment: from error vis- +ibility to structural similarity,” +IEEE transactions on +image processing, vol. 13, no. 4, pp. 600–612, 2004. +[4] Shaolin Su, Qingsen Yan, Yu Zhu, Cheng Zhang, Xin +Ge, Jinqiu Sun, and Yanning Zhang, +“Blindly assess +image quality in the wild guided by a self-adaptive hyper +network,” in Proceedings of the IEEE/CVF Conference +on Computer Vision and Pattern Recognition, 2020, pp. +3667–3676. +[5] Hancheng Zhu, Leida Li, Jinjian Wu, Weisheng Dong, +and Guangming Shi, “Metaiqa: Deep meta-learning for +no-reference image quality assessment,” in Proceedings +of the IEEE/CVF Conference on Computer Vision and +Pattern Recognition, 2020, pp. 14143–14152. +[6] Dingquan Li, Tingting Jiang, Weisi Lin, and Ming Jiang, +“Which has better visual quality: The clear blue sky or a +blurry animal?,” IEEE Transactions on Multimedia, vol. +21, no. 5, pp. 1221–1234, 2018. +[7] IP Pavlov, +“Conditioned reflexes,” +Les Etudes +Philosophiques, vol. 17, no. 4, 1927. +[8] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian +Sun, “Deep residual learning for image recognition,” in +Proceedings of the IEEE conference on computer vision +and pattern recognition, 2016, pp. 770–778. +[9] Diederik P Kingma and Jimmy Ba, +“Adam: +A +method for stochastic optimization,” +arXiv preprint +arXiv:1412.6980, 2014. +[10] Deepti Ghadiyaram and Alan C Bovik, “Massive online +crowdsourced study of subjective and objective picture +quality,” IEEE Transactions on Image Processing, vol. +25, no. 1, pp. 372–387, 2015. +[11] Alexandre Ciancio, Eduardo AB da Silva, Amir Said, +Ramin Samadani, Pere Obrador, et al., “No-reference +blur assessment of digital pictures based on multifeature +classifiers,” +IEEE Transactions on image processing, +vol. 20, no. 1, pp. 64–75, 2010. +[12] Hamid R Sheikh, Muhammad F Sabir, and Alan C +Bovik, “A statistical evaluation of recent full reference +image quality assessment algorithms,” IEEE Transac- +tions on image processing, vol. 15, no. 11, pp. 3440– +3451, 2006. +[13] Eric Cooper Larson and Damon Michael Chandler, +“Most apparent distortion: full-reference image quality +assessment and the role of strategy,” Journal of elec- +tronic imaging, vol. 19, no. 1, pp. 011006, 2010. +[14] Ann Lehman, JMP for basic univariate and multivariate +statistics: a step-by-step guide, SAS Institute, 2005. +[15] Anish Mittal, Anush Krishna Moorthy, and Alan Con- +rad Bovik, “No-reference image quality assessment in +the spatial domain,” IEEE Transactions on image pro- +cessing, vol. 21, no. 12, pp. 4695–4708, 2012. +[16] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hin- +ton, “Imagenet classification with deep convolutional +neural networks,” Advances in neural information pro- +cessing systems, vol. 25, 2012. +[17] Lin Zhang, Lei Zhang, and Alan C Bovik, “A feature- +enriched completely blind image quality evaluator,” +IEEE Transactions on Image Processing, vol. 24, no. 8, +pp. 2579–2591, 2015. +[18] Jingtao Xu, Peng Ye, Qiaohong Li, Haiqing Du, Yong +Liu, and David Doermann, “Blind image quality assess- +ment based on high order statistics aggregation,” IEEE +Transactions on Image Processing, vol. 25, no. 9, pp. +4444–4457, 2016. +[19] Jongyoo Kim and Sanghoon Lee, “Fully deep blind im- +age quality predictor,” IEEE Journal of selected topics +in signal processing, vol. 11, no. 1, pp. 206–220, 2016. +[20] Hui Zeng, Lei Zhang, and Alan C Bovik, “Blind image +quality assessment with a probabilistic quality represen- +tation,” in 2018 25th IEEE International Conference on +Image Processing (ICIP). IEEE, 2018, pp. 609–613. +[21] Weixia Zhang, Kede Ma, Jia Yan, Dexiang Deng, and +Zhou Wang, +“Blind image quality assessment using +a deep bilinear convolutional neural network,” +IEEE +Transactions on Circuits and Systems for Video Tech- +nology, vol. 30, no. 1, pp. 36–47, 2018. + +[22] Takuya Akiba, Shotaro Sano, Toshihiko Yanase, Takeru +Ohta, and Masanori Koyama, +“Optuna: +A next- +generation hyperparameter optimization framework,” in +Proceedings of the 25th ACM SIGKDD international +conference on knowledge discovery data mining, 2019, +pp. 2623–2631. + diff --git a/stAzT4oBgHgl3EQfPPv2/content/tmp_files/load_file.txt b/stAzT4oBgHgl3EQfPPv2/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..ad2540977832a1a0c8e38d7bd8a2b5afe34491cb --- /dev/null +++ b/stAzT4oBgHgl3EQfPPv2/content/tmp_files/load_file.txt @@ -0,0 +1,383 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf,len=382 +page_content='PMT-IQA: PROGRESSIVE MULTI-TASK LEARNING FOR BLIND IMAGE QUALITY ASSESSMENT Qingyi Pan1,2,3 Ning Guo1 Letu Qingge4 Jingyi Zhang2 Pei Yang1,† 1 Tsinghua University, Department of Computer Technology and Application, China 2 Tsinghua University, Center for Statistical Science & Department of Industrial Engineering, China 3 Tsinghua University, Dept.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' of Computer Science & Technology, China 4 North Carolina A&T State University, Department of Computer Science, USA ABSTRACT Blind image quality assessment (BIQA) remains challenging due to the diversity of distortion and image content variation, which complicate the distortion patterns crossing different scales and aggravate the difficulty of the regression problem for BIQA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' However, existing BIQA methods often fail to con- sider multi-scale distortion patterns and image content, and little research has been done on learning strategies to make the regression model produce better performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' In this paper, we propose a simple yet effective Progressive Multi- Task Image Quality Assessment (PMT-IQA) model, which contains a multi-scale feature extraction module (MS) and a progressive multi-task learning module (PMT), to help the model learn complex distortion patterns and better optimize the regression issue to align with the law of human learning process from easy to hard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' To verify the effectiveness of the proposed PMT-IQA model, we conduct experiments on four widely used public datasets, and the experimental re- sults indicate that the performance of PMT-IQA is superior to the comparison approaches, and both MS and PMT modules improve the model’s performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Index Terms— Blind image quality assessment, no- reference image quality assessment, multi-scale feature, pro- gressive multi-task learning 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' INTRODUCTION With the popularity of smartphones and other camera devices in recent years, a vast amount of images have been produced and play an increasingly important role in people’s informa- tion interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' However, these images could be distorted by various factors, including the professional level of the pho- tographer, equipment performance, transmission and device storage, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Therefore, it is of great need to assess the quality of images.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Although people can subjectively evaluate the im- age quality accurately and reliably, it is very limited in prac- tical applications due to time-consuming and laborious [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' This work is supported by the National Natural Science Foundation of China under Grant 61866031.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' † Corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' The motivation of PMT-IQA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Image quality assess- ment can be divided into two steps: multi-scale vision system and human learning procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Consequently, objective image quality assessment (IQA) [2], which aims to explore models for automatically evaluating the image quality in line with the human vision system (HVS), has attracted much attention in the past few years [1, 3, 4, 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Among all the objective IQA methods, blind IQA (BIQA) ap- proaches, which are also called no-reference IQA (NR-IQA) methods, are the most challenging ones as they use no extra reference information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Yet much progress has been made on this topic, it is still an open and challenging issue, and in this study, we are committed to exploring the BIQA problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' The diversity of distortion and image content variation are the main reasons why BIQA is full of challenges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' On the one hand, they complicate the distortion patterns, covering multi- ple scales, from local to global.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' On the other hand, the com- plex input space aggravates the difficulty of the regression problem for BIQA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' However, existing works often fail to con- sider multi-scale distortion patterns and image content.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Some attempts have been made to design end-to-end architectures for IQA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' For example, Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [6] extract global features us- ing a pre-trained deep convolutional neural network (DCNN).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' However, most real-world image data distortion patterns exist in local areas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Therefore, the global features are not enough to capture the complex distortions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' In addition, human learning process follows the law from easy to hard, which is known as the easy-to-hard effect proposed by Pavlov [7] in 1927.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' However, existing BIQA methods tend to solve the complex regression problem directly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='01182v1 [eess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='IV] 3 Jan 2023 Easy Hard hink Score Multi-Scale Image Learning Assessment Vision systemConcat Prediction 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='42 Score Loss Loss Total Loss Assessment Rating Multi-Scale Feature Extraction Progressive Multi-Task learning Image Dataset Flow of Feature map Prediction Label Epoch Epoch Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Progressive Multi-Task learning Image Quality Assessment architecture.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' It divides the task of IQA into two steps: Multi-Scale Semantic Feature Extraction and Progressive Multi-Task learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' In this paper, we proposed a simple yet effective image quality assessment architecture inspired by the multi-scale characteristics of HVS and the from easy to hard law of hu- man learning shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' We name the proposed network as Progressive Multi-Task Image Quality Assessment (PMT- IQA), since it is designed to capture distortion related patterns using a task transfer strategy simulating the from easy to hard human learning law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' The idea behind the proposed model is as below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Firstly, we extract global-to-local distortions by designing a multi-scale semantic feature extraction module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Secondly, inspired by the the from easy to hard learning law, we build a progressive multi-task learning scheme, which can gradually shift from an easy task (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' quality level classifi- cation) to a hard one (quality score regression).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' At last, we evaluate the performance of the proposed PMT-IQA on sev- eral widely used public IQA datasets, and the experimental results validate the effectiveness of the PMT-IQA model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' METHODS 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Overview of the Proposed Model The architecture of the proposed Progressive Mult-Task Im- age Quality Assessment (PMT-IQA) model is presented in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' It contains a multi-scale feature extraction mod- ule (MS) and a progressive multi-task learning module (PMT) to explore the diversity of distortion and image content varia- tion as Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' fθ(·) = gφ ◦ hψ(·) (1) where fθ(·) represents the complete model with paramters θ, hψ is the MS module, which obtains local-to-global distor- tions, and PMT module gφ learns complex regression prob- lems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' The definition of the parameters θ = {φ, ψ} will be declared in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Multi-Scale Semantic Feature Extraction To characterize various distortions, we utilize convolutions to extract multi-scale features (from local to global), each of which corresponding to a feature map si.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Then we concate- nate all features, as shown in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' hψ(xi) = concat(s1, · · · sj, · · · , sn) (2) More specifically, we use a pretrained ResNet50 [8] as the backbone architecture in PMT-IQA, and collect feature maps from four stages of ResNet50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Then we use 1 × 1 convo- lution and global average pooling for dimension alignment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' The output of MS module h(·) is fed into the PMT module for prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Progressive Multi-Task Image Quality Assessment As introduced in section 1, the diversity of distortion and im- age content variation make the input space of quality scalar score regression issue complicated and increase the difficulty of model learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Inspired by the law of the human learn- ing process, we introduce a quality level classification task simplified from the complex quality regression task aiming to help optimize the regression task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Specifically, we divide the range of scalar quality score into discrete sub-intervals, and let each sub-interval be a quality category, which represents a specific quality level, for the quality classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Let w be the interval length, [ymin, ymax] be the range of quality score, then we can obtain K categories as: K = ⌊|ymax − ymin| w ⌋ (3) For sample xi with scalar quality score yi, we can get the cor- responding quality category label yc i ∈ Y = {1, · · · , K} by mapping yi into the corresponding discrete quality interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 2, the PMT gφ contains two parts: scalar image quality score assessment module gφ1 : Rh → R 0 0 0 0l1l2X1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='2 0 25 50 75 100 125 150 175 200 Epoch1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='0 21 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='2 0 25 50 75 100 125 150 175 200 Epochand image quality level classification module gφ2 : Rh → [0, 1]K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Both gφ1 and gφ2 are implemented using a sim- ple Multilayer Perception (MLP), where gφ1 is composed of three fully connected layers and gφ2 contains three fully connected layers and one softmax layer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Suppose φ1 = {W (φ1) 1 , W (φ1) 2 , W (φ1) 3 } and φ2 = {W (φ2) 1 , W (φ2) 2 , W (φ2) 3 }, where W (φ1) i , W (φ2) i are the parameters of the i-th layer of gφ1 and gφ2 respectively, then for an input X (note that X is actually [ ˆX;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 1] corresponding to real input ˆX as W φj i repre- sents weight and bias), gφ1 and gφ2 are defined as follows: gφ1(X) = W (φ1) 3 (W (φ1) 2 (W (φ1) 1 X)) (4) gφ2(X) = ( exp(o1) �K i=1 exp(oi) , · · · , exp(oK) �K i=1 exp(oi) ) (5) where oi is the i-th component of W (φ2) 3 (W (φ2) 2 (W (φ2) 1 X)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Given the definition of gφ1 and gφ2, the objective loss function in PMT-IQA can be defined in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' (6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' λ1 n � i=1 ℓ1(gφ1(h(xi)), yi) + λ2 n � i=1 ℓ2(gφ2(h(xi)), yc i ) (6) where ℓ1 and ℓ2 denote L1 loss and cross-entropy loss respec- tively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Parameters λ1, λ2 > 0 are dynamic hyperparameters in the training procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' To simulate the from easy to hard learning law [7], we make the model focusing on learning the classification task in the early stage of training, and gradually concentrates on scalar quality score assessment with the progress of training by dynamically adjusting the weights of the classification and regression tasks as: λ1(t) = t T + 1ω, λ2(t) = 1 − λ1(t) (7) where t represents the t-th epoch, T denotes the maxi- mum epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' ω is a trade-off to balance the two losses’ scale difference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' We adopt the Adam optimizer [9] to optimize the PMT-IQA parameters φ and ψ jointly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' EXPERIMENT 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Experimental Setup 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Datasets We use four publicly available IQA datasets, including LIVE Challenge (LIVE-C) [10], BID [11], LIVE [12], and CSIQ [13], to evaluate each IQA method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' In these four datasets, BID and LIVE-C are authentic distortion datasets, where BID contains 586 figures with realistic blurry dis- tortions, and LIVE-C includes 1162 real-world images col- lected by various cameras.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' In addition to authentic distortion Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' The hyperparameters obtained by Optuna on the four test datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Dataset LR Batch ω Optimizer BID 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='09e-4 12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='9419 Adam LIVE-C 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='72e-4 12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='9841 Adam LIVE 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='23e-4 12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='9941 Adam CSIQ 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='72e-4 12 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='8931 Adam Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' SRCC and PLCC values of PMT-IQA on BID dataset in the training procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' datasets, we also evaluate PMT-IQA on two synthetic image datasets LIVE and CSIQ, which contain 779 and 866 images with 5 and 6 individual distortions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Evaluation Metrics We select two commonly-used evaluation metrics, Spear- man’s rank-order correlation coefficient (SRCC) [14] and Pearson’s linear correlation coefficient (PLCC) [14], to eval- uate the performances of IQA algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Both SRCC and PLCC range from -1 to 1, and a larger value indicates a better performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Implementation Details Each dataset is divided into training set and test set accord- ing to 4:1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' The quality scores are scaled into [0,1] to improve stability, as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' During training, we augment each training image by randomly cropping and horizontally flipping ten times for LIVE-C and five times for the other three datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' A recently proposed hyperparameter search- ing framework optuna [22] is employed to optimize hyperpa- rameters and the values of hyperparameters of PMT-IQA on four datasets are reported in Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' In addition, dropout and weight-decay strategies are used to avoid overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='90 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='85 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='80 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='70 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='65 SRCC 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='60 PLCC 5 10 15 20 25 30 EpochTable 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' The SRCC and PLCC values of various methods on BID, LIVE-C, LIVE and CSIQ datasets and the average rank of SRCC and PLCC for each method.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Best performance in boldface and numbers in parentheses indicate corresponding ranks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' We report the median SRCC and PLCC in ten runs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' BID LIVE-C LIVE CSIQ Average Rank of Methods SRCC PLCC SRCC PLCC SRCC PLCC SRCC PLCC SRCC PLCC BRISQUE [15] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='562(8) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='593(8) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='608(9) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='629(9) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='939(8) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='935(7) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='746(10) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='829(6) 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='75(10) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='50(8) AlexNet [16] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='766(7) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='807(7) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='932(9) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='841(11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='766(9) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='811(9) 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='33(9) 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='00(10) ResNet50 [8] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='583(7) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='599(7) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='824(5) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='868(5) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='947(6) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='913(8) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='823(5) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='876(5) 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='75(5) 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='25(5) ILNIQE [17] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='516(10) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='554(10) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='432(11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='508(11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='903(10) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='865(10) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='806(7) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='808(10) 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='50(11) 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='25(11) HOSA [18] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='721(6) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='736(6) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='640(8) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='678(8) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='946(7) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='947(6) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='741(11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='823(7) 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='00(8) 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='75(6) BIECON [19] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='539(9) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='576(9) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='595(10) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='613(10) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='961(5) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='962(4) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='815(6) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='803(11) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='50(7) 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='50(9) SFA [6] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='826(4) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='840(4) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='812(6) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='833(6) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='883(11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='895(9) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='796(8) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='818(8) 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='25(6) 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='75(6) PQR [20] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='775(5) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='794(5) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='857(2) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='872(3) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='965(3) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='951(5) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='873(4) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='901(4) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='50(4) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='25(4) DB-CNN [21] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='845(3) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='859(3) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='851(4) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='869(4) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='968(2) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='971(1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='946(1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='959(1) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='50(2) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='25(2) HyperIQA [4] 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='869(2) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='878(2) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='859(1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='882(2) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='962(4) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='966(3) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='923(3) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='942(3) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='50(2) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='50(3) Ours 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='874(1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='883(1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='856(3) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='893(1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='969(1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='971(1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='929(2) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='951(2) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='75(1) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='25(1) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Performance Evaluation We select ten BIQA methods as strong baselines, including BRISQUE [15], ILNIQUE [17], AlexNet [16], ResNet50 [8], HOSA [18], BIECON [19], SFA [6], PQR [20], DB-CNN [21] and HyperIQA [4], to evaluate the performance of our proposed PMT-IQA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' The SRCC and PLCC values of each method on the four test datasets are listed in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' From Table 2, we can find that the PMT-IQA approach outper- forms all the comparison methods on BID, and LIVE for both SRCC and PLCC evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' For the CSIQ dataset, both SRCC and PLCC of PMT-IQA are only weaker than those of DB-CNN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' On the more challenging LIVE-C dataset, PMT- IQA also achieved competitive results, with the largest PLCC value (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='893) and SRCC value (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='856), which are very close to the best result (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='859) obtained by HyperIQA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' In order to compare the performance of each method more intuitively, we also provide the ranks of all methods (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' the numbers in parentheses in Table 2) and the average ranks of SRCC and PLCC of each method (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' the last two columns of Ta- ble 2), and our proposed PMT-IQA obtains the best overall performance according to the average rank metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Ablation Study To further verify the effectiveness of MS and PMT modules, we conduct several subtle ablation studies on BID and LIVE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' The variants include (1) ResNet: Pre-trained ResNet50 ar- chitecture on ImageNet, adding fully-connected layer for pre- diction (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=', without MS and PMT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' (2) Type1: The entire architecture in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 2 with only MS (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=', without PMT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' (3) Type2: The entire architecture in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 2 with MS and PMT using fixed λ1 and λ2, and we use λ1 = λ2 = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='5 in our implementation based on test experiments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' (4) PMT-IQA: The entire architecture PMT-IQA in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 2 with MS and PMT using dynamic task weights as Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' We tune the hidden dimension to ensure variants have (a) BID (b) LIVE Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' The ablation study on the BID and LIVE datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' similar numbers of parameters to the completed PMT-IQA by removing the performance gain induced by model complex- ity for fairness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 4 shows the ablation study results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 4, we can see that PMT-IQA achieves the best performance on both BID and LIVE-C datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' In addition, both the MS and PMT modules improve the image quality assessment results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Compared with MS, PMT improves the overall performance more significantly for SRCC evaluation on both BID and LIVE.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Moreover, the comparison between the results of Type2 and PMT-IQA shows that the strategy of dynamically adjusting the task weights to make the net- work learn from an easy task to a complex task is effective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' The novel progressive shift of tasks in PMT-IQA is essential in the prediction/training strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Therefore, the ablation study results again verify the effectiveness of the proposed PMT-IQA approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' CONCLUSION In this paper, we propose a simple yet effective progressive multi-task learning model for blind image quality assessment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Our model contains a multi-scale feature extraction module and a progressive multi-task learning module to help the model learn complex distortion patterns and better optimize 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='2 ResNet Typel 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='0 Type2 PMT-IQA 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='2 SRCC PLCC1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='00 ResNet Typel 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='98 Type2 PMT-IQA 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='96 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='94 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='92 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='90 SRCC PLCCthe regression problem by simulating the from easy to hard human learning law.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' Extensive experimental results show that although the proposed PMT-IQA method has a simple architecture, it can still achieve superior performance than various baselines on the four test datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' REFERENCES [1] Guangtao Zhai and Xiongkuo Min, “Perceptual image quality assessment: a survey,” Science China Informa- tion Sciences, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 63, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 1–52, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [2] Jongyoo Kim, Hui Zeng, Deepti Ghadiyaram, Sanghoon Lee, Lei Zhang, and Alan C Bovik, “Deep convolutional neural models for picture-quality prediction: Challenges and solutions to data-driven image quality assessment,” IEEE Signal processing magazine, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 34, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 130–141, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [3] Zhou Wang, Alan C Bovik, Hamid R Sheikh, and Eero P Simoncelli, “Image quality assessment: from error vis- ibility to structural similarity,” IEEE transactions on image processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 13, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 600–612, 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [4] Shaolin Su, Qingsen Yan, Yu Zhu, Cheng Zhang, Xin Ge, Jinqiu Sun, and Yanning Zhang, “Blindly assess image quality in the wild guided by a self-adaptive hyper network,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 3667–3676.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [5] Hancheng Zhu, Leida Li, Jinjian Wu, Weisheng Dong, and Guangming Shi, “Metaiqa: Deep meta-learning for no-reference image quality assessment,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 14143–14152.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [6] Dingquan Li, Tingting Jiang, Weisi Lin, and Ming Jiang, “Which has better visual quality: The clear blue sky or a blurry animal?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=',” IEEE Transactions on Multimedia, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 1221–1234, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [7] IP Pavlov, “Conditioned reflexes,” Les Etudes Philosophiques, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 17, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 4, 1927.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [8] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition, 2016, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 770–778.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [9] Diederik P Kingma and Jimmy Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content='6980, 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [10] Deepti Ghadiyaram and Alan C Bovik, “Massive online crowdsourced study of subjective and objective picture quality,” IEEE Transactions on Image Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 25, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 372–387, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [11] Alexandre Ciancio, Eduardo AB da Silva, Amir Said, Ramin Samadani, Pere Obrador, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=', “No-reference blur assessment of digital pictures based on multifeature classifiers,” IEEE Transactions on image processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 20, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 64–75, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [12] Hamid R Sheikh, Muhammad F Sabir, and Alan C Bovik, “A statistical evaluation of recent full reference image quality assessment algorithms,” IEEE Transac- tions on image processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 15, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 3440– 3451, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [13] Eric Cooper Larson and Damon Michael Chandler, “Most apparent distortion: full-reference image quality assessment and the role of strategy,” Journal of elec- tronic imaging, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 19, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 011006, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [14] Ann Lehman, JMP for basic univariate and multivariate statistics: a step-by-step guide, SAS Institute, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [15] Anish Mittal, Anush Krishna Moorthy, and Alan Con- rad Bovik, “No-reference image quality assessment in the spatial domain,” IEEE Transactions on image pro- cessing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 12, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 4695–4708, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [16] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hin- ton, “Imagenet classification with deep convolutional neural networks,” Advances in neural information pro- cessing systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 25, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [17] Lin Zhang, Lei Zhang, and Alan C Bovik, “A feature- enriched completely blind image quality evaluator,” IEEE Transactions on Image Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 24, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 2579–2591, 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [18] Jingtao Xu, Peng Ye, Qiaohong Li, Haiqing Du, Yong Liu, and David Doermann, “Blind image quality assess- ment based on high order statistics aggregation,” IEEE Transactions on Image Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 25, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 9, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 4444–4457, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [19] Jongyoo Kim and Sanghoon Lee, “Fully deep blind im- age quality predictor,” IEEE Journal of selected topics in signal processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 11, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 206–220, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [20] Hui Zeng, Lei Zhang, and Alan C Bovik, “Blind image quality assessment with a probabilistic quality represen- tation,” in 2018 25th IEEE International Conference on Image Processing (ICIP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' IEEE, 2018, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 609–613.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [21] Weixia Zhang, Kede Ma, Jia Yan, Dexiang Deng, and Zhou Wang, “Blind image quality assessment using a deep bilinear convolutional neural network,” IEEE Transactions on Circuits and Systems for Video Tech- nology, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 30, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 36–47, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' [22] Takuya Akiba, Shotaro Sano, Toshihiko Yanase, Takeru Ohta, and Masanori Koyama, “Optuna: A next- generation hyperparameter optimization framework,” in Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery data mining, 2019, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} +page_content=' 2623–2631.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/stAzT4oBgHgl3EQfPPv2/content/2301.01182v1.pdf'} diff --git a/tdE1T4oBgHgl3EQfQQPo/content/2301.03039v1.pdf b/tdE1T4oBgHgl3EQfQQPo/content/2301.03039v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b8e8d25d19ea05e3c873989ad88b2a7f28d09d40 --- /dev/null +++ b/tdE1T4oBgHgl3EQfQQPo/content/2301.03039v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:280996c77ab7e03e2aa7ed5e59025d4933c307ea6bffef60d5cab5ff45760f67 +size 403341 diff --git a/tdE1T4oBgHgl3EQfQQPo/vector_store/index.faiss b/tdE1T4oBgHgl3EQfQQPo/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..0bdc1aeb10abc678ae2faee94086cab3b70446ce --- /dev/null +++ b/tdE1T4oBgHgl3EQfQQPo/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b8eb42608c5e9c945951e54057831cfd03a8711a93d67138af241c8bba72fec0 +size 852013 diff --git a/tdE1T4oBgHgl3EQfQQPo/vector_store/index.pkl b/tdE1T4oBgHgl3EQfQQPo/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..87bafb9c2b78c4c2af0bff190da625e638a2594e --- /dev/null +++ b/tdE1T4oBgHgl3EQfQQPo/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b1ec97c7461905f5ae549df7cff8c2d8eda965209ce362932ded9ef8d4c1e445 +size 42746 diff --git a/ttA0T4oBgHgl3EQfLf_G/content/tmp_files/2301.02120v1.pdf.txt b/ttA0T4oBgHgl3EQfLf_G/content/tmp_files/2301.02120v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..2ce3568c6555c920252e025d3a35b9a4f4752c4b --- /dev/null +++ b/ttA0T4oBgHgl3EQfLf_G/content/tmp_files/2301.02120v1.pdf.txt @@ -0,0 +1,1572 @@ +Reprogramming Pretrained Language Models for Protein Sequence +Representation Learning +Ria Vinod 1, Pin-Yu Chen2, and Payel Das2 +1Department of Computational and Molecular Biology, Brown University +2IBM Research +Abstract +Machine Learning-guided solutions for protein learning tasks have made significant headway in recent years. +However, success in scientific discovery tasks is limited by the accessibility of well-defined and labeled in-domain +data. To tackle the low-data constraint, recent adaptions of deep learning models pretrained on millions of +protein sequences have shown promise; however, the construction of such domain-specific large-scale model is +computationally expensive. Here, we propose Representation Learning via Dictionary Learning (R2DL), an +end-to-end representation learning framework in which we reprogram deep models for alternate-domain tasks +that can perform well on protein property prediction with significantly fewer training samples. R2DL reprograms +a pretrained English language model to learn the embeddings of protein sequences, by learning a sparse linear +mapping between English and protein sequence vocabulary embeddings. Our model can attain better accuracy +and significantly improve the data efficiency by up to 105 times over the baselines set by pretrained and standard +supervised methods. To this end, we reprogram an off-the-shelf pre-trained English language transformer and +benchmark it on a set of protein physicochemical prediction tasks (secondary structure, stability, homology, +stability) as well as on a biomedically relevant set of protein function prediction tasks (antimicrobial, toxicity, +antibody affinity). +Introduction +Recent advances in artificial intelligence (AI), particularly in deep learning, have led to major innovations and +advances in many scientific domains, including biology. These deep learning models aim to learn a highly accurate +and compressed representation of the biological system, which then can be employed for a range of tasks. There has +been notable success across a range of tasks, from high-quality protein structure prediction from protein sequences +[1; 2], accurate prediction of protein properties, to enabling novel and functional peptide discoveries [3; 4]. Many of +these advances rely on developing deep learning models [1; 5; 6] which are trained from scratch on massive amounts +(on the order of billions of tokens) of data. However, labeled data in biology is scarce and sparse, which is also the +case for many other real-world scenarios in the scientific domain. In the biological domain, label annotation can +involve biological assays, high resolution imaging and spectroscopy, which are all costly and time consuming processes. +The technique of pretraining deep learning models was proposed to address this issue. Pretraining methods +leverage large amounts of sequence data and can learn to encode features that can explain the variance seen in +sequences across biological task-specific training samples. In the context of protein sequences, pretraining has enabled +meaningful density modelling across protein functions, structures, and families [7]. In this work, we reference two types +of pretraining methods: (i) unsupervised pretraining, where all data is unlabeled, and (ii) self-supervised pretraining, +where a model learns to assign labels to its unlabeled data. Large models then pretrain on massive amounts of +unlabeled data, specifically biological sequences, which are available at scale. Once pretrained, these foundation +models (FMs) [8] are finetuned on smaller amounts of labeled data, which correspond to a specific downstream task. +Interestingly, for the large-scale models pretrained on protein sequences, biological structure and function seem to +emerge in the learned protein representation, even though such information was not included in model training [5]. +Though highly powerful, the training of those domain-specific foundation models from scratch is highly resource- +intensive [9]. For example, one training run of BERT (the language model considered in this work) learns 110 million +parameters, costs up to $13,000 USD and takes 64 days (without parallelized computing) and results in 0.7 tons +of carbon emissions [10]. A single training run of another popular language model, the T5 transformer, learns 11 +billion parameters, costs up to $1.3 million USD, takes 20 days, and results in 47 tons of carbon emissions [11; 12]. +Such pretrained language models and size variants are abundantly available with the advent of models libraries (e.g., +Hugging Face [13]) which host pretrained models and datasets. The scale of data, compute, and financial resources +required to train these models is not only available to a limited number of researchers, but is also infeasible for +applications with limited labeled data. However, in the scientific domain, we still aim to train models with similar +1 +arXiv:2301.02120v1 [cs.LG] 5 Jan 2023 + +Figure 1: Left: Descriptions of considered predictive tasks. We select the set of physicochemical property prediction +tasks from the well-studied domains in [6], and the biomedical function prediction tasks from works with biomedically +relevant small-szied labeled datasets [3; 14]. Center: We compare R2DL to pretraining and standard supervised +training methods. We refer to supervised methods as standard supervised classifiers that are trained from scratch from +labeled data alone. Depending on how labeled and unlabeled data are used in pretraining, we consider pretraining to +constitute unsupervised/supervised pretraining. Right: The comparative table shows the broad adaptability of the +R2DL framework. In comparison to existing gold standard methods, R2DL is has a broader utility across different +domains, sizes of training datasets, and data efficiency. We categorize supervised methods as cross-domain adaptable, +through various domain adaptation and transfer learning techniques [15]. +representational capacity and predictive performance. To this end, we propose a lightweight, and more accurate +alternative method to large-scale pretraining. Specifically, we introduce a method to reprogram an existing foundation +model of high capacity that is trained on data from a different domain. This situation calls for innovations in +cross-domain transfer learning, which is largely unexplored, particularly in scientific domains. +One known fact is that biological sequences are similar to natural language, as they also contain long-range +dependencies and follow Zipf’s law [16]. These sequences and their associated dependencies are crucial for determining +their structural and functional properties. Such similarity has motivated the use of deep learning architectures +and mechanisms that are widely used in natural language processing (NLP) to build protein sequence models +from scratch. In this work, we explore an alternative warm-start paradigm, i.e. how to effectively and efficiently +reprogram an existing, fully-trained large English language model to learn a meaningful (i.e., biomedically relevant) +representation of protein sequences. The goal is to create a more carbon-friendly, resource-efficient, and broadly +accessible framework to motivate different scientific domains toward democratizing the representation power of large +AI models. This warm-start paradigm is defined by the framework’s ability to achieve the performance of transformers +that are pretrained on billions of tokens, with a lighter-weight training procedure that is similar to that of a standard +supervised classifier trained from scratch. In particular, we consider highly specific biological and biomedical protein +sequence datasets (illustrated in Figure 1) which have much fewer samples than standard supervised language task +datasets. Reprogramming thus provides a more data and resource-efficient approach to developing models to achieve +deep representational capacity and performance for downstream protein tasks. Reprogramming has been previously +explored in the language domain as a sub-problem of transfer learning [17]. [18] explored reprogramming language +models for alternate text classification tasks, [19] reprogrammed acoustic models for time series classification, [20] +reprogrammed ImageNet classification models for alternate image classification tasks. However, none of these methods +investigate mappings between domains that require a very high representational capacity (from natural language to +biological sequence), which is the setting we require in the protein sequence domain. +Toward this goal, we introduce R2DL (Representation Reprogramming via Dictionary Learning), a novel cross- +domain transfer learning framework to reprogram an existing pretrained large-scale deep-learning model of the English +language, namely a English BERT model [10], to learn and predict physicochemical and biomedical properties of +protein sequences. To the best of our knowledge, our work remains the first work to address reprogramming in +any biological, and more broadly, scientific domain. In Figure 1, we illustrate the set of protein physicochemical +and functional property prediction tasks we consider, as well as the baseline methods against which we compare +R2DL performance to, and a brief description of R2DL’s advantages compared to these existing methods. We test +the reprogrammed model for a range of biomedically relevant downstream physicochemical property, structure, and +function prediction tasks, which include prediction of secondary structure, homology, mutational stability, solubility, +as well as antimicrobial nature, toxicity, and antibody affinity of proteins. Each of these tasks involves learning on +datasets which are limited to a few thousands of labeled samples, at least an order of magnitude smaller needed +2 + +Biological Property Prediction Tasks +Comparable Models +Model Comparison +Secondary Structure +Physiochemical +Stability +property +Reprogrammed +Can be +Can be +Can be +Robust +Our Contribution +prediction +(R2DL) +Trained +trained +adapted +to +on Large +on Small +cross- +Reduced +Homology +Data +Data +domain +Samples +ESM-1b [Rives2019], Tasks +R2DL +Solubility +口 +Pretrained +Assessing Protein +Embeddings [Rao 2019] +Peptide WAE [Das 2021] +Pretained +Antimicrobial +Biomedical +Toxicity +function +Supervised +LSTM [Das 2021] +Supervised +prediction +Antibody AffinityFigure 2: System illustration of the Representation Reprogramming via Dictionary Learning (R2DL) framework. In +Step 1, R2DL loads a pretrained language model (source), obtains the source vocabulary embeddings, and specifies the +protein tokens (target). In Step 2, R2DL learns a sparse linear mapping between the source and target embeddings via +dictionary learning, to represent a target token embedding as a sparse linear combination of source token embeddings. +In Step 3, the system maps the source task labels (e.g., positive/negative sentiments) to target task labels (e.g., +toxic/non-toxic proteins) and optimizes the embedding mapping parameters based on the task-specific loss evaluation +on a given protein sequence dataset. Finally, in Step 4 the reprogrammed model is deployed for the test-time +evaluation. +to train a foundation model or a large language model [21]. R2DL uses dictionary learning, a machine learning +framework that finds the optimal sparse linear mapping between the English vocabulary embeddings and the amino +acid embeddings. To do so, a protein property prediction task-specific loss is used to learn the optimal parameters +of the reprogrammed model. We train R2DL in a supervised setting with the downstream protein prediction task +datasets that are labeled and small in size (illustrated in Figure 1). R2DL demonstrates consistent performance +improvement from existing baselines across seven different physicochemical (e.g., up to 11% in stability), structural, +and functional property prediction (e.g., up to 3% in toxicity) tasks of proteins. We estimate R2DL to be over 105 +times more data-efficient than existing pretraining methods. We further demonstrate the performance robustness +of R2DL when trained on a reduced size version of the supervised protein datasets. In addition, we show that that +R2DL learns to encode physicochemical and biomedical properties in the learned representations, even in a limited +data scenarios. This work thus blazes a path toward efficient and large-scale adaptation of existing foundation models +toward different real-world learning tasks and accelerates scientific discovery, which naturally involves learning from +limited real-world data. +Results +Figure 2 illustrates the proposed Representation Reprogramming via Dictionary Learning (R2DL) framework, which +learns to embed a protein sequence dataset of interest by training on the representations of a transformer that is +pretrained on an English text corpus. A one-to-one label mapping function is assigned for each downstream protein +prediction task for cross-domain machine learning, and a class label or a regression value is predicted using R2DL for +each protein sequence during testing. Below we discuss details of the general framework (tasks described in Figure 1). +R2DL Framework Formulation +The R2DL objective is to reprogram a source model (pretrained language model) to be able to correctly classify, +or predict the regression values of, protein sequences (for a target prediction task). We use pretrained instances +of BERT, a bidirectional transformer (termed the source model), which has been finetuned separately for different +language tasks (e.g., sentiment classification, named entity recognition) [10; 22]. For a protein sequence classification +task, we use the source model trained on a language task for which there are n sentence output classes (e.g., positive +and negative for senitiment classification), and n protein sequence classes (e.g., toxic, non-toxic). The output-label +mapping h is then a simple 1-1 correspondence between the source task labels and the target task labels (e.g., positive +→ toxic and negative → non-toxic). For a regression task, R2DL uses a mapping between the regression values in +protein sequence feature space and the classification probability values in the source model embedding space. It does +so by learning optimal thresholds of regression values that map to the source model class labels. +3 + +Domain Data Construction +Token Mapping and Dictionary Learning +3 +Task Specific Training +& Embedding Extraction +source model: +reprogrammed +source +pretrained classifier +amino acid +model +tokens +label +[ positive +→ toxic +SOURCE DOMAIN: +mapping +negative ++ non-toxic +English Vocabulary +Vt1 +Approximate Vt = θVs +Vt2 +"I'm" +"going" +"to" +"the" +Vt3 +biological +property +extract +prediction +output: (positive, negative, neutral) +embeddings Vs +Nt xm +cross entropy loss minimization to +TARGET DOMAIN: +Target Vocabulary +Source Vocabulary +Biochemical Characters +Embedding Matrix (Vs) +update until convergence +Embedding Matrix (V-) +ARND +A +Vt1 +Vs1 +"'m" +Vr~e Vs +output: biological sequence +R +Vt2 +Vs2 +Task Specific Testing +properties (toxic, non-toxic) +Vt3 +Vs3 +"to" +"the" +Use optimized parameters θ* from (3 +D +: +axm +axb +bxmThe input data of the source English language model is tokenized at the word level. These tokens form the atoms +for our dictionary representation of VS, a matrix with its rows corresponding to embedding vectors of source tokens. +The input data to the target task, protein sequences, are tokenized on a character level with only 20 distinct tokens +(corresponding to the set of 20 discrete natural amino acid characters). R2DL obtains VS from the learned embeddings +of the source model and learns to represent VT , the matrix of the target token embedding, as a weighted combination +of the English token embeddings. We propose token reprogramming by approximating a linear mapping between VS +and VT . That is, we aim to find a transformation of the latent representation of the protein sequences, such that it +can be embedded in the pretrained language model’s latent space and enable R2DL to leverage these re-embedded +tokens for learning. Specifically, we learn the linear map Θ by approximating a dictionary using a k-SVD solver [23]. +That is, we want to approximate VT = ΘVS. The k-SVD solver guarantees a task-specific level of sparsity in the +coefficients when linearly combining English token embeddings to represent a protein sequence token embedding. In +other words, it helps select k English tokens and use their linearly combined embeddings as the embedding of a target +token. Additionally, with a one-to-one label mapping function of the protein sequence label to the English text label, +we are able to use the pretrained language model for inference on the embedded protein dataset, VT . We thus design +an end-to-end reprogramming framework for any arbitrary protein sequence classification or regression task. +R2DL Training and Optimization Procedure +We are given a pretrained classifier, C (which has been pretrained on a source-task dataset with source tokens denoted +by {vSi}|VS| +i=1 ) and a target-task dataset with target tokes denoted by {VT j}|VT | +j=1 . The embedding matrices are VS and +VT respectively. We can encode an output label mapping function translating between source and target labels. In +Figure 2, we show how R2DL aims to find a linear mapping function Θ that learns the optimal coefficients for our +atoms in VT to be represented as a sparse encoding of the dictionary VS such that VT = ΘVS. The map Θ is used to +reprogram C to be able to correctly classify the protein sequences through the transformation h(C(θt, t)) where t +is a protein sequence from a protein task and θt is the linear weights associated with the protein sequence t in Θ. +We note that for each of the downstream protein property prediction task, R2DL only trains a corresponding token +mapping function Θ while keeping the pretrained classifier C intact. Therefore, the number of trainable parameters in +R2DL is simply the size of the matrix Θ, which is usually much smaller compared to the number of parameters in the +pretrained deep neural network classifier C. To approximate the dictionary, we use a k-SVD solver to optimize over +the cross entropy loss for updates to Θ. We then apply the assigned label mapping h for protein classification tasks, +or thresholding for regression tasks, and train the mapping function Θ using gradient-based optimization evaluated +on the task-specific cross-entropy loss. Details for R2DL training procedure are given in the Method section. +Benchmark Tasks and Evaluation +We consider four physicochemical structure and property prediction tasks from a well-established protein benchmark +from [6] (represented in Figure 1). Secondary structure prediction involves predicting secondary structure y ∈ +{Helix, Strand, Other} for each amino acid x in a given protein sequence. Solubility prediction considers mapping an +input protein sequence x to a label of y ∈ {Membrane-Bound, Water Soluble}. Homology detection is a sequence +classification task, where each input protein x is mapped to a label y ∈ {1, ..., 1195}, representing different possible +protein folds. Stability prediction is a regression task. We further consider three biomedically relevant function +prediction tasks, which are sequence classification tasks (represented in Figure 1). Using R2DL, we predict for +a given sequence x, its binary class label y ∈ {AMP, non-AMP} for antimicrobial-nature prediction [3] or y ∈ +{Toxic, non-Toxic} for toxicity prediction [3]. Finally, we predict antigen and non-specific binding of antibody variant +sequences from [14]: given a sequence x, the task is to predict y ∈ {on-target, off-target}. Further details on the +protein tasks and datasets are in the Method section. The sizes of the individual datasets vary between 4,000 and +50,000 (see supplementary for details on data sizes and train-test splits). Data efficiency is defined as the ratio of the +R2DL prediction accuracy to the number of biological sequences used during pretraining and finetuning. We use +data efficiency as a metric to compare the performance of R2DL to established benchmarks for the protein tasks +in [6; 3; 14]. For classification tasks, we evaluate prediction accuracy with a top-n accuracy, where n is the number +of classes in the protein sequence classification task. For regression tasks, we evaluate prediction accuracy with +Spearman’s correlation. +Model Baselines and Data +The baseline models we consider in this work are of two types. Firstly, we consider models trained in a supervised +manner, by training standard sequence Long Range Short Term Memory (LSTM) models from scratch. For each +downstream peptide or protein classification task, we have labeled (supervised) datasets. The results of these models +are reported in Figure 3(a). Secondly, we consider models that are pretrained in an unsupervised manner on protein +sequence data and are fintuned for a particular downstream task. Pretraining methods that do not use labeled data +4 + +pose an advantage, as those models can then learn from a significantly larger number of data samples. In the cases of +the toxicity and antimicrobial prediction tasks, the baseline model we compare to has been pretrained on a subset of +the UniProt database where sequences are limited to being 50 residues long [24]. The pretraining corpus size is then +1.7 million peptide sequences. Using unlabeled data for pretraining is thus much more advantage than pretraining +in a supervised scheme. Of these 1.7 million sequences, only 9,000 are labeled (0.005% of sequences). The model +is a Wasserstein Autoencoder, which is a generative model that undergoes unsupervised pretraining on the subset +of UniProt data. The WAE embeddings of the labeled sequences are then used to train a logistic regressor model +on the labeled dataset to obtain a binary classifier for Antimicrobial/non-Antimicrobial (6489 labeled samples) or +for toxic/non-toxic (8153 labeled samples) label prediction. For the physicochemical property prediction tasks, the +baseline model we consider is pretrained on the Pfam corpus [25]. This corpus consists of 31 million protein domains +and is widely used in bioinformatics pipelines. Sequences are grouped by protein families which are categorized by +evolutionarily-related sequences. In contrast, the downstream physicochemical tasks of structure, homology, stability +and solubility prediction have labeled datasets that range from 5,000 to 50,000 samples which the model can be +finetuned on. Pretraining thus poses the advantage of modeling the density over a range of protein families and +structures, but stipulates that there must be sequence datasets that contain structural and functional information +about the downstream task datasets, and typically be of a size on the order of millions of sequences. R2DL eliminates +this requirement by repurposing existing pretrained English language models, and leveraging transferrable information +from models that are not conditioned on protein sequence information. +Data Efficiency and Accuracy of Reprogramming +We report the performance of R2DL for the set of 7 protein predictive and their corresponding baselines in Figure 3. +Baselines for the physicochemical prediction tasks are established by a transformer from [6] that has been pretrained +in an unsupervised setting on the Pfam pretraining corpus [26]. Baselines for the antimicrobial and toxicity prediction +tasks are established in [3], where Das et al. pretrained a Wasserstein Autoencoder on the peptides from the UniProt +corpus [24] using unsupervised training, and then used the latent encodings from autoencoder to train the property +classifiers. Baselines for the antibody affinity task are established in [14] where they train a linear discriminant +analysis model in a supervised setting. Each physicochemical and biomedical function prediction task then has a +relatively small, supervised dataset which we split into training and testing sets to train the R2DL framework and +evaluate its performance on the test set. Henceforth, we refer to these baselines as task-specific baselines, whereas the +baseline model we compare R2DL to varies with the downstream protein prediction task and the best performing +model available (see Supplementary for details on task-specific baselines). +We show that, for every prediction task we achieve a higher test accuracy with R2DL than with the corresponding +task-specific baseline model when both models are trained on the full labeled dataset. R2DL shows performance +improvement up to 11.2% when compared to the pretrained models, and up to 29.3% performance when compared to +a standard, supervised LSTM that is trained from scratch on the same dataset. However, R2DL needs a pretrained +source model and only a small-sized, labeled protein sequence dataset as the input. And, therefore the size of R2DL +training set is limited to the number of samples in the downstream protein prediction dataset. Pretrained models +require a large amount of protein sequence data for pretraining, on the order of 106 samples, in addition to the +downstream supervised protein task sequence data that the pretrained model is fine-tuned on. In Figure 3(a), we +show the number of training samples and corresponding accuracy metric (see Method section for details) of the +R2DL, pretrained, and supervised models. In Figure 3(b), we show the data efficiency, i.e., the ratio of the number +of training samples (including the pretraining corpus only of biological sequences for pretrained source models) to +the accuracy of the model for R2DL and baseline models. We show that R2DL is a maximum of 104 times more +data efficient, as in the case of the toxicity prediction task. This is due to the very large number of pretraining data +samples required relative to the downstream protein task dataset. +Figures 3(c) and 3(d) show the R2DL performance on the antigen affinity prediction task for antibody variant +sequences and its comparison with the baseline LDA model reported in [14]. R2DL achieves a higher predictive +accuracy than the baseline LDA model by 3% and with a higher classification accuracy with imbalanced datasets. +The antibody affinity task dataset has the following distribution on target: 1516, off-target: 2484. For 37% to 62% +class-imbalance ratio of labels, we show that the R2DL model has a better classification accuracy than the LDA +model. The learned representations can therefore be inferred to be more accurate in our model than in the baseline +model. This is important, as in many real-world prediction tasks, the dataset is found to be class-imbalanced. +R2DL Performance vs. Pretraining Performance in Low Data Settings +Motivated by the data efficiency of R2DL as a framework, we tested the task-specific predictive performance of R2DL +in reduced-data training settings. We compared these results to the performance of task-specific baseline models, +when trained and tested in the same restricted data setting. In Figure 4, we show the performance of the R2DL model +and then baseline model when trained on 100%, 80%, 60%, and 40% of a specific task dataset. We show results for +5 + +(a) Downstream supervised protein task dataset sizes and test accuracy +of the 3 comparable methods introduced in Figure 1. +(b) Data efficiency of R2DL vs. pretrained methods as +illustrated in Figure 1. +(c) Confusion matrix of the baseline model trained in [14] +for the antibody affinity prediction task. +(d) Confusion matrix of the R2DL model for the antibody +affinity prediction task. +Figure 3: Task-specific evaluation of R2DL performance compared to the performance of the baseline models. In +Figure 3(a), results for the pretrained baseline models are from unsupervised pretrained transformers for secondary +structure, stability, homology, and solubility prediction tasks [6]. The baseline models for the antimicrobial and toxicity +prediction tasks are logistic regressors trained using sequence embeddings from the pretrained peptide wassertein +variational autoencoder [3]. Results for the supervised classifiers are from sequence-level LSTMs trained from scratch +on the downstream protein prediction data. For classification tasks, we evaluate prediction accuracy with a top-n +accuracy, where n is the number of classes in the protein sequence classification task. For regression tasks, we evaluate +prediction accuracy with Spearman’s correlation coefficient. Results of the pretrained models on the antibody task +dataset have not been previously reported in any work and are hence left out for future work. In 3(b), Data efficiency +is defined as the ratio of the R2DL prediction accuracy to the number of protein sequences used during training. +In Figure 3(c)-(d), we show a comparison between the performance of a linear discriminant analysis (LDA) model +in [14] and R2DL on the antibody affinity dataset. The LDA model is a binary classifier which finds the optimal +classification boundary by projecting the data onto a one-dimensional feature space and finding a threshold. The +antibody affinity dataset consists of 4,000 labeled protein sequences, with labels {1 (on-target binding), 0 (off-target +binding)}. R2DL achieves a predictive accuracy of 95.5% compared to the LDA model performance of 92.8%. +the Antimicrobial, Toxicity, Secondary Structure, Stability, Homology, and Solubility prediction tasks in Figure 4 and +compare the performance of R2DL and pretrained models against the performance of a random guess. We observe, +that for downstream tasks of Toxicity, Secondary Structure, Homology and Solubility, R2DL always performs better +than a pretrained protein language model across the size range of the limited datasets. Furthermore, we observe that, +except in the stability task, the rate of failure to perform better than a random guess is higher for the pretrained +6 + +Protein +R2DL +Pretraining +Supervised +Downstream +Training +Accuracy +Training +Accuracy +Training +Task +Efficiency +Efficiency +Accuracy +Efficiency +Samples +Samples +Samples +Secondary +8678 +0.841 +9.70E-05 +3.10E+07 +0.801 +2.58E-08 +8678 +0.623 +7.18E-05 +Structure +Stability +21446 +0.849 +3.96E-05 +3.10E+07 +0.738 +2.38E-08 +21446 +0.660 +3.08E-05 +Homology +12312 +0.241 +1.96E-05 +3.10E+07 +0.265 +8.56E-09 +12312 +0.245 +1.99E-05 +Solubility +16253 +0.943 +5.80E-05 +1.70E+06 +0.872 +5.13E-07 +16253 +0.856 +5.27E-05 +Antibody Affinity +4000 +0.9456 +2.36E-04 +4000 +0.928 +2.32E-04 +Antimicrobial +6489 +0.900 +1.39E-04 +1.70E+06 +0.883 +5.19E-07 +6489 +0.874 +1.35E-04 +Toxicity +8153 +0.961 +1.18E-04 +1.70E+06 +0.937 +5.51E-07 +8153 +0.689 +8.45E-05Antimicrobial +Method +Pretrained +Toxicity +R2DL +Secondary +Task +Structure +Stability +Homology +Solubility +10°° +8- +10 +-7 +10 +10 +10 +-4 +10 +-3 +(Log Scale) Efficiency = +Accuracy +#TrainingSamples400 +0 +415 +64 +True label +300 +200 +1 +60 +461 +100 +0 +1 +Predictedlabel +False Negative +60 +False Positive RateLDA = +:11.5% +False Negatives + True Positives +60 + 461 +True Positives +461 +True Positive RateLDA = +88.4 % +False Negatives + True Positives +60 + 461400 +0 +494 +6 +True label +300 +200 +1 +27 +473 +100 +0 +1 +Predictedlabel +False Negative +27 +False Positive RateR2DL = +: 5.4% +False Negatives + True Positives +27 + 473 +True Positives +473 +True Positive RateR2DL = += 94.6 % +False Negatives + True Positives +27 + 473(a) Secondary structure prediction. +(b) Mutational stability prediction. +(c) Remote homology prediction. +(d) Membrane solubility prediction. +(e) Antimicrobial-nature prediction. +(f) Toxicity prediction. +Figure 4: Results of the R2DL model and baseline model for each downstream task in reduced training data settings. +models than for R2DL. In both cases, R2DL outperforms pretraining until the cutoff point that is the intersection +of the random guess curve with the accuracy curves (the point at which the model is not learning any meaningful +representation). +Correlation Between Learned Embeddings and Evolutionary Distances +Beyond comparing the R2DL model against the individual protein task benchmarks, we demonstrate that the R2DL +dictionary learning framework shows interpretable correspondences between the learned embeddings in the latent +space and the specific protein property. We show this result for the antibody affinity, secondary structure, and +toxicity prediction tasks. Figures 5(a-c) show the t-SNE projection of task-specific R2DL embeddings VT = ΘVS of +protein sequences for secondary structure, toxicity, and antibody affinity prediction tasks. Clear separation between +different protein classes is evident. We further calculate the similarity between the euclidean distance between the +latent representation at the last layer for each amino acid embedding, and compare it to the pairwise evolutionary +distance with the BioPython module. In Figure 5(d), we show the euclidean distances between the latent embeddings +learned in the R2DL model and the pairwise evolutionary distances between protein sequences, as estimated using +BLOSUM62 matrix implemented in the pairwise function of BioPython modulde. +The matrix shows a correlation of close to 1.0 along the diagonal showing a perfect correspondence between the +learned representation and the empirical observations of amino acid relatedness. R2DL thus captures the underlying +structure of the linear sequence of amino acid residues in protein sequences in the context of the protein task +reprogrammed. +Discussion +We propose a new framework, R2DL, to reprogram large language models for various protein tasks. R2DL demonstrates +powerful predictive performance across tasks that involve evolutionary understanding, structure prediction, property +prediction and protein engineering. We thus provide a strong alternative to pretraining large language models on +upto 106 protein sequences. With only a pretrained natural language model (which are abundantly available at the +time of writing), a small-sized labeled protein data set of interest, and a small amount of cross-domain finetuning, we +can achieve better performance for each protein prediction task with interpretable correspondences between features. +7 + +Solubility +100 +80 +Test Accuracy +60 +40 +20 +0 +40 +60 +80 +100 +%ofOriginalTrainingDataAntimicrobial +100 +80 +Test Accuracy +60 +40 +20 +0 +40 +60 +80 +100 +%of Original Training DataToxicity +100 +80 +Test Accuracy +60 +40 +20 +0 +40 +60 +80 +100 +%ofOriginalTrainingDataSecondaryStructure +100 +80 +Test Accuracy +60 +40 +20 +0 +0 +25 +50 +75 +100 +%ofOriginalTrainingDataStability +100 + Spearman Correlation +80 +60 +40 +20 +0 +40 +60 +80 +100 +%ofOriginalTrainingDataHomology +100 +R2DLAccuracy +Pretrained +Spearman Correlation +80 +Random Guess +60 +40 +20 +0 +40 +60 +80 +100 +% of Original Training Data(a) t-SNE clustering plot for secondary structure predic- +tion. +(b) t-SNE clustering plot for toxicity prediction. +(c) t-SNE plot for antibody affinity prediction. +(d) Correlation plot for pairwise evolutionary distances vs. pair- +wise euclidean distances in R2DL embeddinng space for antibody +affinity prediction. +Figure 5: (a-c) Clustering of R2DL learned embeddings for secondary structure prediction, toxicity prediction, and +antibody affinity prediction tasks. When tagged by protein property classification, we see very high correspondence +between the clusters and protein sequences with the same physicochemical or biomedical property classification. (d) +For the antibody affinity prediction task, we observe a high correlation coefficient along the diagonal. This shows that +the representation learned by R2DL is highly similar to empirical observations of pairwise residue correlations. +Beyond improvements in predictive performance, we show that the ratio of performance improvements to pretraining +and training samples involved in the R2DL framework make R2DL up to 105 times more data-efficient than any +current methods. This work opens many doors to biological prediction tasks that can acquire very few labeled, high +quality data samples. We emphasize the results of the data-efficiency of R2DL, when applied to biomedically relevant +protein predictions, which are critical to advancing scientific understanding and discovery, but have been unsuccessful +until now. +While R2DL does make gradient updates in the framework, the data and resource requirements of the R2DL +method is much lower than any unsupervised or self-supervised pretraining approach for protein sequence modeling. +Though R2DL has the same data and resource requirements as any standard supervised training approach, R2DL +demonstrates much higher task accuracy across a broad and diverse range of property prediction tasks. We claim +that R2DL is able to do this because it can leverage the deep representational capacity induced by reprogramming, +which standard supervised models cannot achieve without an unjustifiably large number of parameters. R2DL is +thus more efficient than existing baseline models in the following aspects: (i) R2DL only requires a pretrained +transformer (trained on English language data) and a small-sized, labeled protein sequence data set of interest. We +do not make any updates to the pretrained model itself, unlike traditional transfer learning methods. Rather we +make updates to the R2DL model during a supervised training process that optimizes over class-mapped labels. (ii) +R2DL does not require large-scale un/self-supervised pretraining on millions of unlabeled protein sequences, as in +[6; 3; 5]. (iii) Further, R2DL does not require any large-scale supervised pretraining, which has been found beneficial +in protein-specific tasks [6] as well as in computer vision [27]. Labeling protein sequences at scale, particularly for +biomedical function, is almost infeasible for the size of dataset that is required for supervised pretraining. With +these three considerations in mind, we pose R2DL as a data-efficient alternative to pretraining methods for protein +prediction tasks of biological and biomedical relevance. To the best of our knowledge, R2DL is the first framework +8 + +40 +Helix +Strand +Other +20 +comp-2 +0 +-20 +-40 +-80 +-60 +-40 +-20 +0 +20 +40 +comp-1Toxic +Non-Toxic +40 +20 - +Z-dwon +-20 +-40 +-40 +-30 +-20 +-10 +0 +10 +20 +30 +40 +comp-160 +Binding +Non-Binding +40 +20 - +comp-2 +0 +-20 +-40 +-60 +-40 +-20 +0 +20 +40 +comp-1NYDGFOAEIWSTVCKMHLPR +N +1.0 +Y +D +G +0.8 +F +Q +A +E +0.6 +1 +W +s +T +0.4 +v +C +K +M +0.2 +H +L +P +R +0.0without explicit pretraining that facilitates accurate predictions across a general suite of protein prediction tasks +and provides interpretable correspondences between amino acid features that are very closely aligned with domain +knowledge (evolutionary distances). The success of R2DL can be attributed to its representational power to encode +a sparse representation by leveraging the natural language modeling entailed in large language models for efficient +learning on protein structure and function prediction tasks, as both English and protein sequences follow Zipf’s law [16]. +We first demonstrate the effectiveness of R2DL on a set of physicochemical structure and property prediction +tasks, and then on a set of biomedically relevant function prediction tasks, for protein sequences. We show predictive +performance improvements against pretrained methods (up to 11% in stability) and standard supervised methods +(up to 3.2% in antibody affinity). Similarly, on the remaining tasks, we show performance improvements over the +best reported baseline in structure prediction (4.1%), homology (2.3%), solubility (7.1%), antibody affinity (3.2%), +toxicity (2.4%). R2DL thus shows the capability to learn a general representation of protein sequences that can be +efficiently adopted to different downstream protein tasks. These powerful representation capabilities as evidenced by +its ability to achieve high performance across protein datasets with a highly varied number of task-specific training +samples. The performance of R2DL across protein tasks show the potential to repurpose and develop powerful models +that can learn from small, curated, and function-specific datasets. This mitigates the need to train large pretrained +models for peptide learning tasks. We thus provide an alternative method to pretraining that is cheaper to run and +more accurate, and therefore adoptable to broader researcher communities who may not have access to large-scale +compute. This potential is critical for many applications, such as discovery of new materials, catalysts, as well as +drugs. Although we establish the efficacy and efficiency of R2DL in a domain where pretrained large language models +already do exist, we hope that our work will pave the path to extending this approach to other domains where +pretrained LLMs do not exist, such as polymers. +Method +Representation of Tokens +In the R2DL framework, we use 2 input datasets, an English language text dataset (source dataset) and a protein +sequence dataset (target dataset). The vocabulary size of a protein sequence dataset at a unigram level is 20, as +proteins are composed of 20 different natural amino acids. We obtain a latent representation of the English text +vocabulary, VS, by extracting the learned embeddings of the data from a pretrained language model (source model). +The protein sequence data is embedded in the same latent space, and is termed the target vocabulary, VT . For each +task, the token embedding matrix is of dimensions (n, m) where n is the number of tokens and m is the length of the +embedding vectors. We use the same encoding scheme of VS and VT across all downstream tasks. +Procedure Description of the R2DL Framework for a Protein Task +• Procedure Inputs: Pretrained English sentence classifier C, target model training data Xℓ for task ℓ, class +mapping label function, hℓ (if classification) where +ℓ ∈ {Secondary Structure, Fluorescence, Homology, Solubility, Antimicrobial, Toxicity, Antibody}. +• Procedure Hyperparameters: Maximum number of iterations T1 for updates to Θ, number of iterations T2 +for k-SVD, step size {αt}T1 +t=1 +• Procedure Initialization: Random initialization of Θ, obtain the source token embedding matrix VS +• Define Objective Function: Objective function for k-SVD: ∥VT − ΘVS∥ ≤ ϵ +• k-SVD Approximation of Θ: If t1 ≤ T1, while t2 ≤ T2 use approximate k-SVD to solve VT ≈ ΘVS, +t2 ←− t2 + 1 +• Calculate the Loss and Perform Gradient Descent: Θ ←− Θ − αt · ∇ΘLoss(Θ, Xℓ, hℓ, C) , t1 ←− t1 + 1 +and return to the previous K-SVD step +• Output Protein Sequence Labels for Protein Sequence x of Task ℓ: hℓ(C(Θ, x)) +We are given a pretrained English classifier, C, and a protein sequence target-task dataset Xℓ. We denote the task +with ℓ, such that ℓ ∈ {Secondary Structure, Fluorescence, Homology, Solubility, Antimicrobial, Toxicity, Antibody}. +We also encode an output label mapping function hℓ specifying the one-to-one correspondence between source and +target labels. As shown in Figure 2, the source vocabulary embedding, VS, is extracted from the pretrained model, +C. The next objective is to learn Θ that approximates the embedding of tokens in Xℓ (denoted by VT ) in the +representation space of the source model. +9 + +We aim to learn Θ ∈ Ra×b that finds the optimal coefficients {θt} for each of the target tokens t ∈ {1, ..., a} +in VT ∈ Ra×m to be represented as a sparse encoding of the dictionary, VS ∈ Rb×m, such that VT = ΘVS. For a +given target protein sequence x from the ℓ-th task, Θ is used to perform the target task through the transformation +hℓ(C(Θ, x)). While we do not make any modification to the parameters or architecture of C, we assume access to the +gradient ∇Θloss(·) for loss evaluation and parameter updates during training. +A target token embedding vt ∈ Rm can be represented as a sparse linear combination of the source token +embeddings (rows) in VS, vt = θtVs. vt is the representation of the protein token in the dictionary space and satisfies +||vt − θtVs||p ≤ ϵ, where ∥ · ∥p is an Lp norm and θt is made to be sparse by satisfying ||θt||0 ≤ k for all t. An +exact solution vt = θtVS is computationally expensive to find, and is subject to various convergence traps, so for +the purpose of our efficient fine-tuning approach we approximate vt ≈ θtVS using k-SVD. We first fix the dictionary +VS, as extracted from C, and then find the optimal Θ according to the optimization problem, by minimizing the +alternative objective �a +t=1 ||θt||0 subject to ∥VT − ΘVS∥2 +F ≤ ϵ as explored in [23]. While algorithms exist to choose +an optimal dictionary (an exact solution to k-SVD) that can be continually updated [23], we penalize computational +expense over performance for the purpose of maintaining an efficient solution (at the cost of statistically insignificant +improvements in accuracy) by using a predetermined number of iterations for k-SVD convergence, which is then used +to evaluate the cross entropy loss on hℓ(C(Θ, x)) and update the mapping function Θ. +Data +Classification +We provide five biologically relevant downstream physicochemical property prediction tasks, adapted from [6] to serve +as benchmarks. We categorize these into property prediction, structure prediction, evolutionary understanding, and +protein engineering tasks. The sizes of the individual datasets vary between 4,000 and 50,00 (see supplementary for +details on data sizes and train-test splits). +Secondary Structure Prediction (Structure Task): Secondary structure (SS) is critical to understanding +the function and stability of a protein, and SS prediction is an important intermediate step in designing designing +protein complexes. This dataset, obtained from [28] has 8,678 data samples. It is derived from the CB513 dataset, +and each amino acid, x in a protein sequence is mapped to y ∈ {Helix, Strand, Other}. The benchmark for this task +is a transformer that reports a best performance of 80% accuracy. +Solubility: This task takes an input protein x and maps it to a label of y ∈ {Membrane-Bound, Water Soluble}. +Determining the solubility of proteins is useful when designing proteins or evaluating their function for particular +cellular tasks. This dataset, obtained from [29] has 16,253 data samples. The benchmark is a pretrained transformer, +that achieves a best performance of 91% on a binary classification task. +Antigen Affinity (Protein Engineering): Therapeutic antibody development requires the selection and +engineering of molecules with high affinity and other drug-like biophysical properties. This dataset, obtained from +[14] has 4,000 data samples. The task is to map an input protein x to a label y ∈ {on-target, off-target}. The task +corresponds to predicting antigen and non-specific binding. The benchmark for this task is a Linear Discriminant +Analysis model with Spearman’s ρ values for antigen binding (0.87) and for non-specific binding (0.67). +Antimicrobial Prediction (AMP) (Property Task): Determining the antimicrobial nature of a peptide is a +critical step in developing antimicrobials to fight against resistant pathogens. The dataset, obtained from [3], consists +of 6,489 labeled protein sequences x, is mapped to a label y ∈ {AMP, non-AMP}. The original model trained on this +data provides a de novo approach for discovering new, broad-spectrum and low-toxic antimicrobials. The benchmark +for this task is a transformer that reports a best performance of 88% accuracy with a pretrained classifier. +Toxicity (Property Task): Improving the functional profile of molecules, especially in the context of drug +discovery, requires optimizing for toxicity and other physicochemical properties. To that end, toxicity is an important +property to predict in AMP development. This dataset, obtained from [3] consists of 8,153 antimicrobial peptide +sequences which are either toxic (positive class), or non-toxic (negative class). The benchmark for this task is a +transformer that reports a best performance of 93.78% accuracy with a pretrained classifier. +Regression +Stability (Protein Engineering Task): This regression task where each protein, xi is mapped to yi ∈ R based on +maintaining its fold beyond a threshold of concentration. This dataset, obtained from [30] has 21,446 data samples. +Stability is an important protein engineering task, as we can use this fold concentration to test protein inputs such +10 + +that design candidates are stable in the settings of different tasks. The benchmark for this task is a transformer that +reports a best performance of 0.73 Spearman’s ρ. +Homology (Evolutionary Understanding Task): This is a sequence classification task where each input +protein, x is mapped to a protein fold represented by y ∈ {1, ..., 1195}. This dataset, obtained from [31] has 12,312 +data samples. Detecting homologs is particularly important in a biomedical context as they inform structural similarity +across a set of sequences, and can indicate emerging resistance of antibiotic genes [cite]. The original model removes +entire homologous groups during model training, thereby enforcing that models generalize well when large evolutionary +gaps are introduced. The benchmark for this task is a LSTM that reports a best performance of 26% Top-1 Accuracy. +R2DL Settings and Hyperparameter Details +AMP +The full AMP dataset size is 8112, we use a training set size of 6489 and a test set size of 812. We use the L0 norm in +our objective function, 10,000 k-SVD iterations and ϵ = 0.045. +Toxicity +The full Toxicity dataset size is 10,192, we use a training set size of 8153 and a test set size of 1020. We use the L0 +norm in our objective function, 10,000 k-SVD iterations and ϵ = 0.045. +Secondary Structure +The full Toxicity dataset size is 9270, we use a training set size of 7416 and a test set size of 1854. We use the L0 +norm in our objective function, 9,000 k-SVD iterations and ϵ = 0.38. +Stability +The full Stability dataset size is 56,126, we use a training set size of 44,900 and a test set size of 11,226. We use the +L0 norm in our objective function, 6,000 k-SVD iterations and ϵ = 0.29. +Homology +The full Homology dataset size is 13,048, we use a training set size of 10,438 and a test set size of 2,610. We use the +L0 norm in our objective function, 4,000 k-SVD iterations and ϵ = 0.73. +Solubility +The full Solubility dataset size is 43,876, we use a training set size of 35,100 and a test set size of 8,775. We use the +L0 norm in our objective function, 9,000 k-SVD iterations and ϵ = 0.42. +Data and Code Availability +Links to protein sequence data and code are available on Github (github.com/riavinod/r2dl) +11 + +References +[1] J. Jumper, R. Evans, A. Pritzel, T. Green, M. Figurnov, O. Ronneberger, K. Tunyasuvunakool, R. Bates, +A. Žídek, A. Potapenko, et al., “Highly accurate protein structure prediction with alphafold,” Nature, vol. 596, +no. 7873, pp. 583–589, 2021. +[2] M. Baek, F. DiMaio, I. Anishchenko, J. Dauparas, S. Ovchinnikov, G. R. Lee, J. Wang, Q. Cong, L. N. Kinch, +R. D. Schaeffer, et al., “Accurate prediction of protein structures and interactions using a three-track neural +network,” Science, vol. 373, no. 6557, pp. 871–876, 2021. +[3] P. Das, T. Sercu, K. Wadhawan, I. Padhi, S. Gehrmann, F. Cipcigan, V. Chenthamarakshan, H. Strobelt, +C. Dos Santos, P.-Y. Chen, et al., “Accelerated antimicrobial discovery via deep generative models and molecular +dynamics simulations,” Nature Biomedical Engineering, vol. 5, no. 6, pp. 613–623, 2021. +[4] J. M. Stokes, K. Yang, K. Swanson, W. Jin, A. Cubillos-Ruiz, N. M. Donghia, C. R. MacNair, S. French, L. A. +Carfrae, Z. Bloom-Ackermann, et al., “A deep learning approach to antibiotic discovery,” Cell, vol. 180, no. 4, +pp. 688–702, 2020. +[5] J. Meier, R. Rao, R. Verkuil, J. Liu, T. Sercu, and A. Rives, “Language models enable zero-shot prediction +of the effects of mutations on protein function,” Advances in Neural Information Processing Systems, vol. 34, +pp. 29287–29303, 2021. +[6] R. Rao, N. Bhattacharya, N. Thomas, Y. Duan, P. Chen, J. Canny, P. Abbeel, and Y. Song, “Evaluating protein +transfer learning with tape,” Advances in neural information processing systems, vol. 32, 2019. +[7] E. Nijkamp, J. Ruffolo, E. N. Weinstein, N. Naik, and A. Madani, “Progen2: Exploring the boundaries of protein +language models,” 2022. +[8] R. Bommasani, D. A. Hudson, E. Adeli, R. Altman, S. Arora, S. von Arx, M. S. Bernstein, J. Bohg, A. Bosselut, +E. Brunskill, et al., “On the opportunities and risks of foundation models,” arXiv preprint arXiv:2108.07258, +2021. +[9] B. Yuan, Y. He, J. Q. Davis, T. Zhang, T. Dao, B. Chen, P. Liang, C. Re, and C. Zhang, “Decentralized training +of foundation models in heterogeneous environments,” arXiv preprint arXiv:2206.01288, 2022. +[10] J. Devlin, M.-W. Chang, K. Lee, and K. Toutanova, “Bert: Pre-training of deep bidirectional transformers for +language understanding,” arXiv preprint arXiv:1810.04805, 2018. +[11] D. Patterson, J. Gonzalez, Q. Le, C. Liang, L.-M. Munguia, D. Rothchild, D. So, M. Texier, and J. Dean, “Carbon +emissions and large neural network training,” arXiv preprint arXiv:2104.10350, 2021. +[12] C. Raffel, N. Shazeer, A. Roberts, K. Lee, S. Narang, M. Matena, Y. Zhou, W. Li, P. J. Liu, et al., “Exploring +the limits of transfer learning with a unified text-to-text transformer.,” J. Mach. Learn. Res., vol. 21, no. 140, +pp. 1–67, 2020. +[13] T. Wolf, L. Debut, V. Sanh, J. Chaumond, C. Delangue, A. Moi, P. Cistac, T. Rault, R. Louf, M. Funtowicz, +J. Davison, S. Shleifer, P. von Platen, C. Ma, Y. Jernite, J. Plu, C. Xu, T. L. Scao, S. Gugger, M. Drame, +Q. Lhoest, and A. M. Rush, “Huggingface’s transformers: State-of-the-art natural language processing,” 2019. +[14] E. K. Makowski, P. C. Kinnunen, J. Huang, L. Wu, M. D. Smith, T. Wang, A. A. Desai, C. N. Streu, Y. Zhang, +J. M. Zupancic, et al., “Co-optimization of therapeutic antibody affinity and specificity using machine learning +models that generalize to novel mutational space,” Nature communications, vol. 13, no. 1, pp. 1–14, 2022. +[15] F. Zhuang, Z. Qi, K. Duan, D. Xi, Y. Zhu, H. Zhu, H. Xiong, and Q. He, “A comprehensive survey on transfer +learning,” Proceedings of the IEEE, vol. 109, no. 1, pp. 43–76, 2020. +[16] M. E. Newman, “Power laws, pareto distributions and zipf’s law,” Contemporary physics, vol. 46, no. 5, pp. 323– +351, 2005. +[17] P.-Y. Chen, “Model reprogramming: +Resource-efficient cross-domain machine learning,” arXiv preprint +arXiv:2202.10629, 2022. +[18] P. Neekhara, S. Hussain, S. Dubnov, and F. Koushanfar, “Adversarial reprogramming of text classification neural +networks,” arXiv preprint arXiv:1809.01829, 2018. +[19] C.-H. H. Yang, Y.-Y. Tsai, and P.-Y. Chen, “Voice2series: Reprogramming acoustic models for time series +classification,” in International Conference on Machine Learning, pp. 11808–11819, PMLR, 2021. +12 + +[20] G. F. Elsayed, I. Goodfellow, and J. Sohl-Dickstein, “Adversarial reprogramming of neural networks,” arXiv +preprint arXiv:1806.11146, 2018. +[21] R. Bommasani, D. A. Hudson, E. Adeli, R. Altman, S. Arora, S. von Arx, M. S. Bernstein, J. Bohg, A. Bosselut, +E. Brunskill, E. Brynjolfsson, S. Buch, D. Card, R. Castellon, N. Chatterji, A. Chen, K. Creel, J. Q. Davis, +D. Demszky, C. Donahue, M. Doumbouya, E. Durmus, S. Ermon, J. Etchemendy, K. Ethayarajh, L. Fei-Fei, +C. Finn, T. Gale, L. Gillespie, K. Goel, N. Goodman, S. Grossman, N. Guha, T. Hashimoto, P. Henderson, +J. Hewitt, D. E. Ho, J. Hong, K. Hsu, J. Huang, T. Icard, S. Jain, D. Jurafsky, P. Kalluri, S. Karamcheti, +G. Keeling, F. Khani, O. Khattab, P. W. Koh, M. Krass, R. Krishna, R. Kuditipudi, A. Kumar, F. Ladhak, +M. Lee, T. Lee, J. Leskovec, I. Levent, X. L. Li, X. Li, T. Ma, A. Malik, C. D. Manning, S. Mirchandani, +E. Mitchell, Z. Munyikwa, S. Nair, A. Narayan, D. Narayanan, B. Newman, A. Nie, J. C. Niebles, H. Nilforoshan, +J. Nyarko, G. Ogut, L. Orr, I. Papadimitriou, J. S. Park, C. Piech, E. Portelance, C. Potts, A. Raghunathan, +R. Reich, H. Ren, F. Rong, Y. Roohani, C. Ruiz, J. Ryan, C. Ré, D. Sadigh, S. Sagawa, K. Santhanam, A. Shih, +K. Srinivasan, A. Tamkin, R. Taori, A. W. Thomas, F. Tramèr, R. E. Wang, W. Wang, B. Wu, J. Wu, Y. Wu, +S. M. Xie, M. Yasunaga, J. You, M. Zaharia, M. Zhang, T. Zhang, X. Zhang, Y. Zhang, L. Zheng, K. Zhou, and +P. Liang, “On the opportunities and risks of foundation models,” 2021. +[22] X. Jiao, Y. Yin, L. Shang, X. Jiang, X. Chen, L. Li, F. Wang, and Q. Liu, “Tinybert: Distilling bert for natural +language understanding,” arXiv preprint arXiv:1909.10351, 2019. +[23] M. Aharon, M. Elad, and A. Bruckstein, “K-svd: An algorithm for designing overcomplete dictionaries for sparse +representation,” IEEE Transactions on Signal Processing, vol. 54, no. 11, pp. 4311–4322, 2006. +[24] U. Consortium, “Uniprot: a worldwide hub of protein knowledge,” Nucleic acids research, vol. 47, no. D1, +pp. D506–D515, 2019. +[25] S. El-Gebali, J. Mistry, A. Bateman, S. R. Eddy, A. Luciani, S. C. Potter, M. Qureshi, L. J. Richardson, G. A. +Salazar, A. Smart, et al., “The pfam protein families database in 2019,” Nucleic acids research, vol. 47, no. D1, +pp. D427–D432, 2019. +[26] M. Punta, P. C. Coggill, R. Y. Eberhardt, J. Mistry, J. Tate, C. Boursnell, N. Pang, K. Forslund, G. Ceric, +J. Clements, et al., “The pfam protein families database,” Nucleic acids research, vol. 40, no. D1, pp. D290–D301, +2012. +[27] A. Dosovitskiy, L. Beyer, A. Kolesnikov, D. Weissenborn, X. Zhai, T. Unterthiner, M. Dehghani, M. Minderer, +G. Heigold, S. Gelly, et al., “An image is worth 16x16 words: Transformers for image recognition at scale,” arXiv +preprint arXiv:2010.11929, 2020. +[28] M. S. Klausen, M. C. Jespersen, H. Nielsen, K. K. Jensen, V. I. Jurtz, C. K. Soenderby, M. O. A. Sommer, +O. Winther, M. Nielsen, B. Petersen, et al., “Netsurfp-2.0: Improved prediction of protein structural features by +integrated deep learning,” Proteins: Structure, Function, and Bioinformatics, vol. 87, no. 6, pp. 520–527, 2019. +[29] J. J. Almagro Armenteros, C. K. Sønderby, S. K. Sønderby, H. Nielsen, and O. Winther, “Deeploc: prediction of +protein subcellular localization using deep learning,” Bioinformatics, vol. 33, no. 21, pp. 3387–3395, 2017. +[30] G. J. Rocklin, T. M. Chidyausiku, I. Goreshnik, A. Ford, S. Houliston, A. Lemak, L. Carter, R. Ravichandran, +V. K. Mulligan, A. Chevalier, et al., “Global analysis of protein folding using massively parallel design, synthesis, +and testing,” Science, vol. 357, no. 6347, pp. 168–175, 2017. +[31] J. Hou, B. Adhikari, and J. Cheng, “Deepsf: deep convolutional neural network for mapping protein sequences to +folds,” Bioinformatics, vol. 34, no. 8, pp. 1295–1303, 2018. +[32] G. F. Elsayed, I. Goodfellow, and J. Sohl-Dickstein, “Adversarial reprogramming of neural networks,” in +International Conference on Learning Representations, 2019. +[33] P. Neekhara, S. Hussain, S. Dubnov, and F. Koushanfar, “Adversarial reprogramming of sequence classification +neural networks,” 2019. +[34] S. J. Pan and Q. Yang, “A survey on transfer learning,” IEEE Transactions on Knowledge and Data Engineering, +vol. 22, no. 10, pp. 1345–1359, 2010. +[35] J. Devlin, M. Chang, K. Lee, and K. Toutanova, “BERT: pre-training of deep bidirectional transformers for +language understanding,” CoRR, vol. abs/1810.04805, 2018. +[36] A. Lauscher, O. Majewska, L. F. R. Ribeiro, I. Gurevych, N. Rozanov, and G. Glavaš, “Common sense or +world knowledge? investigating adapter-based knowledge injection into pretrained transformers,” arXiv preprint +arXiv:2005.11787, 2020. +13 + +[37] Y.-Y. Tsai, P.-Y. Chen, and T.-Y. Ho, “Transfer learning without knowing: Reprogramming black-box machine +learning models with scarce data and limited resources,” in International Coference on International Conference +on Machine Learning, 2020. +[38] N. Papernot, P. D. McDaniel, A. Swami, and R. E. Harang, “Crafting adversarial input sequences for recurrent +neural networks,” CoRR, vol. abs/1604.08275, 2016. +[39] Y. Bengio, A. C. Courville, and P. Vincent, “Unsupervised feature learning and deep learning: A review and new +perspectives,” CoRR, vol. abs/1206.5538, 2012. +[40] I. Goodfellow, H. Lee, Q. V. Le, A. Saxe, and A. Y. Ng, “Measuring invariances in deep networks,” in Advances +in Neural Information Processing Systems, pp. 646–654, 2009. +[41] P. Das, T. Sercu, K. Wadhawan, I. Padhi, S. Gehrmann, F. Cipcigan, V. Chenthamarakshan, H. Strobelt, C. d. +Santos, P.-Y. Chen, et al., “Accelerating antimicrobial discovery with controllable deep generative models and +molecular dynamics,” arXiv preprint arXiv:2005.11248, 2020. +[42] R. Vinod, P.-Y. Chen, and P. Das, “Reprogramming language models for molecular representation learning,” +2020. +[43] Z. Wu, B. Ramsundar, E. N. Feinberg, J. Gomes, C. Geniesse, A. S. Pappu, K. Leswing, and V. S. Pande, +“Moleculenet: A benchmark for molecular machine learning,” CoRR, vol. abs/1703.00564, 2017. +[44] T. Brown, B. Mann, N. Ryder, M. Subbiah, J. D. Kaplan, P. Dhariwal, A. Neelakantan, P. Shyam, G. Sastry, +A. Askell, et al., “Language models are few-shot learners,” Advances in neural information processing systems, +vol. 33, pp. 1877–1901, 2020. +[45] A. Elnaggar, M. Heinzinger, C. Dallago, G. Rihawi, Y. Wang, L. Jones, T. Gibbs, T. Feher, C. Angerer, +M. Steinegger, et al., “Prottrans: towards cracking the language of life’s code through self-supervised deep +learning and high performance computing,” arXiv preprint arXiv:2007.06225, 2020. +14 + +Supplementary Information +Protein Task +Source +Model +Source Task +Regression +or Classifica- +tion +Source +Labels +Target Labels +Antimicrobial +Transformer +Sentiment Classification +Classification +Positive, +Negative +AMP, non-AMP +Toxicity +Transformer +Sentiment Classification +Classification +Positive, +Negative +Toxic, non-Toxic +Secondary +Structure +Transformer +Sentiment Classification +Classification +Positive, +Neutral, +Negative +Helix, Strand, Other +Stability +Transformer +Sentiment Classification +Regression +- +- +Homology +Transformer +Sentiment Classification +Regression +- +- +Solubility +Transformer +Named Entity Recognition +Classification +Positive, +Negative +Soluble, non-Soluble +Binding +Transformer +Sentiment Classification +Classification +Positive, +Negative +On-target, Off-target +Table 1: Summary of the source and target tasks for reprogramming +Figure 6: Summary of protein prediction tasks and evaluation metrics with model performance. +Model Baselines +Table 2: Toxicity and Antimicrobial-nature reported in [3]. +Attribute +Data-Split +Accuracy +Train +Valid +Test +Majority Class +Test +{Toxic, non-Toxic} +8153 +1019 +1020 +0.82 +0.93 +{AMP, non-AMP} +6489 +811 +812 +0.82 +0.88 +R2DL Results +R2DL Results from the Reduced Training Data Setting +0.1 +Restricted Training Data Setting +To further investigate the efficacy of the transfer learning approach, we compare the performance of R2DL versus +the model trained from scratch with AMP data, with a restricted training data set. The test accuracy across tasks +15 + +Evaluation +R2DL +Pretraining +Supervised +Nature +Task +Metric +Training +Training +Training +Accuracy +Efficiency +Accuracy +Efficiency +Accuracy +Efficiency +Samples +Samples +Samples +Secondary +Physicochemical +top-n accuracy +8678 +0.841 +9.70E-05 +3.10E+07 +0.801 +2.58E-08 +8678 +0.623 +7.18E-05 +Structure +Spearman's +Physicochemical +Stability +correlation +21446 +0.849 +3.96E-05 +3.10E+07 +0.738 +2.38E-08 +21446 +0.660 +3.08E-05 +Homology +Spearman's +Physicochemical +12312 +0.241 +1.96E-05 +3.10E+07 +0.265 +8.56E-09 +12312 +0.245 +1.99E-05 +correlation +Physicochemical +Solubility +top-n accuracy +16253 +0.943 +5.80E-05 +1.70E+06 +0.872 +5.13E-07 +16253 +0.856 +5.27E-05 +Biomedical Function +Antibody Affinity +top-n accuracy +4000 +0.9456 +2.36E-04 +4000 +0.928 +2.32E-04 +Biomedical Function +Antimicrobial +top-n accuracy +6489 +0.900 +1.39E-04 +1.70E+06 +0.883 +5.19E-07 +6489 +0.874 +1.35E-04 +Biomedical Function +Toxicity +top-n accuracy +8153 +0.961 +1.18E-04 +1.70E+06 +0.937 +5.51E-07 +8153 +0.689 +8.45E-05Table 3: Structure prediction, Remote Homology, Stability reported in [6]. +Task +Model +Accuracy +Metric +Test Accuracy +Secondary Structure Prediction +One Hot + +Alignment +Accuracy +(3-class) +0.80 +Remote Homology Detection +LSTM +Top 1 +Accuracy +0.26 +Stability +Transformer +Spearman’s +Rho +0.73 +Table 4: Solubility reported in [45] +Task +Model +Test +Accuracy +Solubility +ProtT5-XL- +UniRef50 +0.91 +Table 5: Antibody Affinity Binding reported in [14]. +Task +Model +Test +Accuracy +Antibody Affinity +Linear +Discriminant +Analysis +0.92 +Table 6: R2DL: AMP Classification +Source Model +AMP +Sequence +Samples +k-SVD +Iterations +Training +Accuracy +Test +Accuracy +BERT (Bidirectional +Transformer) +6489 +100 +87.12 +85.64 +BERT (Bidirectional +Transformer) +6489 +250 +85.67 +82.33 +Bi-LSTM +6489 +100 +79.40 +81.90 +Table 7: R2DL: Toxicity Prediction +Source Model +AMP Sequence Samples +k-SVD Iterations +Test Accuracy +BERT (Bidirectional Transformer) +8153 +100 +87.23 +BERT (Bidirectional Transformer) +8153 +250 +86.93 +Bi-LSTM +8153 +100 +81.25 +Table 8: R2DL: Secondary Structure Prediction +Source Model +Training Samples +k-SVD Iterations +Training Accuracy +Test Accuracy +BERT +8,678 +10000 +71.47 +63.65 +BERT +8,678 +15000 +74.34 +69.91 +BERT +8,678 +20000 +76.32 +74.92 +indicate that R2DL performs better when fewer labeled training data samples are available. Below 25% of training +data samples, both methods approximately do worse than random prediction, so we do not reduce the training data +to evaluate performance after this threshold. +16 + +Table 9: R2DL: Remote Homolgy Detection (Top-1 Accuracy) +Source Model +Training Samples +k-SVD Iterations +Training Accuracy +Test Accuracy +BERT +12,312 +10000 +11.34 +10.76 +BERT +12,312 +15000 +16.45 +15.67 +BERT +12,312 +20000 +26.23 +24.50 +Table 10: R2DL: Stability (Spearman’s Rho) +Source Model +Training Samples +k-SVD Iterations +Training Accuracy +Test Accuracy +BERT +53,679 +10000 +60.23 +61.89 +BERT +53,679 +15000 +68.62 +67.20 +BERT +53,679 +20000 +70.78 +69.73 +Table 11: R2DL: Fluorescence (Spearman’s Rho) +Source Model +Training Samples +k-SVD Iterations +Training Accuracy +Test Accuracy +BERT +21,446 +10000 +61.29 +52.82 +BERT +21,446 +15000 +61.02 +59.46 +BERT +21,446 +20000 +70.90 +62.34 +Table 12: R2DL: Solubility +Source Model +Training Samples +k-SVD Iterations +Training Accuracy +Test Accuracy +TinyBERT +6623 +10000 +68.93 +69.82 +TinyBERT +6623 +15000 +87.22 +89.3 +TinyBERT +6623 +20000 +92.85 +93.21 +Table 13: Restricted Data Setting: Toxicity Prediction +Task +Training +Samples +R2DL Test +Accuracy +Bi-LSTM Test +Accuracy +Toxicity Prediction +5000 +42.12 +37.34 +Toxicity Prediction +6000 +62.98 +49.62 +Toxicity Prediction +7000 +86.23 +82.78 +Toxicity Prediction +8153 +89.34 +93.7 +Table 14: Restricted Data Setting: AMP Prediction +Task +Training +Samples +R2DL Test +Accuracy +Bi-LSTM Test +Accuracy +AMP Prediction +3500 +59.82 +64.52 +AMP Prediction +4500 +72.76 +68.41 +AMP Prediction +5500 +84.17 +74.34 +AMP Prediction +6489 +90.01 +88.0 +Table 15: Restricted Data Setting: Secondary Structure Prediction (SSP) +Task +Training +Samples +R2DL Test +Accuracy +Bi-LSTM Test +Accuracy +Structure Prediction +3378 +12.09 +06.23 +Structure Prediction +4478 +34.26 +37.93 +Structure Prediction +6678 +69.28 +66.34 +Structure Prediction +8678 +84.14 +78.0 +17 + +Table 16: Restricted Data Setting: Remote Homology Detection +Task +Training +Samples +R2DL Test +Accuracy +Bi-LSTM Test +Accuracy +Homology +4312 +09.35 +03.69 +Homology +8312 +17.26 +15.93 +Homology +10312 +23.23 +22.34 +Homology +12312 +24.14 +26.0 +Table 17: Restricted Data Setting: Fluorescence +Task +Training +Samples +R2DL Test +Accuracy +Bi-LSTM Test +Accuracy +Fluorescence +10769 +12.09 +06.23 +Fluorescence +25769 +34.26 +37.93 +Fluorescence +45769 +69.28 +66.34 +Fluorescence +53769 +66.34 +68.0 +Table 18: Restricted Data Setting: Solubility Prediction +Task +Training +Samples +R2DL Test +Accuracy +Bi-LSTM Test +Accuracy +Solubility +2500 +011.0 +07.23 +Solubility +4000 +47.26 +39.93 +Solubility +5200 +85.23 +87.34 +Solubility +6623 +94.0 +93.1 +18 + diff --git a/ttA0T4oBgHgl3EQfLf_G/content/tmp_files/load_file.txt b/ttA0T4oBgHgl3EQfLf_G/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..1416dea200f1fc0124a94245e9cae11f371c994b --- /dev/null +++ b/ttA0T4oBgHgl3EQfLf_G/content/tmp_files/load_file.txt @@ -0,0 +1,1317 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf,len=1316 +page_content='Reprogramming Pretrained Language Models for Protein Sequence Representation Learning Ria Vinod 1, Pin-Yu Chen2, and Payel Das2 1Department of Computational and Molecular Biology, Brown University 2IBM Research Abstract Machine Learning-guided solutions for protein learning tasks have made significant headway in recent years.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' However, success in scientific discovery tasks is limited by the accessibility of well-defined and labeled in-domain data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' To tackle the low-data constraint, recent adaptions of deep learning models pretrained on millions of protein sequences have shown promise;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' however, the construction of such domain-specific large-scale model is computationally expensive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Here, we propose Representation Learning via Dictionary Learning (R2DL), an end-to-end representation learning framework in which we reprogram deep models for alternate-domain tasks that can perform well on protein property prediction with significantly fewer training samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R2DL reprograms a pretrained English language model to learn the embeddings of protein sequences, by learning a sparse linear mapping between English and protein sequence vocabulary embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Our model can attain better accuracy and significantly improve the data efficiency by up to 105 times over the baselines set by pretrained and standard supervised methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' To this end, we reprogram an off-the-shelf pre-trained English language transformer and benchmark it on a set of protein physicochemical prediction tasks (secondary structure, stability, homology, stability) as well as on a biomedically relevant set of protein function prediction tasks (antimicrobial, toxicity, antibody affinity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Introduction Recent advances in artificial intelligence (AI), particularly in deep learning, have led to major innovations and advances in many scientific domains, including biology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' These deep learning models aim to learn a highly accurate and compressed representation of the biological system, which then can be employed for a range of tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' There has been notable success across a range of tasks, from high-quality protein structure prediction from protein sequences [1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 2], accurate prediction of protein properties, to enabling novel and functional peptide discoveries [3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Many of these advances rely on developing deep learning models [1;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 6] which are trained from scratch on massive amounts (on the order of billions of tokens) of data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' However, labeled data in biology is scarce and sparse, which is also the case for many other real-world scenarios in the scientific domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In the biological domain, label annotation can involve biological assays, high resolution imaging and spectroscopy, which are all costly and time consuming processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The technique of pretraining deep learning models was proposed to address this issue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Pretraining methods leverage large amounts of sequence data and can learn to encode features that can explain the variance seen in sequences across biological task-specific training samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In the context of protein sequences, pretraining has enabled meaningful density modelling across protein functions, structures, and families [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In this work, we reference two types of pretraining methods: (i) unsupervised pretraining, where all data is unlabeled, and (ii) self-supervised pretraining, where a model learns to assign labels to its unlabeled data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Large models then pretrain on massive amounts of unlabeled data, specifically biological sequences, which are available at scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Once pretrained, these foundation models (FMs) [8] are finetuned on smaller amounts of labeled data, which correspond to a specific downstream task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Interestingly, for the large-scale models pretrained on protein sequences, biological structure and function seem to emerge in the learned protein representation, even though such information was not included in model training [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Though highly powerful, the training of those domain-specific foundation models from scratch is highly resource- intensive [9].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' For example, one training run of BERT (the language model considered in this work) learns 110 million parameters, costs up to $13,000 USD and takes 64 days (without parallelized computing) and results in 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='7 tons of carbon emissions [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' A single training run of another popular language model, the T5 transformer, learns 11 billion parameters, costs up to $1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='3 million USD, takes 20 days, and results in 47 tons of carbon emissions [11;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 12].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Such pretrained language models and size variants are abundantly available with the advent of models libraries (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', Hugging Face [13]) which host pretrained models and datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The scale of data, compute, and financial resources required to train these models is not only available to a limited number of researchers, but is also infeasible for applications with limited labeled data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' However, in the scientific domain, we still aim to train models with similar 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='02120v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='LG] 5 Jan 2023 Figure 1: Left: Descriptions of considered predictive tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We select the set of physicochemical property prediction tasks from the well-studied domains in [6], and the biomedical function prediction tasks from works with biomedically relevant small-szied labeled datasets [3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Center: We compare R2DL to pretraining and standard supervised training methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We refer to supervised methods as standard supervised classifiers that are trained from scratch from labeled data alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Depending on how labeled and unlabeled data are used in pretraining, we consider pretraining to constitute unsupervised/supervised pretraining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Right: The comparative table shows the broad adaptability of the R2DL framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In comparison to existing gold standard methods, R2DL is has a broader utility across different domains, sizes of training datasets, and data efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We categorize supervised methods as cross-domain adaptable, through various domain adaptation and transfer learning techniques [15].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' representational capacity and predictive performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' To this end, we propose a lightweight, and more accurate alternative method to large-scale pretraining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Specifically, we introduce a method to reprogram an existing foundation model of high capacity that is trained on data from a different domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' This situation calls for innovations in cross-domain transfer learning, which is largely unexplored, particularly in scientific domains.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' One known fact is that biological sequences are similar to natural language, as they also contain long-range dependencies and follow Zipf’s law [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' These sequences and their associated dependencies are crucial for determining their structural and functional properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Such similarity has motivated the use of deep learning architectures and mechanisms that are widely used in natural language processing (NLP) to build protein sequence models from scratch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In this work, we explore an alternative warm-start paradigm, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' how to effectively and efficiently reprogram an existing, fully-trained large English language model to learn a meaningful (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', biomedically relevant) representation of protein sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The goal is to create a more carbon-friendly, resource-efficient, and broadly accessible framework to motivate different scientific domains toward democratizing the representation power of large AI models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' This warm-start paradigm is defined by the framework’s ability to achieve the performance of transformers that are pretrained on billions of tokens, with a lighter-weight training procedure that is similar to that of a standard supervised classifier trained from scratch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In particular, we consider highly specific biological and biomedical protein sequence datasets (illustrated in Figure 1) which have much fewer samples than standard supervised language task datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Reprogramming thus provides a more data and resource-efficient approach to developing models to achieve deep representational capacity and performance for downstream protein tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Reprogramming has been previously explored in the language domain as a sub-problem of transfer learning [17].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [18] explored reprogramming language models for alternate text classification tasks, [19] reprogrammed acoustic models for time series classification, [20] reprogrammed ImageNet classification models for alternate image classification tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' However, none of these methods investigate mappings between domains that require a very high representational capacity (from natural language to biological sequence), which is the setting we require in the protein sequence domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Toward this goal, we introduce R2DL (Representation Reprogramming via Dictionary Learning), a novel cross- domain transfer learning framework to reprogram an existing pretrained large-scale deep-learning model of the English language, namely a English BERT model [10], to learn and predict physicochemical and biomedical properties of protein sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' To the best of our knowledge, our work remains the first work to address reprogramming in any biological, and more broadly, scientific domain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In Figure 1, we illustrate the set of protein physicochemical and functional property prediction tasks we consider, as well as the baseline methods against which we compare R2DL performance to, and a brief description of R2DL’s advantages compared to these existing methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We test the reprogrammed model for a range of biomedically relevant downstream physicochemical property, structure, and function prediction tasks, which include prediction of secondary structure, homology, mutational stability, solubility, as well as antimicrobial nature, toxicity, and antibody affinity of proteins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Each of these tasks involves learning on datasets which are limited to a few thousands of labeled samples,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' at least an order of magnitude smaller needed 2 Biological Property Prediction Tasks Comparable Models Model Comparison Secondary Structure Physiochemical Stability property Reprogrammed Can be Can be Can be Robust Our Contribution prediction (R2DL) Trained trained adapted to on Large on Small cross- Reduced Homology Data Data domain Samples ESM-1b [Rives2019],' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Tasks R2DL Solubility 口 Pretrained Assessing Protein Embeddings [Rao 2019] Peptide WAE [Das 2021] Pretained Antimicrobial Biomedical Toxicity function Supervised LSTM [Das 2021] Supervised prediction Antibody AffinityFigure 2: System illustration of the Representation Reprogramming via Dictionary Learning (R2DL) framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In Step 1, R2DL loads a pretrained language model (source), obtains the source vocabulary embeddings, and specifies the protein tokens (target).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In Step 2, R2DL learns a sparse linear mapping between the source and target embeddings via dictionary learning, to represent a target token embedding as a sparse linear combination of source token embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In Step 3, the system maps the source task labels (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', positive/negative sentiments) to target task labels (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', toxic/non-toxic proteins) and optimizes the embedding mapping parameters based on the task-specific loss evaluation on a given protein sequence dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Finally, in Step 4 the reprogrammed model is deployed for the test-time evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' to train a foundation model or a large language model [21].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R2DL uses dictionary learning, a machine learning framework that finds the optimal sparse linear mapping between the English vocabulary embeddings and the amino acid embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' To do so, a protein property prediction task-specific loss is used to learn the optimal parameters of the reprogrammed model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We train R2DL in a supervised setting with the downstream protein prediction task datasets that are labeled and small in size (illustrated in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R2DL demonstrates consistent performance improvement from existing baselines across seven different physicochemical (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', up to 11% in stability), structural, and functional property prediction (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', up to 3% in toxicity) tasks of proteins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We estimate R2DL to be over 105 times more data-efficient than existing pretraining methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We further demonstrate the performance robustness of R2DL when trained on a reduced size version of the supervised protein datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In addition, we show that that R2DL learns to encode physicochemical and biomedical properties in the learned representations, even in a limited data scenarios.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' This work thus blazes a path toward efficient and large-scale adaptation of existing foundation models toward different real-world learning tasks and accelerates scientific discovery, which naturally involves learning from limited real-world data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Results Figure 2 illustrates the proposed Representation Reprogramming via Dictionary Learning (R2DL) framework, which learns to embed a protein sequence dataset of interest by training on the representations of a transformer that is pretrained on an English text corpus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' A one-to-one label mapping function is assigned for each downstream protein prediction task for cross-domain machine learning, and a class label or a regression value is predicted using R2DL for each protein sequence during testing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Below we discuss details of the general framework (tasks described in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R2DL Framework Formulation The R2DL objective is to reprogram a source model (pretrained language model) to be able to correctly classify, or predict the regression values of, protein sequences (for a target prediction task).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We use pretrained instances of BERT, a bidirectional transformer (termed the source model), which has been finetuned separately for different language tasks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', sentiment classification, named entity recognition) [10;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' For a protein sequence classification task, we use the source model trained on a language task for which there are n sentence output classes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', positive and negative for senitiment classification), and n protein sequence classes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', toxic, non-toxic).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The output-label mapping h is then a simple 1-1 correspondence between the source task labels and the target task labels (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', positive → toxic and negative → non-toxic).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' For a regression task, R2DL uses a mapping between the regression values in protein sequence feature space and the classification probability values in the source model embedding space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' It does so by learning optimal thresholds of regression values that map to the source model class labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 3 Domain Data Construction Token Mapping and Dictionary Learning 3 Task Specific Training & Embedding Extraction source model: reprogrammed source pretrained classifier amino acid model tokens label [ positive → toxic SOURCE DOMAIN: mapping negative + non-toxic English Vocabulary Vt1 Approximate Vt = θVs Vt2 "I\'m" "going" "to" "the" Vt3 biological property extract prediction output: (positive,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' negative,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' neutral) embeddings Vs Nt xm cross entropy loss minimization to TARGET DOMAIN: Target Vocabulary Source Vocabulary Biochemical Characters Embedding Matrix (Vs) update until convergence Embedding Matrix (V-) ARND A Vt1 Vs1 "\'m" Vr~e Vs output: biological sequence R Vt2 Vs2 Task Specific Testing properties (toxic,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' non-toxic) Vt3 Vs3 "to" "the" Use optimized parameters θ* from (3 D : axm axb bxmThe input data of the source English language model is tokenized at the word level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' These tokens form the atoms for our dictionary representation of VS, a matrix with its rows corresponding to embedding vectors of source tokens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The input data to the target task, protein sequences, are tokenized on a character level with only 20 distinct tokens (corresponding to the set of 20 discrete natural amino acid characters).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R2DL obtains VS from the learned embeddings of the source model and learns to represent VT , the matrix of the target token embedding, as a weighted combination of the English token embeddings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We propose token reprogramming by approximating a linear mapping between VS and VT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' That is, we aim to find a transformation of the latent representation of the protein sequences, such that it can be embedded in the pretrained language model’s latent space and enable R2DL to leverage these re-embedded tokens for learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Specifically, we learn the linear map Θ by approximating a dictionary using a k-SVD solver [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' That is, we want to approximate VT = ΘVS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The k-SVD solver guarantees a task-specific level of sparsity in the coefficients when linearly combining English token embeddings to represent a protein sequence token embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In other words, it helps select k English tokens and use their linearly combined embeddings as the embedding of a target token.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Additionally, with a one-to-one label mapping function of the protein sequence label to the English text label, we are able to use the pretrained language model for inference on the embedded protein dataset, VT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We thus design an end-to-end reprogramming framework for any arbitrary protein sequence classification or regression task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R2DL Training and Optimization Procedure We are given a pretrained classifier, C (which has been pretrained on a source-task dataset with source tokens denoted by {vSi}|VS| i=1 ) and a target-task dataset with target tokes denoted by {VT j}|VT | j=1 .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The embedding matrices are VS and VT respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We can encode an output label mapping function translating between source and target labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In Figure 2, we show how R2DL aims to find a linear mapping function Θ that learns the optimal coefficients for our atoms in VT to be represented as a sparse encoding of the dictionary VS such that VT = ΘVS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The map Θ is used to reprogram C to be able to correctly classify the protein sequences through the transformation h(C(θt, t)) where t is a protein sequence from a protein task and θt is the linear weights associated with the protein sequence t in Θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We note that for each of the downstream protein property prediction task, R2DL only trains a corresponding token mapping function Θ while keeping the pretrained classifier C intact.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Therefore, the number of trainable parameters in R2DL is simply the size of the matrix Θ, which is usually much smaller compared to the number of parameters in the pretrained deep neural network classifier C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' To approximate the dictionary, we use a k-SVD solver to optimize over the cross entropy loss for updates to Θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We then apply the assigned label mapping h for protein classification tasks, or thresholding for regression tasks, and train the mapping function Θ using gradient-based optimization evaluated on the task-specific cross-entropy loss.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Details for R2DL training procedure are given in the Method section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Benchmark Tasks and Evaluation We consider four physicochemical structure and property prediction tasks from a well-established protein benchmark from [6] (represented in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Secondary structure prediction involves predicting secondary structure y ∈ {Helix, Strand, Other} for each amino acid x in a given protein sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Solubility prediction considers mapping an input protein sequence x to a label of y ∈ {Membrane-Bound, Water Soluble}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Homology detection is a sequence classification task, where each input protein x is mapped to a label y ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', 1195}, representing different possible protein folds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Stability prediction is a regression task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We further consider three biomedically relevant function prediction tasks, which are sequence classification tasks (represented in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Using R2DL, we predict for a given sequence x, its binary class label y ∈ {AMP, non-AMP} for antimicrobial-nature prediction [3] or y ∈ {Toxic, non-Toxic} for toxicity prediction [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Finally, we predict antigen and non-specific binding of antibody variant sequences from [14]: given a sequence x, the task is to predict y ∈ {on-target, off-target}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Further details on the protein tasks and datasets are in the Method section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The sizes of the individual datasets vary between 4,000 and 50,000 (see supplementary for details on data sizes and train-test splits).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Data efficiency is defined as the ratio of the R2DL prediction accuracy to the number of biological sequences used during pretraining and finetuning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We use data efficiency as a metric to compare the performance of R2DL to established benchmarks for the protein tasks in [6;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' For classification tasks, we evaluate prediction accuracy with a top-n accuracy, where n is the number of classes in the protein sequence classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' For regression tasks, we evaluate prediction accuracy with Spearman’s correlation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Model Baselines and Data The baseline models we consider in this work are of two types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Firstly, we consider models trained in a supervised manner, by training standard sequence Long Range Short Term Memory (LSTM) models from scratch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' For each downstream peptide or protein classification task, we have labeled (supervised) datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The results of these models are reported in Figure 3(a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Secondly, we consider models that are pretrained in an unsupervised manner on protein sequence data and are fintuned for a particular downstream task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Pretraining methods that do not use labeled data 4 pose an advantage, as those models can then learn from a significantly larger number of data samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In the cases of the toxicity and antimicrobial prediction tasks, the baseline model we compare to has been pretrained on a subset of the UniProt database where sequences are limited to being 50 residues long [24].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The pretraining corpus size is then 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='7 million peptide sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Using unlabeled data for pretraining is thus much more advantage than pretraining in a supervised scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Of these 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='7 million sequences, only 9,000 are labeled (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='005% of sequences).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The model is a Wasserstein Autoencoder, which is a generative model that undergoes unsupervised pretraining on the subset of UniProt data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The WAE embeddings of the labeled sequences are then used to train a logistic regressor model on the labeled dataset to obtain a binary classifier for Antimicrobial/non-Antimicrobial (6489 labeled samples) or for toxic/non-toxic (8153 labeled samples) label prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' For the physicochemical property prediction tasks, the baseline model we consider is pretrained on the Pfam corpus [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' This corpus consists of 31 million protein domains and is widely used in bioinformatics pipelines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Sequences are grouped by protein families which are categorized by evolutionarily-related sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In contrast, the downstream physicochemical tasks of structure, homology, stability and solubility prediction have labeled datasets that range from 5,000 to 50,000 samples which the model can be finetuned on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Pretraining thus poses the advantage of modeling the density over a range of protein families and structures, but stipulates that there must be sequence datasets that contain structural and functional information about the downstream task datasets, and typically be of a size on the order of millions of sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R2DL eliminates this requirement by repurposing existing pretrained English language models, and leveraging transferrable information from models that are not conditioned on protein sequence information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Data Efficiency and Accuracy of Reprogramming We report the performance of R2DL for the set of 7 protein predictive and their corresponding baselines in Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Baselines for the physicochemical prediction tasks are established by a transformer from [6] that has been pretrained in an unsupervised setting on the Pfam pretraining corpus [26].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Baselines for the antimicrobial and toxicity prediction tasks are established in [3], where Das et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' pretrained a Wasserstein Autoencoder on the peptides from the UniProt corpus [24] using unsupervised training, and then used the latent encodings from autoencoder to train the property classifiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Baselines for the antibody affinity task are established in [14] where they train a linear discriminant analysis model in a supervised setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Each physicochemical and biomedical function prediction task then has a relatively small, supervised dataset which we split into training and testing sets to train the R2DL framework and evaluate its performance on the test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Henceforth, we refer to these baselines as task-specific baselines, whereas the baseline model we compare R2DL to varies with the downstream protein prediction task and the best performing model available (see Supplementary for details on task-specific baselines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We show that, for every prediction task we achieve a higher test accuracy with R2DL than with the corresponding task-specific baseline model when both models are trained on the full labeled dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R2DL shows performance improvement up to 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='2% when compared to the pretrained models, and up to 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='3% performance when compared to a standard, supervised LSTM that is trained from scratch on the same dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' However, R2DL needs a pretrained source model and only a small-sized, labeled protein sequence dataset as the input.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' And, therefore the size of R2DL training set is limited to the number of samples in the downstream protein prediction dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Pretrained models require a large amount of protein sequence data for pretraining, on the order of 106 samples, in addition to the downstream supervised protein task sequence data that the pretrained model is fine-tuned on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In Figure 3(a), we show the number of training samples and corresponding accuracy metric (see Method section for details) of the R2DL, pretrained, and supervised models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In Figure 3(b), we show the data efficiency, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', the ratio of the number of training samples (including the pretraining corpus only of biological sequences for pretrained source models) to the accuracy of the model for R2DL and baseline models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We show that R2DL is a maximum of 104 times more data efficient, as in the case of the toxicity prediction task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' This is due to the very large number of pretraining data samples required relative to the downstream protein task dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Figures 3(c) and 3(d) show the R2DL performance on the antigen affinity prediction task for antibody variant sequences and its comparison with the baseline LDA model reported in [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R2DL achieves a higher predictive accuracy than the baseline LDA model by 3% and with a higher classification accuracy with imbalanced datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The antibody affinity task dataset has the following distribution on target: 1516, off-target: 2484.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' For 37% to 62% class-imbalance ratio of labels, we show that the R2DL model has a better classification accuracy than the LDA model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The learned representations can therefore be inferred to be more accurate in our model than in the baseline model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' This is important, as in many real-world prediction tasks, the dataset is found to be class-imbalanced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R2DL Performance vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Pretraining Performance in Low Data Settings Motivated by the data efficiency of R2DL as a framework, we tested the task-specific predictive performance of R2DL in reduced-data training settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We compared these results to the performance of task-specific baseline models, when trained and tested in the same restricted data setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In Figure 4, we show the performance of the R2DL model and then baseline model when trained on 100%, 80%, 60%, and 40% of a specific task dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We show results for 5 (a) Downstream supervised protein task dataset sizes and test accuracy of the 3 comparable methods introduced in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' (b) Data efficiency of R2DL vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' pretrained methods as illustrated in Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' (c) Confusion matrix of the baseline model trained in [14] for the antibody affinity prediction task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' (d) Confusion matrix of the R2DL model for the antibody affinity prediction task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Figure 3: Task-specific evaluation of R2DL performance compared to the performance of the baseline models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In Figure 3(a), results for the pretrained baseline models are from unsupervised pretrained transformers for secondary structure, stability, homology, and solubility prediction tasks [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The baseline models for the antimicrobial and toxicity prediction tasks are logistic regressors trained using sequence embeddings from the pretrained peptide wassertein variational autoencoder [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Results for the supervised classifiers are from sequence-level LSTMs trained from scratch on the downstream protein prediction data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' For classification tasks, we evaluate prediction accuracy with a top-n accuracy, where n is the number of classes in the protein sequence classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' For regression tasks, we evaluate prediction accuracy with Spearman’s correlation coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Results of the pretrained models on the antibody task dataset have not been previously reported in any work and are hence left out for future work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In 3(b), Data efficiency is defined as the ratio of the R2DL prediction accuracy to the number of protein sequences used during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In Figure 3(c)-(d), we show a comparison between the performance of a linear discriminant analysis (LDA) model in [14] and R2DL on the antibody affinity dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The LDA model is a binary classifier which finds the optimal classification boundary by projecting the data onto a one-dimensional feature space and finding a threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The antibody affinity dataset consists of 4,000 labeled protein sequences, with labels {1 (on-target binding), 0 (off-target binding)}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R2DL achieves a predictive accuracy of 95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='5% compared to the LDA model performance of 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='8%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' the Antimicrobial, Toxicity, Secondary Structure, Stability, Homology, and Solubility prediction tasks in Figure 4 and compare the performance of R2DL and pretrained models against the performance of a random guess.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We observe, that for downstream tasks of Toxicity, Secondary Structure, Homology and Solubility, R2DL always performs better than a pretrained protein language model across the size range of the limited datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Furthermore, we observe that, except in the stability task, the rate of failure to perform better than a random guess is higher for the pretrained 6 Protein R2DL Pretraining Supervised Downstream Training Accuracy Training Accuracy Training Task Efficiency Efficiency Accuracy Efficiency Samples Samples Samples Secondary 8678 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='841 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='70E-05 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='10E+07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='801 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='58E-08 8678 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='623 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='18E-05 Structure Stability 21446 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='849 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='96E-05 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='10E+07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='738 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='38E-08 21446 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='660 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='08E-05 Homology 12312 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='241 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='96E-05 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='10E+07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='265 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='56E-09 12312 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='245 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='99E-05 Solubility 16253 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='943 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='80E-05 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='70E+06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='872 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='13E-07 16253 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='856 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='27E-05 Antibody Affinity 4000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='9456 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='36E-04 4000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='928 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='32E-04 Antimicrobial 6489 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='900 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='39E-04 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='70E+06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='883 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='19E-07 6489 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='874 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='35E-04 Toxicity 8153 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='961 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='18E-04 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='70E+06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='937 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='51E-07 8153 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='689 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='45E-05Antimicrobial Method Pretrained Toxicity R2DL Secondary Task Structure Stability Homology Solubility 10°° 8- 10 7 10 10 10 4 10 3 (Log Scale) Efficiency = Accuracy #TrainingSamples400 0 415 64 True label 300 200 1 60 461 100 0 1 Predictedlabel False Negative 60 False Positive RateLDA = :11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='5% False Negatives + True Positives 60 + 461 True Positives 461 True Positive RateLDA = 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='4 % False Negatives + True Positives 60 + 461400 0 494 6 True label 300 200 1 27 473 100 0 1 Predictedlabel False Negative 27 False Positive RateR2DL = : 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='4% False Negatives + True Positives 27 + 473 True Positives 473 True Positive RateR2DL = = 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='6 % False Negatives + True Positives 27 + 473(a) Secondary structure prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' (b) Mutational stability prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' (c) Remote homology prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' (d) Membrane solubility prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' (e) Antimicrobial-nature prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' (f) Toxicity prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Figure 4: Results of the R2DL model and baseline model for each downstream task in reduced training data settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' models than for R2DL.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In both cases, R2DL outperforms pretraining until the cutoff point that is the intersection of the random guess curve with the accuracy curves (the point at which the model is not learning any meaningful representation).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Correlation Between Learned Embeddings and Evolutionary Distances Beyond comparing the R2DL model against the individual protein task benchmarks, we demonstrate that the R2DL dictionary learning framework shows interpretable correspondences between the learned embeddings in the latent space and the specific protein property.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We show this result for the antibody affinity, secondary structure, and toxicity prediction tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Figures 5(a-c) show the t-SNE projection of task-specific R2DL embeddings VT = ΘVS of protein sequences for secondary structure, toxicity, and antibody affinity prediction tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Clear separation between different protein classes is evident.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We further calculate the similarity between the euclidean distance between the latent representation at the last layer for each amino acid embedding, and compare it to the pairwise evolutionary distance with the BioPython module.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' In Figure 5(d), we show the euclidean distances between the latent embeddings learned in the R2DL model and the pairwise evolutionary distances between protein sequences, as estimated using BLOSUM62 matrix implemented in the pairwise function of BioPython modulde.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The matrix shows a correlation of close to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0 along the diagonal showing a perfect correspondence between the learned representation and the empirical observations of amino acid relatedness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R2DL thus captures the underlying structure of the linear sequence of amino acid residues in protein sequences in the context of the protein task reprogrammed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Discussion We propose a new framework, R2DL, to reprogram large language models for various protein tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R2DL demonstrates powerful predictive performance across tasks that involve evolutionary understanding, structure prediction, property prediction and protein engineering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We thus provide a strong alternative to pretraining large language models on upto 106 protein sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' With only a pretrained natural language model (which are abundantly available at the time of writing), a small-sized labeled protein data set of interest, and a small amount of cross-domain finetuning, we can achieve better performance for each protein prediction task with interpretable correspondences between features.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='7 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='Solubility ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='Test Accuracy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='%ofOriginalTrainingDataAntimicrobial ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='Test Accuracy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='%of Original Training DataToxicity ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='Test Accuracy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='%ofOriginalTrainingDataSecondaryStructure ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='Test Accuracy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='25 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='50 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='75 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='%ofOriginalTrainingDataStability ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='Spearman Correlation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='%ofOriginalTrainingDataHomology ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='R2DLAccuracy ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='Pretrained ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='Spearman Correlation ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='Random Guess ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='20 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='40 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='60 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='80 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='100 ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='% of Original Training Data(a) t-SNE clustering plot for secondary structure predic- ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' (b) t-SNE clustering plot for toxicity prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' (c) t-SNE plot for antibody affinity prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' (d) Correlation plot for pairwise evolutionary distances vs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' pair- wise euclidean distances in R2DL embeddinng space for antibody affinity prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Figure 5: (a-c) Clustering of R2DL learned embeddings for secondary structure prediction, toxicity prediction, and antibody affinity prediction tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' When tagged by protein property classification, we see very high correspondence between the clusters and protein sequences with the same physicochemical or biomedical property classification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' (d) For the antibody affinity prediction task, we observe a high correlation coefficient along the diagonal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' This shows that the representation learned by R2DL is highly similar to empirical observations of pairwise residue correlations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Beyond improvements in predictive performance, we show that the ratio of performance improvements to pretraining and training samples involved in the R2DL framework make R2DL up to 105 times more data-efficient than any current methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' This work opens many doors to biological prediction tasks that can acquire very few labeled, high quality data samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We emphasize the results of the data-efficiency of R2DL, when applied to biomedically relevant protein predictions, which are critical to advancing scientific understanding and discovery, but have been unsuccessful until now.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' While R2DL does make gradient updates in the framework, the data and resource requirements of the R2DL method is much lower than any unsupervised or self-supervised pretraining approach for protein sequence modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Though R2DL has the same data and resource requirements as any standard supervised training approach, R2DL demonstrates much higher task accuracy across a broad and diverse range of property prediction tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We claim that R2DL is able to do this because it can leverage the deep representational capacity induced by reprogramming, which standard supervised models cannot achieve without an unjustifiably large number of parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R2DL is thus more efficient than existing baseline models in the following aspects: (i) R2DL only requires a pretrained transformer (trained on English language data) and a small-sized, labeled protein sequence data set of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We do not make any updates to the pretrained model itself, unlike traditional transfer learning methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Rather we make updates to the R2DL model during a supervised training process that optimizes over class-mapped labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' (ii) R2DL does not require large-scale un/self-supervised pretraining on millions of unlabeled protein sequences, as in [6;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 3;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' (iii) Further, R2DL does not require any large-scale supervised pretraining, which has been found beneficial in protein-specific tasks [6] as well as in computer vision [27].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Labeling protein sequences at scale, particularly for biomedical function, is almost infeasible for the size of dataset that is required for supervised pretraining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' With these three considerations in mind, we pose R2DL as a data-efficient alternative to pretraining methods for protein prediction tasks of biological and biomedical relevance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' To the best of our knowledge, R2DL is the first framework 8 40 Helix Strand Other 20 comp-2 0 20 40 80 60 40 20 0 20 40 comp-1Toxic Non-Toxic 40 20 - Z-dwon 20 40 40 30 20 10 0 10 20 30 40 comp-160 Binding Non-Binding 40 20 - comp-2 0 20 40 60 40 20 0 20 40 comp-1NYDGFOAEIWSTVCKMHLPR N 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0 Y D G 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='8 F Q A E 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='6 1 W s T 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='4 v C K M 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='2 H L P R 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0without explicit pretraining that facilitates accurate predictions across a general suite of protein prediction tasks and provides interpretable correspondences between amino acid features that are very closely aligned with domain knowledge (evolutionary distances).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The success of R2DL can be attributed to its representational power to encode a sparse representation by leveraging the natural language modeling entailed in large language models for efficient learning on protein structure and function prediction tasks, as both English and protein sequences follow Zipf’s law [16].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We first demonstrate the effectiveness of R2DL on a set of physicochemical structure and property prediction tasks, and then on a set of biomedically relevant function prediction tasks, for protein sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We show predictive performance improvements against pretrained methods (up to 11% in stability) and standard supervised methods (up to 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='2% in antibody affinity).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Similarly, on the remaining tasks, we show performance improvements over the best reported baseline in structure prediction (4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='1%), homology (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='3%), solubility (7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='1%), antibody affinity (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='2%), toxicity (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='4%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R2DL thus shows the capability to learn a general representation of protein sequences that can be efficiently adopted to different downstream protein tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' These powerful representation capabilities as evidenced by its ability to achieve high performance across protein datasets with a highly varied number of task-specific training samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The performance of R2DL across protein tasks show the potential to repurpose and develop powerful models that can learn from small, curated, and function-specific datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' This mitigates the need to train large pretrained models for peptide learning tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We thus provide an alternative method to pretraining that is cheaper to run and more accurate, and therefore adoptable to broader researcher communities who may not have access to large-scale compute.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' This potential is critical for many applications, such as discovery of new materials, catalysts, as well as drugs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Although we establish the efficacy and efficiency of R2DL in a domain where pretrained large language models already do exist, we hope that our work will pave the path to extending this approach to other domains where pretrained LLMs do not exist, such as polymers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Method Representation of Tokens In the R2DL framework, we use 2 input datasets, an English language text dataset (source dataset) and a protein sequence dataset (target dataset).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The vocabulary size of a protein sequence dataset at a unigram level is 20, as proteins are composed of 20 different natural amino acids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We obtain a latent representation of the English text vocabulary, VS, by extracting the learned embeddings of the data from a pretrained language model (source model).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The protein sequence data is embedded in the same latent space, and is termed the target vocabulary, VT .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' For each task, the token embedding matrix is of dimensions (n, m) where n is the number of tokens and m is the length of the embedding vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We use the same encoding scheme of VS and VT across all downstream tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Procedure Description of the R2DL Framework for a Protein Task Procedure Inputs: Pretrained English sentence classifier C, target model training data Xℓ for task ℓ, class mapping label function, hℓ (if classification) where ℓ ∈ {Secondary Structure, Fluorescence, Homology, Solubility, Antimicrobial, Toxicity, Antibody}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Procedure Hyperparameters: Maximum number of iterations T1 for updates to Θ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' number of iterations T2 for k-SVD,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' step size {αt}T1 t=1 Procedure Initialization: Random initialization of Θ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' obtain the source token embedding matrix VS Define Objective Function: Objective function for k-SVD: ∥VT − ΘVS∥ ≤ ϵ k-SVD Approximation of Θ: If t1 ≤ T1,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' while t2 ≤ T2 use approximate k-SVD to solve VT ≈ ΘVS,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' t2 ←− t2 + 1 Calculate the Loss and Perform Gradient Descent: Θ ←− Θ − αt · ∇ΘLoss(Θ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Xℓ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' hℓ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' C) ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' t1 ←− t1 + 1 and return to the previous K-SVD step Output Protein Sequence Labels for Protein Sequence x of Task ℓ: hℓ(C(Θ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' x)) We are given a pretrained English classifier,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' C,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' and a protein sequence target-task dataset Xℓ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We denote the task with ℓ, such that ℓ ∈ {Secondary Structure, Fluorescence, Homology, Solubility, Antimicrobial, Toxicity, Antibody}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We also encode an output label mapping function hℓ specifying the one-to-one correspondence between source and target labels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' As shown in Figure 2, the source vocabulary embedding, VS, is extracted from the pretrained model, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The next objective is to learn Θ that approximates the embedding of tokens in Xℓ (denoted by VT ) in the representation space of the source model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 9 We aim to learn Θ ∈ Ra×b that finds the optimal coefficients {θt} for each of the target tokens t ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', a} in VT ∈ Ra×m to be represented as a sparse encoding of the dictionary, VS ∈ Rb×m, such that VT = ΘVS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' For a given target protein sequence x from the ℓ-th task, Θ is used to perform the target task through the transformation hℓ(C(Θ, x)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' While we do not make any modification to the parameters or architecture of C, we assume access to the gradient ∇Θloss(·) for loss evaluation and parameter updates during training.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' A target token embedding vt ∈ Rm can be represented as a sparse linear combination of the source token embeddings (rows) in VS, vt = θtVs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' vt is the representation of the protein token in the dictionary space and satisfies ||vt − θtVs||p ≤ ϵ, where ∥ · ∥p is an Lp norm and θt is made to be sparse by satisfying ||θt||0 ≤ k for all t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' An exact solution vt = θtVS is computationally expensive to find, and is subject to various convergence traps, so for the purpose of our efficient fine-tuning approach we approximate vt ≈ θtVS using k-SVD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We first fix the dictionary VS, as extracted from C, and then find the optimal Θ according to the optimization problem, by minimizing the alternative objective �a t=1 ||θt||0 subject to ∥VT − ΘVS∥2 F ≤ ϵ as explored in [23].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' While algorithms exist to choose an optimal dictionary (an exact solution to k-SVD) that can be continually updated [23], we penalize computational expense over performance for the purpose of maintaining an efficient solution (at the cost of statistically insignificant improvements in accuracy) by using a predetermined number of iterations for k-SVD convergence, which is then used to evaluate the cross entropy loss on hℓ(C(Θ, x)) and update the mapping function Θ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Data Classification We provide five biologically relevant downstream physicochemical property prediction tasks, adapted from [6] to serve as benchmarks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We categorize these into property prediction, structure prediction, evolutionary understanding, and protein engineering tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The sizes of the individual datasets vary between 4,000 and 50,00 (see supplementary for details on data sizes and train-test splits).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Secondary Structure Prediction (Structure Task): Secondary structure (SS) is critical to understanding the function and stability of a protein, and SS prediction is an important intermediate step in designing designing protein complexes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' This dataset, obtained from [28] has 8,678 data samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' It is derived from the CB513 dataset, and each amino acid, x in a protein sequence is mapped to y ∈ {Helix, Strand, Other}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The benchmark for this task is a transformer that reports a best performance of 80% accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Solubility: This task takes an input protein x and maps it to a label of y ∈ {Membrane-Bound, Water Soluble}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Determining the solubility of proteins is useful when designing proteins or evaluating their function for particular cellular tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' This dataset, obtained from [29] has 16,253 data samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The benchmark is a pretrained transformer, that achieves a best performance of 91% on a binary classification task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Antigen Affinity (Protein Engineering): Therapeutic antibody development requires the selection and engineering of molecules with high affinity and other drug-like biophysical properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' This dataset, obtained from [14] has 4,000 data samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The task is to map an input protein x to a label y ∈ {on-target, off-target}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The task corresponds to predicting antigen and non-specific binding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The benchmark for this task is a Linear Discriminant Analysis model with Spearman’s ρ values for antigen binding (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='87) and for non-specific binding (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='67).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Antimicrobial Prediction (AMP) (Property Task): Determining the antimicrobial nature of a peptide is a critical step in developing antimicrobials to fight against resistant pathogens.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The dataset, obtained from [3], consists of 6,489 labeled protein sequences x, is mapped to a label y ∈ {AMP, non-AMP}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The original model trained on this data provides a de novo approach for discovering new, broad-spectrum and low-toxic antimicrobials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The benchmark for this task is a transformer that reports a best performance of 88% accuracy with a pretrained classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Toxicity (Property Task): Improving the functional profile of molecules, especially in the context of drug discovery, requires optimizing for toxicity and other physicochemical properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' To that end, toxicity is an important property to predict in AMP development.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' This dataset, obtained from [3] consists of 8,153 antimicrobial peptide sequences which are either toxic (positive class), or non-toxic (negative class).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The benchmark for this task is a transformer that reports a best performance of 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='78% accuracy with a pretrained classifier.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Regression Stability (Protein Engineering Task): This regression task where each protein, xi is mapped to yi ∈ R based on maintaining its fold beyond a threshold of concentration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' This dataset, obtained from [30] has 21,446 data samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Stability is an important protein engineering task, as we can use this fold concentration to test protein inputs such 10 that design candidates are stable in the settings of different tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The benchmark for this task is a transformer that reports a best performance of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='73 Spearman’s ρ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Homology (Evolutionary Understanding Task): This is a sequence classification task where each input protein, x is mapped to a protein fold represented by y ∈ {1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', 1195}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' This dataset, obtained from [31] has 12,312 data samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Detecting homologs is particularly important in a biomedical context as they inform structural similarity across a set of sequences, and can indicate emerging resistance of antibiotic genes [cite].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The original model removes entire homologous groups during model training, thereby enforcing that models generalize well when large evolutionary gaps are introduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The benchmark for this task is a LSTM that reports a best performance of 26% Top-1 Accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R2DL Settings and Hyperparameter Details AMP The full AMP dataset size is 8112, we use a training set size of 6489 and a test set size of 812.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We use the L0 norm in our objective function, 10,000 k-SVD iterations and ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='045.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Toxicity The full Toxicity dataset size is 10,192, we use a training set size of 8153 and a test set size of 1020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We use the L0 norm in our objective function, 10,000 k-SVD iterations and ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='045.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Secondary Structure The full Toxicity dataset size is 9270, we use a training set size of 7416 and a test set size of 1854.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We use the L0 norm in our objective function, 9,000 k-SVD iterations and ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Stability The full Stability dataset size is 56,126, we use a training set size of 44,900 and a test set size of 11,226.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We use the L0 norm in our objective function, 6,000 k-SVD iterations and ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Homology The full Homology dataset size is 13,048, we use a training set size of 10,438 and a test set size of 2,610.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We use the L0 norm in our objective function, 4,000 k-SVD iterations and ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Solubility The full Solubility dataset size is 43,876, we use a training set size of 35,100 and a test set size of 8,775.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' We use the L0 norm in our objective function, 9,000 k-SVD iterations and ϵ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Data and Code Availability Links to protein sequence data and code are available on Github (github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='com/riavinod/r2dl) 11 References [1] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Jumper, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Evans, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Pritzel, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Green, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Figurnov, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ronneberger, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Tunyasuvunakool, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Bates, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Žídek, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Potapenko, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', “Highly accurate protein structure prediction with alphafold,” Nature, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 596, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 7873, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 583–589, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [2] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Baek, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' DiMaio, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Anishchenko, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Dauparas, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ovchinnikov, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Wang, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Cong, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Kinch, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Schaeffer, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', “Accurate prediction of protein structures and interactions using a three-track neural network,” Science, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 373, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 6557, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 871–876, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [3] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Das, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Sercu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Wadhawan, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Padhi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Gehrmann, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Cipcigan, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chenthamarakshan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Strobelt, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Dos Santos, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chen, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', “Accelerated antimicrobial discovery via deep generative models and molecular dynamics simulations,” Nature Biomedical Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 5, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 613–623, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [4] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Stokes, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Yang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Swanson, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Jin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Cubillos-Ruiz, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Donghia, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' MacNair, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' French, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Carfrae, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Bloom-Ackermann, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', “A deep learning approach to antibiotic discovery,” Cell, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 180, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 4, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 688–702, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [5] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Meier, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Rao, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Verkuil, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Liu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Sercu, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Rives, “Language models enable zero-shot prediction of the effects of mutations on protein function,” Advances in Neural Information Processing Systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 34, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 29287–29303, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [6] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Rao, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Bhattacharya, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Thomas, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Duan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Canny, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Abbeel, and Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Song, “Evaluating protein transfer learning with tape,” Advances in neural information processing systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 32, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [7] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Nijkamp, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ruffolo, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Weinstein, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Naik, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Madani, “Progen2: Exploring the boundaries of protein language models,” 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [8] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Bommasani, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Hudson, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Adeli, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Altman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Arora, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' von Arx, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Bernstein, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Bohg, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Bosselut, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Brunskill, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', “On the opportunities and risks of foundation models,” arXiv preprint arXiv:2108.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='07258, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [9] B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Yuan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' He, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Davis, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Zhang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Dao, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chen, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Liang, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Re, and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Zhang, “Decentralized training of foundation models in heterogeneous environments,” arXiv preprint arXiv:2206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='01288, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [10] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Devlin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Lee, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Toutanova, “Bert: Pre-training of deep bidirectional transformers for language understanding,” arXiv preprint arXiv:1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='04805, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [11] D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Patterson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Gonzalez, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Le, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Liang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Munguia, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Rothchild, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' So, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Texier, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Dean, “Carbon emissions and large neural network training,” arXiv preprint arXiv:2104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='10350, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [12] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Raffel, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Shazeer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Roberts, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Lee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Narang, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Matena, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Zhou, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Li, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Liu, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', “Exploring the limits of transfer learning with a unified text-to-text transformer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=',” J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Mach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Learn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Res.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 21, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 140, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 1–67, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [13] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Wolf, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Debut, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Sanh, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chaumond, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Delangue, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Moi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Cistac, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Rault, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Louf, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Funtowicz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Davison, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Shleifer, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' von Platen, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ma, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Jernite, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Plu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Xu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Scao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Gugger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Drame, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Lhoest, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Rush, “Huggingface’s transformers: State-of-the-art natural language processing,” 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [14] E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Makowski, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Kinnunen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Huang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Wu, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Smith, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Wang, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Desai, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Streu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Zhang, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Zupancic, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', “Co-optimization of therapeutic antibody affinity and specificity using machine learning models that generalize to novel mutational space,” Nature communications, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 13, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 1–14, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [15] F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Zhuang, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Qi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Duan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Xi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Zhu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Zhu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Xiong, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' He, “A comprehensive survey on transfer learning,” Proceedings of the IEEE, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 109, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 43–76, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [16] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Newman, “Power laws, pareto distributions and zipf’s law,” Contemporary physics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 46, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 5, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 323– 351, 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [17] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chen, “Model reprogramming: Resource-efficient cross-domain machine learning,” arXiv preprint arXiv:2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='10629, 2022.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [18] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Neekhara, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Hussain, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Dubnov, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Koushanfar, “Adversarial reprogramming of text classification neural networks,” arXiv preprint arXiv:1809.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='01829, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [19] C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Yang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Tsai, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chen, “Voice2series: Reprogramming acoustic models for time series classification,” in International Conference on Machine Learning, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 11808–11819, PMLR, 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 12 [20] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Elsayed, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Goodfellow, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Sohl-Dickstein, “Adversarial reprogramming of neural networks,” arXiv preprint arXiv:1806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='11146, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [21] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Bommasani, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Hudson, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Adeli, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Altman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Arora, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' von Arx, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Bernstein, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Bohg, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Bosselut, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Brunskill, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Brynjolfsson, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Buch, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Card, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Castellon, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chatterji, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Creel, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Davis, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Demszky, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Donahue, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Doumbouya, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Durmus, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ermon, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Etchemendy, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ethayarajh, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Fei-Fei, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Finn, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Gale, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Gillespie, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Goel, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Goodman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Grossman, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Guha, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Hashimoto, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Henderson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Hewitt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ho, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Hong, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Hsu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Huang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Icard, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Jain, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Jurafsky, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Kalluri, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Karamcheti, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Keeling, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Khani, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Khattab, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Koh, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Krass, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Krishna, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Kuditipudi, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Kumar, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ladhak, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Lee, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Lee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Leskovec, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Levent, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Li, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ma, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Malik, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Manning, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Mirchandani, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Mitchell, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Munyikwa, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Nair, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Narayan, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Narayanan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Newman, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Nie, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Niebles, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Nilforoshan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Nyarko, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ogut, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Orr, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Papadimitriou, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Park, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Piech, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Portelance, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Potts, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Raghunathan, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Reich, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ren, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Rong, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Roohani, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ruiz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ryan, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ré, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Sadigh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Sagawa, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Santhanam, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Shih, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Srinivasan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Tamkin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Taori, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Thomas, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Tramèr, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Wang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Wang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Wu, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Wu, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Wu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Xie, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Yasunaga, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' You, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Zaharia, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Zhang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Zhang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Zhang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Zhang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Zheng, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Zhou, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Liang, “On the opportunities and risks of foundation models,” 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [22] X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Jiao, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Yin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Shang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Jiang, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chen, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Li, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Wang, and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Liu, “Tinybert: Distilling bert for natural language understanding,” arXiv preprint arXiv:1909.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='10351, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [23] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Aharon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Elad, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Bruckstein, “K-svd: An algorithm for designing overcomplete dictionaries for sparse representation,” IEEE Transactions on Signal Processing, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 54, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 11, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 4311–4322, 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [24] U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Consortium, “Uniprot: a worldwide hub of protein knowledge,” Nucleic acids research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 47, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' D1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' D506–D515, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [25] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' El-Gebali, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Mistry, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Bateman, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Eddy, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Luciani, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Potter, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Qureshi, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Richardson, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Salazar, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Smart, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', “The pfam protein families database in 2019,” Nucleic acids research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 47, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' D1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' D427–D432, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [26] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Punta, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Coggill, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Eberhardt, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Mistry, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Tate, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Boursnell, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Pang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Forslund, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ceric, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Clements, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', “The pfam protein families database,” Nucleic acids research, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 40, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' D1, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' D290–D301, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [27] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Dosovitskiy, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Beyer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Kolesnikov, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Weissenborn, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Zhai, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Unterthiner, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Dehghani, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Minderer, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Heigold, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Gelly, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', “An image is worth 16x16 words: Transformers for image recognition at scale,” arXiv preprint arXiv:2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='11929, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [28] M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Klausen, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Jespersen, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Nielsen, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Jensen, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Jurtz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Soenderby, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Sommer, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Winther, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Nielsen, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Petersen, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', “Netsurfp-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0: Improved prediction of protein structural features by integrated deep learning,” Proteins: Structure, Function, and Bioinformatics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 87, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 6, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 520–527, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [29] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Almagro Armenteros, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Sønderby, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Sønderby, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Nielsen, and O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Winther, “Deeploc: prediction of protein subcellular localization using deep learning,” Bioinformatics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 33, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 21, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 3387–3395, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [30] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Rocklin, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chidyausiku, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Goreshnik, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ford, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Houliston, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Lemak, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Carter, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ravichandran, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Mulligan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chevalier, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', “Global analysis of protein folding using massively parallel design, synthesis, and testing,” Science, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 357, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 6347, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 168–175, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [31] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Hou, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Adhikari, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Cheng, “Deepsf: deep convolutional neural network for mapping protein sequences to folds,” Bioinformatics, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 34, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 8, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 1295–1303, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [32] G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Elsayed, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Goodfellow, and J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Sohl-Dickstein, “Adversarial reprogramming of neural networks,” in International Conference on Learning Representations, 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [33] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Neekhara, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Hussain, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Dubnov, and F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Koushanfar, “Adversarial reprogramming of sequence classification neural networks,” 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [34] S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Pan and Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Yang, “A survey on transfer learning,” IEEE Transactions on Knowledge and Data Engineering, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 22, no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 10, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 1345–1359, 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [35] J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Devlin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chang, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Lee, and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Toutanova, “BERT: pre-training of deep bidirectional transformers for language understanding,” CoRR, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' abs/1810.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='04805, 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [36] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Lauscher, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Majewska, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ribeiro, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Gurevych, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Rozanov, and G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Glavaš, “Common sense or world knowledge?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' investigating adapter-based knowledge injection into pretrained transformers,” arXiv preprint arXiv:2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='11787, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 13 [37] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Tsai, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chen, and T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ho, “Transfer learning without knowing: Reprogramming black-box machine learning models with scarce data and limited resources,” in International Coference on International Conference on Machine Learning, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [38] N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Papernot, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' McDaniel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Swami, and R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Harang, “Crafting adversarial input sequences for recurrent neural networks,” CoRR, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' abs/1604.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='08275, 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [39] Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Bengio, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Courville, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Vincent, “Unsupervised feature learning and deep learning: A review and new perspectives,” CoRR, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' abs/1206.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='5538, 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [40] I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Goodfellow, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Lee, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Le, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Saxe, and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ng, “Measuring invariances in deep networks,” in Advances in Neural Information Processing Systems, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 646–654, 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [41] P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Das, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Sercu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Wadhawan, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Padhi, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Gehrmann, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Cipcigan, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chenthamarakshan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Strobelt, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' d.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Santos, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chen, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', “Accelerating antimicrobial discovery with controllable deep generative models and molecular dynamics,” arXiv preprint arXiv:2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='11248, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [42] R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Vinod, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Chen, and P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Das, “Reprogramming language models for molecular representation learning,” 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [43] Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Wu, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ramsundar, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Feinberg, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Gomes, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Geniesse, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Pappu, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Leswing, and V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Pande, “Moleculenet: A benchmark for molecular machine learning,” CoRR, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' abs/1703.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='00564, 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [44] T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Brown, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Mann, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Ryder, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Subbiah, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Kaplan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Dhariwal, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Neelakantan, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Shyam, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Sastry, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Askell, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', “Language models are few-shot learners,” Advances in neural information processing systems, vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 33, pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 1877–1901, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' [45] A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Elnaggar, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Heinzinger, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Dallago, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Rihawi, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Wang, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Jones, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Gibbs, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Feher, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Angerer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Steinegger, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=', “Prottrans: towards cracking the language of life’s code through self-supervised deep learning and high performance computing,” arXiv preprint arXiv:2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='06225, 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 14 Supplementary Information Protein Task Source Model Source Task Regression or Classifica- tion Source Labels Target Labels Antimicrobial Transformer Sentiment Classification Classification Positive,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Negative AMP,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' non-AMP Toxicity Transformer Sentiment Classification Classification Positive,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Negative Toxic,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' non-Toxic Secondary Structure Transformer Sentiment Classification Classification Positive,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Neutral,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Negative Helix,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Strand,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Other Stability Transformer Sentiment Classification Regression Homology Transformer Sentiment Classification Regression Solubility Transformer Named Entity Recognition Classification Positive,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Negative Soluble,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' non-Soluble Binding Transformer Sentiment Classification Classification Positive,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Negative On-target,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Off-target Table 1: Summary of the source and target tasks for reprogramming Figure 6: Summary of protein prediction tasks and evaluation metrics with model performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Model Baselines Table 2: Toxicity and Antimicrobial-nature reported in [3].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Attribute Data-Split Accuracy Train Valid Test Majority Class Test {Toxic, non-Toxic} 8153 1019 1020 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='82 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='93 {AMP, non-AMP} 6489 811 812 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='82 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='88 R2DL Results R2DL Results from the Reduced Training Data Setting 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='1 Restricted Training Data Setting To further investigate the efficacy of the transfer learning approach, we compare the performance of R2DL versus the model trained from scratch with AMP data, with a restricted training data set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' The test accuracy across tasks 15 Evaluation R2DL Pretraining Supervised Nature Task Metric Training Training Training Accuracy Efficiency Accuracy Efficiency Accuracy Efficiency Samples Samples Samples Secondary Physicochemical top-n accuracy 8678 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='841 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='70E-05 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='10E+07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='801 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='58E-08 8678 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='623 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content="18E-05 Structure Spearman's Physicochemical Stability correlation 21446 0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='849 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='96E-05 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='10E+07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='738 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='38E-08 21446 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='660 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content="08E-05 Homology Spearman's Physicochemical 12312 0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='241 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='96E-05 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='10E+07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='265 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='56E-09 12312 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='245 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='99E-05 correlation Physicochemical Solubility top-n accuracy 16253 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='943 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='80E-05 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='70E+06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='872 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='13E-07 16253 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='856 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='27E-05 Biomedical Function Antibody Affinity top-n accuracy 4000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='9456 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='36E-04 4000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='928 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='32E-04 Biomedical Function Antimicrobial top-n accuracy 6489 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='900 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='39E-04 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='70E+06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='883 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='19E-07 6489 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='874 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='35E-04 Biomedical Function Toxicity top-n accuracy 8153 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='961 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='18E-04 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='70E+06 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='937 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='51E-07 8153 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='689 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='45E-05Table 3: Structure prediction, Remote Homology, Stability reported in [6].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Task Model Accuracy Metric Test Accuracy Secondary Structure Prediction One Hot + Alignment Accuracy (3-class) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='80 Remote Homology Detection LSTM Top 1 Accuracy 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='26 Stability Transformer Spearman’s Rho 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='73 Table 4: Solubility reported in [45] Task Model Test Accuracy Solubility ProtT5-XL- UniRef50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='91 Table 5: Antibody Affinity Binding reported in [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Task Model Test Accuracy Antibody Affinity Linear Discriminant Analysis 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='92 Table 6: R2DL: AMP Classification Source Model AMP Sequence Samples k-SVD Iterations Training Accuracy Test Accuracy BERT (Bidirectional Transformer) 6489 100 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='12 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='64 BERT (Bidirectional Transformer) 6489 250 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='67 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='33 Bi-LSTM 6489 100 79.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='40 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='90 Table 7: R2DL: Toxicity Prediction Source Model AMP Sequence Samples k-SVD Iterations Test Accuracy BERT (Bidirectional Transformer) 8153 100 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='23 BERT (Bidirectional Transformer) 8153 250 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='93 Bi-LSTM 8153 100 81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='25 Table 8: R2DL: Secondary Structure Prediction Source Model Training Samples k-SVD Iterations Training Accuracy Test Accuracy BERT 8,678 10000 71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='47 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='65 BERT 8,678 15000 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='34 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='91 BERT 8,678 20000 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='32 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='92 indicate that R2DL performs better when fewer labeled training data samples are available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' Below 25% of training data samples, both methods approximately do worse than random prediction, so we do not reduce the training data to evaluate performance after this threshold.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content=' 16 Table 9: R2DL: Remote Homolgy Detection (Top-1 Accuracy) Source Model Training Samples k-SVD Iterations Training Accuracy Test Accuracy BERT 12,312 10000 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='34 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='76 BERT 12,312 15000 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='45 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='67 BERT 12,312 20000 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='23 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='50 Table 10: R2DL: Stability (Spearman’s Rho) Source Model Training Samples k-SVD Iterations Training Accuracy Test Accuracy BERT 53,679 10000 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='23 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='89 BERT 53,679 15000 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='62 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='20 BERT 53,679 20000 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='78 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='73 Table 11: R2DL: Fluorescence (Spearman’s Rho) Source Model Training Samples k-SVD Iterations Training Accuracy Test Accuracy BERT 21,446 10000 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='29 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='82 BERT 21,446 15000 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='02 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='46 BERT 21,446 20000 70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='90 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='34 Table 12: R2DL: Solubility Source Model Training Samples k-SVD Iterations Training Accuracy Test Accuracy TinyBERT 6623 10000 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='93 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='82 TinyBERT 6623 15000 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='22 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='3 TinyBERT 6623 20000 92.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='85 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='21 Table 13: Restricted Data Setting: Toxicity Prediction Task Training Samples R2DL Test Accuracy Bi-LSTM Test Accuracy Toxicity Prediction 5000 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='12 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='34 Toxicity Prediction 6000 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='98 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='62 Toxicity Prediction 7000 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='23 82.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='78 Toxicity Prediction 8153 89.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='34 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='7 Table 14: Restricted Data Setting: AMP Prediction Task Training Samples R2DL Test Accuracy Bi-LSTM Test Accuracy AMP Prediction 3500 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='82 64.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='52 AMP Prediction 4500 72.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='76 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='41 AMP Prediction 5500 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='17 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='34 AMP Prediction 6489 90.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='01 88.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0 Table 15: Restricted Data Setting: Secondary Structure Prediction (SSP) Task Training Samples R2DL Test Accuracy Bi-LSTM Test Accuracy Structure Prediction 3378 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='09 06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='23 Structure Prediction 4478 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='26 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='93 Structure Prediction 6678 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='28 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='34 Structure Prediction 8678 84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='14 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0 17 Table 16: Restricted Data Setting: Remote Homology Detection Task Training Samples R2DL Test Accuracy Bi-LSTM Test Accuracy Homology 4312 09.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='35 03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='69 Homology 8312 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='26 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='93 Homology 10312 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='23 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='34 Homology 12312 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='14 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0 Table 17: Restricted Data Setting: Fluorescence Task Training Samples R2DL Test Accuracy Bi-LSTM Test Accuracy Fluorescence 10769 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='09 06.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='23 Fluorescence 25769 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='26 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='93 Fluorescence 45769 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='28 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='34 Fluorescence 53769 66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='34 68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0 Table 18: Restricted Data Setting: Solubility Prediction Task Training Samples R2DL Test Accuracy Bi-LSTM Test Accuracy Solubility 2500 011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0 07.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='23 Solubility 4000 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='26 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='93 Solubility 5200 85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='23 87.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='34 Solubility 6623 94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='0 93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} +page_content='1 18' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ttA0T4oBgHgl3EQfLf_G/content/2301.02120v1.pdf'} diff --git a/uNAzT4oBgHgl3EQfc_zP/content/2301.01414v1.pdf b/uNAzT4oBgHgl3EQfc_zP/content/2301.01414v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..31c8285e6d07f29a1d484d19b47d42827d93dc68 --- /dev/null +++ b/uNAzT4oBgHgl3EQfc_zP/content/2301.01414v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fcdcbc473bc2f51f81ba97a162bc1c494d03f68ac9fc431d96ff87b1834e8d82 +size 849032 diff --git a/w9E_T4oBgHgl3EQf_xxJ/vector_store/index.faiss b/w9E_T4oBgHgl3EQf_xxJ/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..262c4764f154b0307740092d7848ff1d5c3bb29c --- /dev/null +++ b/w9E_T4oBgHgl3EQf_xxJ/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:51da62250ce75b1b366541124860b7d1282b26c0f39e1101aa673fe7173826e4 +size 9109549 diff --git a/x9FST4oBgHgl3EQfSzhz/content/2301.13767v1.pdf b/x9FST4oBgHgl3EQfSzhz/content/2301.13767v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..71cdf57c01a1b4f15d3ae0b868581c63d3657ad8 --- /dev/null +++ b/x9FST4oBgHgl3EQfSzhz/content/2301.13767v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:07e64dc4418987fcf9a212a954b2d09bce4bcbc6394d4aafdc2c5328d5369bdc +size 12188176 diff --git a/xtE4T4oBgHgl3EQfYAyx/content/tmp_files/2301.05046v1.pdf.txt b/xtE4T4oBgHgl3EQfYAyx/content/tmp_files/2301.05046v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..84ab2b93353d7fdd3cc2f4ce28168ece57fa710d --- /dev/null +++ b/xtE4T4oBgHgl3EQfYAyx/content/tmp_files/2301.05046v1.pdf.txt @@ -0,0 +1,1659 @@ +Taking Search to Task +Chirag Shah +University of Washington +Seattle, USA +chirags@uw.edu +Ryen W. White +Microsoft Research +Redmond, USA +ryenw@microsoft.com +Paul Thomas +Microsoft +Canberra, Australia +pathom@microsoft.com +Bhaskar Mitra +Microsoft Research +Montréal, Canada +bmitra@microsoft.com +Shawon Sarkar +University of Washington +Seattle, USA +ss288@uw.edu +Nicholas Belkin +Rutgers University +New Brunswick, USA +belkin@comminfo.rutgers.edu +ABSTRACT +The importance of tasks in information retrieval (IR) has been long +argued for, addressed in different ways, often ignored, and fre- +quently revisited. For decades, scholars made a case for the role +that a user’s task plays in how and why that user engages in search +and what a search system should do to assist. But for the most +part, the IR community has been too focused on query processing +and assuming a search task to be a collection of user queries, often +ignoring if or how such an assumption addresses the users accom- +plishing their tasks. With emerging areas of conversational agents +and proactive IR, understanding and addressing users’ tasks has +become more important than ever before. In this paper, we provide +various perspectives on where the state-of-the-art is with regard to +tasks in IR, what are some of the bottlenecks in deriving and using +task information, and how do we go forward from here. In addition +to covering relevant literature, the paper provides a synthesis of +historical and current perspectives on understanding, extracting, +and addressing task-focused search. To ground ongoing and future +research in this area, we present a new framing device for tasks +using a tree-like structure and various moves on that structure +that allow different interpretations and applications. Presented as a +combination of synthesis of ideas and past works, proposals for fu- +ture research, and our perspectives on technical, social, and ethical +considerations, this paper is meant to help revitalize the interest +and future work in task-based IR. +CCS CONCEPTS +• Information systems → Information retrieval. +KEYWORDS +Tasks; Contextual search; Proactive search +ACM Reference Format: +Chirag Shah, Ryen W. White, Paul Thomas, Bhaskar Mitra, Shawon Sarkar, +and Nicholas Belkin. 2023. Taking Search to Task. In ACM SIGIR Conference +on Human Information Interaction and Retrieval (CHIIR ’23), March 19–23, +Permission to make digital or hard copies of part or all of this work for personal or +classroom use is granted without fee provided that copies are not made or distributed +for profit or commercial advantage and that copies bear this notice and the full citation +on the first page. Copyrights for third-party components of this work must be honored. +For all other uses, contact the owner/author(s). +CHIIR ’23, March 19–23, 2023, Austin, TX, USA +© 2023 Copyright held by the owner/author(s). +ACM ISBN 979-8-4007-0035-4/23/03. +https://doi.org/10.1145/3576840.3578288 +2023, Austin, TX, USA. ACM, New York, NY, USA, 14 pages. https://doi.org/ +10.1145/3576840.3578288 +1 +INTRODUCTION +Scholars have long argued for the importance of considering task in- +formation in information retrieval (IR) for truly helping people with +complex, unexpressed, or unclear needs [17, 45]. Over the decades, +the concept of task has been studied by many researchers who +have produced notable theoretical and practical outcomes. Several +attempts have been made to understand search tasks, characterize +and extract them, and use task knowledge to better provide support +in search and recommendation applications. There are several small +and practical successes along the way, including search services +incorporating spatial and temporal information in understanding or +expanding a query, as well as using the current context and history +activity to provide contextual recommendations. However, these +efforts can be limiting at best and harmful at worst as they fail to +regard user intents or goals as a way to model the ongoing task. +Can we meaningfully connect operationalization of search to +conceptualization of task (take search to task)? How do we create +a framing device with tasks with the explicit purpose of applying +it to various IR applications? What do we gain (and lose) if we are +successful with this? These are some of the core questions that trig- +gered our investigations – some theoretical, some empirical, and +others simply thought experiments – resulting in this perspective +paper. Thus, the purpose of this perspective paper is to shine the +light, once again, on this very important area of IR and provide a +new foundation built with current understanding and future pos- +sibilities that include emerging domains of conversational agents, +multi-device search, and proactive recommenders to guide users to +complete their tasks step by step. +The remainder of the paper is organized as follows. The next +section reviews some of the most important and transformative +research on tasks in IR over the last few decades. We also list several +recent events and activities to demonstrate the importance of this +area and emphasize the scholarly interest. In Section 3, we present +a framing device to think through possibilities and challenges for +capturing task-related information in IR. Section 4 extends this by +providing paths and perspectives as we move forward, specifically +focusing on task representation and using such representations in +IR applications. Some of such applications that are taking shape +now and are important in the future of IR are outlined in Section 5. +In Section 6, we briefly discuss methods and metrics for evaluating +task-based applications. Finally, we conclude in Section 7 with our +1 +arXiv:2301.05046v1 [cs.IR] 12 Jan 2023 + +thoughts on task futures, along with a discussion of ethical consid- +erations regarding using tasks in search and other applications. +2 +A BRIEF HISTORY OF TASKS IN IR +A task is generally considered as a set of connected physical, cogni- +tive, and affective actions through which individuals try to accom- +plish some goals in their work or everyday lives [26, 168]. In the +context of IR, the concept of task has taken on explicit meanings +related to understanding and supporting information seeking and +searching. In this section, we give an overview of the ways in which +task has been understood in previous IR-related research, beginning +with a general survey of different approaches, then considering +some specific aspects of task that have been investigated, followed +by discussion of some significant attempts to apply knowledge of +task in IR, and concluding with a discussion of recent workshops +concerning task in IR. +2.1 +Overview of Approaches to Task in IR +Some of the earliest prior research in IR related to task can be traced +back to the cognitive perspective in IR [18], which was centrally +concerned with understanding what motivated a person to engage +in information seeking and searching. This perspective influenced +works by Vakkari [167] and Ingwersen and Järvelin [77], which +consider tasks in the design of IR systems to find out for what +purposes the system is used [139] and thus provides implications +for IR system design to personalize information search according +to the task at hand. Based on a series of empirical works, Vakkari +[167] developed a framework of task-based information searching +comprising three stages: pre-focus, focus formulation, and post-focus. +Tasks are often considered multi-level information seeking pro- +cesses in which people need information to achieve a goal [e.g., +29, 139, 143, 166]. Many existing task models [e.g., 34, 88, 99] have +investigated and identified searchers’ tasks as static and overar- +ching goals that motivate search actions, but this is not always +desired as the task evolves with time and changing cognitive states. +Conversely, different characteristics or facets of tasks [99] influence +people’s interaction with intelligent systems, such as search engines +[107]. Search tasks are influenced by the work task or everyday life +task that drives them to seek information or are associated with a +problematic situation [28]. +Identification of task, at various levels, has been an area of focus. +Broder [23] proposed that a person’s intent or goal in engaging with +a search engine could be one of three types: informational, transac- +tional, and navigational. This scheme has been successfully used in +a great deal of research, to classify tasks according to search behav- +iors and for study and support of search according to type. Rose +and Levinson [137] extended Broder’s scheme by specifying types +of information goals, and adding a new goal type (resource). They +tested their scheme of motivating goals (or tasks), by classifying +search engine queries. +Many early works investigated and identified various aspects of +task which could influence a variety of search behaviors, including +task complexity [e.g., 29], task difficulty [e.g., 92] and work context +[e.g., 58]. Others considered the interactive and dynamic nature of +search tasks themselves [e.g., 13]. +Apart from task, existing studies in IR segment information seek- +ing behaviors into various levels of explicit and implicit signals. +While performing tasks, searchers’ actions are also driven by inten- +tions and can be well-defined or ill-defined [77]. These studies have +indicated that there is a close association between searchers’ per- +formance of a task and the information need, the search strategies +employed, and the assessment of document relevance and utility. +Beyond search, tasks permeate almost every aspect of our daily +work and personal lives [5]. They involve different activities, have +different constraints, and take different amounts of time to complete. +Users of task management applications would benefit from assis- +tance with many aspects of task management, especially task plan- +ning [20] and prioritization [128]. There has been recent progress +in task intelligence, in areas such as discovering digital assistant ca- +pabilities [176], estimating task durations [181], and automatically +tracking task status [182]. +It should be noted that not all research concerned with tasks +in IR has been explicitly about modeling or using task. Some such +examples include research on task trails [101], personalized search +[178], trail recommendation [150], cross-session tasks [174], task +continuation [1], and cross-device tasks [175]. +2.2 +Task Levels +According to Byström and Hansen [27, 28], task contexts in infor- +mation practices can be represented by a nested model consisting of +three levels (from outer level to inner level): work task, information +seeking task, and search task. Specifically, work tasks are separable +parts of a person’s duties in his or her workplace [28]. Everyday +life tasks that emerge from non-work scenarios can also lead to +active information seeking and searching practices (e.g., search for +and book a hotel for travel) [2]. +In addition to Byström and Hansen’s nested model of task, Xie +[190] also explored the multilevel nature of user goals and tasks and +developed a four-level hierarchical framework of goals. This four- +level typology covers a wide range of user goals and tasks (from +long-term task-independent goals to local goals behind specific +search tactics) and was verified via user studies [103, 190]. +2.3 +Task Facets +Focusing on different dimensions or task taxonomies, previous +research has examined the impacts of task types and facets on +search interactions from different perspectives. Liu et al. [105] and +Jiang et al. [82] examined the associations between user behaviors +and objective task features (i.e., task product, task goal, task type) +and discussed to what extent these behavioral features can help +disambiguate search tasks of different types. Capra et al. [34] found +that manipulating task a priori determinability via modifying task +items and dimensions can significantly affect users’ perceived task +difficulty and choices of search strategies. +With respect to task-user combined features, Wildemuth [186] +argued that in task-based information search, search tactics are in- +fluenced by users’ topical knowledge. Liu et al. [106] demonstrated +that both whole-session level and within-session search behaviors +are affected by task difficulty, and that the dynamic relationships +between search behavior and task perception are influenced by task +type. Similarly, Aula et al. [7] investigated search behavioral varia- +tions under tasks of different levels of difficulty, and found more +query variance, more usage of advanced syntax, and longer time +on search engine result pages (SERPs) with more difficult tasks. +2 + +Li and Belkin [99] developed a faceted approach to conceptualiz- +ing tasks in IR based on related literature on task classification as +well as their empirical studies on task-based information search- +ing [97, 98]. The faceted framework provides a holistic approach to +exploring the nature of tasks and conceptually supported a series +of empirical studies on task-based search interactions. +2.4 +Task Stages +Task process is an aspect of task which differs from static task prop- +erties or facets [99] (e.g., predefined task goal, task product). When +conceptualizing tasks from the process-oriented perspective, we are +essentially looking at the process of doing or performing tasks. The +core argument here is that in the context of information seeking, +we cannot define or study a task without examining how the task +was actually completed (or failed). Therefore, to fully understand a +task, we need to explore both the objective task features and users’ +responses to the evolving task environments at multiple levels (e.g., +behavioral, cognitive, emotional). +Many search process models focus on behavioral aspects and +examine the transitions of information seeking and search actions. +For instance, to describe the general process of information seek- +ing, Ellis [53] studied the information seeking patterns of academic +social scientists and broke it down into six characteristics: start- +ing, chaining, browsing, differentiating, monitoring, and extracting. +Wilson [188] suggests that in some circumstances, Ellis’ “charac- +teristics” can be organized as a sequence of information seeking +stages. Ellis’ model clearly identifies the features of information +seeking patterns and has been modified and tested empirically [e.g., +54, 55]. However, this model only describes the behavioral level of +task-based information seeking. It does not consider the interaction +between the information seeker and the multi-dimensional context +in which task states and information seeking activities evolve. +2.5 +Applying Task Knowledge in IR +Applications of task knowledge to IR have demonstrated that task +representations can be used to provide users with better query sug- +gestions [8], build user models for improved personalized search +[115, 178] and recommendation [199], and help in satisfaction pre- +diction [68, 173]. Mehrotra et al. [114] used a tensor-based approach, +representing each user as a combination of their topical interests +and their search task behaviors for personalization. Other works +have developed various novel task context embeddings to represent +queries via search logs to provide task-based personalization, query +suggestion, and re-ranking [115, 119]. Tolomei et al. [160] investi- +gated the concept of task flows and analyzed query logs to generate +task-based query suggestions. Baraglia et al. [12] introduced the +notion of search shortcuts and offered query suggestions to drive +goal attainment. +Vu et al. [171] has also used tasks to model user interests in +search. In a similar vein but in other contexts, several scholars +have leveraged task information to provide long-term support for +task completion [e.g., 1, 84, 181]. Cai et al. [31] used task models +to improve the ranking of retrieved search results to provide task- +based support to users. Tasks help users achieve their search goals +and understand and evaluate a system’s competency in helping +users do so. Hassan et al. [68] used search task constructs to predict +satisfaction. White and Kelly [185] used them to improve relevance +feedback. Song and Guo [152] demonstrated that task information +could help to automate tasks to reduce user burden. +Other researchers have focused on assistive systems in terms of +tours or trails to lead users through their search process [70, 120, +132], predicting users’ next search action based on the current ac- +tions, either by predicting the next result click [32] or by predicting +short-term interests based on task topic information [177]. +2.6 +Recent Research, Development, Activities +There continues to be significant interest and activity surrounding +tasks from the research community. Several workshops have been +held on task-based IR, focusing on search interactions, searcher +intents, and tasks in information search. This includes the SIGCHI +2012 workshop on End-user Interactions with Intelligent Systems +[156], and the Second Strategic Workshop on Information Retrieval +in Lorne (SWIRL) [4]. The Task-based and Aggregated Search work- +shop held in 2012 [96] focused on the challenges of task-based and +aggregated search, such as the mismatch between search interface +and specialized task-based functionalities, the lack of homogeneous +systems to support different tasks, and so on. In the same year, +the SIGIR 2012 workshop entitled “Entertain Me” Supporting Com- +plex Search Tasks [19] focused on fostering potential solutions to +problems faced by searchers with complex information needs. +An NSF-sponsored workshop on Task-Based Information Search +Systems, held in 2013, discussed challenges in developing systems +and tools to support tasks and user needs Kelly et al. [87]. The SIGIR +2013 workshop on Modeling User Behavior for Information Retrieval +Evaluation [39], examined ways to model search intent based on +queries. Workshops on Supporting Complex Search Tasks held in +2015 [61] and 2017 [16] initiated interdisciplinary dialog on many +task-related open research questions, including evaluation and the +role of context. The WSDM 2018 workshop on Learning from User +Interactions [113], focused on task-based intelligent systems, more +specifically on six related topics – user needs and task understand- +ing, user modeling and personalization, metrics and evaluation, user +interaction processes and context, intelligent interface design and +applications. The WSDM 2019 workshop on Task Intelligence [71], +focused on tasks in the context of system development, including +areas such search assistance, personalization, and recommendation. +Shah and White [146] also delivered a well-attended tutorial on +this topic at SIGIR 2020. +3 +TASK COMPOSITION AND SUPPORT +These decades of work have led to many different mechanisms for +representing tasks, which we can divide into two sets: explicit and +implicit representations. Explicitly represented tasks are often pre- +sented as hierarchies, trees, or lists of aspects. These are explainable +and readily interpretable. Implicit representations often use a prob- +ability distribution (over latent aspects of tasks) or encoded vectors. +Such representations are usually not meant to be interpreted by +humans, but they can offer more flexibility. +We have experimented with both of these representations over +the years [e.g., 42, 107, 121], recognizing their advantages and disad- +vantages. However, we have started to converge on ideas that offer +the best of both worlds—providing the interpretability of an explicit +representation, with the scalability of an implicit representation. +For example, we focused on task completion, defining three stages +3 + +Figure 1: An abstract task “tree”. Larger tasks may be decom- +posed into smaller tasks, and ultimately to actions. Some +of these may be unobservable (dotted lines). Task support +needs us to move “up”, “down”, and “across” the tree. See +text for notes 1○, 2○, and 3○. +of a task: beginning, continuing/exploration, and ending/terminal. For +a given task and its stage, we also attempted to identify the kinds of +support the user could use. Such support may include query or doc- +ument suggestions, snippets or answers, as well as external tools. +The goal here was to do manual (explicit) annotations for many +search sessions with known tasks to then learn a model that could +create an implicit representation (e.g., vector embeddings) of a task +with respect to some application, such as next query prediction. +However, as we worked with several real-world datasets of +search sessions, we realized that our coding scheme for task stage +and support annotations was not as comprehensive or robust as we +had hoped. We need a better framework that offers both compre- +hensive representation of a task as well as enough flexibility to be +able to accommodate various applications and datasets. We discuss +a possible approach next. +3.1 +Tasks as Trees +We now consider some mechanisms and times for a search sys- +tem to support a searcher’s tasks. Simplifying the nested model of +Byström and Järvelin [29] and the hierarchies of Xie [190], we can +say that a task (also called a “macrotask” [37]) is composed of sub- +tasks, sub-sub-tasks, and so on. For example, “arrange a vacation in +Austin” may consist of “find the best dates” and “make bookings”; +“make bookings” might be composed of “book flights” and “book +a hotel”; etc. Each of these sub-tasks could be at any of Byström +and Järvelin’s levels (Figure 1). At the lowest level, a simple task is +instead composed by “actions”: the observable things people (or as +we will discuss later, systems) might do. These could be instances of +queries, or clicks; but could also be reading books, conversing with +friends, or other moves (bottom level of Figure 1). In some cases this +structure will be explicit, as in a project plan or a hierarchical to-do +list, but more often it will not be. The structure might not be mapped +out at the start, will certainly be dynamic in all but the simplest +cases, and different strategies will be useful at different points. As +searchers may be simultaneously engaged in multiple tasks, the cor- +responding hierarchies of sub-tasks and actions may also interleave +in interesting and dynamic ways. It is our perspective that hierar- +chical representations are key to task modeling that is supported +by a body of existing literature [28, 29, 37, 80, 154, 163, 190, 191]. +In principle, a search system can offer support at each level of +this hierarchy, although in practice search support tends to be small- +scale. For example, actions are supported by techniques such as +query auto-completion (supporting the current action) or query +suggestion (supporting the next action), and these supports are +relatively well-studied [30]. Some low-level tasks are also supported +in search systems: for example, major web search engines offer +booking widgets for flights and hotels, directly supporting these +small transactional tasks. Mid-level tasks can be supported by, for +example, recognizing a flight booking and offering to book a hotel +and transport. Although only partially search applications, airline +websites routinely offer this. High-level tasks, such as planning an +entire vacation, are not at all well supported in software but are +routinely supported by (human) agents and delegates. +3.2 +Moves +The tree of (sub)tasks and actions also suggests certain moves that +competent software should make. To move left to right in the tree +is to predict or suggest the next thing in a sequence. To move up +the tree, action to task or sub-task to super-task, is to recognize a +more complex task, having recognized its constituents [e.g., 82, 108]. +Finally, to move down the tree is to decompose a task [e.g., 73, 198]. +For example, by re-ranking search results, Bennett et al. [21] +consider short-term and long-term context information for person- +alization which in our framework corresponds to moving left to +right for short and longer distances but without explicitly modeling +the hierarchy. Similarly, Mitra [120] considers sessions as paths in +query embedding spaces, again moving left to right without specifi- +cally modeling the hierarchical relationships. Finally, Sordoni et al. +[153] use a hierarchical recurrent encoder-decoder architecture to +simultaneously model the sequential relationship between terms in +a query and between queries in a session. While they do not con- +sider higher level relationships between search sessions, sub-tasks, +and tasks, it may be natural to employ such methods to model task +hierarchies. +3.3 +Challenges +This model illustrates some challenges we face, if we are to build +task-aware search completent in long run. First, some moves around +the tree are easier than others. For example, at the time of writing, +popular web search engines support small, transactional tasks— +such as booking a flight—only when the most-recent query looks +promising. Research on building longer-term task models is still +limited [95, 174], even at the scale of consecutive searches [100, 178], +meaning this move is currently only possible when there is a 1:1 +correspondence between task and action (point 1○ in Figure 1). +Some actions are also unobserved, or unobservable, from soft- +ware, even in practice ( 2○). For example, a web search engine will +most likely be unaware of a searcher’s other activity online; all +online services will be blind to a face-to-face conversation. +Finally, observed actions are sparse signals and more than one +task will have similar steps, so moving up the tree is more difficult +than moving down or sideways. We can easily imagine support for +decomposing tasks, and can also imagine going across the tree at +any level: for example, we could predict the next action given a +sequence of actions, or we could predict the next microtask given +4 + +a sequence of microtasks. It is harder to imagine getting from ob- +served actions to the uppermost (macro-) task or goal 3○, especially +when observations are incomplete 2○. We must also note that the +data searchers give us will be bound by the affordances we give +them; in practice, that means that searchers will express themselves +in short keyword phrases (“lhr lax flights”) rather than explain a +task (“I need to get to the LA office for Wednesday’s big meeting”). +Challenges for supporting tasks in search therefore include: +(1) Representing tasks in ways that allows the system to take actions. +This representation needs to handle tasks at different granular- +ity, with different topics and strategies, and tasks which persist +over time. +(2) Observing more task-relevant context, to better identify and track +tasks as they happen. This needs to include tracking across dif- +ferent devices and different timescales, so we can better identify +tasks from actions and “move up” the tree. +(3) Developing task-oriented interfaces that encourage descriptions +of task, not need and not short queries; and which support tasks +as they happen, either in the search interface or elsewhere. +4 +TASK MODELING +There are different ways we can extract, represent, and apply task +information to address the challenges discussed in Section 3.3. In +this section, we review some possible approaches we could take in +modeling and extracting complex task structures composed of any +number of tasks or sub-tasks. +4.1 +Task Representation +In the model shown in Figure 1, tasks can be defined at differ- +ent granularity levels. This flexibility provides ways to represent +tasks from different theoretical and methodological perspectives. +At the same time, it asks for a far-reaching representation capa- +ble of modeling work at multiple levels of abstraction [135]. Task +descriptions can range from a high level of abstraction to a con- +crete, granular action-oriented level with precise information need +strongly associated to the task. As mentioned by Paterno [134], to +build an intelligent task-aware search system, it is necessary to +support tasks at each level of the task hierarchy not only from top +to down but also from left to right. There are many possibilities to +instantiate our task framework by applying diverse supervised and +unsupervised techniques depending on the availability of search +interaction signals. Assuming that there may be multiple sub-tasks +associated with a user’s information need and that these sub-tasks +could be interleaved across different sessions, a bare tree extraction +algorithm has the potential to extract a hierarchical representa- +tion of tasks/sub-tasks embedded in search processes as considered +by Mehrotra and Yilmaz [117] (e.g., decomposing a macro task into +microtasks as moving down the tree in Figure 1). The approach +allows us to go across the tree at any level. +Another possible approach could be a vector representation of +tasks implicit in search behaviors (i.e., points 1○ and 3○ in Figure 1) +by triangulating observable search events with other situational and +contextual information related to the search process. This abstract +representation of tasks can especially be helpful in search scenarios +where searchers’ tasks are not clearly expressed or manifested. For +example, existing research has shown how such signals indicate +the nature of the task being done [e.g., 38, 107, 108, 122]. +To move up and down the task hierarchy, action to task or sub- +task to macro-task, it is crucial to know the connections among +the contextual components of the search session. Based on the idea +that in a real-world information network, proximal nodes in the +network structure tend to be similar or related to one another, it is +intuitive to visualize user-system interactions initiated by a specific +task as a complex graph network structure of users’ actions (i.e., +query submission, clicks on a document) and systems’ reactions +(i.e., analyze, retrieve, and display relevant related items). Similarly, +queries issued and actions performed by a user and documents +viewed within a short time period are more likely to be different +stages of the same task, sub-tasks, or sub-sub-tasks; therefore, the +search state can be extracted based on similar node representation +patterns. Therefore, a sequential heterogeneous graph embedding- +based task model [e.g., 60] could potentially capture the structural +features of interactive search sessions and represent tasks from +observable behavioral signals. This way, the model can represent +the macro-task (moving up in the tree) or the next microtask given +a sequence of microtasks (moving down or right in the tree). +We have seen several attempts to model search sessions as +Markov Decision Proceses [e.g., 36, 194], Hidden Markov Mod- +els [e.g., 33, 50] or Partially Observed Markov Models [e.g., 193]. +Taking the idea further, we could apply reinforcement learning +approaches to learn to predict or suggest the next action/task given +a sequence of actions or tasks. This is similar to search intent pre- +diction by Yao et al. [195]. +4.2 +Inferring Tasks from Observable Events +Many studies used lexical and content-based features, such as the +lexical content of queries, for determining topical and task change +in the sequence of query formulations. For example, Verma and +Yilmaz [169] tried to identify entities and clusters of terms related +to entities in queries (e.g., using tagging, TF-IDF scoring, term filter- +ing, category terms) to represent a task as a set of terms related to +an entity. Other studies have used latent search interaction events +to infer tasks (query-based features: query term cosine similarity; +URL-based features: URL domain clicked, Jaccard coefficient be- +tween clicked URL sets; session-based features: same session and +the number of sessions in between, query reformulations, click +entropy, query length, post-click actions, and session lengths; tem- +poral features: dwell time for action events). Studies have shown +how such signals indicate the nature of the task being performed, +even when there is no explicit statement [107–109, 122, 175]. De- +pending on the availability of search interaction features at a given +time, we could exploit several clustering algorithms to extract tasks. +5 +APPLICATIONS OF TASK IN SEARCH +Task information applications can pave the way for simulating, +developing, and evaluating task-aware support. Although exist- +ing search systems have improved incredibly and support users +with specific factual information tasks, their support is still lack- +ing for complex and exploratory search tasks. Given the nature of +these tasks, they need to be decomposed into multiple actionable +sub-tasks (i.e., move down the task tree shown in Figure 1). They +may require numerous rounds of interaction (queries/clicks, from +5 + +a search engine perspective) to complete those tasks [7]. Track- +ing and completing those sub-tasks increases cognitive demands, +regardless of user experience level. The task tree can be applied +to decompose exploratory and complex tasks into smaller goals, +hence reducing cognitive load. This can also help narrow the focus +of the assistance offered to the specific task at hand, which could +be represented in a semantic space (the so-called “implicit repre- +sentations” referenced earlier) to better identify the task and more +fully capture the user’s underlying goals and intentions. +In this section, we examine four applications where such consid- +erations of task-based knowledge are valuable. +5.1 +Contextual Search +Searches are performed within a situational context. Understand- +ing and modeling this context, especially the current task, is vital +for search systems in finding the most relevant information. Task +models derived from recent queries and clicks (i.e., the observable +actions in the leaf nodes of Figure 1) within the current session can +be applied to improve search engine performance [148, 189]. These +task representations can assume many forms, including distribu- +tions over topical categories [21] or semantic vectors [118]. +As we try to model tasks in a short-term search context, we +often find ourselves discussing sessions (sequences of interactions +demarcated by topic or time [84]), which are not exactly the same +as tasks (especially given multi-tasking [155]) but are a reasonable +proxy for task in a search setting and are a valuable source of +tasks data [100, 101]. Task models must evolve over time as more +evidence is collected about user interests and intentions (implicitly, +explicitly, or both) and ideally be transferable across sessions as +tasks are suspended and resume over time [1]. Other search-related +applications of task models that span the leaves of our task tree +include personalizing search results [116] and generating query +suggestions [62]. +5.2 +Multi-device Search +Complex tasks can span both time and space. Another way that the +leaves on the task tree can be related is in terms of the devices used. +As mentioned in the previous section, there has been some focus +in IR on supporting cross-session tasks [1]. Cross-device search- +ing [126, 175], where people initiate a task at one time and/or on +one device and resume it later, perhaps on a different device, is re- +lated to cross-session and may be simply because of necessity, but +also the device capabilities (e.g., larger display, availability during +commute). Supporting both types of searching requires a task rep- +resentation that is transferable between devices (something more +abstract and consistent than a sequence of observable actions). This +involves moving up in our task tree, from actions to micro-tasks, +sub-tasks, and so on, stopping at the point where the device space +can be most fully represented without being so broad that the task +representation is meaningless. Multi-device experiences capitalize +on the strengths of multiple devices simultaneously to support +complex tasks (e.g., recipe preparation, home or auto repair) [180]. +For example, we can combine a smart speaker such as an Ama- +zon Echo with a tablet such as an Apple iPad capitalizes on the +far-field speech recognition capabilities of the speaker and the high- +resolution display of the tablet. In these experiences, the evolving +task representation (implicit, explicit, or both) plays a central role +in connecting the devices and providing dynamic context. +In multi-device scenarios, as with many other task scenarios, +task assistance can be offered to users at different stages of the +task (e.g., proactively searching for resources related to the current +action [130]) depending on an understanding of the task and the +affordances available. This multi-device paradigm can also apply +directly to a search context, where, for convenience, people can +pose natural language questions to smart speakers via voice, ob- +tain quick answers, and use their smartphones or tablet devices +to review supporting information (videos, websites, documents, +etc.). For example, a child getting quick responses from a digital +assistant (e.g., an answer to a math question) on a smart speaker or +smart watch can also be shown explanatory information on a larger +display device. Supporting the use of combinations of devices in +multi-device search can provide a way for people to maximize the +quality and diversity of the information that they utilize. More fully +representing tasks, and their dynamism and context sensitivity, is +critical in supporting these multi-device behaviors. +5.3 +Conversational Agents +One of the active areas of application for task-based IR is con- +versational agents. One can imagine the following conversation +happening with an agent over voice using, for example, a smart +speaker or a smartphone. +User: I think I would like to go do some outside ac- +tivity today. Do I need to wear a face mask if I go +running? +Agent: It depends where you are running, but if you +are concerned about safety or compliance and still +want an outdoor activity, may I suggest biking? +User: Oh.. ya, sure, that could work. Do I need to +know anything? +Agent: While you don’t need to wear a mask while +biking, you should still bring one with you. There is +also a chance of some rain showers, so plan for that. +And yes, definitely carry some water. +Now let us examine what may be going on here. There are four +distinct capabilities that we see the agent exhibiting. +• Understanding the intention behind a user seeking information. +The agent understands that the user wants to do outdoor activity +while being safe. This understanding enables the agent to make +other recommendations beyond simply answering the question. +• Addressing the effects of unknown unknowns (i.e., “people don’t +know what they don’t know”). The user asked “what do I need to +know if I go biking?”, indicating their lack of knowledge about +even what may be the right questions to ask. This often happens +in human-human interactions. Here, the agent understands the +situation (task), as well as the intention behind that question and +responds with relevant suggestions. +• Zero-query recommendations. The user does not ask about weather, +but the agent deems it important to convey that information as it +may affect the outdoor activity. Also, given the nature of the ac- +tivity (biking), the agent also recommends carrying water. These +are examples of zero-query recommendations, in which an answer +is provided without there being a clear question. Again, doing +6 + +something like this requires a deep understanding of the situation +(task), the user, and their intentions. +• Proactive recommendations. The conversation starts by the user +asking a question about running, but rather than completely an- +swering that question, the agent makes a different suggestion +(biking), which turns out to be a better one. This is a case of the +agent being proactive. In order to go beyond the user’s need (at +least the expressed need) and provide a relevant and compelling +answers or recommendations, an agent needs to be able to under- +stand the purpose behind the potential task, the user’s intention +behind asking a question, and the world knowledge about how +different tasks are executed. +In short, to create an intelligent agent like the one envisioned in +the scenario above, we need to bring in the following capabilities: +• Abstracting out from a query or a question or even an observation +to the task and/or context. +• Leveraging world knowledge (in this case, public health guide- +lines and mask mandates). +• Generating recommendations from that task/context and weigh- +ing whether that would outperform query/question-based rec- +ommendation. +• Learning how to perform a task. +As one can see, much of what we need revolves around tasks. +This is just a simple example of a short conversation. Imagine hav- +ing discussions (and even debates) about health, politics, and more. +Imagine carrying out such conversations across multiple sessions, +multiple devices, and multiple people. There are tremendous possi- +bilities here for a giant leap for IR systems. We believe at its core is +the notion of task and ways to capture, represent, and address it. +5.4 +Proactive Search and Recommender +Systems +The ability to identify and automatically extract and represent tasks +accurately has implications for search or recommender systems in +understanding users’ information needs at different task levels as +well as supporting people in task completion. Therefore, it is crucial +to understand how to utilize this knowledge about tasks behind the +request to improve a system’s offerings to its users. Also, the ability +to model users’ tasks from their observable actions (at different +levels per Figure 1) unlocks new directions for solving many prob- +lems and improving user engagement and satisfaction for building +intelligent and proactive systems that can retrieve and recommend +information implicitly without requiring explicit queries or other +interactions [49]. This is important because research has shown +that people often struggle to get their tasks done due to a lack of +knowledge, motivation, or information literacy [142]. +The observable actions covered earlier are primarily those taken +by the user on their initiative, but this need not always be the case. In +mixed-initiative systems, these actions can be prompted by the sys- +tem or even taken by the system on the user’s behalf [74], i.e., new +leaf actions in the task tree can be proposed or created automatically. +The notion of proactive search systems is not new. Letizia [102] was +one of the earliest applications that provided proactive recommen- +dations during web browsing. Commercially deployed proactive, +intelligent systems such as Google Now and Microsoft Cortana can +model short-term and long-term search intents and tasks based +on search log history [64]. In recent times, Song and Guo [152] +proposed proactive recommendations to the user at specific times +based on repeated pattern recognition over time. Incorporating task +understanding into a proactive system could support users in each +task stage and help enable task completion. A task-aware intelli- +gent system could proactively identify potential problems in users’ +search paths and guide users at various task levels by providing +help recommendations or what actions could be executed next to +avoid future problems. The aforementioned task representation can +be incorporated into various sequence-to-sequence models, proba- +bilistic, or Markov decision-based reinforcement learning models +to generate proactive recommendations. +6 +EVALUATING TASK-BASED APPLICATIONS +Evaluation is central in IR [85] and this is no different in task-based +search and recommendation systems. Many of the same methodolo- +gies (user studies, simulations, etc.) used in IR to evaluate system +performance can be used to evaluate systems to support tasks in +search and recommendation settings. Non-task-based IR systems +tend to focus on ad hoc retrieval and consider each query indepen- +dently. Task-based systems consider tasks holistically, spanning +multiple queries and/or sessions, the associated context, and task +outcomes. The metrics used to determine task-based system perfor- +mance deserve special attention given the focus of these systems +on supporting full task processes (not individual queries) and at- +taining task completion (not only result relevance). We now offer a +perspective on methods and metrics for task-based evaluation. +6.1 +Methodologies +Many standard evaluation methods (user study protocols, instru- +ments, etc.) apply to the evaluation of task-based systems [85]. In +IR, the Cranfield experiments [41] and TREC [170] have driven +considerable progress, including in tasks research [197]. Beyond +Cranfield and TREC, evaluation in IR must now take a broader view +on tasks, users, and context [83], to improve experimental realism +and the reliability of conclusions drawn. Methods such as living +laboratories [91] bridge user- and system-centered research via re- +sources, tools, and infrastructure for collaborative experimentation +[11]. Mixed methods studies can provide a more complete picture +of task performance, albeit with more complexity and greater cost +than single-method studies. As mentioned earlier, tasks can extend +over time and be part of larger macrotasks. This additional context +should also factor into task-based evaluation [47]. +6.2 +Metrics +Evaluating systems on the basis of search task performance has been +explored for decades [72]. All metrics make assumptions about task +behavior, which must be validated [51]. Conceptualizing tasks and +creating task models are important in determining appropriate task- +based evaluation metrics. It is insufficient to solely target system +functionality (or even more narrowly: specific components) when +systems and users must collaborate to complete tasks successfully +[14]. We should evaluate task-based systems holistically to reach +actionable conclusions and understand system performance [10]. +We discuss that now, targeting task processes and task outcomes. +7 + +6.2.1 +Task Processes. Process metrics are focused on how people +attempt to complete the task, regardless of the task outcome. They +include: (1) Task completion time, both actual time and perceived +time. Time has been used in search evaluation [57, 192]. Task has +been shown to affect document dwell times [89, 185]. Smucker and +Clarke [151] studied time from the perspective of gain per unit +time. Perceived time can differ from stopwatch time per factors +such as attentional demand [44]; (2) Effort expended to complete the +task (e.g., the number of actions taken, recommendations reviewed, +dialog turns). In search, effort typically describes the number of +searches or clicks [9, 43]. Kelly [86] discussed the relationship be- +tween expected and experienced effort (e.g., if experienced effort +is less than expected, the task is considered easy). Effort underlies +many user models in IR evaluation [e.g., 79, 125]. Kiseleva et al. +[94] showed that user satisfaction is negatively correlated with the +amount of effort to complete a task: more effort means less user +satisfaction; (3) Engagement covers the connection between the +user and the system, spanning emotional, cognitive, and behavioral +aspects [78]. It is affected by many factors, including user and task +characteristics, user experience, and biases [131]. It can be a goal in +task-based systems (e.g., in open-domain dialog [76]) but also a side +effect (e.g., in task-oriented dialog systems [35]), and; (4) Progress +through the task. Detecting task completion can be straightforward +for some tasks, e.g., transactional tasks, but complex for others, e.g., +learning tasks [183]. Progress can be tracked using dedicated tools +[20] or inferred [182]. Recent research has built benchmarks for +measuring task progress in digital assistants [104]. Task-oriented +dialog systems, focus on metrics such as number of slots filled (𝑥 of +𝑦) [25]. These four popular metrics are broadly applicable, are easy +to define in task-based search and recommendation settings, and +can be computed at low-cost at large scale. There are other met- +rics including cognitive load [15], learning [136], affect [56], and +usability [3], which are more challenging to define and measure. +6.2.2 +Task Outcomes. Outcome metrics focus on the product of +tasks, either a real outcome (e.g., task completion) or a user-perceived +outcome (e.g., satisfaction). Salient examples include: (1) Task utility, +denoting the value of information obtained to complete the task, +e.g., relevance [123]. Relevance is affected by task stage [158] and +relevance metrics help estimate support for task completion [124]. +Relevance metrics are usually computed per query but session-level +metrics must also be considered in task scenarios [110], as must +task support beyond result pages [46]. Relevance is personal and +situational [141] and task-based evaluation must consider that, e.g., +during contextual search [21]; (2) Satisfaction with the outcome of +the task and the process, often modeled at the task/session level +[69]. Satisfaction is non-binary and impacted by task and user ef- +fects [89, 93, 185] and even query position in the session [81]. More +observations of on-task behavior enable more accurate models of +satisfaction [75, 94], and; (3) Task success, covering whether task +objectives were accomplished. This relates to satisfaction but not +entirely and can be modeled based on behavioral signals [67]. Com- +pletion events such as in-world activities may be unobservable to +online systems, making it difficult to measure task success, although +proxies e.g., conversions [24] may offer insight. Other task outcome +metrics, including novelty and diversity [40], creativity [149], and +adoption and retention, e.g., search engine switching [184] and +sustained use over time [48], are promising but are also less well +defined and require data that can be difficult to obtain. +6.3 +Additional Considerations +There are many other metrics that can apply to task-based systems +including robustness, privacy, adaptivity, and scalability [147]. In +developing task-based metrics, we also must consider user models +(e.g., personas) and task models (e.g., search strategies and goals). +Task performance is affected by many factors, including intrinsic +properties of the task (e.g., nature of the task [121], topic [112], +difficulty [187], complexity [29]) as well as extrinsic properties +such as user attributes (e.g., expertise [179], familiarity [90]), the +situation [77, 80, 144], and other factors such as meta-cognitive +skills in task planning and reflective assessment [22]. We must also +understand the nature of the user experience, which impacts how +metrics are defined and interpreted. Metrics also interact, e.g., effort +affects satisfaction [196] and they trade off, e.g., time taken versus +coverage [162]. Metrics must be contextualized, e.g., not all effort +is detrimental and more effort could also mean more learning. +Task support systems also contain multiple connected compo- +nents [128]. Evaluating per component performance has limited +value in appraising what the user would experience [162]; hence +our focus here on holistic metrics. However, the metrics may not +be correlated [59]. Integrated metrics combine multiple variables +[131, 157, 164], although these can be difficult to interpret. Sets of +metrics are commonly employed in the evaluation of task-oriented +dialog systems [172] and defining such a set of metrics that are +agreed upon by the community could help evaluate task-based +search and recommendation systems. Meta-analysis frameworks +[6, 140] analyze the extent to which metrics capture key properties +and align with user preferences; they may also be applicable here. +7 +TASK FUTURES +Considering user tasks in IR is not a new idea, but every new gener- +ation of IR students and scholars seem to encounter it in a new light +– sometimes leading to groundbreaking advancements, and other +times redoing or incrementally adding to previous work. With the +increasing attention to and importance of emerging IR applications, +we believe the time is ripe for a new generation of scholars to +not only rediscover task-based IR, but also take a conceptual and +practical leap to finally realize the vision of supporting users in +accomplishing their tasks, regardless of their information literacy +or specificity in queries. We now consider some future directions +and conclude by discussing key ethical considerations. +7.1 +Research Threads and Directions +Here, we identify some big challenges, each suitable for one or +more PhD dissertations or grant proposals: +• Task understanding +– Formalize and validate various task representations (both im- +plicit and explicit, as mentioned earlier), potentially tying them +to different contexts or applications. +– Investigate different ways to use contextual information (e.g., +spatiotemporal signals, concurrent running applications) to +better understand tasks. +8 + +– Extend task understanding across multiple sessions and/or +devices. +– Attributing and aggregating observed actions into higher-level +tasks (moving up the task tree). +• Task support +– Make task a first class object in search support, e.g., surface +guided tours in response to exploratory queries. +– Provide support for task completion (not just providing search +results), including recommending search as a means of task +completion, where appropriate. +– Integrate IR applications with existing task applications such +as Microsoft To Do and Google Tasks, as well as email and +calendar, to seamlessly surface task-related information and +actions. +– Better support complex tasks comprising multiple steps, includ- +ing decomposing complex tasks into more manageable sub- +tasks, and supporting search across multiple sessions and/or +devices. +– Support team tasks (direct collaboration, sub-task assignment, +load balancing, etc.) in addition to individual tasks. +– Cooperate with users directly, e.g., task-oriented dialog sys- +tems, to address tasks more explicitly and also to better educate +users about the role of IR systems in solving tasks. +– Explore task automation, starting with frequent or recurring +tasks, e.g., travel planning, finding job opportunities, and re- +searching a socio-political issue, including extending work on +standing queries [127] and slow search [159]. +• Task data and experimentation +– Provide lightweight task capture mechanisms, as ground truth +for machine learning models and to build trust in task assis- +tance with users by giving them agency over what task-related +information is shared with the system. +– Find ways to uncover more unobservable events related to the +task process (triangulate data sources, with user consent). +– Create shared datasets and challenges, with user consent, to +promote task-related research and mitigate risk of leaking +sensitive data via methods such as differential privacy [52]. +We believe the framing device presented in this paper (Figure +1) as well as our proposals for how such a device can be useful +in modeling and using task in search applications (Sections 4 and +5) can help for at least some of these directions. For example, the +task tree structure along with the formulations of various moves +presented in Section 3 can be used to define a set of support actions +(e.g., offer within-task query recommendations with traversal to a +sibling node, suggest related tasks with a jump to a new parallel +branch in the tree) in interactive search. This structure can be +comprised of (1) identifying which part of this task tree the user +is at a given moment; (2) deciding what could be the next set of +sub/super/related tasks could be from this tree; and (3) making and +revising recommendations based on user actions (moves). +7.2 +Ethical Considerations +Capturing and representing tasks can have benefits, but at what +cost? Many scholars have argued that low information literacy can +lead to users not being able to fully utilize the available informa- +tion or the tools to their most potential [138]. Even for users with +reasonable or high information literacy, they often “don’t know +what they don’t know” [17, 145]. In other words, if an IR system is +relying on a user explicitly and at least partially expressing their +information needs in order to provide them results or recommen- +dations, it is likely to face challenges serving these populations of +users. Extracting and using task information, and being proactive +in search can help such users [185]. However, what is often ignored +are the ethical considerations and responsibility of researchers and +developers. +As we move toward systems that go beyond serving explicit +requests from users, with task-based IR systems being one of the +examples, there are dangers in how such systems could unduly +influence user behaviors and nudge them in ways that perpetuate +bias and a false sense of trust. With rapid development in artificial +intelligence techniques that are being deployed in search systems, +those systems become less and less trustworthy, even while usu- +ally remaining trusted [133]. The feedback loops created between +systems recommending information and users selecting among +recommendations make the selections less and less useful for train- +ing: we are no longer observing human behavior, but controlling +it [111, 129]. This effect, along with other systemic effects, means +that the datasets on which models are trained include significant +biases [63, 161, 165]. +This vicious cycle of a system getting ahead of user requests to +recommend results and the users clicking on them as they either +lack motivation or enough information literacy can be manifested +in several ways. For instance, this proactive, task-based recommen- +dation could lead to a search engine promoting its own services and +tools simply because it has access to a lot more data and insights +about those entities than those from their competitors. +Identifying and modeling tasks may call for more data collection +from more people, even those who do not actively use the system. +We need to balance the need for more data and the dangers of +ubiquitous data collection such as surveillance capitalism and other +forms of abuse [65, 66, 200]. +As task modeling inherently necessitates predicting users’ next +actions/needs, we must consider the cost of false prediction (e.g., +requiring user to perform even more actions to counter the system’s +false beliefs regarding user goals or intentions). A related question +is how to recognize and respect user agency in their tasks and not +overtly influence their course of action. +We should also not assume that a task modeling system can easily +identify and address a singular objective or interest. When different +stakeholder interests are involved, how do we balance across the +different dimensions and control for unintended consequences? +For example, a tool that makes it really easy to book a flight may +unintentionally discourage users to do more research that may lead +to cheaper tickets. Finally, if task modeling is inherently complex +and resource intensive, it might mean that system designers need to +prioritize which tasks they support, raising questions about fairness +across different user populations. In short, explicating and using +task information, while important and desired, must be done with +ethical issues in mind. We should, in general, create a practice of +integrating such considerations from the outset rather than trying +to address them later or fix problems resulting from not considering +them as a posthoc activity. +9 + +ACKNOWLEDGMENTS +This work was partially supported by National Science Foundation +(NSF) grant III-1717488. +REFERENCES +[1] Eugene Agichtein, Ryen W. White, Susan T. Dumais, and Paul N. Bennett. 2012. +Search, interrupted: understanding and predicting search task continuation. +In Proceedings of the ACM SIGIR Conference on Research and Development in +Information Retrieval. 315–324. +[2] Denise E Agosto and Sandra Hughes-Hassell. 2006. Toward a model of the +everyday life information needs of urban teenagers, part 2: Empirical model. +Journal of the American Society for Information Science and Technology 57, 11 +(2006), 1418–1426. +[3] William Albert and Thomas Tullis. 2013. Measuring the User Experience: Collect- +ing, Analyzing, and Presenting Usability Metrics. Morgan Kaufmann. +[4] James Allan, Bruce Croft, Alistair Moffat, and Mark Sanderson. 2012. Frontiers, +challenges, and opportunities for information retrieval: Report from SWIRL +2012 the second strategic workshop on information retrieval in Lorne. ACM +SIGIR Forum 46, 1 (2012), 2–32. +[5] David Allen. 2015. Getting Things Done: The Art of Stress-free Productivity. +Penguin. +[6] Enrique Amigó, Damiano Spina, and Jorge Carrillo-de Albornoz. 2018. An +axiomatic analysis of diversity evaluation metrics: Introducing the rank-biased +utility metric. In Proceedings of the ACM SIGIR Conference on Research and +Development in Information Retrieval. 625–634. +[7] Anne Aula, Rehan M. Khan, and Zhiwei Guan. 2010. How Does Search Behavior +Change As Search Becomes More Difficult?. In Proceedings of the ACM SIGCHI +Conference on Human Factors in Computing Systems (Atlanta, Georgia, USA). +35–44. +[8] Ahmed Hassan Awadallah, Ryen W. White, Patrick Pantel, Susan T. Dumais, +and Yi-Min Wang. 2014. Supporting complex search tasks. In Proceedings of the +ACM CIKM Conference on Information and Knowledge Management. 829–838. +[9] Leif Azzopardi, Diane Kelly, and Kathy Brennan. 2013. How query cost affects +search behavior. In Proceedings of the ACM SIGIR Conference on Research and +Development in Information Retrieval. 23–32. +[10] Krisztian Balog. 2015. Task-completion Engines: A Vision with a Plan.. In +Proceedings of the Supporting Complex Search Task Workshop. +[11] Krisztian Balog, Liadh Kelly, and Anne Schuth. 2014. Head first: Living labs +for ad-hoc search evaluation. In Proceedings of the ACM CIKM Conference on +Information and Knowledge Management. 1815–1818. +[12] Ranieri Baraglia, Fidel Cacheda, Victor Carneiro, Vreixo Formoso, Raffaele +Perego, and Fabrizio Silvestri. 2009. Search shortcuts: Driving users towards +their goals. In Proceedings of the International Conference on the World Wide Web. +1073–1074. +[13] Marcia J Bates. 1989. The design of browsing and berrypicking techniques for +the online search interface. Online Review 13, 5 (1989), 407–424. +[14] Marcia J Bates. 1990. Where should the person stop and the information search +interface start? Information Processing and Management 26, 5 (1990), 575–591. +[15] Micheline Beaulieu. 1997. Experiments on interfaces to support query expansion. +Journal of Documentation 53, 1 (1997), 8–15. +[16] Nicholas Belkin, Toine Bogers, Jaap Kamps, Diane Kelly, Marijn Koolen, and +Emine Yilmaz. 2017. Second workshop on supporting complex search tasks. In +Proceedings of the ACM CHIIR Conference on Human Information Interaction and +Retrieval. 433–435. +[17] Nicholas J Belkin. 1980. Anomalous states of knowledge as a basis for informa- +tion retrieval. Canadian Journal of Information Science 5, 1 (1980), 133–143. +[18] Nicholas J Belkin. 1990. The cognitive viewpoint in information science. Journal +of information science 16, 1 (1990), 11–15. +[19] Nicholas J Belkin, Charles LA Clarke, Ning Gao, Jaap Kamps, and Jussi Karlgren. +2012. Report on the SIGIR workshop on “entertain me” supporting complex +search tasks. ACM SIGIR Forum 45, 2 (2012), 51–59. +[20] Victoria Bellotti, Brinda Dalal, Nathaniel Good, Peter Flynn, Daniel G Bobrow, +and Nicolas Ducheneaut. 2004. What a to-do: Studies of task management +towards the design of a personal task list manager. In Proceedings of the ACM +SIGCHI Conference on Human Factors in Computing Systems. 735–742. +[21] Paul N Bennett, Ryen W White, Wei Chu, Susan T Dumais, Peter Bailey, Fedor +Borisyuk, and Xiaoyuan Cui. 2012. Modeling the impact of short-and long-term +behavior on search personalization. In Proceedings of the 35th international ACM +SIGIR conference on Research and development in information retrieval. 185–194. +[22] John Biggs. 1988. The role of metacognition in enhancing learning. Australian +Journal of Education 32, 2 (1988), 127–138. +[23] Andrei Broder. 2002. A taxonomy of web search. In ACM Sigir forum, Vol. 36. +ACM New York, NY, USA, 3–10. +[24] Yuri M Brovman, Marie Jacob, Natraj Srinivasan, Stephen Neola, Daniel Galron, +Ryan Snyder, and Paul Wang. 2016. Optimizing similar item recommendations +in a semi-structured marketplace to maximize conversion. In Proceedings of the +ACM RecSys Conference on Recommender Systems. 199–202. +[25] Paweł Budzianowski, Tsung-Hsien Wen, Bo-Hsiang Tseng, Iñigo Casanueva, +Stefan Ultes, Osman Ramadan, and Milica Gasic. 2018. MultiWOZ-A Large-Scale +Multi-Domain Wizard-of-Oz Dataset for Task-Oriented Dialogue Modelling. +In Proceedings of the Conference on Empirical Methods in Natural Language +Processing. 5016–5026. +[26] Katriina Byström. 2007. Approaches to “task” in contemporary information +studies. In Proceedings of the International Conference on Conceptions of Library +and Information Science, Vol. 12. 1–10. +[27] Katriina Byström and Preben Hansen. 2002. Work tasks as units for analysis +in information seeking and retrieval studies. In Proceedings of the International +Conference on Conceptions of Library and Information Science. 239–251. +[28] Katriina Byström and Preben Hansen. 2005. Conceptual framework for tasks in +information studies. Journal of the American Society for Information Science and +Technology 56, 10 (2005), 1050–1061. +[29] Katriina Byström and Kalervo Järvelin. 1995. Task complexity affects infor- +mation seeking and use. Information Processing and Management 31, 2 (1995), +191–213. +[30] Fei Cai and Maarten de Rijke. 2016. A Survey of Query Auto Completion in +Information Retrieval. Foundations and Trends in Information Retrieval 10, 4 +(2016), 273–363. https://doi.org/10.1561/1500000055 +[31] Fei Cai, Shangsong Liang, and Maarten De Rijke. 2014. Personalized document +re-ranking based on bayesian probabilistic matrix factorization. In Proceedings of +the ACM SIGIR Conference on Research and Development in Information Retrieval. +835–838. +[32] Huanhuan Cao, Daxin Jiang, Jian Pei, Enhong Chen, and Hang Li. 2009. Towards +context-aware search by learning a very large variable length hidden markov +model from search logs. In Proceedings of the International Conference on the +World Wide Web. 191–200. +[33] Huanhuan Cao, Daxin Jiang, Jian Pei, Enhong Chen, and Hang Li. 2009. Towards +context-aware search by learning a very large variable length hidden markov +model from search logs. In Proceedings of the 18th international conference on +World wide web. 191–200. +[34] Robert Capra, Jaime Arguello, Heather O’Brien, Yuan Li, and Bogeum Choi. +2018. The effects of manipulating task determinability on search behaviors +and outcomes. In Proceedings of the ACM SIGIR Conference on Research and +Development in Information Retrieval. 445–454. +[35] Hongshen Chen, Xiaorui Liu, Dawei Yin, and Jiliang Tang. 2017. A survey on +dialogue systems: Recent advances and new frontiers. ACM SIGKDD Explorations +Newsletter 19, 2 (2017), 25–35. +[36] Jia Chen, Yiqun Liu, Cheng Luo, Jiaxin Mao, Min Zhang, and Shaoping Ma. +2018. Improving session search performance with a multi-MDP model. In Asia +Information Retrieval Symposium. Springer, 45–59. +[37] Justin Cheng, Jaime Teevan, Shamsi T Iqbal, and Michael S Bernstein. 2015. +Break it down: A comparison of macro-and microtasks. In Proceedings of the +33rd Annual ACM Conference on Human Factors in Computing Systems. 4061– +4064. +[38] Dongho Choi, Chirag Shah, and Vivek Singh. 2016. Probing the interconnections +between geo-exploration and information exploration behavior. In Proceedings +of the 2016 ACM International Joint Conference on Pervasive and Ubiquitous +Computing. 1170–1175. +[39] Charles LA Clarke, Luanne Freund, Mark D Smucker, and Emine Yilmaz. 2013. +Report on the SIGIR 2013 workshop on modeling user behavior for information +retrieval evaluation. ACM SIGIR Forum 47, 2 (2013), 84–95. +[40] Charles LA Clarke, Maheedhar Kolla, Gordon V Cormack, Olga Vechtomova, +Azin Ashkan, Stefan Büttcher, and Ian MacKinnon. 2008. Novelty and diversity +in information retrieval evaluation. In Proceedings of the ACM SIGIR Conference +on Research and Development in Information Retrieval. 659–666. +[41] Cyril Cleverdon. 1967. The Cranfield tests on index language devices. Aslib +Proceedings 19, 6 (1967), 173–194. +[42] Michael J Cole, Chathra Hendahewa, Nicholas J Belkin, and Chirag Shah. 2014. +Discrimination between tasks with user activity patterns during information +search. In Proceedings of the 37th international ACM SIGIR conference on Research +& development in information retrieval. 567–576. +[43] William S Cooper. 1968. Expected search length: A single measure of retrieval +effectiveness based on the weak ordering action of retrieval systems. American +Documentation 19, 1 (1968), 30–41. +[44] Mihaly Csikszentmihalyi. 1990. Flow: The Psychology of Optimal Experience. +Harper and Row. +[45] Brenda Dervin. 1998. Sense-making theory and practice: an overview of user +interests in knowledge seeking and use. Journal of Knowledge Management 2, 2 +(1998), 36–46. +[46] Doug Downey, Susan Dumais, Dan Liebling, and Eric Horvitz. 2008. Under- +standing the relationship between searchers’ queries and information goals. +In Proceedings of the ACM CIKM Conference on Information and Knowledge +Management. 449–458. +[47] Susan Dumais. 2009. Evaluating IR in situ. In Proceedings of the SIGIR Workshop +on the Future of IR Evaluation. 2. +10 + +[48] Susan Dumais. 2013. Task-based search: a search engine perspective. In Pro- +ceedings of the NSF Workshop on Task-Based Search. +[49] Susan Dumais, Edward Cutrell, Raman Sarin, and Eric Horvitz. 2004. Implicit +queries (IQ) for contextualized search. In Proceedings of the 27th annual in- +ternational ACM SIGIR conference on Research and development in information +retrieval. 594–594. +[50] Sebastian Dungs and Norbert Fuhr. 2017. Advanced hidden markov models +for recognizing search phases. In Proceedings of the ACM SIGIR International +Conference on Theory of Information Retrieval. 257–260. +[51] Georges E Dupret and Benjamin Piwowarski. 2008. A user browsing model to +predict search engine click data from past observations.. In Proceedings of the +ACM SIGIR Conference on Research and Development in Information Retrieval. +331–338. +[52] Cynthia Dwork. 2008. Differential privacy: A survey of results. In International +conference on theory and applications of models of computation. Springer, 1–19. +[53] David Ellis. 1989. A behavioural approach to information retrieval system +design. Journal of Documentation 45, 3 (1989), 171–212. +[54] David Ellis. 1993. Modeling the information-seeking patterns of academic +researchers: A grounded theory approach. The Library Quarterly 63, 4 (1993), +469–486. +[55] David Ellis, Deborah Cox, and Katherine Hall. 1993. A comparison of the +information seeking patterns of researchers in the physical and social sciences. +Journal of Documentation 49, 4 (1993), 356–369. +[56] Henry A Feild, James Allan, and Rosie Jones. 2010. Predicting searcher frustra- +tion. In Proceedings of the ACM SIGIR Conference on Research and Development +in Information Retrieval. 34–41. +[57] Steve Fox, Kuldeep Karnawat, Mark Mydland, Susan Dumais, and Thomas White. +2005. Evaluating implicit measures to improve web search. ACM Transactions +on Information Systems 23, 2 (2005), 147–168. +[58] Luanne Freund, Elaine G. Toms, and Charles L.A. Clarke. 2005. Modeling Task- +Genre Relationships for IR in the Workplace. In Proceedings of the ACM SIGIR +Conference on Research and Development in Information Retrieval. Association +for Computing Machinery, New York, NY, USA, 441–448. +[59] Erik Frøkjær, Morten Hertzum, and Kasper Hornbæk. 2000. Measuring usability: +are effectiveness, efficiency, and satisfaction really correlated?. In Proceedings of +the ACM SIGCHI Conference on Human Factors in Computing Systems. 345–352. +[60] Xinyu Fu, Jiani Zhang, Ziqiao Meng, and Irwin King. 2020. Magnn: Metap- +ath aggregated graph neural network for heterogeneous graph embedding. In +Proceedings of The Web Conference 2020. 2331–2341. +[61] Maria Gäde, Mark M Hall, Hugo Huurdeman, Jaap Kamps, Marijn Koolen, Mette +Skove, Elaine Toms, and David Walsh. 2015. Report on the first workshop on +supporting complex search tasks. ACM SIGIR Forum 49, 1 (2015), 50–56. +[62] Darío Garigliotti and Krisztian Balog. 2017. Generating query suggestions to +support task-based search. In Proceedings of the 40th International ACM SIGIR +Conference on Research and Development in Information Retrieval. 1153–1156. +[63] Robert Geirhos, Patricia Rubisch, Claudio Michaelis, Matthias Bethge, Felix A +Wichmann, and Wieland Brendel. 2018. ImageNet-trained CNNs are biased +towards texture; increasing shape bias improves accuracy and robustness. arXiv +preprint arXiv:1811.12231 (2018). +[64] Ramanathan Guha, Vineet Gupta, Vivek Raghunathan, and Ramakrishnan +Srikant. 2015. User modeling for a personal assistant. In Proceedings of the +Eighth ACM International Conference on Web Search and Data Mining. 275–284. +[65] Drew +Harwell. +2019. +Doorbell-camera +firm +Ring +has +partnered +with 400 police forces, extending surveillance concerns. +https: +//www.washingtonpost.com/technology/2019/08/28/doorbell-camera- +firm-ring-has-partnered-with-police-forces-extending-surveillance-reach/. +Downloaded 2022-02-14.. +[66] Paul Haskell-Dowland. 2021. How Apple’s AirTag turns us into unwitting spies +in a vast surveillance network. +https://www.theguardian.com/technology/ +2021/may/17/how-apples-airtag-turns-us-into-unwitting-spies-in-a-vast- +surveillance-network. Downloaded 2022-02-14.. +[67] Ahmed Hassan, Rosie Jones, and Kristina Lisa Klinkner. 2010. Beyond DCG: +user behavior as a predictor of a successful search. In Proceedings of the ACM +WSDM International Conference on Web Search and Data Mining. 221–230. +[68] Ahmed Hassan, Xiaolin Shi, Nick Craswell, and Bill Ramsey. 2013. Beyond clicks: +query reformulation as a predictor of search satisfaction. In Proceedings of the +ACM CIKM Conference on Information and Knowledge Management. 2019–2028. +[69] Ahmed Hassan, Yang Song, and Li-wei He. 2011. A task level metric for measur- +ing web search satisfaction and its application on improving relevance estima- +tion. In Proceedings of the ACM CIKM Conference on Information and Knowledge +Management. 125–134. +[70] Ahmed Hassan and Ryen W White. 2012. Task tours: helping users tackle +complex search tasks. In Proceedings of the ACM CIKM Conference on Information +and Knowledge Management. 1885–1889. +[71] Ahmed Hassan Awadallah, Cathal Gurrin, Mark Sanderson, and Ryen W White. +2019. Task Intelligence Workshop@ WSDM 2019. In Proceedings of the ACM +WSDM International Conference on Web Search and Data Mining. 848–849. +[72] William Hersh, Jeffrey Pentecost, and David Hickam. 1996. A task-oriented +approach to information retrieval evaluation. Journal of the American Society +for Information Science 47, 1 (1996), 50–56. +[73] H Ulrich Hoppe and Franz Schiele. 1992. Towards task models for embedded +information retrieval. In Proceedings of the ACM SIGCHI Conference on Human +Factors in Computing Systems. +[74] Eric Horvitz. 1999. Principles of mixed-initiative user interfaces. In Proceedings +of the SIGCHI conference on Human Factors in Computing Systems. 159–166. +[75] Jeff Huang, Ryen W White, Georg Buscher, and Kuansan Wang. 2012. Improving +searcher models using mouse cursor activity. In Proceedings of the ACM SIGIR +Conference on Research and Development in Information Retrieval. 195–204. +[76] Minlie Huang, Xiaoyan Zhu, and Jianfeng Gao. 2020. Challenges in building +intelligent open-domain dialog systems. ACM Transactions on Information +Systems 38, 3 (2020), 1–32. +[77] Peter Ingwersen and Kalervo Järvelin. 2006. The Turn: Integration of Information +Seeking and Retrieval in Context. Springer. +[78] Richard David Jacques. 1996. The nature of engagement and its role in hypermedia +evaluation and design. Ph. D. Dissertation. South Bank University. +[79] Kalervo Järvelin, Susan L Price, Lois ML Delcambre, and Marianne Lykke Nielsen. +2008. Discounted cumulated gain based evaluation of multiple-query IR sessions. +In Proceedings of the European Conference on Information Retrieval. 4–15. +[80] Kalervo Järvelin, Pertti Vakkari, Paavo Arvola, Feza Baskaya, Anni Järvelin, +Jaana Kekäläinen, Heikki Keskustalo, Sanna Kumpulainen, Miamaria Saasta- +moinen, Reijo Savolainen, et al. 2015. Task-based information interaction eval- +uation: The viewpoint of program theory. ACM Transactions on Information +Systems 33, 1 (2015), 1–30. +[81] Jiepu Jiang and James Allan. 2016. Correlation between system and user met- +rics in a session. In Proceedings of the ACM CHIIR on Conference on Human +Information Interaction and Retrieval. 285–288. +[82] Jiepu Jiang, Daqing He, and James Allan. 2014. Searching, browsing, and clicking +in a search session: changes in user behavior by task and over time. In Proceed- +ings of the ACM SIGIR Conference on Research and Development in Information +Retrieval. 607–616. +[83] Karen Sparck Jones. 2006. What’s the value of TREC: is there a gap to jump or +a chasm to bridge? ACM SIGIR Forum 40, 1 (2006), 10–20. +[84] Rosie Jones and Kristina Lisa Klinkner. 2008. Beyond the session timeout: auto- +matic hierarchical segmentation of search topics in query logs. In Proceedings of +the 17th ACM conference on Information and knowledge management. 699–708. +[85] Diane Kelly. 2009. Methods for evaluating interactive information retrieval +systems with users. Foundations and Trends in Information Retrieval 3, 1-2 (2009), +1–224. +[86] Diane Kelly. 2015. When effort exceeds expectations: A theory of search task +difficulty. In Proceedings of the ECIR Workshop on Supporting Complex Search +Tasks. +[87] Diane Kelly, Jamie Arguello, and Robert Capra. 2013. NSF Workshop on Task- +Based Search Systems. SIGIR Forum 47, 2 (2013), 116–127. +[88] Diane Kelly, Jaime Arguello, Ashlee Edwards, and Wan-ching Wu. 2015. Devel- +opment and evaluation of search tasks for IIR experiments using a cognitive +complexity framework. In Proceedings of the ACM ICTIR International Conference +on the Theory of Information Retrieval. 101–110. +[89] Diane Kelly and Nicholas J Belkin. 2004. Display time as implicit feedback: +understanding task effects. In Proceedings of the ACM SIGIR Conference on +Research and Development in Information Retrieval. 377–384. +[90] Diane Kelly and Colleen Cool. 2002. The effects of topic familiarity on informa- +tion search behavior. In Proceedings of the ACM/IEEE-CS JCDL Joint Conference +on Digital Libraries. 74–75. +[91] Diane Kelly, Susan Dumais, and Jan O Pedersen. 2009. Evaluation challenges +and directions for information-seeking support systems. Computer 3 (2009), +60–66. +[92] Jeonghyun Kim. 2006. Task difficulty as a predictor and indicator of web +searching interaction. In CHI EA ’06: CHI ’06 Extended Abstracts on Human +Factors in Computing Systems. Association for Computing Machinery, New York, +NY, USA, 959–964. +[93] Youngho Kim, Ahmed Hassan, Ryen W White, and Imed Zitouni. 2014. Modeling +dwell time to predict click-level satisfaction. In Proceedings of the ACM WSDM +International Conference on Web Search and Data Mining. 193–202. +[94] Julia Kiseleva, Kyle Williams, Jiepu Jiang, Ahmed Hassan Awadallah, Aidan C +Crook, Imed Zitouni, and Tasos Anastasakos. 2016. Understanding user satis- +faction with intelligent assistants. In Proceedings of the ACM CHIIR Conference +on Human Information Interaction and Retrieval. 121–130. +[95] Alexander Kotov, Paul N Bennett, Ryen W White, Susan T Dumais, and Jaime +Teevan. 2011. Modeling and analysis of cross-session search tasks. In Proceedings +of the 34th international ACM SIGIR conference on Research and development in +Information Retrieval. 5–14. +[96] Birger Larsen, Christina Lioma, and Arjen de Vries. 2012. Report on TBAS 2012: +workshop on task-based and aggregated search. ACM SIGIR Forum 46, 1 (2012), +71–77. +[97] Yuelin Li. 2009. Exploring the relationships between work task and search task +in information search. Journal of the American Society for Information Science +11 + +and Technology 60, 2 (2009), 275–291. +[98] Yuelin Li. 2010. An exploration of the relationships between work tasks and +users’ interaction performance. In Proceedings of the ASIS&T Annual Meeting. +1–9. +[99] Yuelin Li and Nicholas J Belkin. 2008. A faceted approach to conceptualizing +tasks in information seeking. Information Processing and Management 44, 6 +(2008), 1822–1837. +[100] Zhen Liao, Yang Song, Li-wei He, and Yalou Huang. 2012. Evaluating the effec- +tiveness of search task trails. In Proceedings of the 21st international conference +on World Wide Web. 489–498. +[101] Zhen Liao, Yang Song, Yalou Huang, Li-wei He, and Qi He. 2014. Task trail: An +effective segmentation of user search behavior. IEEE Transactions on Knowledge +and Data Engineering 26, 12 (2014), 3090–3102. +[102] Henry Lieberman et al. 1995. Letizia: An agent that assists web browsing. IJCAI +(1) 1995 (1995), 924–929. +[103] Shin-Jeng Lin and Nicholas J Belkin. 2005. Validation of a model of information +seeking over multiple search sessions. Journal of the American Society for +Information Science and Technology 56, 4 (2005), 393–415. +[104] Jonathan Liono, Johanne R Trippas, Damiano Spina, Mohammad S Rahaman, +Yongli Ren, Flora D Salim, Mark Sanderson, Falk Scholer, and Ryen W White. +2019. Building a benchmark for task progress in digital assistants. In Proceedings +of the WSDM Task Intelligence Workshop. +[105] Jingjing Liu, Michael J Cole, Chang Liu, Ralf Bierig, Jacek Gwizdka, Nicholas J +Belkin, Jun Zhang, and Xiangmin Zhang. 2010. Search behaviors in different +task types. In Proceedings of the Annual Joint Conference on Digital Libraries. +69–78. +[106] Jingjing Liu, Jacek Gwizdka, Chang Liu, and Nicholas J. Belkin. 2010. Predicting +Task Difficulty for Different Task Types. In Proceedings of the ASIS&T Annual +Meeting. 1–16. +[107] Jiqun Liu, Matthew Mitsui, Nicholas J Belkin, and Chirag Shah. 2019. Task, +information seeking Intentions, and user behavior: Toward a multi-level under- +standing of web search. In Proceedings of the ACM CHIIR Conference on Human +Information Interaction and Retrieval. 123–132. +[108] Jiqun Liu, Shawon Sarkar, and Chirag Shah. 2020. Identifying and predicting the +states of complex search tasks. In Proceedings of the 2020 Conference on Human +Information Interaction and Retrieval. 193–202. +[109] Claudio Lucchese, Salvatore Orlando, Raffaele Perego, Fabrizio Silvestri, and +Gabriele Tolomei. 2011. Identifying task-based sessions in search engine query +logs. In Proceedings of the fourth ACM international conference on Web search +and data mining. 277–286. +[110] Jiyun Luo, Christopher Wing, Hui Yang, and Marti Hearst. 2013. The water filling +model and the cube test: multi-dimensional evaluation for professional search. +In Proceedings of the ACM CIKM Conference on Information and Knowledge +Management. 709–714. +[111] Christoph Lutz. 2019. Digital inequalities in the age of artificial intelligence and +big data. Human Behavior and Emerging Technologies 1, 2 (2019), 141–148. +[112] Rishabh Mehrotra, A Hassan Awadallah, Ahmed E Kholy, and Imed Zitouni. +2017. Hey Cortana! Exploring the use cases of a Desktop based Digital Assistant. +In Proceedings of the SIGIR Workshop on Conversational Approaches to Information +Retrieval. +[113] Rishabh Mehrotra, Ahmed Hassan Awadallah, and Emine Yilmaz. 2018. Learnir: +Wsdm 2018 workshop on learning from user interactions. In Proceedings of the +ACM WSDM International Conference on Web Search and Data Mining. 797–798. +[114] Rishabh Mehrotra, Prasanta Bhattacharya, and Emine Yilmaz. 2016. Character- +izing users’ multi-tasking behavior in web search. In Proceedings of the ACM +CHIIR Conference on Human Information Interaction and Retrieval. 297–300. +[115] Rishabh Mehrotra and Emine Yilmaz. 2015. Terms, topics & tasks: Enhanced +user modelling for better personalization. In Proceedings of the ACM ICTIR +International Conference on The Theory of Information Retrieval. 131–140. +[116] Rishabh Mehrotra and Emine Yilmaz. 2015. Terms, topics & tasks: Enhanced +user modelling for better personalization. In Proceedings of the 2015 international +conference on the theory of information retrieval. 131–140. +[117] Rishabh Mehrotra and Emine Yilmaz. 2015. Towards hierarchies of search tasks +and subtasks. In Proceedings of the International Conference on the World Wide +Web. 73–74. +[118] Rishabh Mehrotra and Emine Yilmaz. 2017. Task embeddings: Learning query +embeddings using task context. In Proceedings of the 2017 ACM on conference on +information and knowledge management. 2199–2202. +[119] Rishabh Mehrotra, Emine Yilmaz, and Manisha Verma. 2014. Task-Based User +Modelling for Personalization via Probabilistic Matrix Factorization. In RecSys +Posters. +[120] Bhaskar Mitra. 2015. Exploring session context using distributed representations +of queries and reformulations. In Proceedings of the 38th international ACM SIGIR +conference on research and development in information retrieval. 3–12. +[121] Matthew Mitsui and Chirag Shah. 2018. The broad view of task type using path +analysis. In Proceedings of the ACM ICTIR International Conference on Theory of +Information Retrieval. 131–138. +[122] Matthew Mitsui and Chirag Shah. 2019. Bridging gaps: Predicting user and +task characteristics from partial user information. In Proceedings of the 42nd +International ACM SIGIR Conference on Research and Development in Information +Retrieval. 415–424. +[123] Stefano Mizzaro. 1997. Relevance: The whole history. Journal of the American +Society for Information Science 48, 9 (1997), 810–832. +[124] Alistair Moffat, Peter Bailey, Falk Scholer, and Paul Thomas. 2017. Incorporating +user expectations and behavior into the measurement of search effectiveness. +ACM Transactions on Information Systems 35, 3 (2017), 1–38. +[125] Alistair Moffat and Justin Zobel. 2008. Rank-biased precision for measurement +of retrieval effectiveness. ACM Transactions on Information Systems 27, 1 (2008), +1–27. +[126] George D Montanez, Ryen W White, and Xiao Huang. 2014. Cross-device +search. In Proceedings of the 23rd ACM international conference on conference on +information and knowledge management. 1669–1678. +[127] Meredith Ringel Morris and Eric Horvitz. 2007. S 3: storable, shareable search. +In IFIP Conference on Human-Computer Interaction. Springer, 120–123. +[128] Karen Myers, Pauline Berry, Jim Blythe, Ken Conley, Melinda Gervasio, Deb- +orah L McGuinness, David Morley, Avi Pfeffer, Martha Pollack, and Milind +Tambe. 2007. An intelligent personal assistant for task and time management. +AI Magazine 28, 2 (2007), 47–47. +[129] Hugo Neri and Fabio Cozman. 2020. The role of experts in the public perception +of risk of artificial intelligence. AI & SOCIETY 35, 3 (2020), 663–673. +[130] Elnaz Nouri, Robert Sim, Adam Fourney, and Ryen W White. 2020. Proac- +tive suggestion generation: Data and methods for stepwise task assistance. In +Proceedings of the 43rd International ACM SIGIR Conference on Research and +Development in Information Retrieval. 1585–1588. +[131] Heather L O’Brien and Elaine G Toms. 2008. What is user engagement? A +conceptual framework for defining user engagement with technology. Journal +of the American Society for Information Science and Technology 59, 6 (2008), +938–955. +[132] Brendan O’Connor, Michel Krieger, and David Ahn. 2010. Tweetmotif: Ex- +ploratory search and topic summarization for twitter. In Proceedings of the +International AAAI Conference on Web and Social Media, Vol. 4. +[133] Bing Pan, Helene Hembrooke, Thorsten Joachims, Lori Lorigo, Geri Gay, and +Laura Granka. 2007. In Google we trust: Users’ decisions on rank, position, and +relevance. Journal of computer-mediated communication 12, 3 (2007), 801–823. +[134] Fabio Paterno. 1999. Model-based design and evaluation of interactive applications. +Springer Science & Business Media. +[135] Fabio Paternò. 2004. ConcurTaskTrees: an engineered notation for task models. +The handbook of task analysis for human-computer interaction (2004), 483–503. +[136] Soo Young Rieh, Kevyn Collins-Thompson, Preben Hansen, and Hye-Jung Lee. +2016. Towards searching as a learning process: A review of current perspectives +and future directions. Journal of Information Science 42, 1 (2016), 19–34. +[137] Daniel E Rose and Danny Levinson. 2004. Understanding user goals in web +search. In Proceedings of the International Conference on the World Wide Web. +ACM, 13–19. +[138] Daniel M Russell. 2019. The Joy of Search: A Google Insider’s Guide to Going +Beyond the Basics. MIT Press. +[139] Miamaria Saastamoinen and Kalervo Järvelin. 2017. Search task features in work +tasks of varying types and complexity. Journal of the Association for Information +Science and Technology 68, 5 (2017), 1111–1123. +[140] Tetsuya Sakai. 2012. Evaluation with informational and navigational intents. In +Proceedings of the International Conference on the World Wide Web. 499–508. +[141] Tefko Saracevic. 2007. Relevance: A review of the literature and a framework for +thinking on the notion in information science. Part III: Behavior and effects of +relevance. Journal of the American Society for Information Science and Technology +58, 13 (2007), 2126–2144. +[142] Shawon Sarkar, Matthew Mitsui, Jiqun Liu, and Chirag Shah. 2020. Implicit +information need as explicit problems, help, and behavioral signals. Information +Processing & Management 57, 2 (2020), 102069. +[143] Reijo Savolainen. 2012. Expectancy-value beliefs and information needs as +motivators for task-based information seeking. Journal of Documentation 68, 4 +(2012), 492–511. +[144] Chirag Shah. 2017. Social Information Seeking. Springer. +[145] Chirag Shah. 2018. Information Fostering-Being Proactive with Information +Seeking and Retrieval: Perspective Paper. In Proceedings of the ACM CHIIR +Conference on Human Information Interaction and Retrieval. 62–71. +[146] Chirag Shah and Ryen W White. 2020. Tutorial on Task-Based Search and Assis- +tance. In Proceedings of the ACM SIGIR Conference on Research and Development +in Information Retrieval. 2436–2439. +[147] Guy Shani and Asela Gunawardana. 2011. Evaluating recommendation systems. +In Recommender Systems Handbook, Francesco Ricci, Lior Rokach, and Bracha +Shapira (Eds.). Springer, 257–297. +[148] Xuehua Shen, Bin Tan, and ChengXiang Zhai. 2005. Context-sensitive in- +formation retrieval using implicit feedback. In Proceedings of the 28th annual +international ACM SIGIR conference on Research and development in information +retrieval. 43–50. +12 + +[149] Ben Shneiderman. 2000. Creating creativity: user interfaces for supporting +innovation. ACM Transactions on Computer-Human Interaction 7, 1 (2000), +114–138. +[150] Adish Singla, Ryen White, and Jeff Huang. 2010. Studying trailfinding algorithms +for enhanced web search. In Proceedings of the 33rd international ACM SIGIR +conference on Research and development in information retrieval. 443–450. +[151] Mark D Smucker and Charles LA Clarke. 2012. Time-based calibration of +effectiveness measures. In Proceedings of the ACM SIGIR Conference on Research +and Development in Information Retrieval. 95–104. +[152] Yang Song and Qi Guo. 2016. Query-less: Predicting task repetition for nextgen +proactive search and recommendation engines. In Proceedings of the International +Conference on the World Wide Web. 543–553. +[153] Alessandro Sordoni, Yoshua Bengio, Hossein Vahabi, Christina Lioma, Jakob +Grue Simonsen, and Jian-Yun Nie. 2015. A hierarchical recurrent encoder- +decoder for generative context-aware query suggestion. In proceedings of the +24th ACM international on conference on information and knowledge management. +553–562. +[154] Ayah Soufan, Ian Ruthven, and Leif Azzopardi. 2021. Untangling the concept of +task in information seeking and retrieval. In Proceedings of the 2021 ACM SIGIR +International Conference on Theory of Information Retrieval. 73–81. +[155] Amanda Spink, Minsoo Park, Bernard J Jansen, and Jan Pedersen. 2006. Multi- +tasking during web search sessions. Information Processing & Management 42, 1 +(2006), 264–275. +[156] Simone Stumpf, Margaret Burnett, Volkmar Pipek, and Weng-Keen Wong. 2012. +End-user interactions with intelligent and autonomous systems. In Proceedings +of the ACM SIGCHI Extended Abstracts on Human Factors in Computing Systems. +2755–2758. +[157] Jean Tague-Sutcliffe. 1992. Measuring the informativeness of a retrieval process. +In Proceedings of the ACM SIGIR Conference on Research and Development in +Information Retrieval. 23–36. +[158] Arthur R Taylor, Colleen Cool, Nicholas J Belkin, and William J Amadio. 2007. +Relationships between categories of relevance criteria and stage in task comple- +tion. Information Processing and Management 43, 4 (2007), 1071–1084. +[159] Jaime Teevan, Kevyn Collins-Thompson, Ryen W White, and Susan Dumais. +2014. Slow search. Commun. ACM 57, 8 (2014), 36–38. +[160] Gabriele Tolomei, Salvatore Orlando, and Fabrizio Silvestri. 2010. Towards task- +based search and recommender systems. In Proceedings of the IEEE International +Conference on Data Engineering Workshops. 333–336. +[161] Tatiana Tommasi, Novi Patricia, Barbara Caputo, and Tinne Tuytelaars. 2017. A +deeper look at dataset bias. In Domain adaptation in computer vision applications. +Springer, 37–55. +[162] E Toms and H O’Brien. 2009. The ISSS Measurement Dilemma. IEEE Computer +42, 3 (2009), 48. +[163] Elaine G Toms. 2019. Information activities and tasks. Information at work: +information management in the workplace. London: Facet Publishing (2019), 33– +62. +[164] Elaine G Toms, Heather L O’Brien, Rick Kopak, and Luanne Freund. 2005. Search- +ing for relevance in the relevance of search. In Proceedings of the International +Conference on Conceptions of Library and Information Sciences. 59–78. +[165] Antonio Torralba and Alexei A Efros. 2011. Unbiased look at dataset bias. In +CVPR 2011. IEEE, 1521–1528. +[166] Pertti Vakkari. 1999. Task complexity, problem structure and information actions: +Integrating studies on information seeking and retrieval. Information Processing +and Management 35, 6 (1999), 819–837. +[167] Pertti Vakkari. 2001. A theory of the task-based information retrieval process: a +summary and generalisation of a longitudinal study. Journal of Documentation +57, 1 (2001). +[168] Pertti Vakkari. 2003. Task-based information searching. Annual Review of +Information Science and Technology 37, 1 (2003), 413–464. +[169] Manisha Verma and Emine Yilmaz. 2014. Entity oriented task extraction from +query logs. In Proceedings of the 23rd ACM International Conference on Conference +on Information and Knowledge Management. 1975–1978. +[170] Ellen M Voorhees and Donna K Harman (Eds.). 2005. TREC: Experiment and +evaluation in information retrieval. MIT Press, Cambridge. +[171] Thanh Vu, Alistair Willis, Son N Tran, and Dawei Song. 2015. Temporal latent +topic user profiles for search personalisation. In Proceedings of the European +Conference on Information Retrieval. 605–616. +[172] Marilyn Walker, Diane Litman, Candace A Kamm, and Alicia Abella. 1997. PAR- +ADISE: A Framework for Evaluating Spoken Dialogue Agents. In Proceedings of +the Annual Meeting of the Association for Computational Linguistics and Confer- +ence of the European Chapter of the Association for Computational Linguistics. +271–280. +[173] Hongning Wang, Yang Song, Ming-Wei Chang, Xiaodong He, Ahmed Hassan +Awadallah, and Ryen W. White. 2014. Modeling action-level satisfaction for +search task satisfaction prediction. In Proceedings of the ACM SIGIR Conference +on Research and Development in Information Retrieval. 123–132. +[174] Hongning Wang, Yang Song, Ming-Wei Chang, Xiaodong He, Ryen W White, +and Wei Chu. 2013. Learning to extract cross-session search tasks. In Proceedings +of the 22nd international conference on World Wide Web. 1353–1364. +[175] Yu Wang, Xiao Huang, and Ryen W White. 2013. Characterizing and supporting +cross-device search tasks. In Proceedings of the sixth ACM international conference +on Web search and data mining. 707–716. +[176] Ryen W White. 2018. Skill discovery in virtual assistants. Commun. ACM 61, 11 +(2018), 106–113. +[177] Ryen W White, Paul N Bennett, and Susan T Dumais. 2010. Predicting short- +term interests using activity-based search context. In Proceedings of the ACM +CIKM Conference on Information and Knowledge Management. 1009–1018. +[178] Ryen W White, Wei Chu, Ahmed Hassan, Xiaodong He, Yang Song, and Hongn- +ing Wang. 2013. Enhancing personalized search by mining and modeling task +behavior. In Proceedings of the 22nd international conference on World Wide Web. +1411–1420. +[179] Ryen W White, Susan T Dumais, and Jaime Teevan. 2009. Characterizing the +influence of domain expertise on web search behavior. In Proceedings of the +ACM WSDM International Conference on Web Search and Data Mining. 132–141. +[180] Ryen W White, Adam Fourney, Allen Herring, Paul N Bennett, Nirupama Chan- +drasekaran, Robert Sim, Elnaz Nouri, and Mark J Encarnación. 2019. Multi-device +digital assistance. Commun. ACM 62, 10 (2019), 28–31. +[181] Ryen W White and Ahmed Hassan Awadallah. 2019. Task duration estimation. +In Proceedings of the ACM WSDM International Conference on Web Search and +Data Mining. 636–644. +[182] Ryen W White, Ahmed Hassan Awadallah, and Robert Sim. 2019. Task Comple- +tion Detection: A Study in the Context of Intelligent Systems. In Proceedings of +the ACM SIGIR Conference on Research and Development in Information Retrieval. +405–414. +[183] Ryen W White and Jeff Huang. 2010. Assessing the scenic route: measuring the +value of search trails in web logs. In Proceedings of the ACM SIGIR Conference +on Research and Development in Information Retrieval. 587–594. +[184] Ryen W White, Ashish Kapoor, and Susan T Dumais. 2010. Modeling long- +term search engine usage. In Proceedings of the International Conference on User +Modeling, Adaptation, and Personalization. 28–39. +[185] Ryen W White and Diane Kelly. 2006. A study on the effects of personalization +and task information on implicit feedback performance. In Proceedings of the +15th ACM international conference on Information and knowledge management. +297–306. +[186] Barbara M Wildemuth. 2004. The effects of domain knowledge on search +tactic formulation. Journal of the American Society for Information Science and +Technology 55, 3 (2004), 246–258. +[187] Barbara M Wildemuth, Luanne Freund, and Elaine G Toms. 2014. Studies +of search task complexity or difficulty. Science and Technology 62, 9 (2014), +1676–1695. +[188] Tom D Wilson. 1999. Models in information behaviour research. Journal of +Documentation 55, 3 (1999), 249–270. +[189] Biao Xiang, Daxin Jiang, Jian Pei, Xiaohui Sun, Enhong Chen, and Hang Li. 2010. +Context-aware ranking in web search. In Proceedings of the 33rd international +ACM SIGIR conference on Research and development in information retrieval. +451–458. +[190] Iris Xie. 2008. Interactive Information Retrieval in Digital Environments. IGI +Global. +[191] Iris Xie. 2009. Dimensions of tasks: influences on information-seeking and +retrieving process. Journal of Documentation (2009). +[192] Ya Xu and David Mease. 2009. Evaluating web search using task completion +time. In Proceedings of the ACM SIGIR Conference on Research and Development +in Information Retrieval. 676–677. +[193] Grace Hui Yang, Xuchu Dong, Jiyun Luo, and Sicong Zhang. 2018. Session +search modeling by partially observable Markov decision process. Information +Retrieval Journal 21, 1 (2018), 56–80. +[194] Hui Yang, Dongyi Guan, and Sicong Zhang. 2015. The query change model: +Modeling session search as a markov decision process. ACM Transactions on +Information Systems (TOIS) 33, 4 (2015), 1–33. +[195] Jing Yao, Zhicheng Dou, Jun Xu, and Ji-Rong Wen. 2021. RLPS: A Reinforcement +Learning–Based Framework for Personalized Search. ACM Transactions on +Information Systems (TOIS) 39, 3 (2021), 1–29. +[196] Emine Yilmaz, Manisha Verma, Nick Craswell, Filip Radlinski, and Peter Bailey. +2014. Relevance and effort: An analysis of document utility. In Proceedings of +the ACM CIKM Conference on Information and Knowledge Management. 91–100. +[197] Emine Yilmaz, Manisha Verma, Rishabh Mehrotra, Evangelos Kanoulas, Ben +Carterette, and Nick Craswell. 2015. Overview of the TREC 2015 Tasks Track.. +In Proceedings of the Text Retrieval Conference. +[198] Yi Zhang, Sujay Kumar Jauhar, Julia Kiseleva, Ryen White, and Dan Roth. 2021. +Learning to decompose and organize complex tasks. In Proceedings of the 2021 +Conference of the North American Chapter of the Association for Computational +Linguistics: Human Language Technologies. 2726–2735. +[199] Yongfeng Zhang, Min Zhang, Yiqun Liu, Chua Tat-Seng, Yi Zhang, and Shaoping +Ma. 2015. Task-based recommendation on a web-scale. In Proceedings of the +IEEE International Conference on Big Data. 827–836. +13 + +[200] Shoshana Zuboff. 2019. Surveillance capitalism and the challenge of collective +action. In New labor forum, Vol. 28. SAGE Publications Sage CA: Los Angeles, +CA, 10–29. +14 + diff --git a/xtE4T4oBgHgl3EQfYAyx/content/tmp_files/load_file.txt b/xtE4T4oBgHgl3EQfYAyx/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..4679f8f335cc2a56a276f8d4bf5fe01d44f84147 --- /dev/null +++ b/xtE4T4oBgHgl3EQfYAyx/content/tmp_files/load_file.txt @@ -0,0 +1,1533 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf,len=1532 +page_content='Taking Search to Task Chirag Shah University of Washington Seattle, USA chirags@uw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='edu Ryen W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' White Microsoft Research Redmond, USA ryenw@microsoft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='com Paul Thomas Microsoft Canberra, Australia pathom@microsoft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='com Bhaskar Mitra Microsoft Research Montréal, Canada bmitra@microsoft.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='com Shawon Sarkar University of Washington Seattle, USA ss288@uw.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='edu Nicholas Belkin Rutgers University New Brunswick, USA belkin@comminfo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='rutgers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='edu ABSTRACT The importance of tasks in information retrieval (IR) has been long argued for, addressed in different ways, often ignored, and fre- quently revisited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For decades, scholars made a case for the role that a user’s task plays in how and why that user engages in search and what a search system should do to assist.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' But for the most part, the IR community has been too focused on query processing and assuming a search task to be a collection of user queries, often ignoring if or how such an assumption addresses the users accom- plishing their tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' With emerging areas of conversational agents and proactive IR, understanding and addressing users’ tasks has become more important than ever before.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In this paper, we provide various perspectives on where the state-of-the-art is with regard to tasks in IR, what are some of the bottlenecks in deriving and using task information, and how do we go forward from here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In addition to covering relevant literature, the paper provides a synthesis of historical and current perspectives on understanding, extracting, and addressing task-focused search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' To ground ongoing and future research in this area, we present a new framing device for tasks using a tree-like structure and various moves on that structure that allow different interpretations and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Presented as a combination of synthesis of ideas and past works, proposals for fu- ture research, and our perspectives on technical, social, and ethical considerations, this paper is meant to help revitalize the interest and future work in task-based IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' CCS CONCEPTS Information systems → Information retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' KEYWORDS Tasks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Contextual search;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Proactive search ACM Reference Format: Chirag Shah, Ryen W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' White, Paul Thomas, Bhaskar Mitra, Shawon Sarkar, and Nicholas Belkin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Taking Search to Task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In ACM SIGIR Conference on Human Information Interaction and Retrieval (CHIIR ’23), March 19–23, Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Copyrights for third-party components of this work must be honored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For all other uses, contact the owner/author(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' CHIIR ’23, March 19–23, 2023, Austin, TX, USA © 2023 Copyright held by the owner/author(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM ISBN 979-8-4007-0035-4/23/03.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='1145/3576840.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='3578288 2023, Austin, TX, USA.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM, New York, NY, USA, 14 pages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='org/ 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='1145/3576840.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='3578288 1 INTRODUCTION Scholars have long argued for the importance of considering task in- formation in information retrieval (IR) for truly helping people with complex, unexpressed, or unclear needs [17, 45].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Over the decades, the concept of task has been studied by many researchers who have produced notable theoretical and practical outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Several attempts have been made to understand search tasks, characterize and extract them, and use task knowledge to better provide support in search and recommendation applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' There are several small and practical successes along the way, including search services incorporating spatial and temporal information in understanding or expanding a query, as well as using the current context and history activity to provide contextual recommendations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' However, these efforts can be limiting at best and harmful at worst as they fail to regard user intents or goals as a way to model the ongoing task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Can we meaningfully connect operationalization of search to conceptualization of task (take search to task)?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' How do we create a framing device with tasks with the explicit purpose of applying it to various IR applications?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' What do we gain (and lose) if we are successful with this?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' These are some of the core questions that trig- gered our investigations – some theoretical, some empirical, and others simply thought experiments – resulting in this perspective paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Thus, the purpose of this perspective paper is to shine the light, once again, on this very important area of IR and provide a new foundation built with current understanding and future pos- sibilities that include emerging domains of conversational agents, multi-device search, and proactive recommenders to guide users to complete their tasks step by step.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The remainder of the paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The next section reviews some of the most important and transformative research on tasks in IR over the last few decades.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We also list several recent events and activities to demonstrate the importance of this area and emphasize the scholarly interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Section 3, we present a framing device to think through possibilities and challenges for capturing task-related information in IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Section 4 extends this by providing paths and perspectives as we move forward, specifically focusing on task representation and using such representations in IR applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Some of such applications that are taking shape now and are important in the future of IR are outlined in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Section 6, we briefly discuss methods and metrics for evaluating task-based applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Finally, we conclude in Section 7 with our 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='05046v1 [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='IR] 12 Jan 2023 thoughts on task futures, along with a discussion of ethical consid- erations regarding using tasks in search and other applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2 A BRIEF HISTORY OF TASKS IN IR A task is generally considered as a set of connected physical, cogni- tive, and affective actions through which individuals try to accom- plish some goals in their work or everyday lives [26, 168].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In the context of IR, the concept of task has taken on explicit meanings related to understanding and supporting information seeking and searching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In this section, we give an overview of the ways in which task has been understood in previous IR-related research, beginning with a general survey of different approaches, then considering some specific aspects of task that have been investigated, followed by discussion of some significant attempts to apply knowledge of task in IR, and concluding with a discussion of recent workshops concerning task in IR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='1 Overview of Approaches to Task in IR Some of the earliest prior research in IR related to task can be traced back to the cognitive perspective in IR [18], which was centrally concerned with understanding what motivated a person to engage in information seeking and searching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This perspective influenced works by Vakkari [167] and Ingwersen and Järvelin [77], which consider tasks in the design of IR systems to find out for what purposes the system is used [139] and thus provides implications for IR system design to personalize information search according to the task at hand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Based on a series of empirical works, Vakkari [167] developed a framework of task-based information searching comprising three stages: pre-focus, focus formulation, and post-focus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Tasks are often considered multi-level information seeking pro- cesses in which people need information to achieve a goal [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 29, 139, 143, 166].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Many existing task models [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 34, 88, 99] have investigated and identified searchers’ tasks as static and overar- ching goals that motivate search actions, but this is not always desired as the task evolves with time and changing cognitive states.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Conversely, different characteristics or facets of tasks [99] influence people’s interaction with intelligent systems, such as search engines [107].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Search tasks are influenced by the work task or everyday life task that drives them to seek information or are associated with a problematic situation [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Identification of task, at various levels, has been an area of focus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Broder [23] proposed that a person’s intent or goal in engaging with a search engine could be one of three types: informational, transac- tional, and navigational.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This scheme has been successfully used in a great deal of research, to classify tasks according to search behav- iors and for study and support of search according to type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Rose and Levinson [137] extended Broder’s scheme by specifying types of information goals, and adding a new goal type (resource).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' They tested their scheme of motivating goals (or tasks), by classifying search engine queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Many early works investigated and identified various aspects of task which could influence a variety of search behaviors, including task complexity [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 29], task difficulty [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 92] and work context [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 58].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Others considered the interactive and dynamic nature of search tasks themselves [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 13].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Apart from task, existing studies in IR segment information seek- ing behaviors into various levels of explicit and implicit signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' While performing tasks, searchers’ actions are also driven by inten- tions and can be well-defined or ill-defined [77].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' These studies have indicated that there is a close association between searchers’ per- formance of a task and the information need, the search strategies employed, and the assessment of document relevance and utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Beyond search, tasks permeate almost every aspect of our daily work and personal lives [5].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' They involve different activities, have different constraints, and take different amounts of time to complete.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Users of task management applications would benefit from assis- tance with many aspects of task management, especially task plan- ning [20] and prioritization [128].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' There has been recent progress in task intelligence, in areas such as discovering digital assistant ca- pabilities [176], estimating task durations [181], and automatically tracking task status [182].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' It should be noted that not all research concerned with tasks in IR has been explicitly about modeling or using task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Some such examples include research on task trails [101], personalized search [178], trail recommendation [150], cross-session tasks [174], task continuation [1], and cross-device tasks [175].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='2 Task Levels According to Byström and Hansen [27, 28], task contexts in infor- mation practices can be represented by a nested model consisting of three levels (from outer level to inner level): work task, information seeking task, and search task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Specifically, work tasks are separable parts of a person’s duties in his or her workplace [28].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Everyday life tasks that emerge from non-work scenarios can also lead to active information seeking and searching practices (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', search for and book a hotel for travel) [2].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In addition to Byström and Hansen’s nested model of task, Xie [190] also explored the multilevel nature of user goals and tasks and developed a four-level hierarchical framework of goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This four- level typology covers a wide range of user goals and tasks (from long-term task-independent goals to local goals behind specific search tactics) and was verified via user studies [103, 190].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='3 Task Facets Focusing on different dimensions or task taxonomies, previous research has examined the impacts of task types and facets on search interactions from different perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [105] and Jiang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [82] examined the associations between user behaviors and objective task features (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', task product, task goal, task type) and discussed to what extent these behavioral features can help disambiguate search tasks of different types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Capra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [34] found that manipulating task a priori determinability via modifying task items and dimensions can significantly affect users’ perceived task difficulty and choices of search strategies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' With respect to task-user combined features, Wildemuth [186] argued that in task-based information search, search tactics are in- fluenced by users’ topical knowledge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [106] demonstrated that both whole-session level and within-session search behaviors are affected by task difficulty, and that the dynamic relationships between search behavior and task perception are influenced by task type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Similarly, Aula et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [7] investigated search behavioral varia- tions under tasks of different levels of difficulty, and found more query variance, more usage of advanced syntax, and longer time on search engine result pages (SERPs) with more difficult tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2 Li and Belkin [99] developed a faceted approach to conceptualiz- ing tasks in IR based on related literature on task classification as well as their empirical studies on task-based information search- ing [97, 98].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The faceted framework provides a holistic approach to exploring the nature of tasks and conceptually supported a series of empirical studies on task-based search interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='4 Task Stages Task process is an aspect of task which differs from static task prop- erties or facets [99] (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', predefined task goal, task product).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' When conceptualizing tasks from the process-oriented perspective, we are essentially looking at the process of doing or performing tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The core argument here is that in the context of information seeking, we cannot define or study a task without examining how the task was actually completed (or failed).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Therefore, to fully understand a task, we need to explore both the objective task features and users’ responses to the evolving task environments at multiple levels (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', behavioral, cognitive, emotional).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Many search process models focus on behavioral aspects and examine the transitions of information seeking and search actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For instance, to describe the general process of information seek- ing, Ellis [53] studied the information seeking patterns of academic social scientists and broke it down into six characteristics: start- ing, chaining, browsing, differentiating, monitoring, and extracting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Wilson [188] suggests that in some circumstances, Ellis’ “charac- teristics” can be organized as a sequence of information seeking stages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Ellis’ model clearly identifies the features of information seeking patterns and has been modified and tested empirically [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 54, 55].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' However, this model only describes the behavioral level of task-based information seeking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' It does not consider the interaction between the information seeker and the multi-dimensional context in which task states and information seeking activities evolve.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='5 Applying Task Knowledge in IR Applications of task knowledge to IR have demonstrated that task representations can be used to provide users with better query sug- gestions [8], build user models for improved personalized search [115, 178] and recommendation [199], and help in satisfaction pre- diction [68, 173].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Mehrotra et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [114] used a tensor-based approach, representing each user as a combination of their topical interests and their search task behaviors for personalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Other works have developed various novel task context embeddings to represent queries via search logs to provide task-based personalization, query suggestion, and re-ranking [115, 119].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Tolomei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [160] investi- gated the concept of task flows and analyzed query logs to generate task-based query suggestions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Baraglia et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [12] introduced the notion of search shortcuts and offered query suggestions to drive goal attainment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Vu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [171] has also used tasks to model user interests in search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In a similar vein but in other contexts, several scholars have leveraged task information to provide long-term support for task completion [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 1, 84, 181].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Cai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [31] used task models to improve the ranking of retrieved search results to provide task- based support to users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Tasks help users achieve their search goals and understand and evaluate a system’s competency in helping users do so.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Hassan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [68] used search task constructs to predict satisfaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' White and Kelly [185] used them to improve relevance feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Song and Guo [152] demonstrated that task information could help to automate tasks to reduce user burden.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Other researchers have focused on assistive systems in terms of tours or trails to lead users through their search process [70, 120, 132], predicting users’ next search action based on the current ac- tions, either by predicting the next result click [32] or by predicting short-term interests based on task topic information [177].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='6 Recent Research, Development, Activities There continues to be significant interest and activity surrounding tasks from the research community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Several workshops have been held on task-based IR, focusing on search interactions, searcher intents, and tasks in information search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This includes the SIGCHI 2012 workshop on End-user Interactions with Intelligent Systems [156], and the Second Strategic Workshop on Information Retrieval in Lorne (SWIRL) [4].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The Task-based and Aggregated Search work- shop held in 2012 [96] focused on the challenges of task-based and aggregated search, such as the mismatch between search interface and specialized task-based functionalities, the lack of homogeneous systems to support different tasks, and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In the same year, the SIGIR 2012 workshop entitled “Entertain Me” Supporting Com- plex Search Tasks [19] focused on fostering potential solutions to problems faced by searchers with complex information needs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' An NSF-sponsored workshop on Task-Based Information Search Systems, held in 2013, discussed challenges in developing systems and tools to support tasks and user needs Kelly et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [87].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The SIGIR 2013 workshop on Modeling User Behavior for Information Retrieval Evaluation [39], examined ways to model search intent based on queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Workshops on Supporting Complex Search Tasks held in 2015 [61] and 2017 [16] initiated interdisciplinary dialog on many task-related open research questions, including evaluation and the role of context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The WSDM 2018 workshop on Learning from User Interactions [113], focused on task-based intelligent systems, more specifically on six related topics – user needs and task understand- ing, user modeling and personalization, metrics and evaluation, user interaction processes and context, intelligent interface design and applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The WSDM 2019 workshop on Task Intelligence [71], focused on tasks in the context of system development, including areas such search assistance, personalization, and recommendation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Shah and White [146] also delivered a well-attended tutorial on this topic at SIGIR 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 3 TASK COMPOSITION AND SUPPORT These decades of work have led to many different mechanisms for representing tasks, which we can divide into two sets: explicit and implicit representations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Explicitly represented tasks are often pre- sented as hierarchies, trees, or lists of aspects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' These are explainable and readily interpretable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Implicit representations often use a prob- ability distribution (over latent aspects of tasks) or encoded vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Such representations are usually not meant to be interpreted by humans, but they can offer more flexibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We have experimented with both of these representations over the years [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 42, 107, 121], recognizing their advantages and disad- vantages.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' However, we have started to converge on ideas that offer the best of both worlds—providing the interpretability of an explicit representation, with the scalability of an implicit representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For example, we focused on task completion, defining three stages 3 Figure 1: An abstract task “tree”.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Larger tasks may be decom- posed into smaller tasks, and ultimately to actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Some of these may be unobservable (dotted lines).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task support needs us to move “up”, “down”, and “across” the tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' See text for notes 1○, 2○, and 3○.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' of a task: beginning, continuing/exploration, and ending/terminal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For a given task and its stage, we also attempted to identify the kinds of support the user could use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Such support may include query or doc- ument suggestions, snippets or answers, as well as external tools.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The goal here was to do manual (explicit) annotations for many search sessions with known tasks to then learn a model that could create an implicit representation (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', vector embeddings) of a task with respect to some application, such as next query prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' However, as we worked with several real-world datasets of search sessions, we realized that our coding scheme for task stage and support annotations was not as comprehensive or robust as we had hoped.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We need a better framework that offers both compre- hensive representation of a task as well as enough flexibility to be able to accommodate various applications and datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We discuss a possible approach next.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='1 Tasks as Trees We now consider some mechanisms and times for a search sys- tem to support a searcher’s tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Simplifying the nested model of Byström and Järvelin [29] and the hierarchies of Xie [190], we can say that a task (also called a “macrotask” [37]) is composed of sub- tasks, sub-sub-tasks, and so on.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For example, “arrange a vacation in Austin” may consist of “find the best dates” and “make bookings”;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' “make bookings” might be composed of “book flights” and “book a hotel”;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Each of these sub-tasks could be at any of Byström and Järvelin’s levels (Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' At the lowest level, a simple task is instead composed by “actions”: the observable things people (or as we will discuss later, systems) might do.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' These could be instances of queries, or clicks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' but could also be reading books, conversing with friends, or other moves (bottom level of Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In some cases this structure will be explicit, as in a project plan or a hierarchical to-do list, but more often it will not be.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The structure might not be mapped out at the start, will certainly be dynamic in all but the simplest cases, and different strategies will be useful at different points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' As searchers may be simultaneously engaged in multiple tasks, the cor- responding hierarchies of sub-tasks and actions may also interleave in interesting and dynamic ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' It is our perspective that hierar- chical representations are key to task modeling that is supported by a body of existing literature [28, 29, 37, 80, 154, 163, 190, 191].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In principle, a search system can offer support at each level of this hierarchy, although in practice search support tends to be small- scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For example, actions are supported by techniques such as query auto-completion (supporting the current action) or query suggestion (supporting the next action), and these supports are relatively well-studied [30].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Some low-level tasks are also supported in search systems: for example, major web search engines offer booking widgets for flights and hotels, directly supporting these small transactional tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Mid-level tasks can be supported by, for example, recognizing a flight booking and offering to book a hotel and transport.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Although only partially search applications, airline websites routinely offer this.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' High-level tasks, such as planning an entire vacation, are not at all well supported in software but are routinely supported by (human) agents and delegates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='2 Moves The tree of (sub)tasks and actions also suggests certain moves that competent software should make.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' To move left to right in the tree is to predict or suggest the next thing in a sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' To move up the tree, action to task or sub-task to super-task, is to recognize a more complex task, having recognized its constituents [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 82, 108].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Finally, to move down the tree is to decompose a task [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 73, 198].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For example, by re-ranking search results, Bennett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [21] consider short-term and long-term context information for person- alization which in our framework corresponds to moving left to right for short and longer distances but without explicitly modeling the hierarchy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Similarly, Mitra [120] considers sessions as paths in query embedding spaces, again moving left to right without specifi- cally modeling the hierarchical relationships.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Finally, Sordoni et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [153] use a hierarchical recurrent encoder-decoder architecture to simultaneously model the sequential relationship between terms in a query and between queries in a session.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' While they do not con- sider higher level relationships between search sessions, sub-tasks, and tasks, it may be natural to employ such methods to model task hierarchies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='3 Challenges This model illustrates some challenges we face, if we are to build task-aware search completent in long run.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' First, some moves around the tree are easier than others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For example, at the time of writing, popular web search engines support small, transactional tasks— such as booking a flight—only when the most-recent query looks promising.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Research on building longer-term task models is still limited [95, 174], even at the scale of consecutive searches [100, 178], meaning this move is currently only possible when there is a 1:1 correspondence between task and action (point 1○ in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Some actions are also unobserved, or unobservable, from soft- ware, even in practice ( 2○).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For example, a web search engine will most likely be unaware of a searcher’s other activity online;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' all online services will be blind to a face-to-face conversation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Finally, observed actions are sparse signals and more than one task will have similar steps, so moving up the tree is more difficult than moving down or sideways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We can easily imagine support for decomposing tasks, and can also imagine going across the tree at any level: for example, we could predict the next action given a sequence of actions, or we could predict the next microtask given 4 a sequence of microtasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' It is harder to imagine getting from ob- served actions to the uppermost (macro-) task or goal 3○, especially when observations are incomplete 2○.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We must also note that the data searchers give us will be bound by the affordances we give them;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' in practice, that means that searchers will express themselves in short keyword phrases (“lhr lax flights”) rather than explain a task (“I need to get to the LA office for Wednesday’s big meeting”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Challenges for supporting tasks in search therefore include: (1) Representing tasks in ways that allows the system to take actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This representation needs to handle tasks at different granular- ity, with different topics and strategies, and tasks which persist over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' (2) Observing more task-relevant context, to better identify and track tasks as they happen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This needs to include tracking across dif- ferent devices and different timescales, so we can better identify tasks from actions and “move up” the tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' (3) Developing task-oriented interfaces that encourage descriptions of task, not need and not short queries;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' and which support tasks as they happen, either in the search interface or elsewhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 4 TASK MODELING There are different ways we can extract, represent, and apply task information to address the challenges discussed in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In this section, we review some possible approaches we could take in modeling and extracting complex task structures composed of any number of tasks or sub-tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='1 Task Representation In the model shown in Figure 1, tasks can be defined at differ- ent granularity levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This flexibility provides ways to represent tasks from different theoretical and methodological perspectives.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' At the same time, it asks for a far-reaching representation capa- ble of modeling work at multiple levels of abstraction [135].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task descriptions can range from a high level of abstraction to a con- crete, granular action-oriented level with precise information need strongly associated to the task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' As mentioned by Paterno [134], to build an intelligent task-aware search system, it is necessary to support tasks at each level of the task hierarchy not only from top to down but also from left to right.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' There are many possibilities to instantiate our task framework by applying diverse supervised and unsupervised techniques depending on the availability of search interaction signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Assuming that there may be multiple sub-tasks associated with a user’s information need and that these sub-tasks could be interleaved across different sessions, a bare tree extraction algorithm has the potential to extract a hierarchical representa- tion of tasks/sub-tasks embedded in search processes as considered by Mehrotra and Yilmaz [117] (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', decomposing a macro task into microtasks as moving down the tree in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The approach allows us to go across the tree at any level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Another possible approach could be a vector representation of tasks implicit in search behaviors (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', points 1○ and 3○ in Figure 1) by triangulating observable search events with other situational and contextual information related to the search process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This abstract representation of tasks can especially be helpful in search scenarios where searchers’ tasks are not clearly expressed or manifested.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For example, existing research has shown how such signals indicate the nature of the task being done [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 38, 107, 108, 122].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' To move up and down the task hierarchy, action to task or sub- task to macro-task, it is crucial to know the connections among the contextual components of the search session.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Based on the idea that in a real-world information network, proximal nodes in the network structure tend to be similar or related to one another, it is intuitive to visualize user-system interactions initiated by a specific task as a complex graph network structure of users’ actions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', query submission, clicks on a document) and systems’ reactions (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', analyze, retrieve, and display relevant related items).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Similarly, queries issued and actions performed by a user and documents viewed within a short time period are more likely to be different stages of the same task, sub-tasks, or sub-sub-tasks;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' therefore, the search state can be extracted based on similar node representation patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Therefore, a sequential heterogeneous graph embedding- based task model [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 60] could potentially capture the structural features of interactive search sessions and represent tasks from observable behavioral signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This way, the model can represent the macro-task (moving up in the tree) or the next microtask given a sequence of microtasks (moving down or right in the tree).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We have seen several attempts to model search sessions as Markov Decision Proceses [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 36, 194], Hidden Markov Mod- els [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 33, 50] or Partially Observed Markov Models [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 193].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Taking the idea further, we could apply reinforcement learning approaches to learn to predict or suggest the next action/task given a sequence of actions or tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This is similar to search intent pre- diction by Yao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [195].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='2 Inferring Tasks from Observable Events Many studies used lexical and content-based features, such as the lexical content of queries, for determining topical and task change in the sequence of query formulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For example, Verma and Yilmaz [169] tried to identify entities and clusters of terms related to entities in queries (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', using tagging, TF-IDF scoring, term filter- ing, category terms) to represent a task as a set of terms related to an entity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Other studies have used latent search interaction events to infer tasks (query-based features: query term cosine similarity;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' URL-based features: URL domain clicked, Jaccard coefficient be- tween clicked URL sets;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' session-based features: same session and the number of sessions in between, query reformulations, click entropy, query length, post-click actions, and session lengths;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' tem- poral features: dwell time for action events).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Studies have shown how such signals indicate the nature of the task being performed, even when there is no explicit statement [107–109, 122, 175].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' De- pending on the availability of search interaction features at a given time, we could exploit several clustering algorithms to extract tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 5 APPLICATIONS OF TASK IN SEARCH Task information applications can pave the way for simulating, developing, and evaluating task-aware support.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Although exist- ing search systems have improved incredibly and support users with specific factual information tasks, their support is still lack- ing for complex and exploratory search tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Given the nature of these tasks, they need to be decomposed into multiple actionable sub-tasks (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', move down the task tree shown in Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' They may require numerous rounds of interaction (queries/clicks, from 5 a search engine perspective) to complete those tasks [7].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Track- ing and completing those sub-tasks increases cognitive demands, regardless of user experience level.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The task tree can be applied to decompose exploratory and complex tasks into smaller goals, hence reducing cognitive load.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This can also help narrow the focus of the assistance offered to the specific task at hand, which could be represented in a semantic space (the so-called “implicit repre- sentations” referenced earlier) to better identify the task and more fully capture the user’s underlying goals and intentions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In this section, we examine four applications where such consid- erations of task-based knowledge are valuable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='1 Contextual Search Searches are performed within a situational context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Understand- ing and modeling this context, especially the current task, is vital for search systems in finding the most relevant information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task models derived from recent queries and clicks (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', the observable actions in the leaf nodes of Figure 1) within the current session can be applied to improve search engine performance [148, 189].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' These task representations can assume many forms, including distribu- tions over topical categories [21] or semantic vectors [118].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' As we try to model tasks in a short-term search context, we often find ourselves discussing sessions (sequences of interactions demarcated by topic or time [84]), which are not exactly the same as tasks (especially given multi-tasking [155]) but are a reasonable proxy for task in a search setting and are a valuable source of tasks data [100, 101].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task models must evolve over time as more evidence is collected about user interests and intentions (implicitly, explicitly, or both) and ideally be transferable across sessions as tasks are suspended and resume over time [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Other search-related applications of task models that span the leaves of our task tree include personalizing search results [116] and generating query suggestions [62].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='2 Multi-device Search Complex tasks can span both time and space.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Another way that the leaves on the task tree can be related is in terms of the devices used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' As mentioned in the previous section, there has been some focus in IR on supporting cross-session tasks [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Cross-device search- ing [126, 175], where people initiate a task at one time and/or on one device and resume it later, perhaps on a different device, is re- lated to cross-session and may be simply because of necessity, but also the device capabilities (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', larger display, availability during commute).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Supporting both types of searching requires a task rep- resentation that is transferable between devices (something more abstract and consistent than a sequence of observable actions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This involves moving up in our task tree, from actions to micro-tasks, sub-tasks, and so on, stopping at the point where the device space can be most fully represented without being so broad that the task representation is meaningless.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Multi-device experiences capitalize on the strengths of multiple devices simultaneously to support complex tasks (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', recipe preparation, home or auto repair) [180].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For example, we can combine a smart speaker such as an Ama- zon Echo with a tablet such as an Apple iPad capitalizes on the far-field speech recognition capabilities of the speaker and the high- resolution display of the tablet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In these experiences, the evolving task representation (implicit, explicit, or both) plays a central role in connecting the devices and providing dynamic context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In multi-device scenarios, as with many other task scenarios, task assistance can be offered to users at different stages of the task (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', proactively searching for resources related to the current action [130]) depending on an understanding of the task and the affordances available.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This multi-device paradigm can also apply directly to a search context, where, for convenience, people can pose natural language questions to smart speakers via voice, ob- tain quick answers, and use their smartphones or tablet devices to review supporting information (videos, websites, documents, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For example, a child getting quick responses from a digital assistant (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', an answer to a math question) on a smart speaker or smart watch can also be shown explanatory information on a larger display device.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Supporting the use of combinations of devices in multi-device search can provide a way for people to maximize the quality and diversity of the information that they utilize.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' More fully representing tasks, and their dynamism and context sensitivity, is critical in supporting these multi-device behaviors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='3 Conversational Agents One of the active areas of application for task-based IR is con- versational agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' One can imagine the following conversation happening with an agent over voice using, for example, a smart speaker or a smartphone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' User: I think I would like to go do some outside ac- tivity today.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Do I need to wear a face mask if I go running?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Agent: It depends where you are running, but if you are concerned about safety or compliance and still want an outdoor activity, may I suggest biking?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' User: Oh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='. ya, sure, that could work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Do I need to know anything?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Agent: While you don’t need to wear a mask while biking, you should still bring one with you.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' There is also a chance of some rain showers, so plan for that.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' And yes, definitely carry some water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Now let us examine what may be going on here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' There are four distinct capabilities that we see the agent exhibiting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Understanding the intention behind a user seeking information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The agent understands that the user wants to do outdoor activity while being safe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This understanding enables the agent to make other recommendations beyond simply answering the question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Addressing the effects of unknown unknowns (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', “people don’t know what they don’t know”).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The user asked “what do I need to know if I go biking?”' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', indicating their lack of knowledge about even what may be the right questions to ask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This often happens in human-human interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Here, the agent understands the situation (task), as well as the intention behind that question and responds with relevant suggestions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Zero-query recommendations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The user does not ask about weather, but the agent deems it important to convey that information as it may affect the outdoor activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Also, given the nature of the ac- tivity (biking), the agent also recommends carrying water.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' These are examples of zero-query recommendations, in which an answer is provided without there being a clear question.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Again, doing 6 something like this requires a deep understanding of the situation (task), the user, and their intentions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Proactive recommendations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The conversation starts by the user asking a question about running, but rather than completely an- swering that question, the agent makes a different suggestion (biking), which turns out to be a better one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This is a case of the agent being proactive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In order to go beyond the user’s need (at least the expressed need) and provide a relevant and compelling answers or recommendations, an agent needs to be able to under- stand the purpose behind the potential task, the user’s intention behind asking a question, and the world knowledge about how different tasks are executed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In short, to create an intelligent agent like the one envisioned in the scenario above, we need to bring in the following capabilities: Abstracting out from a query or a question or even an observation to the task and/or context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Leveraging world knowledge (in this case, public health guide- lines and mask mandates).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Generating recommendations from that task/context and weigh- ing whether that would outperform query/question-based rec- ommendation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Learning how to perform a task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' As one can see, much of what we need revolves around tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This is just a simple example of a short conversation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Imagine hav- ing discussions (and even debates) about health, politics, and more.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Imagine carrying out such conversations across multiple sessions, multiple devices, and multiple people.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' There are tremendous possi- bilities here for a giant leap for IR systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We believe at its core is the notion of task and ways to capture, represent, and address it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='4 Proactive Search and Recommender Systems The ability to identify and automatically extract and represent tasks accurately has implications for search or recommender systems in understanding users’ information needs at different task levels as well as supporting people in task completion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Therefore, it is crucial to understand how to utilize this knowledge about tasks behind the request to improve a system’s offerings to its users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Also, the ability to model users’ tasks from their observable actions (at different levels per Figure 1) unlocks new directions for solving many prob- lems and improving user engagement and satisfaction for building intelligent and proactive systems that can retrieve and recommend information implicitly without requiring explicit queries or other interactions [49].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This is important because research has shown that people often struggle to get their tasks done due to a lack of knowledge, motivation, or information literacy [142].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The observable actions covered earlier are primarily those taken by the user on their initiative, but this need not always be the case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In mixed-initiative systems, these actions can be prompted by the sys- tem or even taken by the system on the user’s behalf [74], i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', new leaf actions in the task tree can be proposed or created automatically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The notion of proactive search systems is not new.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Letizia [102] was one of the earliest applications that provided proactive recommen- dations during web browsing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Commercially deployed proactive, intelligent systems such as Google Now and Microsoft Cortana can model short-term and long-term search intents and tasks based on search log history [64].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In recent times, Song and Guo [152] proposed proactive recommendations to the user at specific times based on repeated pattern recognition over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Incorporating task understanding into a proactive system could support users in each task stage and help enable task completion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' A task-aware intelli- gent system could proactively identify potential problems in users’ search paths and guide users at various task levels by providing help recommendations or what actions could be executed next to avoid future problems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The aforementioned task representation can be incorporated into various sequence-to-sequence models, proba- bilistic, or Markov decision-based reinforcement learning models to generate proactive recommendations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 6 EVALUATING TASK-BASED APPLICATIONS Evaluation is central in IR [85] and this is no different in task-based search and recommendation systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Many of the same methodolo- gies (user studies, simulations, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=') used in IR to evaluate system performance can be used to evaluate systems to support tasks in search and recommendation settings.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Non-task-based IR systems tend to focus on ad hoc retrieval and consider each query indepen- dently.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task-based systems consider tasks holistically, spanning multiple queries and/or sessions, the associated context, and task outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The metrics used to determine task-based system perfor- mance deserve special attention given the focus of these systems on supporting full task processes (not individual queries) and at- taining task completion (not only result relevance).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We now offer a perspective on methods and metrics for task-based evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='1 Methodologies Many standard evaluation methods (user study protocols, instru- ments, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=') apply to the evaluation of task-based systems [85].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In IR, the Cranfield experiments [41] and TREC [170] have driven considerable progress, including in tasks research [197].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Beyond Cranfield and TREC, evaluation in IR must now take a broader view on tasks, users, and context [83], to improve experimental realism and the reliability of conclusions drawn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Methods such as living laboratories [91] bridge user- and system-centered research via re- sources, tools, and infrastructure for collaborative experimentation [11].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Mixed methods studies can provide a more complete picture of task performance, albeit with more complexity and greater cost than single-method studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' As mentioned earlier, tasks can extend over time and be part of larger macrotasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This additional context should also factor into task-based evaluation [47].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='2 Metrics Evaluating systems on the basis of search task performance has been explored for decades [72].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' All metrics make assumptions about task behavior, which must be validated [51].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Conceptualizing tasks and creating task models are important in determining appropriate task- based evaluation metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' It is insufficient to solely target system functionality (or even more narrowly: specific components) when systems and users must collaborate to complete tasks successfully [14].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We should evaluate task-based systems holistically to reach actionable conclusions and understand system performance [10].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We discuss that now, targeting task processes and task outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 7 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='1 Task Processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Process metrics are focused on how people attempt to complete the task, regardless of the task outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' They include: (1) Task completion time, both actual time and perceived time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Time has been used in search evaluation [57, 192].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task has been shown to affect document dwell times [89, 185].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Smucker and Clarke [151] studied time from the perspective of gain per unit time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Perceived time can differ from stopwatch time per factors such as attentional demand [44];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' (2) Effort expended to complete the task (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', the number of actions taken, recommendations reviewed, dialog turns).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In search, effort typically describes the number of searches or clicks [9, 43].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Kelly [86] discussed the relationship be- tween expected and experienced effort (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', if experienced effort is less than expected, the task is considered easy).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Effort underlies many user models in IR evaluation [e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', 79, 125].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Kiseleva et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [94] showed that user satisfaction is negatively correlated with the amount of effort to complete a task: more effort means less user satisfaction;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' (3) Engagement covers the connection between the user and the system, spanning emotional, cognitive, and behavioral aspects [78].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' It is affected by many factors, including user and task characteristics, user experience, and biases [131].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' It can be a goal in task-based systems (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', in open-domain dialog [76]) but also a side effect (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', in task-oriented dialog systems [35]), and;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' (4) Progress through the task.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Detecting task completion can be straightforward for some tasks, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', transactional tasks, but complex for others, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', learning tasks [183].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Progress can be tracked using dedicated tools [20] or inferred [182].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Recent research has built benchmarks for measuring task progress in digital assistants [104].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task-oriented dialog systems, focus on metrics such as number of slots filled (𝑥 of 𝑦) [25].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' These four popular metrics are broadly applicable, are easy to define in task-based search and recommendation settings, and can be computed at low-cost at large scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' There are other met- rics including cognitive load [15], learning [136], affect [56], and usability [3], which are more challenging to define and measure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='2 Task Outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Outcome metrics focus on the product of tasks, either a real outcome (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', task completion) or a user-perceived outcome (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', satisfaction).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Salient examples include: (1) Task utility, denoting the value of information obtained to complete the task, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', relevance [123].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Relevance is affected by task stage [158] and relevance metrics help estimate support for task completion [124].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Relevance metrics are usually computed per query but session-level metrics must also be considered in task scenarios [110], as must task support beyond result pages [46].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Relevance is personal and situational [141] and task-based evaluation must consider that, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', during contextual search [21];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' (2) Satisfaction with the outcome of the task and the process, often modeled at the task/session level [69].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Satisfaction is non-binary and impacted by task and user ef- fects [89, 93, 185] and even query position in the session [81].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' More observations of on-task behavior enable more accurate models of satisfaction [75, 94], and;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' (3) Task success, covering whether task objectives were accomplished.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This relates to satisfaction but not entirely and can be modeled based on behavioral signals [67].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Com- pletion events such as in-world activities may be unobservable to online systems, making it difficult to measure task success, although proxies e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', conversions [24] may offer insight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Other task outcome metrics, including novelty and diversity [40], creativity [149], and adoption and retention, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', search engine switching [184] and sustained use over time [48], are promising but are also less well defined and require data that can be difficult to obtain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='3 Additional Considerations There are many other metrics that can apply to task-based systems including robustness, privacy, adaptivity, and scalability [147].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In developing task-based metrics, we also must consider user models (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', personas) and task models (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', search strategies and goals).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task performance is affected by many factors, including intrinsic properties of the task (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', nature of the task [121], topic [112], difficulty [187], complexity [29]) as well as extrinsic properties such as user attributes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', expertise [179], familiarity [90]), the situation [77, 80, 144], and other factors such as meta-cognitive skills in task planning and reflective assessment [22].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We must also understand the nature of the user experience, which impacts how metrics are defined and interpreted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Metrics also interact, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', effort affects satisfaction [196] and they trade off, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', time taken versus coverage [162].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Metrics must be contextualized, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', not all effort is detrimental and more effort could also mean more learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task support systems also contain multiple connected compo- nents [128].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Evaluating per component performance has limited value in appraising what the user would experience [162];' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' hence our focus here on holistic metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' However, the metrics may not be correlated [59].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Integrated metrics combine multiple variables [131, 157, 164], although these can be difficult to interpret.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Sets of metrics are commonly employed in the evaluation of task-oriented dialog systems [172] and defining such a set of metrics that are agreed upon by the community could help evaluate task-based search and recommendation systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Meta-analysis frameworks [6, 140] analyze the extent to which metrics capture key properties and align with user preferences;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' they may also be applicable here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 7 TASK FUTURES Considering user tasks in IR is not a new idea, but every new gener- ation of IR students and scholars seem to encounter it in a new light – sometimes leading to groundbreaking advancements, and other times redoing or incrementally adding to previous work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' With the increasing attention to and importance of emerging IR applications, we believe the time is ripe for a new generation of scholars to not only rediscover task-based IR, but also take a conceptual and practical leap to finally realize the vision of supporting users in accomplishing their tasks, regardless of their information literacy or specificity in queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We now consider some future directions and conclude by discussing key ethical considerations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='1 Research Threads and Directions Here, we identify some big challenges, each suitable for one or more PhD dissertations or grant proposals: Task understanding – Formalize and validate various task representations (both im- plicit and explicit, as mentioned earlier), potentially tying them to different contexts or applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' – Investigate different ways to use contextual information (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', spatiotemporal signals, concurrent running applications) to better understand tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 8 – Extend task understanding across multiple sessions and/or devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' – Attributing and aggregating observed actions into higher-level tasks (moving up the task tree).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task support – Make task a first class object in search support, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', surface guided tours in response to exploratory queries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' – Provide support for task completion (not just providing search results), including recommending search as a means of task completion, where appropriate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' – Integrate IR applications with existing task applications such as Microsoft To Do and Google Tasks, as well as email and calendar, to seamlessly surface task-related information and actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' – Better support complex tasks comprising multiple steps, includ- ing decomposing complex tasks into more manageable sub- tasks, and supporting search across multiple sessions and/or devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' – Support team tasks (direct collaboration, sub-task assignment, load balancing, etc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=') in addition to individual tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' – Cooperate with users directly, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', task-oriented dialog sys- tems, to address tasks more explicitly and also to better educate users about the role of IR systems in solving tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' – Explore task automation, starting with frequent or recurring tasks, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', travel planning, finding job opportunities, and re- searching a socio-political issue, including extending work on standing queries [127] and slow search [159].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task data and experimentation – Provide lightweight task capture mechanisms, as ground truth for machine learning models and to build trust in task assis- tance with users by giving them agency over what task-related information is shared with the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' – Find ways to uncover more unobservable events related to the task process (triangulate data sources, with user consent).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' – Create shared datasets and challenges, with user consent, to promote task-related research and mitigate risk of leaking sensitive data via methods such as differential privacy [52].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We believe the framing device presented in this paper (Figure 1) as well as our proposals for how such a device can be useful in modeling and using task in search applications (Sections 4 and 5) can help for at least some of these directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For example, the task tree structure along with the formulations of various moves presented in Section 3 can be used to define a set of support actions (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', offer within-task query recommendations with traversal to a sibling node, suggest related tasks with a jump to a new parallel branch in the tree) in interactive search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This structure can be comprised of (1) identifying which part of this task tree the user is at a given moment;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' (2) deciding what could be the next set of sub/super/related tasks could be from this tree;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' and (3) making and revising recommendations based on user actions (moves).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='2 Ethical Considerations Capturing and representing tasks can have benefits, but at what cost?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Many scholars have argued that low information literacy can lead to users not being able to fully utilize the available informa- tion or the tools to their most potential [138].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Even for users with reasonable or high information literacy, they often “don’t know what they don’t know” [17, 145].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In other words, if an IR system is relying on a user explicitly and at least partially expressing their information needs in order to provide them results or recommen- dations, it is likely to face challenges serving these populations of users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Extracting and using task information, and being proactive in search can help such users [185].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' However, what is often ignored are the ethical considerations and responsibility of researchers and developers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' As we move toward systems that go beyond serving explicit requests from users, with task-based IR systems being one of the examples, there are dangers in how such systems could unduly influence user behaviors and nudge them in ways that perpetuate bias and a false sense of trust.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' With rapid development in artificial intelligence techniques that are being deployed in search systems, those systems become less and less trustworthy, even while usu- ally remaining trusted [133].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The feedback loops created between systems recommending information and users selecting among recommendations make the selections less and less useful for train- ing: we are no longer observing human behavior, but controlling it [111, 129].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This effect, along with other systemic effects, means that the datasets on which models are trained include significant biases [63, 161, 165].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' This vicious cycle of a system getting ahead of user requests to recommend results and the users clicking on them as they either lack motivation or enough information literacy can be manifested in several ways.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For instance, this proactive, task-based recommen- dation could lead to a search engine promoting its own services and tools simply because it has access to a lot more data and insights about those entities than those from their competitors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Identifying and modeling tasks may call for more data collection from more people, even those who do not actively use the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We need to balance the need for more data and the dangers of ubiquitous data collection such as surveillance capitalism and other forms of abuse [65, 66, 200].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' As task modeling inherently necessitates predicting users’ next actions/needs, we must consider the cost of false prediction (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=', requiring user to perform even more actions to counter the system’s false beliefs regarding user goals or intentions).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' A related question is how to recognize and respect user agency in their tasks and not overtly influence their course of action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We should also not assume that a task modeling system can easily identify and address a singular objective or interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' When different stakeholder interests are involved, how do we balance across the different dimensions and control for unintended consequences?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' For example, a tool that makes it really easy to book a flight may unintentionally discourage users to do more research that may lead to cheaper tickets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Finally, if task modeling is inherently complex and resource intensive, it might mean that system designers need to prioritize which tasks they support, raising questions about fairness across different user populations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In short, explicating and using task information, while important and desired, must be done with ethical issues in mind.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' We should, in general, create a practice of integrating such considerations from the outset rather than trying to address them later or fix problems resulting from not considering them as a posthoc activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 9 ACKNOWLEDGMENTS This work was partially supported by National Science Foundation (NSF) grant III-1717488.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' REFERENCES [1] Eugene Agichtein, Ryen W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' White, Susan T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Dumais, and Paul N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Bennett.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Search, interrupted: understanding and predicting search task continuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 315–324.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [2] Denise E Agosto and Sandra Hughes-Hassell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Toward a model of the everyday life information needs of urban teenagers, part 2: Empirical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of the American Society for Information Science and Technology 57, 11 (2006), 1418–1426.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [3] William Albert and Thomas Tullis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Measuring the User Experience: Collect- ing, Analyzing, and Presenting Usability Metrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Morgan Kaufmann.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [4] James Allan, Bruce Croft, Alistair Moffat, and Mark Sanderson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Frontiers, challenges, and opportunities for information retrieval: Report from SWIRL 2012 the second strategic workshop on information retrieval in Lorne.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM SIGIR Forum 46, 1 (2012), 2–32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [5] David Allen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Getting Things Done: The Art of Stress-free Productivity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Penguin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [6] Enrique Amigó, Damiano Spina, and Jorge Carrillo-de Albornoz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' An axiomatic analysis of diversity evaluation metrics: Introducing the rank-biased utility metric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 625–634.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [7] Anne Aula, Rehan M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Khan, and Zhiwei Guan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' How Does Search Behavior Change As Search Becomes More Difficult?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='. In Proceedings of the ACM SIGCHI Conference on Human Factors in Computing Systems (Atlanta, Georgia, USA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 35–44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [8] Ahmed Hassan Awadallah, Ryen W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' White, Patrick Pantel, Susan T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Dumais, and Yi-Min Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Supporting complex search tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM CIKM Conference on Information and Knowledge Management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 829–838.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [9] Leif Azzopardi, Diane Kelly, and Kathy Brennan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' How query cost affects search behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 23–32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [10] Krisztian Balog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task-completion Engines: A Vision with a Plan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='. In Proceedings of the Supporting Complex Search Task Workshop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [11] Krisztian Balog, Liadh Kelly, and Anne Schuth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Head first: Living labs for ad-hoc search evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM CIKM Conference on Information and Knowledge Management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1815–1818.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [12] Ranieri Baraglia, Fidel Cacheda, Victor Carneiro, Vreixo Formoso, Raffaele Perego, and Fabrizio Silvestri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Search shortcuts: Driving users towards their goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the International Conference on the World Wide Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1073–1074.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [13] Marcia J Bates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The design of browsing and berrypicking techniques for the online search interface.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Online Review 13, 5 (1989), 407–424.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [14] Marcia J Bates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Where should the person stop and the information search interface start?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Information Processing and Management 26, 5 (1990), 575–591.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [15] Micheline Beaulieu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Experiments on interfaces to support query expansion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of Documentation 53, 1 (1997), 8–15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [16] Nicholas Belkin, Toine Bogers, Jaap Kamps, Diane Kelly, Marijn Koolen, and Emine Yilmaz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Second workshop on supporting complex search tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM CHIIR Conference on Human Information Interaction and Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 433–435.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [17] Nicholas J Belkin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1980.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Anomalous states of knowledge as a basis for informa- tion retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Canadian Journal of Information Science 5, 1 (1980), 133–143.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [18] Nicholas J Belkin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The cognitive viewpoint in information science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of information science 16, 1 (1990), 11–15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [19] Nicholas J Belkin, Charles LA Clarke, Ning Gao, Jaap Kamps, and Jussi Karlgren.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Report on the SIGIR workshop on “entertain me” supporting complex search tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM SIGIR Forum 45, 2 (2012), 51–59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [20] Victoria Bellotti, Brinda Dalal, Nathaniel Good, Peter Flynn, Daniel G Bobrow, and Nicolas Ducheneaut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' What a to-do: Studies of task management towards the design of a personal task list manager.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGCHI Conference on Human Factors in Computing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 735–742.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [21] Paul N Bennett, Ryen W White, Wei Chu, Susan T Dumais, Peter Bailey, Fedor Borisyuk, and Xiaoyuan Cui.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Modeling the impact of short-and long-term behavior on search personalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 35th international ACM SIGIR conference on Research and development in information retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 185–194.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [22] John Biggs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1988.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The role of metacognition in enhancing learning.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Australian Journal of Education 32, 2 (1988), 127–138.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [23] Andrei Broder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' A taxonomy of web search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In ACM Sigir forum, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM New York, NY, USA, 3–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [24] Yuri M Brovman, Marie Jacob, Natraj Srinivasan, Stephen Neola, Daniel Galron, Ryan Snyder, and Paul Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Optimizing similar item recommendations in a semi-structured marketplace to maximize conversion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM RecSys Conference on Recommender Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 199–202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [25] Paweł Budzianowski, Tsung-Hsien Wen, Bo-Hsiang Tseng, Iñigo Casanueva, Stefan Ultes, Osman Ramadan, and Milica Gasic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' MultiWOZ-A Large-Scale Multi-Domain Wizard-of-Oz Dataset for Task-Oriented Dialogue Modelling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the Conference on Empirical Methods in Natural Language Processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 5016–5026.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [26] Katriina Byström.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Approaches to “task” in contemporary information studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the International Conference on Conceptions of Library and Information Science, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1–10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [27] Katriina Byström and Preben Hansen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Work tasks as units for analysis in information seeking and retrieval studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the International Conference on Conceptions of Library and Information Science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 239–251.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [28] Katriina Byström and Preben Hansen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Conceptual framework for tasks in information studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of the American Society for Information Science and Technology 56, 10 (2005), 1050–1061.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [29] Katriina Byström and Kalervo Järvelin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task complexity affects infor- mation seeking and use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Information Processing and Management 31, 2 (1995), 191–213.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [30] Fei Cai and Maarten de Rijke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' A Survey of Query Auto Completion in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Foundations and Trends in Information Retrieval 10, 4 (2016), 273–363.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' https://doi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='org/10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='1561/1500000055 [31] Fei Cai, Shangsong Liang, and Maarten De Rijke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Personalized document re-ranking based on bayesian probabilistic matrix factorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 835–838.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [32] Huanhuan Cao, Daxin Jiang, Jian Pei, Enhong Chen, and Hang Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Towards context-aware search by learning a very large variable length hidden markov model from search logs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the International Conference on the World Wide Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 191–200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [33] Huanhuan Cao, Daxin Jiang, Jian Pei, Enhong Chen, and Hang Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Towards context-aware search by learning a very large variable length hidden markov model from search logs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 18th international conference on World wide web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 191–200.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [34] Robert Capra, Jaime Arguello, Heather O’Brien, Yuan Li, and Bogeum Choi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The effects of manipulating task determinability on search behaviors and outcomes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 445–454.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [35] Hongshen Chen, Xiaorui Liu, Dawei Yin, and Jiliang Tang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' A survey on dialogue systems: Recent advances and new frontiers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM SIGKDD Explorations Newsletter 19, 2 (2017), 25–35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [36] Jia Chen, Yiqun Liu, Cheng Luo, Jiaxin Mao, Min Zhang, and Shaoping Ma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Improving session search performance with a multi-MDP model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Asia Information Retrieval Symposium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Springer, 45–59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [37] Justin Cheng, Jaime Teevan, Shamsi T Iqbal, and Michael S Bernstein.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Break it down: A comparison of macro-and microtasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 33rd Annual ACM Conference on Human Factors in Computing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 4061– 4064.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [38] Dongho Choi, Chirag Shah, and Vivek Singh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Probing the interconnections between geo-exploration and information exploration behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 2016 ACM International Joint Conference on Pervasive and Ubiquitous Computing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1170–1175.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [39] Charles LA Clarke, Luanne Freund, Mark D Smucker, and Emine Yilmaz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Report on the SIGIR 2013 workshop on modeling user behavior for information retrieval evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM SIGIR Forum 47, 2 (2013), 84–95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [40] Charles LA Clarke, Maheedhar Kolla, Gordon V Cormack, Olga Vechtomova, Azin Ashkan, Stefan Büttcher, and Ian MacKinnon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Novelty and diversity in information retrieval evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 659–666.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [41] Cyril Cleverdon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1967.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The Cranfield tests on index language devices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Aslib Proceedings 19, 6 (1967), 173–194.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [42] Michael J Cole, Chathra Hendahewa, Nicholas J Belkin, and Chirag Shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Discrimination between tasks with user activity patterns during information search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 37th international ACM SIGIR conference on Research & development in information retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 567–576.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [43] William S Cooper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1968.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Expected search length: A single measure of retrieval effectiveness based on the weak ordering action of retrieval systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' American Documentation 19, 1 (1968), 30–41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [44] Mihaly Csikszentmihalyi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1990.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Flow: The Psychology of Optimal Experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Harper and Row.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [45] Brenda Dervin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1998.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Sense-making theory and practice: an overview of user interests in knowledge seeking and use.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of Knowledge Management 2, 2 (1998), 36–46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [46] Doug Downey, Susan Dumais, Dan Liebling, and Eric Horvitz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Under- standing the relationship between searchers’ queries and information goals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM CIKM Conference on Information and Knowledge Management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 449–458.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [47] Susan Dumais.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Evaluating IR in situ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the SIGIR Workshop on the Future of IR Evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 10 [48] Susan Dumais.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task-based search: a search engine perspective.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Pro- ceedings of the NSF Workshop on Task-Based Search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [49] Susan Dumais, Edward Cutrell, Raman Sarin, and Eric Horvitz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Implicit queries (IQ) for contextualized search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 27th annual in- ternational ACM SIGIR conference on Research and development in information retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 594–594.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [50] Sebastian Dungs and Norbert Fuhr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Advanced hidden markov models for recognizing search phases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR International Conference on Theory of Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 257–260.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [51] Georges E Dupret and Benjamin Piwowarski.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' A user browsing model to predict search engine click data from past observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='. In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 331–338.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [52] Cynthia Dwork.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Differential privacy: A survey of results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In International conference on theory and applications of models of computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Springer, 1–19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [53] David Ellis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1989.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' A behavioural approach to information retrieval system design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of Documentation 45, 3 (1989), 171–212.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [54] David Ellis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Modeling the information-seeking patterns of academic researchers: A grounded theory approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The Library Quarterly 63, 4 (1993), 469–486.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [55] David Ellis, Deborah Cox, and Katherine Hall.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1993.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' A comparison of the information seeking patterns of researchers in the physical and social sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of Documentation 49, 4 (1993), 356–369.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [56] Henry A Feild, James Allan, and Rosie Jones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Predicting searcher frustra- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 34–41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [57] Steve Fox, Kuldeep Karnawat, Mark Mydland, Susan Dumais, and Thomas White.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Evaluating implicit measures to improve web search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM Transactions on Information Systems 23, 2 (2005), 147–168.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [58] Luanne Freund, Elaine G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Toms, and Charles L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Clarke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Modeling Task- Genre Relationships for IR in the Workplace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Association for Computing Machinery, New York, NY, USA, 441–448.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [59] Erik Frøkjær, Morten Hertzum, and Kasper Hornbæk.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Measuring usability: are effectiveness, efficiency, and satisfaction really correlated?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='. In Proceedings of the ACM SIGCHI Conference on Human Factors in Computing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 345–352.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [60] Xinyu Fu, Jiani Zhang, Ziqiao Meng, and Irwin King.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Magnn: Metap- ath aggregated graph neural network for heterogeneous graph embedding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of The Web Conference 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2331–2341.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [61] Maria Gäde, Mark M Hall, Hugo Huurdeman, Jaap Kamps, Marijn Koolen, Mette Skove, Elaine Toms, and David Walsh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Report on the first workshop on supporting complex search tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM SIGIR Forum 49, 1 (2015), 50–56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [62] Darío Garigliotti and Krisztian Balog.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Generating query suggestions to support task-based search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 40th International ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1153–1156.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [63] Robert Geirhos, Patricia Rubisch, Claudio Michaelis, Matthias Bethge, Felix A Wichmann, and Wieland Brendel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ImageNet-trained CNNs are biased towards texture;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' increasing shape bias improves accuracy and robustness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' arXiv preprint arXiv:1811.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='12231 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [64] Ramanathan Guha, Vineet Gupta, Vivek Raghunathan, and Ramakrishnan Srikant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' User modeling for a personal assistant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the Eighth ACM International Conference on Web Search and Data Mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 275–284.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [65] Drew Harwell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Doorbell-camera firm Ring has partnered with 400 police forces, extending surveillance concerns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' https: //www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='washingtonpost.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='com/technology/2019/08/28/doorbell-camera- firm-ring-has-partnered-with-police-forces-extending-surveillance-reach/.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Downloaded 2022-02-14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='. [66] Paul Haskell-Dowland.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' How Apple’s AirTag turns us into unwitting spies in a vast surveillance network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='theguardian.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='com/technology/ 2021/may/17/how-apples-airtag-turns-us-into-unwitting-spies-in-a-vast- surveillance-network.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Downloaded 2022-02-14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='. [67] Ahmed Hassan, Rosie Jones, and Kristina Lisa Klinkner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Beyond DCG: user behavior as a predictor of a successful search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM WSDM International Conference on Web Search and Data Mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 221–230.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [68] Ahmed Hassan, Xiaolin Shi, Nick Craswell, and Bill Ramsey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Beyond clicks: query reformulation as a predictor of search satisfaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM CIKM Conference on Information and Knowledge Management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2019–2028.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [69] Ahmed Hassan, Yang Song, and Li-wei He.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' A task level metric for measur- ing web search satisfaction and its application on improving relevance estima- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM CIKM Conference on Information and Knowledge Management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 125–134.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [70] Ahmed Hassan and Ryen W White.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task tours: helping users tackle complex search tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM CIKM Conference on Information and Knowledge Management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1885–1889.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [71] Ahmed Hassan Awadallah, Cathal Gurrin, Mark Sanderson, and Ryen W White.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task Intelligence Workshop@ WSDM 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM WSDM International Conference on Web Search and Data Mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 848–849.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [72] William Hersh, Jeffrey Pentecost, and David Hickam.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' A task-oriented approach to information retrieval evaluation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of the American Society for Information Science 47, 1 (1996), 50–56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [73] H Ulrich Hoppe and Franz Schiele.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Towards task models for embedded information retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGCHI Conference on Human Factors in Computing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [74] Eric Horvitz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Principles of mixed-initiative user interfaces.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the SIGCHI conference on Human Factors in Computing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 159–166.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [75] Jeff Huang, Ryen W White, Georg Buscher, and Kuansan Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Improving searcher models using mouse cursor activity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 195–204.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [76] Minlie Huang, Xiaoyan Zhu, and Jianfeng Gao.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Challenges in building intelligent open-domain dialog systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM Transactions on Information Systems 38, 3 (2020), 1–32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [77] Peter Ingwersen and Kalervo Järvelin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The Turn: Integration of Information Seeking and Retrieval in Context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [78] Richard David Jacques.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1996.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The nature of engagement and its role in hypermedia evaluation and design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Dissertation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' South Bank University.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [79] Kalervo Järvelin, Susan L Price, Lois ML Delcambre, and Marianne Lykke Nielsen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Discounted cumulated gain based evaluation of multiple-query IR sessions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the European Conference on Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 4–15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [80] Kalervo Järvelin, Pertti Vakkari, Paavo Arvola, Feza Baskaya, Anni Järvelin, Jaana Kekäläinen, Heikki Keskustalo, Sanna Kumpulainen, Miamaria Saasta- moinen, Reijo Savolainen, et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task-based information interaction eval- uation: The viewpoint of program theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM Transactions on Information Systems 33, 1 (2015), 1–30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [81] Jiepu Jiang and James Allan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Correlation between system and user met- rics in a session.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM CHIIR on Conference on Human Information Interaction and Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 285–288.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [82] Jiepu Jiang, Daqing He, and James Allan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Searching, browsing, and clicking in a search session: changes in user behavior by task and over time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceed- ings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 607–616.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [83] Karen Sparck Jones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' What’s the value of TREC: is there a gap to jump or a chasm to bridge?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM SIGIR Forum 40, 1 (2006), 10–20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [84] Rosie Jones and Kristina Lisa Klinkner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Beyond the session timeout: auto- matic hierarchical segmentation of search topics in query logs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 17th ACM conference on Information and knowledge management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 699–708.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [85] Diane Kelly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Methods for evaluating interactive information retrieval systems with users.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Foundations and Trends in Information Retrieval 3, 1-2 (2009), 1–224.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [86] Diane Kelly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' When effort exceeds expectations: A theory of search task difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ECIR Workshop on Supporting Complex Search Tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [87] Diane Kelly, Jamie Arguello, and Robert Capra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' NSF Workshop on Task- Based Search Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' SIGIR Forum 47, 2 (2013), 116–127.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [88] Diane Kelly, Jaime Arguello, Ashlee Edwards, and Wan-ching Wu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Devel- opment and evaluation of search tasks for IIR experiments using a cognitive complexity framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM ICTIR International Conference on the Theory of Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 101–110.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [89] Diane Kelly and Nicholas J Belkin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Display time as implicit feedback: understanding task effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 377–384.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [90] Diane Kelly and Colleen Cool.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2002.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The effects of topic familiarity on informa- tion search behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM/IEEE-CS JCDL Joint Conference on Digital Libraries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 74–75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [91] Diane Kelly, Susan Dumais, and Jan O Pedersen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Evaluation challenges and directions for information-seeking support systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Computer 3 (2009), 60–66.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [92] Jeonghyun Kim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task difficulty as a predictor and indicator of web searching interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In CHI EA ’06: CHI ’06 Extended Abstracts on Human Factors in Computing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Association for Computing Machinery, New York, NY, USA, 959–964.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [93] Youngho Kim, Ahmed Hassan, Ryen W White, and Imed Zitouni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Modeling dwell time to predict click-level satisfaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM WSDM International Conference on Web Search and Data Mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 193–202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [94] Julia Kiseleva, Kyle Williams, Jiepu Jiang, Ahmed Hassan Awadallah, Aidan C Crook, Imed Zitouni, and Tasos Anastasakos.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Understanding user satis- faction with intelligent assistants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM CHIIR Conference on Human Information Interaction and Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 121–130.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [95] Alexander Kotov, Paul N Bennett, Ryen W White, Susan T Dumais, and Jaime Teevan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Modeling and analysis of cross-session search tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 34th international ACM SIGIR conference on Research and development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 5–14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [96] Birger Larsen, Christina Lioma, and Arjen de Vries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Report on TBAS 2012: workshop on task-based and aggregated search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM SIGIR Forum 46, 1 (2012), 71–77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [97] Yuelin Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Exploring the relationships between work task and search task in information search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of the American Society for Information Science 11 and Technology 60, 2 (2009), 275–291.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [98] Yuelin Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' An exploration of the relationships between work tasks and users’ interaction performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ASIS&T Annual Meeting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1–9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [99] Yuelin Li and Nicholas J Belkin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' A faceted approach to conceptualizing tasks in information seeking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Information Processing and Management 44, 6 (2008), 1822–1837.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [100] Zhen Liao, Yang Song, Li-wei He, and Yalou Huang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Evaluating the effec- tiveness of search task trails.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 21st international conference on World Wide Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 489–498.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [101] Zhen Liao, Yang Song, Yalou Huang, Li-wei He, and Qi He.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task trail: An effective segmentation of user search behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' IEEE Transactions on Knowledge and Data Engineering 26, 12 (2014), 3090–3102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [102] Henry Lieberman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1995.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Letizia: An agent that assists web browsing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' IJCAI (1) 1995 (1995), 924–929.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [103] Shin-Jeng Lin and Nicholas J Belkin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Validation of a model of information seeking over multiple search sessions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of the American Society for Information Science and Technology 56, 4 (2005), 393–415.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [104] Jonathan Liono, Johanne R Trippas, Damiano Spina, Mohammad S Rahaman, Yongli Ren, Flora D Salim, Mark Sanderson, Falk Scholer, and Ryen W White.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Building a benchmark for task progress in digital assistants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the WSDM Task Intelligence Workshop.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [105] Jingjing Liu, Michael J Cole, Chang Liu, Ralf Bierig, Jacek Gwizdka, Nicholas J Belkin, Jun Zhang, and Xiangmin Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Search behaviors in different task types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the Annual Joint Conference on Digital Libraries.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 69–78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [106] Jingjing Liu, Jacek Gwizdka, Chang Liu, and Nicholas J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Belkin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Predicting Task Difficulty for Different Task Types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ASIS&T Annual Meeting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1–16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [107] Jiqun Liu, Matthew Mitsui, Nicholas J Belkin, and Chirag Shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task, information seeking Intentions, and user behavior: Toward a multi-level under- standing of web search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM CHIIR Conference on Human Information Interaction and Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 123–132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [108] Jiqun Liu, Shawon Sarkar, and Chirag Shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Identifying and predicting the states of complex search tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 2020 Conference on Human Information Interaction and Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 193–202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [109] Claudio Lucchese, Salvatore Orlando, Raffaele Perego, Fabrizio Silvestri, and Gabriele Tolomei.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Identifying task-based sessions in search engine query logs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the fourth ACM international conference on Web search and data mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 277–286.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [110] Jiyun Luo, Christopher Wing, Hui Yang, and Marti Hearst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The water filling model and the cube test: multi-dimensional evaluation for professional search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM CIKM Conference on Information and Knowledge Management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 709–714.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [111] Christoph Lutz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Digital inequalities in the age of artificial intelligence and big data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Human Behavior and Emerging Technologies 1, 2 (2019), 141–148.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [112] Rishabh Mehrotra, A Hassan Awadallah, Ahmed E Kholy, and Imed Zitouni.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Hey Cortana!' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Exploring the use cases of a Desktop based Digital Assistant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the SIGIR Workshop on Conversational Approaches to Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [113] Rishabh Mehrotra, Ahmed Hassan Awadallah, and Emine Yilmaz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Learnir: Wsdm 2018 workshop on learning from user interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM WSDM International Conference on Web Search and Data Mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 797–798.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [114] Rishabh Mehrotra, Prasanta Bhattacharya, and Emine Yilmaz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Character- izing users’ multi-tasking behavior in web search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM CHIIR Conference on Human Information Interaction and Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 297–300.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [115] Rishabh Mehrotra and Emine Yilmaz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Terms, topics & tasks: Enhanced user modelling for better personalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM ICTIR International Conference on The Theory of Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 131–140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [116] Rishabh Mehrotra and Emine Yilmaz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Terms, topics & tasks: Enhanced user modelling for better personalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 2015 international conference on the theory of information retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 131–140.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [117] Rishabh Mehrotra and Emine Yilmaz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Towards hierarchies of search tasks and subtasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the International Conference on the World Wide Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 73–74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [118] Rishabh Mehrotra and Emine Yilmaz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task embeddings: Learning query embeddings using task context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 2017 ACM on conference on information and knowledge management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2199–2202.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [119] Rishabh Mehrotra, Emine Yilmaz, and Manisha Verma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task-Based User Modelling for Personalization via Probabilistic Matrix Factorization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In RecSys Posters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [120] Bhaskar Mitra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Exploring session context using distributed representations of queries and reformulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 38th international ACM SIGIR conference on research and development in information retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 3–12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [121] Matthew Mitsui and Chirag Shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The broad view of task type using path analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM ICTIR International Conference on Theory of Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 131–138.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [122] Matthew Mitsui and Chirag Shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Bridging gaps: Predicting user and task characteristics from partial user information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 42nd International ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 415–424.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [123] Stefano Mizzaro.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Relevance: The whole history.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of the American Society for Information Science 48, 9 (1997), 810–832.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [124] Alistair Moffat, Peter Bailey, Falk Scholer, and Paul Thomas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Incorporating user expectations and behavior into the measurement of search effectiveness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM Transactions on Information Systems 35, 3 (2017), 1–38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [125] Alistair Moffat and Justin Zobel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Rank-biased precision for measurement of retrieval effectiveness.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM Transactions on Information Systems 27, 1 (2008), 1–27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [126] George D Montanez, Ryen W White, and Xiao Huang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Cross-device search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 23rd ACM international conference on conference on information and knowledge management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1669–1678.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [127] Meredith Ringel Morris and Eric Horvitz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' S 3: storable, shareable search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In IFIP Conference on Human-Computer Interaction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Springer, 120–123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [128] Karen Myers, Pauline Berry, Jim Blythe, Ken Conley, Melinda Gervasio, Deb- orah L McGuinness, David Morley, Avi Pfeffer, Martha Pollack, and Milind Tambe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' An intelligent personal assistant for task and time management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' AI Magazine 28, 2 (2007), 47–47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [129] Hugo Neri and Fabio Cozman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The role of experts in the public perception of risk of artificial intelligence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' AI & SOCIETY 35, 3 (2020), 663–673.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [130] Elnaz Nouri, Robert Sim, Adam Fourney, and Ryen W White.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Proac- tive suggestion generation: Data and methods for stepwise task assistance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 43rd International ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1585–1588.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [131] Heather L O’Brien and Elaine G Toms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' What is user engagement?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' A conceptual framework for defining user engagement with technology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of the American Society for Information Science and Technology 59, 6 (2008), 938–955.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [132] Brendan O’Connor, Michel Krieger, and David Ahn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Tweetmotif: Ex- ploratory search and topic summarization for twitter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the International AAAI Conference on Web and Social Media, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [133] Bing Pan, Helene Hembrooke, Thorsten Joachims, Lori Lorigo, Geri Gay, and Laura Granka.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Google we trust: Users’ decisions on rank, position, and relevance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of computer-mediated communication 12, 3 (2007), 801–823.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [134] Fabio Paterno.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Model-based design and evaluation of interactive applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Springer Science & Business Media.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [135] Fabio Paternò.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ConcurTaskTrees: an engineered notation for task models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The handbook of task analysis for human-computer interaction (2004), 483–503.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [136] Soo Young Rieh, Kevyn Collins-Thompson, Preben Hansen, and Hye-Jung Lee.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Towards searching as a learning process: A review of current perspectives and future directions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of Information Science 42, 1 (2016), 19–34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [137] Daniel E Rose and Danny Levinson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Understanding user goals in web search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the International Conference on the World Wide Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM, 13–19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [138] Daniel M Russell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The Joy of Search: A Google Insider’s Guide to Going Beyond the Basics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' MIT Press.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [139] Miamaria Saastamoinen and Kalervo Järvelin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Search task features in work tasks of varying types and complexity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of the Association for Information Science and Technology 68, 5 (2017), 1111–1123.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [140] Tetsuya Sakai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Evaluation with informational and navigational intents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the International Conference on the World Wide Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 499–508.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [141] Tefko Saracevic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Relevance: A review of the literature and a framework for thinking on the notion in information science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Part III: Behavior and effects of relevance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of the American Society for Information Science and Technology 58, 13 (2007), 2126–2144.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [142] Shawon Sarkar, Matthew Mitsui, Jiqun Liu, and Chirag Shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Implicit information need as explicit problems, help, and behavioral signals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Information Processing & Management 57, 2 (2020), 102069.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [143] Reijo Savolainen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Expectancy-value beliefs and information needs as motivators for task-based information seeking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of Documentation 68, 4 (2012), 492–511.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [144] Chirag Shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Social Information Seeking.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Springer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [145] Chirag Shah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Information Fostering-Being Proactive with Information Seeking and Retrieval: Perspective Paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM CHIIR Conference on Human Information Interaction and Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 62–71.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [146] Chirag Shah and Ryen W White.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2020.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Tutorial on Task-Based Search and Assis- tance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2436–2439.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [147] Guy Shani and Asela Gunawardana.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Evaluating recommendation systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Recommender Systems Handbook, Francesco Ricci, Lior Rokach, and Bracha Shapira (Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Springer, 257–297.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [148] Xuehua Shen, Bin Tan, and ChengXiang Zhai.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Context-sensitive in- formation retrieval using implicit feedback.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 28th annual international ACM SIGIR conference on Research and development in information retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 43–50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 12 [149] Ben Shneiderman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2000.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Creating creativity: user interfaces for supporting innovation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM Transactions on Computer-Human Interaction 7, 1 (2000), 114–138.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [150] Adish Singla, Ryen White, and Jeff Huang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Studying trailfinding algorithms for enhanced web search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 33rd international ACM SIGIR conference on Research and development in information retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 443–450.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [151] Mark D Smucker and Charles LA Clarke.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Time-based calibration of effectiveness measures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 95–104.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [152] Yang Song and Qi Guo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2016.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Query-less: Predicting task repetition for nextgen proactive search and recommendation engines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the International Conference on the World Wide Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 543–553.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [153] Alessandro Sordoni, Yoshua Bengio, Hossein Vahabi, Christina Lioma, Jakob Grue Simonsen, and Jian-Yun Nie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' A hierarchical recurrent encoder- decoder for generative context-aware query suggestion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In proceedings of the 24th ACM international on conference on information and knowledge management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 553–562.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [154] Ayah Soufan, Ian Ruthven, and Leif Azzopardi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Untangling the concept of task in information seeking and retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 2021 ACM SIGIR International Conference on Theory of Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 73–81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [155] Amanda Spink, Minsoo Park, Bernard J Jansen, and Jan Pedersen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Multi- tasking during web search sessions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Information Processing & Management 42, 1 (2006), 264–275.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [156] Simone Stumpf, Margaret Burnett, Volkmar Pipek, and Weng-Keen Wong.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2012.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' End-user interactions with intelligent and autonomous systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGCHI Extended Abstracts on Human Factors in Computing Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2755–2758.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [157] Jean Tague-Sutcliffe.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1992.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Measuring the informativeness of a retrieval process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 23–36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [158] Arthur R Taylor, Colleen Cool, Nicholas J Belkin, and William J Amadio.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2007.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Relationships between categories of relevance criteria and stage in task comple- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Information Processing and Management 43, 4 (2007), 1071–1084.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [159] Jaime Teevan, Kevyn Collins-Thompson, Ryen W White, and Susan Dumais.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Slow search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM 57, 8 (2014), 36–38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [160] Gabriele Tolomei, Salvatore Orlando, and Fabrizio Silvestri.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Towards task- based search and recommender systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the IEEE International Conference on Data Engineering Workshops.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 333–336.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [161] Tatiana Tommasi, Novi Patricia, Barbara Caputo, and Tinne Tuytelaars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2017.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' A deeper look at dataset bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Domain adaptation in computer vision applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Springer, 37–55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [162] E Toms and H O’Brien.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The ISSS Measurement Dilemma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' IEEE Computer 42, 3 (2009), 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [163] Elaine G Toms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Information activities and tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Information at work: information management in the workplace.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' London: Facet Publishing (2019), 33– 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [164] Elaine G Toms, Heather L O’Brien, Rick Kopak, and Luanne Freund.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Search- ing for relevance in the relevance of search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the International Conference on Conceptions of Library and Information Sciences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 59–78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [165] Antonio Torralba and Alexei A Efros.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Unbiased look at dataset bias.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In CVPR 2011.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' IEEE, 1521–1528.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [166] Pertti Vakkari.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task complexity, problem structure and information actions: Integrating studies on information seeking and retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Information Processing and Management 35, 6 (1999), 819–837.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [167] Pertti Vakkari.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' A theory of the task-based information retrieval process: a summary and generalisation of a longitudinal study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of Documentation 57, 1 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [168] Pertti Vakkari.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2003.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task-based information searching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Annual Review of Information Science and Technology 37, 1 (2003), 413–464.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [169] Manisha Verma and Emine Yilmaz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Entity oriented task extraction from query logs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 23rd ACM International Conference on Conference on Information and Knowledge Management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1975–1978.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [170] Ellen M Voorhees and Donna K Harman (Eds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=').' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2005.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' TREC: Experiment and evaluation in information retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' MIT Press, Cambridge.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [171] Thanh Vu, Alistair Willis, Son N Tran, and Dawei Song.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Temporal latent topic user profiles for search personalisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the European Conference on Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 605–616.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [172] Marilyn Walker, Diane Litman, Candace A Kamm, and Alicia Abella.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' PAR- ADISE: A Framework for Evaluating Spoken Dialogue Agents.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the Annual Meeting of the Association for Computational Linguistics and Confer- ence of the European Chapter of the Association for Computational Linguistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 271–280.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [173] Hongning Wang, Yang Song, Ming-Wei Chang, Xiaodong He, Ahmed Hassan Awadallah, and Ryen W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' White.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Modeling action-level satisfaction for search task satisfaction prediction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 123–132.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [174] Hongning Wang, Yang Song, Ming-Wei Chang, Xiaodong He, Ryen W White, and Wei Chu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Learning to extract cross-session search tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 22nd international conference on World Wide Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1353–1364.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [175] Yu Wang, Xiao Huang, and Ryen W White.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Characterizing and supporting cross-device search tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the sixth ACM international conference on Web search and data mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 707–716.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [176] Ryen W White.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Skill discovery in virtual assistants.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM 61, 11 (2018), 106–113.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [177] Ryen W White, Paul N Bennett, and Susan T Dumais.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Predicting short- term interests using activity-based search context.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM CIKM Conference on Information and Knowledge Management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1009–1018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [178] Ryen W White, Wei Chu, Ahmed Hassan, Xiaodong He, Yang Song, and Hongn- ing Wang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2013.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Enhancing personalized search by mining and modeling task behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 22nd international conference on World Wide Web.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1411–1420.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [179] Ryen W White, Susan T Dumais, and Jaime Teevan.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Characterizing the influence of domain expertise on web search behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM WSDM International Conference on Web Search and Data Mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 132–141.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [180] Ryen W White, Adam Fourney, Allen Herring, Paul N Bennett, Nirupama Chan- drasekaran, Robert Sim, Elnaz Nouri, and Mark J Encarnación.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Multi-device digital assistance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Commun.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM 62, 10 (2019), 28–31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [181] Ryen W White and Ahmed Hassan Awadallah.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task duration estimation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM WSDM International Conference on Web Search and Data Mining.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 636–644.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [182] Ryen W White, Ahmed Hassan Awadallah, and Robert Sim.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task Comple- tion Detection: A Study in the Context of Intelligent Systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 405–414.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [183] Ryen W White and Jeff Huang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Assessing the scenic route: measuring the value of search trails in web logs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 587–594.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [184] Ryen W White, Ashish Kapoor, and Susan T Dumais.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Modeling long- term search engine usage.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the International Conference on User Modeling, Adaptation, and Personalization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 28–39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [185] Ryen W White and Diane Kelly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2006.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' A study on the effects of personalization and task information on implicit feedback performance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 15th ACM international conference on Information and knowledge management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 297–306.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [186] Barbara M Wildemuth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2004.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The effects of domain knowledge on search tactic formulation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of the American Society for Information Science and Technology 55, 3 (2004), 246–258.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [187] Barbara M Wildemuth, Luanne Freund, and Elaine G Toms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Studies of search task complexity or difficulty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Science and Technology 62, 9 (2014), 1676–1695.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [188] Tom D Wilson.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 1999.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Models in information behaviour research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of Documentation 55, 3 (1999), 249–270.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [189] Biao Xiang, Daxin Jiang, Jian Pei, Xiaohui Sun, Enhong Chen, and Hang Li.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2010.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Context-aware ranking in web search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 33rd international ACM SIGIR conference on Research and development in information retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 451–458.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [190] Iris Xie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2008.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Interactive Information Retrieval in Digital Environments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' IGI Global.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [191] Iris Xie.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Dimensions of tasks: influences on information-seeking and retrieving process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Journal of Documentation (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [192] Ya Xu and David Mease.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2009.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Evaluating web search using task completion time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM SIGIR Conference on Research and Development in Information Retrieval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 676–677.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [193] Grace Hui Yang, Xuchu Dong, Jiyun Luo, and Sicong Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2018.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Session search modeling by partially observable Markov decision process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Information Retrieval Journal 21, 1 (2018), 56–80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [194] Hui Yang, Dongyi Guan, and Sicong Zhang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' The query change model: Modeling session search as a markov decision process.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM Transactions on Information Systems (TOIS) 33, 4 (2015), 1–33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [195] Jing Yao, Zhicheng Dou, Jun Xu, and Ji-Rong Wen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' RLPS: A Reinforcement Learning–Based Framework for Personalized Search.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' ACM Transactions on Information Systems (TOIS) 39, 3 (2021), 1–29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [196] Emine Yilmaz, Manisha Verma, Nick Craswell, Filip Radlinski, and Peter Bailey.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2014.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Relevance and effort: An analysis of document utility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the ACM CIKM Conference on Information and Knowledge Management.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 91–100.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [197] Emine Yilmaz, Manisha Verma, Rishabh Mehrotra, Evangelos Kanoulas, Ben Carterette, and Nick Craswell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Overview of the TREC 2015 Tasks Track.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content='. In Proceedings of the Text Retrieval Conference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [198] Yi Zhang, Sujay Kumar Jauhar, Julia Kiseleva, Ryen White, and Dan Roth.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2021.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Learning to decompose and organize complex tasks.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2726–2735.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' [199] Yongfeng Zhang, Min Zhang, Yiqun Liu, Chua Tat-Seng, Yi Zhang, and Shaoping Ma.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2015.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Task-based recommendation on a web-scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In Proceedings of the IEEE International Conference on Big Data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 827–836.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 13 [200] Shoshana Zuboff.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 2019.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' Surveillance capitalism and the challenge of collective action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' In New labor forum, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' SAGE Publications Sage CA: Los Angeles, CA, 10–29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} +page_content=' 14' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/xtE4T4oBgHgl3EQfYAyx/content/2301.05046v1.pdf'} diff --git a/ydE0T4oBgHgl3EQfcgDn/content/2301.02365v1.pdf b/ydE0T4oBgHgl3EQfcgDn/content/2301.02365v1.pdf new file mode 100644 index 0000000000000000000000000000000000000000..389c8aa14ff6b5b7b96a1339fb0453b08c918382 --- /dev/null +++ b/ydE0T4oBgHgl3EQfcgDn/content/2301.02365v1.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6a51231fae2259d6e24767e137ebf3f0b40b947df6421f75c1483400ee868239 +size 140499 diff --git a/ydE0T4oBgHgl3EQfcgDn/vector_store/index.faiss b/ydE0T4oBgHgl3EQfcgDn/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..594800f5a581ae70d5646bc73bdac7b69c4e01c8 --- /dev/null +++ b/ydE0T4oBgHgl3EQfcgDn/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:043054919c67e54916ebd3723b5eb1dd872aa6fce57dc9990856794838c089c8 +size 1507373 diff --git a/ydE0T4oBgHgl3EQfcgDn/vector_store/index.pkl b/ydE0T4oBgHgl3EQfcgDn/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..cd2d4731e896253cf04260a902300f98b2537140 --- /dev/null +++ b/ydE0T4oBgHgl3EQfcgDn/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:187159f8b8923f815df52e3749abb32977a7fb9fdc19e68be44bfd04c2ee2473 +size 52658 diff --git a/ydE2T4oBgHgl3EQf3wjf/vector_store/index.faiss b/ydE2T4oBgHgl3EQf3wjf/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..444c2fe5763700de0222f315559fc73044e33a2c --- /dev/null +++ b/ydE2T4oBgHgl3EQf3wjf/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3a046d438accddd90ca0942453ebadee64329b472504da78730d4f8837c2914d +size 4718637 diff --git a/ydE2T4oBgHgl3EQf3wjf/vector_store/index.pkl b/ydE2T4oBgHgl3EQf3wjf/vector_store/index.pkl new file mode 100644 index 0000000000000000000000000000000000000000..944ffbe9196028259c7f4c6766ea7594aa914f7a --- /dev/null +++ b/ydE2T4oBgHgl3EQf3wjf/vector_store/index.pkl @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:2ccf344e7c0bbc27e5eda2a3bce3cbcad66c93463265f457734437487279b3c4 +size 151358 diff --git a/zNE4T4oBgHgl3EQfAQs4/vector_store/index.faiss b/zNE4T4oBgHgl3EQfAQs4/vector_store/index.faiss new file mode 100644 index 0000000000000000000000000000000000000000..508086d277a93f8c62a7ecbcd96ac49d6f90cf9a --- /dev/null +++ b/zNE4T4oBgHgl3EQfAQs4/vector_store/index.faiss @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f953bedb85f75ae3caca2f78dc6c4c7d1162619ae8715021cbc9afcd72df4885 +size 6684717 diff --git a/ztE1T4oBgHgl3EQf4gVZ/content/tmp_files/2301.03501v1.pdf.txt b/ztE1T4oBgHgl3EQf4gVZ/content/tmp_files/2301.03501v1.pdf.txt new file mode 100644 index 0000000000000000000000000000000000000000..5bd2e2e2cde8c70a3954a5488ec7afa7ac760b10 --- /dev/null +++ b/ztE1T4oBgHgl3EQf4gVZ/content/tmp_files/2301.03501v1.pdf.txt @@ -0,0 +1,1156 @@ +Discovery of enhanced lattice dynamics in a single- +layered hybrid perovskite +Zhuquan Zhang1†, Jiahao Zhang2†, Zi-Jie Liu1†, Nabeel S. Dahod3, Watcharaphol Paritmongkol1,3, +Niamh Brown1,3, Yu-Che Chien1, Zhenbang Dai2, Keith A. Nelson1∗, William A. Tisdale3, +Andrew M. Rappe2, Edoardo Baldini4∗ +1Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Mas- +sachusetts, USA, 02139 +2Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania, +USA, 19104-6323 +3Department of Chemical Engineering, Massachusetts Institute of Technology, Cam- +bridge, Massachusetts, USA, 02139 +4Department of Physics, The University of Texas at Austin, Austin, Texas, USA, 78712 +∗E-mail: edoardo.baldini@austin.utexas.edu, kanelson@mit.edu +†These authors contributed equally to this work +1 +arXiv:2301.03501v1 [cond-mat.mtrl-sci] 9 Jan 2023 + +Abstract +Layered hybrid perovskites have attracted much attention in recent years due to their +emergent physical properties and exceptional functional performances, but the coex- +istence of lattice order and structural disorder severely hinders our understanding of +these materials. One unsolved problem regards how the lattice dynamics are affected +by the dimensional engineering of the inorganic frameworks and the interaction with +the molecular moieties. Here, we address this question by using a combination of high- +resolution spontaneous Raman scattering, high field terahertz spectroscopy, and molec- +ular dynamics simulations. This approach enables us to reveal the structural vibrations +and disorder in and out of equilibrium and provides surprising observables that differ- +entiate single- and double-layered perovskites. While no distinct vibrational coherence +is observed in double-layer perovskites, we discover that an off-resonant terahertz pulse +can selectively drive a long-lived coherent phonon mode through a two-photon process +in the single-layered system. This difference highlights the dramatic change in the lat- +tice environment as the dimension is reduced. The present findings pave the way for the +ultrafast structural engineering of hybrid lattices as well as for developing high-speed +optical modulators based on layered perovskites. +2 + +Main Text +Over the past decade, two-dimensional hybrid perovskites (2DHPs) have emerged as +natural quantum-well-like semiconductors with marked light absorption, large lumines- +cence quantum yield 1,2, and strong exciton binding energy3,4. Unlike their 3D coun- +terparts, 2DHPs also show wider chemical variability and structural diversity, as their +composition can be tuned by altering organic spacer cations, inorganic networks, and +the number of octahedral layers.5–8 This richness may also lead to a plethora of emer- +gent properties including ferroelectricity9,10, spin selectivity11, and multifunctionality12. +Although substantial efforts have been made to exploit this versatility by dimensional +tailoring, it is an ongoing task to establish the structure-function relationships in these +materials. Key to this goal is an understanding of the interplay between the inorganic +lattice framework and the organic cations.13,14 Previous mechanistic studies have sug- +gested that the hybrid lattice features significant anharmonicity and polarizability, in +conjunction with structural disorder15–17. However, it remains an open question whether +these properties persist to the single-layer limit when the octahedral framework does not +fully resemble the lead-halide backbone of the bulk perovskite structure. +Here, we present a joint experimental-theoretical study aimed at uncovering the +origin of the dynamic structural complexity in 2DHPs. By means of steady-state and +ultrafast spectroscopy experiments, we identify unique fingerprints that distinguish the +3 + +structural dynamics of the hybrid lattices in the crossover between quasi-2D and 2D. +We observe that the collective motion of the octahedral cages is significantly enhanced +as the number of layers per repeating unit is altered from two to one. Our results are +rationalized via molecular dynamics calculations, which provide an atomic-level under- +standing of the hybrid lattice in and out of equilibrium. +We focus on two prototypical 2DHPs, which differ in the number of corner- +sharing octahedral layers n: (BA)2PbBr4 (single-layer, n=1) and (BA)2MAPb2Br7 (dou- +ble layer, n=2). As shown in Fig.1a, n=1 2DHP only contains organic spacer ligands +(BA=butylammonium) that separate the octahedral layers, while the double-layered +2DHP consists of additional A-site cations (MA=methylammonium) that occupy cuboc- +tahedral pockets formed by eight octahedra. +As a first step in the study of the lattice dynamics in thermal equilibrium, we mon- +itor low-energy collective responses and structural disorder via high-resolution sponta- +neous Raman scattering. We map the Raman spectra of both 2DHPs across a wide range +of temperatures as shown in Fig. 1b (n=1) and Fig. 1c (n=2). For n=1 2DHP, the Raman +spectra are characterized by eight well-defined peaks that include a dominant mode at +1.8 THz.18 In contrast, the Raman data of n=2 2DHP exhibit broad features at all tem- +peratures. In Fig. 1d, we provide a detailed comparison by selecting the Raman spectra +of both materials at room temperature and at 77 K. The room temperature spectra for +4 + +both n=1 and n=2 crystals show a prominent spectral continuum below 5 THz, which +is reminiscent of quasi-elastic peaks due to disorder19–21; however, the 1.8 THz peak in +the n=1 compound stands out from the underlying continuum. When the temperature is +decreased to 77 K, the continuum background contribution to the n=1 Raman response +is dramatically reduced, and several additional modes become distinct. In contrast, the +low-temperature spectrum of n=2 2DHP exhibits persistent broad features, suggesting +the coexistence of phonon peaks and structural disorder. This is because that in the n=2 +system, the presence of the MA cation introduces both dynamic and orientational disor- +der. From the steady-state Raman data, we establish a thermal equilibrium view of the +structural complexity in 2DHPs and conclude that the structural disorder is significantly +reduced in the single-layer limit. +Next, we track the time evolution of lattice response at ultrafast timescales to +attain more insights into the structural dynamics and separate the collective modes from +the dynamic disorder22,23. To monitor the lattice behavior in real-time, we employ THz +field-induced Kerr effect (TKE) spectroscopy24 (see Fig. 2a). Unlike previous studies +that used optical pump pulses for Kerr effect spectroscopy25 to investigate the lattice +dynamics26, molecular reorientation27, and light propagation28 in hybrid perovskites, +we take advantage of the slowly varying electric field of THz pulses to induce giant +polarizability responses29 that may not be accessible with the pump pulses in the optical +frequency range. +5 + +Figure 2b shows the TKE data recorded at several temperatures for both 2DHPs. +For the n=2 sample at room temperature (green curve), only non-oscillatory signals are +observed after the initial electronic response induced by the THz pulse. When the tem- +perature is lowered below 160 K, oscillations emerge but only last for a few cycles, less +than 5 ps. These observations indicate that in n=2 2DHP, any excited phonon mode loses +its coherence quickly, consistent with the observation of broad features in the steady- +state Raman spectra. In contrast, TKE signals from the n=1 2DHP exhibit a strikingly +different behavior. First, the response is 10 times larger than its n=2 counterpart. This +distinction indicates the presence of an enhanced polarizability at THz frequencies, as +the two materials have similar dielectric properties at the probe photon energy (see Sup- +plementary Note 1). Second, the initial response shows a bipolar character, signaled +by the two lobes with opposite signs that do not follow the incident THz waveform. +This type of signal has only been reported in aqueous systems where it has been at- +tributed to different components of the liquid dynamics.30,31 It is therefore surprising +to observe such a response in a crystalline material, and we attribute its origin to the +BA organic ligands and the unique response of the single-layer octahedral networks32 +(see Supplementary Note 1). More importantly, we observe that a long-lived sinusoidal +modulation appears promptly after the initial electronic response. The oscillation fre- +quency of 1.8 THz (see Fig. 2c) corresponds to the most prominent phonon mode in the +equilibrium Raman spectra. Even at room temperature, this coherent phonon response +6 + +remains detectable for more than 10 ps. Decreasing the temperature results in a simul- +taneous increase in the oscillation amplitude and decay time (see Fig. 2d and 2e), which +is a manifestation of the suppressed structural disorder and reduced anharmonic decay +of the excited mode. +To identify the underlying mechanism that drives this long-lived coherent phonon +response, we obtain the THz field-dependent TKE signals for n=1 2DHP at 10 K. As +shown in Fig. 3a, the time-domain oscillatory responses increase monotonically with +the THz field strengths. Fourier transformation of the oscillatory parts of the TKE sig- +nals shows that the spectral amplitude scales as the square of the pump electric field +(see Fig. 3b). This observation indicates that the Raman mode at 1.8 THz is driven +through a second-order interaction with the THz pump field. Such a nonlinear excita- +tion process can proceed through two distinct pathways, which are ionic or photonic +in nature (see Supplementary Note 2).33 In the ionic scenario, the THz field drives a +dipole-active mode and nonlinear excitation of the Raman mode is mediated by anhar- +monic phonon-phonon coupling,34,35 whereas in the photonic mechanism, the THz field +drives the Raman mode directly through the nonlinear polarizability.36–38 Since the fre- +quency of the Raman mode is well above the bandwidth of the incident THz pulse (see +Fig. 2c), we can also exclude the scenario of impulsive stimulated Raman scattering36,39 +or impulsive ionic Raman scattering40–42, in which difference-frequency components of +the photon or phonon field drives the Raman mode. Rather, the sum-frequency exci- +7 + +tation pathway should be responsible for the observed Raman excitation. For such a +process to be ionic, there must be an infrared-active phonon mode directly driven by the +THz pump, whose phonon frequency is ideally at half of the Raman mode frequency +(i.e., ΩIR = ΩR/2 ∼ 0.9 THz). Since the crystal is centrosymmetric, only Raman- +active modes produce transient birefringent signals, and therefore oscillations in the +TKE responses do not reflect coherent excitation of infrared modes directly driven by +the THz field.43,44 To provide further clues, we apply time-domain THz spectroscopy, +which directly measures dipole-allowed transitions in the THz frequency range. Figure +3c shows the imaginary part of dielectric permittivity at various temperatures below 200 +K, which reveals two infrared-active modes (i.e., at 0.5 and 0.75 THz) emerging at low +temperatures. There is no phonon mode at 0.9 THz that fulfills the resonance condition. +Furthermore, it was previously established that the sum-frequency ionic Raman scatter- +ing would lead to beat signals in the time-domain, resulting from the mutual exchange +of energy between the driven infrared-active and Raman-active phonon modes.35 In our +data, we only observe an exponential decay of the Raman coherence. This rules out any +possibility that the 1.8 THz Raman-active mode is driven by anharmonic coupling to an +excited infrared-active phonon mode. Therefore, we can conclude that the observed co- +herent collective response is generated by sum-frequency photonic excitation (see Fig. +3d).38,45 However, we cannot exclude that the 0.75 THz infrared active phonon mode +in the bandwidth of our THz field acts as a real intermediate state to our Raman-like +8 + +process, especially at low temperature. This mechanism, which has been recently dis- +covered theoretically and dubbed as infrared resonant Raman effect33, depends on the +ionic degrees of freedom but relies on the nonlinear lattice polarizability rather than on +anharmonic phonon-phonon interactions. Such an effect may therefore explain why we +observe a much more prominent Raman excitation response at low temperature. +To gain deeper insight into the nature of both thermal and coherent dynamics, +we conduct ab initio molecular dynamics (MD) simulations for a +√ +2 × +√ +2 × 2 cell. +To simulate equilibrium states, we use the canonical (NVT) ensemble for calculating +the spontaneous Raman responses. Figure 4a displays the simulated Raman spectra for +both n=1 and n=2 2DHPs at 77 K, which agree well with the experimental data at the +same temperature. While the n=2 2DHP exhibits a more disorder-dominated Raman re- +sponse, the Raman spectrum of the n=1 2DHP shows a distinct peak at around 1.9 THz, +which is close to the frequency of the most prominent phonon mode observed in the ex- +perimental data (i.e., 1.8 THz). Based on real-space analysis of the MD simulations, we +identify this mode as the bending and twisting of the octahedral cages in the single-layer +inorganic framework. Since in the 2DHP with n=2, the two adjacent layers of lead bro- +mide octahedra are bonded to each other, the octahedral motions are significantly more +coupled as compared to the n=1 system. The rotation and rattling motions of additional +MA organic cations also introduce additional local static disorder, leading to much more +spatially uncorrelated lattice dynamics associated with heterogeneous responses. This +9 + +naturally explains why the Raman spectra show much broader features for the n=2 sys- +tem. We also investigate the nonlinear THz light-matter interaction in the n=1 2DHP. To +capture coherent dynamics rather than the thermal fluctuation of the lattice response, we +conduct MD simulations in the microcanonical ensemble (NVE). We apply the experi- +mentally measured THz electric field waveform to our system, setting its polarization in +the plane of the octahedral layers. We then project the MD trajectory into the eigenmode +basis calculated from density functional perturbation theory (DFPT).46–48 As shown in +Fig. 4b, we find that the driving THz field generates a long-lived oscillatory response +that does not decay to zero up to 20 ps. The Fourier-transform spectrum in Fig. 4c +reveals a sharp peak centered at around 1.9 THz, in excellent agreement with our exper- +imental data. +Discussion +Our spectroscopic measurements combined with the MD simulations establish that the +single-layered hybrid perovskite features a giant polarizable lattice response that does +not exist in the double-layered perovskite counterparts. This finding highlights the use +of tailored THz light excitation to study hybrid lattices exhibiting a complex interplay of +molecular and ionic dynamics. From the fundamental point of view, this approach can +be applied to explore many other structurally complex materials, including artificially +engineered heterostructures and moiré superlattices, and opens the door to desirably +10 + +controlling their emergent properties and novel functionalities with light.49 Given that +our sample thickness is ∼ 100 µm, the estimated modulation depth of the THz field- +induced polarization rotation is ∼ 2 dB/mm at room temperature (see Supplementary +Note 4). Although we only demonstrate the polarization modulation for light of a sin- +gle wavelength (800 nm), we expect that similar results will hold for a broad range of +wavelengths below the material’s bandgap (i.e., > 400 nm). For these reasons, we be- +lieve that 2DHPs are promising candidates for achieving all-optical, broadband refrac- +tive modulators at high speeds with tailored THz stimuli50, offering new perspectives +for the development of novel optical devices51. +11 + +Methods +Synthesis of bromide-lead 2DHPs +Crystals of bromide-lead 2DHPs were synthesized by slow-cooling crystallization fol- +lowing a previously reported procedure8. Firstly, a solution of lead (II) bromide (PbBr2) +was prepared by dissolving PbO (99.9+%, (trace metal basis) <10 microns, powder, +ACROS Organic) in an aqueous hydrogen bromide solution (HBr, ACS reagent, 48%, +MilliporeSigma). Then, a small volume of butylamine (BA) was added to the PbBr2 +solution to form a white precipitate of (BA)2PbBr4 (single-layer, n=1). To prepare +(BA)2MAPb2Br7 (double layer, n=2), a solution of methylammonium bromide (MABr) +salt was prepared in a separate vial by dissolving the salt in an aqueous HBr solution. +The MABr solution was subsequently added into the solution of (BA)2PbBr4 to form +a (BA)2MAPb2Br7 solution. Next, the solutions of (BA)2PbBr4 and (BA)2MAPb2Br7 +were further diluted by additional volumes of HBr before being heated to 130 °C until +they became clear. After that, they were allowed to cool slowly to room temperature +inside a thermos filled with hot sand at 110 °C to induce crystallization. Crystals were +then collected by suction filtration and dried under reduced pressure for at least 12 hours. +The quantities of reagents used can be found in Table S1. +High-resolution spontaneous Raman scattering +Steady-state Raman spectra were collected in a backscattered geometry using a home- +12 + +built micro-Raman instrument. Samples were housed within an optical cryostat (Janis +ST-500, fused quartz window) mounted to an inverted Nikon microscope (60x, 0.6 NA +objective), and kept under vacuum during all measurements. A 785 nm narrow-band +continuous wave excitation source was filtered from undesirable amplified spontaneous +emission using a series of cleanup filters (laser and filters from Ondax). The Rayleigh +line was minimized by passing the collected signal through a set of volume holographic +grating notch filters (from Ondax) before being dispersed in a 0.5 m focal length spec- +trograph (SP-2500, Princeton Instruments) using a 1200 g/mm and 750 nm blaze grat- +ing. The resulting spectrum was imaged with a cooled charge-coupled device camera +(Princeton Instruments Pixis) with a typical signal integration time of 15-30 s. The +Rayleigh notch filters, centered at 0 cm−1, have a full attenuation bandwidth of ± 10 +cm−1. The overall spectral resolution of the instrument is 0.9 cm−1. The spectra were +calibrated by comparison to the longitudinal optical phonon position of a CdSe standard. +TKE spectroscopy +The majority of the output of a 1 kHz Ti:Sapphire laser amplifier (Coherent Legend Elite +Duo, 800nm, 12 mJ, 35 fs) was chopped at 500 Hz and used to generate single-cycle +THz pulses via optical rectification process with a tilted pulse front52. The THz pulse +was collected and focused by a pair of 90° off-axis parabolic mirrors. The remainder +of the laser output was attenuated and used as a probe pulse, that was focused along +with the THz pulse onto the sample inside the cryostat. In the TKE experiment, the +13 + +800 nm probe pulse polarized at 45° relative to the polarization of the THz pulse was +transmitted through the sample. The transmitted probe pulse was depolarized by the +THz-field-induced anisotropic responses, resulting in transient birefringence. The signal +was measured by a pair of balanced photodiodes after a half-wave plate and a Wollaston +prism. +Time-domain THz spectroscopy +In time-domain THz spectroscopy experiments, The THz field was attenuated by a +pair of wire-grid polarizers so that the measured signals were in the linear response +regime. The transmitted THz waveform was focused into a ZnTe crystal and was over- +lapped with a gate pulse at 800 nm for the electro-optic sampling. We determined the +frequency-dependent complex transmission coefficient by comparing the THz electric +field through the sample to that through a reference aperture of the same size. From +the measured complex transmission coefficient, we numerically extracted the real and +imaginary part of the dielectric permittivity as a function of frequency. +MD simulation +The Raman spectrum was calculated via an MD approach as described before53–55: +Iij(ω) = +ω +1 − exp(− hω +KbT ) +� +< αij(τ)αij(t + τ) >τ e−iwtdt +(1) +where Iij(ω) is the Raman scattering intensity at frequency ω, and αij is the electronic +14 + +polarizability tensor obtained from DFPT47,48,56. The polarizability αij(t) was calcu- +lated based on snapshots of MD trajectories. We used Wiener-Khinchin theorem to cal- +culate the auto-correlation function of the Raman susceptibility.57,58 The MD simulation +is first equilibriated for 10 ps, and then sampled every 100 fs with a total 60 ps time win- +dow. The MD and Raman simulation were conducted using Quantum-Espresso59,60 and +the temperature was controlled with the Nosé-Hoover thermostat (see Supplementary +Note 3).61,62 +Data availability All data that support the findings of this study are available from the +corresponding authors on reasonable request. +Acknowledgments Z.Z., Z.-J.L. and K.A.N acknowledge support from the U.S. Depart- +ment of Energy, Office of Basic Energy Sciences, under Award No. DE-SC0019126. +E.B. acknowledge support from the Robert A. Welch Foundation (grant F-2092-20220331). +Y.-C.C. acknowledges direct funding from the MIT UROP. J. Z. and A. M. R. acknowl- +edge the support from U.S. Department of Energy, Office of Science, Basic Energy Sci- +ences, under Award No. DE-FG02-07ER46431. National Energy Research Scientific +Computing Center (NERSC) provides the computational support by Office of Science +User Facility located at Lawrence Berkeley National Laboratory, operated under Con- +tract No. DE-AC02-05CH11231. N.S.D., W.P., N.B., and W.A.T. acknowledge support +from the U.S. Department of Energy, Office of Science, Basic Energy Sciences under +15 + +award DE-SC0019345. +Funding U.S. Department of Energy, Office of Basic Energy Sciences, Award No. DE- +SC0019126 (ZZ, ZJL, KAN) Robert A. Welch Foundation grant F-2092-20220331(EB) +U.S. Department of Energy, Office of Science, Basic Energy Sciences, Award No. DE- +FG02-07ER46431 (JZ, AMR) Office of Science User Facility located at Lawrence +Berkeley National Laboratory No. DE-AC02-05CH11231 (JZ, AMR) U.S. Depart- +ment of Energy, Office of Science, Basic Energy Sciences, Award No. DE-SC0019345. +(NSD, WP, NB, WAT) MIT UROP (YCC) +Author contributions Z.Z. and E.B. designed the project. Z.Z. and Z.-J.L. performed +the THz measurements, assisted by Y.-C.C.. N.S.D. performed the steady-state Raman +measurements. W.P. and N.B. synthesized the 2DHP crystals. J.Z. performed the MD +and Raman simulations, supported by Z.D.. Z.Z., J.Z., and Z.-J.L. analyzed the data. +Z.Z., J.Z., Z.-J.L., E.B. and K.A.N. wrote the paper with inputs from all authors. E.B., +W.A.T., A.M.R. and K.A.N. supervised the research. +Competing interests The authors declare no competing interests. +16 + +References +1. Gong, X. et al. Electron–phonon interaction in efficient perovskite blue emitters. Nature materials +17, 550–556 (2018). +2. Grancini, G. & Nazeeruddin, M. K. Dimensional tailoring of hybrid perovskites for photovoltaics. +Nature Reviews Materials 4, 4–22 (2019). +3. Smith, M. D., Connor, B. A. & Karunadasa, H. I. Tuning the luminescence of layered halide per- +ovskites. Chemical Reviews 119, 3104–3139 (2019). +4. Mauck, C. M. & Tisdale, W. A. Excitons in 2d organic–inorganic halide perovskites. Trends in +Chemistry 1, 380–393 (2019). +5. Li, X., Hoffman, J. M. & Kanatzidis, M. G. The 2D halide perovskite rulebook: how the spacer +influences everything from the structure to optoelectronic device efficiency. Chemical Reviews 121, +2230–2291 (2021). +6. Shi, E. et al. Two-dimensional halide perovskite nanomaterials and heterostructures. Chemical +Society Reviews 47, 6046–6072 (2018). +7. Saparov, B. & Mitzi, D. B. Organic–inorganic perovskites: structural versatility for functional mate- +rials design. Chemical Reviews 116, 4558–4596 (2016). +8. Paritmongkol, W. et al. Synthetic variation and structural trends in layered two-dimensional alky- +lammonium lead halide perovskites. Chemistry of Materials 31, 5592–5607 (2019). +9. Hang, T., Zhang, W., Ye, H.-Y. & Xiong, R.-G. Metal-organic complex ferroelectrics. Chemical +Society Reviews 40, 3577–3598 (2011). +10. Chen, X.-G. et al. Two-dimensional layered perovskite ferroelectric with giant piezoelectric voltage +coefficient. Journal of the American Chemical Society 142, 1077–1082 (2019). +17 + +11. Kim, Y.-H. et al. Chiral-induced spin selectivity enables a room-temperature spin light-emitting +diode. Science 371, 1129–1133 (2021). +12. Li, W. et al. Chemically diverse and multifunctional hybrid organic–inorganic perovskites. Nature +Reviews Materials 2, 1–18 (2017). +13. Menahem, M. et al. Strongly anharmonic octahedral tilting in two-dimensional hybrid halide per- +ovskites. ACS Nano 15, 10153–10162 (2021). +14. Mayers, M. Z., Tan, L. Z., Egger, D. A., Rappe, A. M. & Reichman, D. R. How lattice and charge +fluctuations control carrier dynamics in halide perovskites. Nano Letters 18, 8041–8046 (2018). +15. Egger, D. A. et al. What remains unexplained about the properties of halide perovskites? Advanced +Materials 30, 1800691 (2018). +16. Miyata, K. & Zhu, X.-Y. Ferroelectric large polarons. Nature Materials 17, 379–381 (2018). +17. Rivett, J. P. et al. Long-lived polarization memory in the electronic states of lead-halide perovskites +from local structural dynamics. Nature Communications 9, 1–8 (2018). +18. Dhanabalan, B. et al. Directional anisotropy of the vibrational modes in 2D-layered perovskites. +ACS Nano 14, 4689–4697 (2020). +19. Hlinka, J. et al. Coexistence of the phonon and relaxation soft modes in the terahertz dielectric +response of tetragonal BaTiO3. Physical Review Letters 101, 167402 (2008). +20. Yaffe, O. et al. Local polar fluctuations in lead halide perovskite crystals. Physical Review Letters +118, 136001 (2017). +21. Dahod, N. S., France-Lanord, A., Paritmongkol, W., Grossman, J. C. & Tisdale, W. A. +Low- +frequency Raman spectrum of 2D layered perovskites: Local atomistic motion or superlattice modes? +The Journal of Chemical Physics 153, 044710 (2020). +18 + +22. Yan, Y.-X. & Nelson, K. A. Impulsive stimulated light scattering. ii. comparison to frequency-domain +light-scattering spectroscopy. The Journal of Chemical Physics 87, 6257–6265 (1987). +23. Dougherty, T. P. et al. Femtosecond resolution of soft mode dynamics in structural phase transitions. +Science 258, 770–774 (1992). +24. Hoffmann, M. C., Brandt, N. C., Hwang, H. Y., Yeh, K.-L. & Nelson, K. A. Terahertz Kerr effect. +Applied Physics Letters 95, 231105 (2009). +25. Zhong, Q. & Fourkas, J. T. Optical Kerr effect spectroscopy of simple liquids. The Journal of +Physical Chemistry B 112, 15529–15539 (2008). +26. Miyata, K. et al. Large polarons in lead halide perovskites. Science Advances 3, e1701217 (2017). +27. Zhu, H. et al. Screening in crystalline liquids protects energetic carriers in hybrid perovskites. Sci- +ence 353, 1409–1413 (2016). +28. Maehrlein, S. F. et al. Decoding ultrafast polarization responses in lead halide perovskites by the two- +dimensional optical Kerr effect. Proceedings of the National Academy of Sciences 118, e2022268118 +(2021). +29. Melnikov, A., Anikeeva, V., Semenova, O. & Chekalin, S. Terahertz kerr effect in a methylammo- +nium lead bromide perovskite crystal. Physical Review B 105, 174304 (2022). +30. Elgabarty, H. et al. Energy transfer within the hydrogen bonding network of water following resonant +terahertz excitation. Science Advances 6, eaay7074 (2020). +31. Zhao, H. et al. Ultrafast hydrogen bond dynamics of liquid water revealed by terahertz-induced +transient birefringence. Light: Science & Applications 9, 1–10 (2020). +32. Reyes-Martinez, M. A. et al. Unraveling the elastic properties of (quasi) two-dimensional hybrid +perovskites: a joint experimental and theoretical study. ACS Applied Materials & Interfaces 12, +17881–17892 (2020). +19 + +33. Khalsa, G., Benedek, N. A. & Moses, J. Ultrafast control of material optical properties via the +infrared resonant Raman effect. Physical Review X 11, 021067 (2021). +34. Först, M. et al. Nonlinear phononics as an ultrafast route to lattice control. Nature Physics 7, 854–856 +(2011). +35. Juraschek, D. M. & Maehrlein, S. F. Sum-frequency ionic Raman scattering. Physical Review B 97, +174302 (2018). +36. Aku-Leh, C., Zhao, J., Merlin, R., Menendez, J. & Cardona, M. Long-lived optical phonons in ZnO +studied with impulsive stimulated Raman scattering. Physical Review B 71, 205211 (2005). +37. Johnson, C. L., Knighton, B. E. & Johnson, J. A. +Distinguishing nonlinear terahertz excitation +pathways with two-dimensional spectroscopy. Physical Review Letters 122, 073901 (2019). +38. Maehrlein, S., Paarmann, A., Wolf, M. & Kampfrath, T. Terahertz sum-frequency excitation of a +Raman-active phonon. Physical Review Letters 119, 127402 (2017). +39. Yan, Y.-X., Gamble Jr, E. B. & Nelson, K. A. Impulsive stimulated scattering: General importance +in femtosecond laser pulse interactions with matter, and spectroscopic applications. The Journal of +Chemical Physics 83, 5391–5399 (1985). +40. Maradudin, A. & Wallis, R. Ionic raman effect. i. scattering by localized vibration modes. Physical +Review B 2, 4294 (1970). +41. Wallis, R. & Maradudin, A. Ionic raman effect. ii. the first-order ionic raman effect. Physical Review +B 3, 2063 (1971). +42. Humphreys, L. Ionic raman effect. iii. first-and second-order ionic raman effects. Physical Review B +6, 3886 (1972). +43. Li, X. et al. Terahertz field–induced ferroelectricity in quantum paraelectric SrTiO3. Science 364, +1079–1082 (2019). +20 + +44. von Hoegen, A. et al. Amplification of superconducting fluctuations in driven YBa2Cu3O6+x. Phys- +ical Review X 12, 031008 (2022). +45. Mead, G., Lin, H.-W., Magdau, I.-B., Miller III, T. F. & Blake, G. A. Sum-frequency signals in +2d-terahertz-terahertz-raman spectroscopy. The Journal of Physical Chemistry B 124, 8904–8908 +(2020). +46. Gonze, X. Adiabatic density-functional perturbation theory. Physical Review A 52, 1096 (1995). +47. Baroni, S., Giannozzi, P. & Testa, A. Green’s-function approach to linear response in solids. Physical +Review Letters 58, 1861 (1987). +48. Baroni, S., De Gironcoli, S., Dal Corso, A. & Giannozzi, P. Phonons and related crystal properties +from density-functional perturbation theory. Reviews of Modern Physics 73, 515 (2001). +49. Disa, A. S., Nova, T. F. & Cavalleri, A. Engineering crystal structures with light. Nature Physics 17, +1087–1092 (2021). +50. Grinblat, G. et al. Ultrafast all-optical modulation in 2D hybrid perovskites. ACS Nano 13, 9504– +9510 (2019). +51. Sun, Z., Martinez, A. & Wang, F. Optical modulators with 2D layered materials. Nature Photonics +10, 227–238 (2016). +52. Yeh, K.-L., Hebling, J., Hoffmann, M. C. & Nelson, K. A. Generation of high average power 1 kHz +shaped thz pulses via optical rectification. Optics Communications 281, 3567–3570 (2008). +53. Thomas, M., Brehm, M., Fligg, R., Vöhringer, P. & Kirchner, B. Computing vibrational spectra from +ab initio molecular dynamics. Physical Chemistry Chemical Physics 15, 6608–6622 (2013). +54. Sharma, R. et al. Elucidating the atomistic origin of anharmonicity in tetragonal CH3NH3PbI3 with +Raman scattering. Physical Review Materials 4, 092401 (2020). +21 + +55. Sharma, R. et al. Lattice mode symmetry analysis of the orthorhombic phase of methylammonium +lead iodide using polarized Raman. Physical Review Materials 4, 051601 (2020). +56. Gonze, X. Adiabatic density-functional perturbation theory. Phys. Rev. A 52, 1096–1114 (1995). +57. Wiener, N. Generalized harmonic analysis. Acta mathematica 55, 117–258 (1930). +58. Khintchine, A. Korrelationstheorie der stationären stochastischen prozesse. Mathematische Annalen +109, 604–615 (1934). +59. Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quan- +tum simulations of materials. Journal of Physics: Condensed Matter 21, 395502 (2009). +60. Giannozzi, P. et al. Advanced capabilities for materials modelling with Quantum ESPRESSO. Jour- +nal of Physics: Condensed Matter 29, 465901 (2017). +61. Nosé, S. +A unified formulation of the constant temperature molecular dynamics methods. +The +Journal of Chemical Physics 81, 511–519 (1984). +62. Hoover, W. G. Canonical dynamics: Equilibrium phase-space distributions. Physical Review A 31, +1695 (1985). +63. Hase, M., Mizoguchi, K., Harima, H., Nakashima, S.-i. & Sakai, K. Dynamics of coherent phonons +in bismuth generated by ultrashort laser pulses. Physical Review B 58, 5448 (1998). +22 + +20 +60 +100 +140 +Raman Shift (cm ) +-1 +100 +150 +200 +250 +300 +Temperature (K) +100 +150 +200 +250 +300 +Temperature (K) +MA +Pb +Br +BA +Raman Shift (cm ) +-1 +n = 1 +n = 2 +a +b +c +20 +60 +100 +140 +Raman Shift (cm ) +-1 +Frequency (THz) +χ’’(ω) (a.u.) +Frequency (THz) +20 +60 +100 +140 +Frequency (THz) +0 +0 +0 +0 +d +n = 2 +298 K +n = 2 +77 K +n = 1 +298 K +n = 1 +77 K +1 +2 +3 +4 +5 +1 +2 +3 +4 +5 +1 +2 +3 +4 +5 +0 +1.4 +0 +1.4 +Fig. 1: Crystal structure and static Raman responses of 2DHPs. a, Schematic illus- +tration of crystal structure for both single-layer (n=1) and double-layer (n=2) bromide +perovskites. BA: butylammonium; MA: methylammonium; Pb: lead; Br: bromide. b, +and c, Temperature-dependent Raman spectra of n=1 and n=2 2DHPs from 77 to 298 K. +d, Selected Raman spectra of n=1 (bottom) and n=2 (top) 2DHPs at 77 K (bright purple +and green) and 298 K (light purple and green). All the phonon modes are indicated by +dashed lines. The quasi-elastic peaks are marked by black arrows. +23 + +40 K +-2 +0 +2 +4 +6 +10 +20 +30 +Time (ps) +TKE siganls (deg) +0 +0.5 +1.0 +1.5 +2.0 +2.5 +Frequency (THz) +10K +THz pump +THz waveform +0 +100 +200 +300 +Temperature (K) +0 +0.2 +0.4 +0.6 +0.8 +1.0 +Amplitude (a.u.) +0 +100 +200 +300 +Temperature (K) +0.10 +0.15 +0.20 +0.25 + (ps-1) +Spectral Amplitude (a.u.) +0 +5 +10 +15 +20 +10 K +80 K +120 K +180 K +295 K +10 K +160 K +295 K +x 10 +x 10 +x 10 +x 10 +x 10 +x 10 +x 10 +x 10 +x 10 +d +Wollaston +prism +Balanced +detector +θ +800 nm probe pulse +450 +THz pump +pulse +n=1 +n=2 +MA +Pb +Br +HWP +800 nm depolarized signal +BA +2D Perovskites +b +c +a +e +0.30 +0.35 +0.05 +Fig. 2: THz Kerr effect spectroscopy measurements. a, The single-cycle THz pump +is focused on both 2DHP single crystals to induce a nonlinear polarization response. +The time-delayed 800-nm probe pulse is polarized at 45◦ relative to the vertical THz +polarization and the transiently depolarized signal is measured by a balanced detection +scheme. HWP, half-wave plate. b, Time-resolved THz-Raman signals for both n=1 +(purple) and n=2 (green) 2DHPs at various temperatures. The TKE signals for n=2 +2DHP and the long-lived oscillations in the n=1 sample are magnified by 10. Data are +vertically shifted for clarity. The THz pump waveform (grey) is also shown at the top. c, +Fourier transform analysis of the oscillatory signal in n=1 sample at 10 K in a reveals a +single peak at 1.8 THz, which is above the spectral component of the incident THz pulse +(grey area). d, Temperature dependence of the mode amplitude. The amplitude becomes +non-zero below 200 K and increases monotonically as the temperature is decreased. +e, The mode dephasing rate as a function of temperature below 200 K. The dashed +blue curve is a fit to an anharmonic decay model63. The error bars represent the 95% +confidence interval. +24 + +0 +1 +0 +0.5 +1 +THz Peak Electric Field (norm.) +0 +10 +20 +30 +40 +50 +60 +Spectral Amplitude (a. u.) +THz Peak Electric Field +0 +1 +2 +3 +4 +5 +6 +TKE Signals (deg) +0 +5 +10 +15 +20 +25 +Time (ps) +a +b +c +d +155 kV/cm +255 kV/cm +360 kV/cm +460 kV/cm +540 kV/cm +610 kV/cm +'' +10K +20K +40K +60K +80K +120K +160K +200K +0 +1 +2 +3 +4 +0.2 +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1.0 +Frequency (THz) +Fig. 3: Generation mechanism of the long-lived phonon oscillation in the n=1 2DHP. +a, TKE signals at 10 K are shown as a function of THz pump electric field strength. Data +are vertically shifted for clarity. b, Fourier transform analysis of signals in a shows the +spectral amplitudes of the mode as a function of THz pump electric field strength. The +light purple line represents a quadratic fit. c, The real part of dielectric permittivity in +the n=1 sample as a function of temperature is measured by time-domain THz spec- +troscopy. The low-temperature curves show two resonance peaks corresponding to two +infrared-active phonon modes. d, The sum frequency of two incident THz electric- +field components is resonant with the transition between the ground and the first excited +states to drive the Raman-active mode. +25 + +0 +1 +2 +3 +4 +Raman Shift (cm ) +-1 +0 +40 +80 +120 +Frequency (THz) +χ’’(ω) (a.u.) +0 +0 +n = 1 +77 K +n = 2 +77 K +10 +15 +20 +Time (ps) +-0.05 +0 +0.05 +Mode Projection (a.u.) +Amplitude (a.u.) +0 +1 +2 +3 +4 +Frequency (THz) +0 +1 +0 +5 +a +b +c +Fig. 4: MD simulation results. a, Simulated Raman spectra of both n=1 (bottom) and +n=2 (top) 2DHPs at finite temperature (77 K). The insets depict the corresponding octa- +hedral tilting and rotation motion for n=1 and n=2 2DHPs. b, MD simulation trajectory +projection onto the 1.8 THz mode (solid purple) along with the input THz electric field +waveform (dashed grey). c, Fourier transform of the trajectory projection in b. +26 + +Supplementary Information for "Discovery of en- +hanced lattice dynamics in a single-layered hybrid +perovskite" +Supplementary Note 1: Comparison of TKE signals for n=1 and n=2 2DHPs +A. Dielectric properties of lead-bromide 2DHPs +In our TKE experiments, the THz-field-induced anisotropic responses are detected by +the depolarization of the probe pulse at 1.55 eV. This photon energy is much lower than +the bandgaps of both n=1 and n=2 2DHPs, and therefore their dielectric properties at +1.55 eV are very similar. To clarify this, we show the optical absorption and photolumi- +nescence spectra1 in Fig. S1. For the n=1 samples, the lowest excitonic resonance lies at +around 3.10 eV and this value is shifted to ∼ 2.76 eV for n=2. This set of data demon- +strate that our probe photon energy is indeed well below the optical gaps and the TKE +signals are not affected by the difference in the dielectric properties of both samples. +B. TKE response of n-butylammonium bromide +To identify the origins of the initial bipolar responses in the TKE signals from the n=1 +sample, we also performed TKE experiments on crystalline n-butylammonium bromide +(98%, SIGMA-ALDRICH) at room temperature. As shown in Fig. S2, the TKE sig- +nal from n-butylammonium bromide also displays a strong bipolar response, similar to +1 + +what is observed in the n=1 2DHP. Thus, we attribute the origin of the observed bipolar +response in the n=1 2DHP to the presence of the BA spacers. However, this bipolar +response is not observed in the n=2 2DHP, which has an additional lead bromide octa- +hedral layer and more crucially, the methylammonium organic cations. Therefore, it is +likely that this more complicated structure of the n=2 system leads to the suppression of +the bipolar response. +Supplementary Note 2: Sum-frequency excitation of the Raman mode +In this section, we provide a comparison of the two nonlinear excitation pathways to +drive the Raman mode. For a two-photon Raman scattering process, we assume a har- +monic lattice potential V (QR) = +1 +2ΩRQ2 +R, and the corresponding Lagrange equation +with a classical Raman type harmonic-oscillator can be derived as 2,3 +( ∂2 +∂t2 + ΓR +∂ +∂t + Ω2 +R)QR = E(t)2 ∂χ +∂QR +, +(1) +where QR is the normal Raman mode coordinate; ΓR is a phenomenological damping +term; ΩR is the eigenfrequency of the Raman mode; E(t) represents the driving electric +field; and χ is the linear dielectric susceptibility. Therefore, the excitation of the Raman +mode is mediated by the Raman tensor +∂χ +∂QR. Since the driving term on the right-hand +side of the equation scales as the square of the pump electric field, which can couple to +2 + +the Raman mode through either difference- (i.e., Ω1 −Ω2 = ΩR) or sum-frequency (i.e., +Ω1 + Ω2 = ΩR) components of light, this equation of motion describes impulsive stim- +ulated Raman scattering as well as sum-frequency excitation observed here. It is worth +noting that the dielectric responses of hybrid perovskites feature large jumps in the THz +range as the frequency decreases across several broad transverse optical phonon reso- +nances. Since for both Raman excitation processes, the pump electric field interacts with +virtual electronic dipole transitions, THz off-resonance excitation gives rise to colossal +nonlinear polarizability response compared to that in the optical range. This can be also +viewed in the time domain as a cloud of electrons bound to a nucleus displaces more +strongly in response to a slowly varying electric field. +In contrast, the ionic Raman scattering requires an anharmonic lattice potential +and its simplest form can be described as V (QR) = 1 +2ΩRQ2 +R + 1 +2ΩIRQ2 +IR + cQIRQ2 +R, +where c is the anharmonic coupling coefficient. The corresponding equations of motion +are4 +( ∂2 +∂t2 + ΓIR +∂ +∂t + Ω2 +IR + 2cQR)QIR = ZIRE(t), +(2) +( ∂2 +∂t2 + ΓR +∂ +∂t + Ω2 +R)QR = cQIR(t)2, +(3) +where in the first equation ZIR is the effective charge of the infrared-active phonon +mode. In this case, the Raman mode is activated by anharmonic coupling to the di- +rectly driven infrared-active mode. For this process to be efficient, there should exist an +3 + +infrared-active phonon mode with its eigenfrequency that matches the sum-frequency +excitation condition (ΩIR = +1 +2ΩR, i.e., ∼ 0.9 THz), which is ruled out by the time- +domain THz spectroscopy measurement. Therefore, we confirm that the driven Raman +mode excited through large polarizability rather than anharmonicity. +Supplementary Note 3: MD simulation details +A. Finite temperature calculations +We used a Nosé-Hoover thermostat reference to sample the thermodynamics of the sys- +tem, with the thermal damping time and the targeted temperature set at 0.1 ps5 and 77 K, +respectively. Figure S3 shows the time evolution of the non-zero tensor elements of the +dielectric susceptibility in thermal equilibrium along with the temperature fluctuations +(See inset plots). The spontaneous Raman scattering intensity was calculated based on +the isotropic average condition,6 +I// ∝ (ωin − ωp)4 +ωp +45a2 +p + 4γ2 +p +45 +1 +1 − exp(− ℏωp +kBT ) +, +(4) +I⊥ ∝ (ωin − ωp)4 +ωp +3γ2 +p +45 +1 +1 − exp(− ℏωp +kBT ) +, +(5) +where I// and I⊥ denote the Raman scattering intensity polarized parallel and perpen- +dicular to the incident light polarization; ωin, ωp are the frequencies of the incident +and scattered light; and Qp represents the normal mode coordinate; ap is the isotropic +4 + +polarizability, defined as +ap = 1 +3(∂χxx +∂Qp ++ ∂χyy +∂Qp ++ ∂χzz +∂Qp +), +(6) +and γp is the anisotropic polarizability, defined as +γ2 +p = 1 +2(∂χxx +∂Qp +− ∂χyy +∂Qp +)2 + 1 +2(∂χyy +∂Qp +− ∂χzz +∂Qp +)2 + 1 +2(∂χzz +∂Qp +− ∂χxx +∂Qp +)2 ++ 3(∂χxy +∂Qp +)2 + 3(∂χyz +∂Qp +)2 + 3(∂χxz +∂Qp +)2. +(7) +The Raman tensor ∂χij +∂Qp was calculated by computing the time-domain auto-correlation +function +(∂χij +∂Qp +)2 ∝ +� +< χij(τ)χij(t + τ) >τ e−iwptdt. +(8) +B. Real-space analysis +To identify the lattice displacements corresponding to the Raman peaks, we filtered the +trajectories of the system ⃗X(t) with each peak frequency ωR and a window ∆ω to get +the real-space trajectory with the mode frequency equals to ωR: +⃗X +′(t, ωR) = FT −1{Θ(ω − ωR + ∆ω)Θ(ω − ωR − ∆ω) FT{ ⃗X(t)}} +(9) +5 + +where Θ is the Heaviside step function, and FT denotes the Fourier transform. We +attached GIF files for each distinct lattice motion, corresponding to Raman peaks at +0.7 THz, 1.1 THz, 1.5 THz and 1.8 THz frequencies. The 0.7 THz mode coincides the +shearing motion of the two adjacent octahedral layers. The 1.1 THz mode represents the +breathing motion of the octahedral layers. The 1.5 THz and 1.8 THz modes correspond +to the octahedral bending and twisting. +Supplementary Note 4: Evaluation of Kerr constant and refractive modulation +depth +In this section, we provide an estimate of the Kerr nonlinear coefficient and the refractive +modulation depth of the n=1 2DHP under the intense THz fields. When irradiating the +material with a peak THz electric field strength of 610 kV/cm at room temperature, we +observe a 1.2% deviation from the balanced signals at the arrival of the THz peak. In +the balanced detection scheme using a half-wave plate7, the differential signal is +∆I +I0 += I1 − I2 +I1 + I2 += 1 +2sin(2Γ), +(10) +where I1 and I2 are intensities of the two orthogonally polarized beams measured by a +pair of identical photodiodes. The phase shift is Γ = 2π∆nL/λ800nm, with L being the +sample thickness (i.e., ∼ 100µm) and ∆n being the THz-induced change in refractive +6 + +index. For small polarization rotations, ∆I/I0 ∼ 2π∆nL/λ800nm, from which we +calculate ∆n = 1.528×10−5, and the Kerr constant K = ∆n/(λ800nmE2 +THz) = 5.132× +10−15m · V −2. The modulation amplitude is calculated as 10 × log((I0 + ∆I)/(I0 + +∆I)) = 0.24 dB, which means the modulation depth is approximately 2.4 dB/mm. This +suggests that 2DHPs are promising candidates for achieving high-speed, all-optical, and +broadband refractive modulators. +7 + +References +1. Paritmongkol, W. et al. Synthetic variation and structural trends in layered two-dimensional alkylam- +monium lead halide perovskites. Chemistry of Materials 31, 5592–5607 (2019). +2. Maehrlein, S., Paarmann, A., Wolf, M. & Kampfrath, T. Terahertz sum-frequency excitation of a +Raman-active phonon. Physical Review Letters 119, 127402 (2017). +3. Dhar, L., Rogers, J. A. & Nelson, K. A. Time-resolved vibrational spectroscopy in the impulsive limit. +Chemical Reviews 94, 157–193 (1994). +4. Juraschek, D. M. & Maehrlein, S. F. Sum-frequency ionic Raman scattering. Physical Review B 97, +174302 (2018). +5. Thompson, A. P. et al. Lammps-a flexible simulation tool for particle-based materials modeling at the +atomic, meso, and continuum scales. Computer Physics Communications 271, 108171 (2022). +6. Thomas, M., Brehm, M., Fligg, R., Vöhringer, P. & Kirchner, B. Computing vibrational spectra from +ab initio molecular dynamics. Physical Chemistry Chemical Physics 15, 6608–6622 (2013). +7. Kumar, V. et al. Balanced-detection Raman-induced Kerr-effect spectroscopy. Physical Review A 86, +053810 (2012). +8 + +Photon Energy (eV) +0 +0.5 +1.0 +Normalized Absorbance +Photon Energy (eV) +0 +0.5 +1.0 +Normalized PL Intensity +a +b +1 +2 +3 +4 +1 +2 +3 +4 +n=1 +n=2 +n=1 +n=2 +Fig. S1: Absorption (a) and photoluminescence (b) spectra of n=1 and n=2 2DHPs +adapted from Ref [1]. +-5 +5 +10 +15 +20 +25 +30 +Time (ps) +-3 +-2 +-1 +0 +1 +2 +3 +TKE Signal (a.u.) +0 +Fig. S2: TKE signals of n-butylammonium bromide crystal at room temperature. +The initial TKE signal shows a bipolar response similar to that observed in the n=1 +sample. The second peak at ∼ 5 ps is due to the reflection of the THz pulse within +crystal. +9 + +Time (ps) +Temperature (K) +0 +60 +20 +40 +60 +70 +80 +90 +Time (ps) +Temperature (K) +0 +60 +20 +40 +60 +70 +80 +90 +100 +Time (ps) +10 +30 +50 +70 +χ +3 +2 +1 +0 +Time (ps) +10 +30 +50 +70 +χ +3 +2 +1 +0 +a +b +Fig. S3: Time evolution of susceptibilities of 2DHPs at 77 K. Non-zero tensor com- +ponents of n=1 (a) and n=2 (b) of time-dependent susceptibilities sampled from finite- +temperature trajectories at every 100 fs. Inset plots show the corresponding thermal +fluctuations during the same time interval. +Table S1:Reagent quantities used for bromide 2D LHP syntheses +Items +(BA)2PbBr4 +(BA)2MAPb2Br7 +PbO mass (g) +0.558 +0.279 +Number of moles of PbO (mmol) +2.5 +1.25 +HBr volume to make PbBr2 solution (mL) +3 +1.5 +MABr mass (g) +- +0.0700 +Number of moles of MABr (mmol) +- +0.625 +HBr volume to make MABr solution (mL) +- +0.4 +BA volume (µL) +247 +74 +Number of moles of BA (mmol) +2.5 +0.75 +Additional volume of HBr for dilution (mL) +5 +0.5 +Total volume of HBr used (mL) +8 +2.4 +10 + diff --git a/ztE1T4oBgHgl3EQf4gVZ/content/tmp_files/load_file.txt b/ztE1T4oBgHgl3EQf4gVZ/content/tmp_files/load_file.txt new file mode 100644 index 0000000000000000000000000000000000000000..bb5f6d029ea052ed1dca7d644618394b858b9891 --- /dev/null +++ b/ztE1T4oBgHgl3EQf4gVZ/content/tmp_files/load_file.txt @@ -0,0 +1,939 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf,len=938 +page_content='Discovery of enhanced lattice dynamics in a single- layered hybrid perovskite Zhuquan Zhang1†, Jiahao Zhang2†, Zi-Jie Liu1†, Nabeel S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Dahod3, Watcharaphol Paritmongkol1,3, Niamh Brown1,3, Yu-Che Chien1, Zhenbang Dai2, Keith A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Nelson1∗, William A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Tisdale3, Andrew M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Rappe2, Edoardo Baldini4∗ 1Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Mas- sachusetts, USA, 02139 2Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania, USA, 19104-6323 3Department of Chemical Engineering, Massachusetts Institute of Technology, Cam- bridge, Massachusetts, USA, 02139 4Department of Physics, The University of Texas at Austin, Austin, Texas, USA, 78712 ∗E-mail: edoardo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='baldini@austin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='utexas.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='edu, kanelson@mit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='edu †These authors contributed equally to this work 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='03501v1 [cond-mat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='mtrl-sci] 9 Jan 2023 Abstract Layered hybrid perovskites have attracted much attention in recent years due to their emergent physical properties and exceptional functional performances, but the coex- istence of lattice order and structural disorder severely hinders our understanding of these materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' One unsolved problem regards how the lattice dynamics are affected by the dimensional engineering of the inorganic frameworks and the interaction with the molecular moieties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Here, we address this question by using a combination of high- resolution spontaneous Raman scattering, high field terahertz spectroscopy, and molec- ular dynamics simulations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' This approach enables us to reveal the structural vibrations and disorder in and out of equilibrium and provides surprising observables that differ- entiate single- and double-layered perovskites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' While no distinct vibrational coherence is observed in double-layer perovskites, we discover that an off-resonant terahertz pulse can selectively drive a long-lived coherent phonon mode through a two-photon process in the single-layered system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' This difference highlights the dramatic change in the lat- tice environment as the dimension is reduced.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The present findings pave the way for the ultrafast structural engineering of hybrid lattices as well as for developing high-speed optical modulators based on layered perovskites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 2 Main Text Over the past decade, two-dimensional hybrid perovskites (2DHPs) have emerged as natural quantum-well-like semiconductors with marked light absorption, large lumines- cence quantum yield 1,2, and strong exciton binding energy3,4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Unlike their 3D coun- terparts, 2DHPs also show wider chemical variability and structural diversity, as their composition can be tuned by altering organic spacer cations, inorganic networks, and the number of octahedral layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='5–8 This richness may also lead to a plethora of emer- gent properties including ferroelectricity9,10, spin selectivity11, and multifunctionality12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Although substantial efforts have been made to exploit this versatility by dimensional tailoring, it is an ongoing task to establish the structure-function relationships in these materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Key to this goal is an understanding of the interplay between the inorganic lattice framework and the organic cations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='13,14 Previous mechanistic studies have sug- gested that the hybrid lattice features significant anharmonicity and polarizability, in conjunction with structural disorder15–17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' However, it remains an open question whether these properties persist to the single-layer limit when the octahedral framework does not fully resemble the lead-halide backbone of the bulk perovskite structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Here, we present a joint experimental-theoretical study aimed at uncovering the origin of the dynamic structural complexity in 2DHPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' By means of steady-state and ultrafast spectroscopy experiments, we identify unique fingerprints that distinguish the 3 structural dynamics of the hybrid lattices in the crossover between quasi-2D and 2D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' We observe that the collective motion of the octahedral cages is significantly enhanced as the number of layers per repeating unit is altered from two to one.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Our results are rationalized via molecular dynamics calculations, which provide an atomic-level under- standing of the hybrid lattice in and out of equilibrium.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' We focus on two prototypical 2DHPs, which differ in the number of corner- sharing octahedral layers n: (BA)2PbBr4 (single-layer, n=1) and (BA)2MAPb2Br7 (dou- ble layer, n=2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='1a, n=1 2DHP only contains organic spacer ligands (BA=butylammonium) that separate the octahedral layers, while the double-layered 2DHP consists of additional A-site cations (MA=methylammonium) that occupy cuboc- tahedral pockets formed by eight octahedra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' As a first step in the study of the lattice dynamics in thermal equilibrium, we mon- itor low-energy collective responses and structural disorder via high-resolution sponta- neous Raman scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' We map the Raman spectra of both 2DHPs across a wide range of temperatures as shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 1b (n=1) and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 1c (n=2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' For n=1 2DHP, the Raman spectra are characterized by eight well-defined peaks that include a dominant mode at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='8 THz.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='18 In contrast, the Raman data of n=2 2DHP exhibit broad features at all tem- peratures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' In Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 1d, we provide a detailed comparison by selecting the Raman spectra of both materials at room temperature and at 77 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The room temperature spectra for 4 both n=1 and n=2 crystals show a prominent spectral continuum below 5 THz, which is reminiscent of quasi-elastic peaks due to disorder19–21;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' however, the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='8 THz peak in the n=1 compound stands out from the underlying continuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' When the temperature is decreased to 77 K, the continuum background contribution to the n=1 Raman response is dramatically reduced, and several additional modes become distinct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' In contrast, the low-temperature spectrum of n=2 2DHP exhibits persistent broad features, suggesting the coexistence of phonon peaks and structural disorder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' This is because that in the n=2 system, the presence of the MA cation introduces both dynamic and orientational disor- der.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' From the steady-state Raman data, we establish a thermal equilibrium view of the structural complexity in 2DHPs and conclude that the structural disorder is significantly reduced in the single-layer limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Next, we track the time evolution of lattice response at ultrafast timescales to attain more insights into the structural dynamics and separate the collective modes from the dynamic disorder22,23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' To monitor the lattice behavior in real-time, we employ THz field-induced Kerr effect (TKE) spectroscopy24 (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 2a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Unlike previous studies that used optical pump pulses for Kerr effect spectroscopy25 to investigate the lattice dynamics26, molecular reorientation27, and light propagation28 in hybrid perovskites, we take advantage of the slowly varying electric field of THz pulses to induce giant polarizability responses29 that may not be accessible with the pump pulses in the optical frequency range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 5 Figure 2b shows the TKE data recorded at several temperatures for both 2DHPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' For the n=2 sample at room temperature (green curve), only non-oscillatory signals are observed after the initial electronic response induced by the THz pulse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' When the tem- perature is lowered below 160 K, oscillations emerge but only last for a few cycles, less than 5 ps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' These observations indicate that in n=2 2DHP, any excited phonon mode loses its coherence quickly, consistent with the observation of broad features in the steady- state Raman spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' In contrast, TKE signals from the n=1 2DHP exhibit a strikingly different behavior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' First, the response is 10 times larger than its n=2 counterpart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' This distinction indicates the presence of an enhanced polarizability at THz frequencies, as the two materials have similar dielectric properties at the probe photon energy (see Sup- plementary Note 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Second, the initial response shows a bipolar character, signaled by the two lobes with opposite signs that do not follow the incident THz waveform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' This type of signal has only been reported in aqueous systems where it has been at- tributed to different components of the liquid dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='30,31 It is therefore surprising to observe such a response in a crystalline material, and we attribute its origin to the BA organic ligands and the unique response of the single-layer octahedral networks32 (see Supplementary Note 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' More importantly, we observe that a long-lived sinusoidal modulation appears promptly after the initial electronic response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The oscillation fre- quency of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='8 THz (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 2c) corresponds to the most prominent phonon mode in the equilibrium Raman spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Even at room temperature, this coherent phonon response 6 remains detectable for more than 10 ps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Decreasing the temperature results in a simul- taneous increase in the oscillation amplitude and decay time (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 2d and 2e), which is a manifestation of the suppressed structural disorder and reduced anharmonic decay of the excited mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' To identify the underlying mechanism that drives this long-lived coherent phonon response, we obtain the THz field-dependent TKE signals for n=1 2DHP at 10 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 3a, the time-domain oscillatory responses increase monotonically with the THz field strengths.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Fourier transformation of the oscillatory parts of the TKE sig- nals shows that the spectral amplitude scales as the square of the pump electric field (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 3b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' This observation indicates that the Raman mode at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='8 THz is driven through a second-order interaction with the THz pump field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Such a nonlinear excita- tion process can proceed through two distinct pathways, which are ionic or photonic in nature (see Supplementary Note 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='33 In the ionic scenario, the THz field drives a dipole-active mode and nonlinear excitation of the Raman mode is mediated by anhar- monic phonon-phonon coupling,34,35 whereas in the photonic mechanism, the THz field drives the Raman mode directly through the nonlinear polarizability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='36–38 Since the fre- quency of the Raman mode is well above the bandwidth of the incident THz pulse (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 2c), we can also exclude the scenario of impulsive stimulated Raman scattering36,39 or impulsive ionic Raman scattering40–42, in which difference-frequency components of the photon or phonon field drives the Raman mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Rather, the sum-frequency exci- 7 tation pathway should be responsible for the observed Raman excitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' For such a process to be ionic, there must be an infrared-active phonon mode directly driven by the THz pump, whose phonon frequency is ideally at half of the Raman mode frequency (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', ΩIR = ΩR/2 ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='9 THz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Since the crystal is centrosymmetric, only Raman- active modes produce transient birefringent signals, and therefore oscillations in the TKE responses do not reflect coherent excitation of infrared modes directly driven by the THz field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='43,44 To provide further clues, we apply time-domain THz spectroscopy, which directly measures dipole-allowed transitions in the THz frequency range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Figure 3c shows the imaginary part of dielectric permittivity at various temperatures below 200 K, which reveals two infrared-active modes (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='5 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='75 THz) emerging at low temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' There is no phonon mode at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='9 THz that fulfills the resonance condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Furthermore, it was previously established that the sum-frequency ionic Raman scatter- ing would lead to beat signals in the time-domain, resulting from the mutual exchange of energy between the driven infrared-active and Raman-active phonon modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='35 In our data, we only observe an exponential decay of the Raman coherence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' This rules out any possibility that the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='8 THz Raman-active mode is driven by anharmonic coupling to an excited infrared-active phonon mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Therefore, we can conclude that the observed co- herent collective response is generated by sum-frequency photonic excitation (see Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 3d).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='38,45 However, we cannot exclude that the 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='75 THz infrared active phonon mode in the bandwidth of our THz field acts as a real intermediate state to our Raman-like 8 process, especially at low temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' This mechanism, which has been recently dis- covered theoretically and dubbed as infrared resonant Raman effect33, depends on the ionic degrees of freedom but relies on the nonlinear lattice polarizability rather than on anharmonic phonon-phonon interactions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Such an effect may therefore explain why we observe a much more prominent Raman excitation response at low temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' To gain deeper insight into the nature of both thermal and coherent dynamics, we conduct ab initio molecular dynamics (MD) simulations for a √ 2 × √ 2 × 2 cell.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' To simulate equilibrium states, we use the canonical (NVT) ensemble for calculating the spontaneous Raman responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Figure 4a displays the simulated Raman spectra for both n=1 and n=2 2DHPs at 77 K, which agree well with the experimental data at the same temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' While the n=2 2DHP exhibits a more disorder-dominated Raman re- sponse, the Raman spectrum of the n=1 2DHP shows a distinct peak at around 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='9 THz, which is close to the frequency of the most prominent phonon mode observed in the ex- perimental data (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='8 THz).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Based on real-space analysis of the MD simulations, we identify this mode as the bending and twisting of the octahedral cages in the single-layer inorganic framework.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Since in the 2DHP with n=2, the two adjacent layers of lead bro- mide octahedra are bonded to each other, the octahedral motions are significantly more coupled as compared to the n=1 system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The rotation and rattling motions of additional MA organic cations also introduce additional local static disorder, leading to much more spatially uncorrelated lattice dynamics associated with heterogeneous responses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' This 9 naturally explains why the Raman spectra show much broader features for the n=2 sys- tem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' We also investigate the nonlinear THz light-matter interaction in the n=1 2DHP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' To capture coherent dynamics rather than the thermal fluctuation of the lattice response, we conduct MD simulations in the microcanonical ensemble (NVE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' We apply the experi- mentally measured THz electric field waveform to our system, setting its polarization in the plane of the octahedral layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' We then project the MD trajectory into the eigenmode basis calculated from density functional perturbation theory (DFPT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='46–48 As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 4b, we find that the driving THz field generates a long-lived oscillatory response that does not decay to zero up to 20 ps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The Fourier-transform spectrum in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 4c reveals a sharp peak centered at around 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='9 THz, in excellent agreement with our exper- imental data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Discussion Our spectroscopic measurements combined with the MD simulations establish that the single-layered hybrid perovskite features a giant polarizable lattice response that does not exist in the double-layered perovskite counterparts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' This finding highlights the use of tailored THz light excitation to study hybrid lattices exhibiting a complex interplay of molecular and ionic dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' From the fundamental point of view, this approach can be applied to explore many other structurally complex materials, including artificially engineered heterostructures and moiré superlattices, and opens the door to desirably 10 controlling their emergent properties and novel functionalities with light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='49 Given that our sample thickness is ∼ 100 µm, the estimated modulation depth of the THz field- induced polarization rotation is ∼ 2 dB/mm at room temperature (see Supplementary Note 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Although we only demonstrate the polarization modulation for light of a sin- gle wavelength (800 nm), we expect that similar results will hold for a broad range of wavelengths below the material’s bandgap (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', > 400 nm).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' For these reasons, we be- lieve that 2DHPs are promising candidates for achieving all-optical, broadband refrac- tive modulators at high speeds with tailored THz stimuli50, offering new perspectives for the development of novel optical devices51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 11 Methods Synthesis of bromide-lead 2DHPs Crystals of bromide-lead 2DHPs were synthesized by slow-cooling crystallization fol- lowing a previously reported procedure8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Firstly, a solution of lead (II) bromide (PbBr2) was prepared by dissolving PbO (99.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='9+%, (trace metal basis) <10 microns, powder, ACROS Organic) in an aqueous hydrogen bromide solution (HBr, ACS reagent, 48%, MilliporeSigma).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Then, a small volume of butylamine (BA) was added to the PbBr2 solution to form a white precipitate of (BA)2PbBr4 (single-layer, n=1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' To prepare (BA)2MAPb2Br7 (double layer, n=2), a solution of methylammonium bromide (MABr) salt was prepared in a separate vial by dissolving the salt in an aqueous HBr solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The MABr solution was subsequently added into the solution of (BA)2PbBr4 to form a (BA)2MAPb2Br7 solution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Next, the solutions of (BA)2PbBr4 and (BA)2MAPb2Br7 were further diluted by additional volumes of HBr before being heated to 130 °C until they became clear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' After that, they were allowed to cool slowly to room temperature inside a thermos filled with hot sand at 110 °C to induce crystallization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Crystals were then collected by suction filtration and dried under reduced pressure for at least 12 hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The quantities of reagents used can be found in Table S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' High-resolution spontaneous Raman scattering Steady-state Raman spectra were collected in a backscattered geometry using a home- 12 built micro-Raman instrument.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Samples were housed within an optical cryostat (Janis ST-500, fused quartz window) mounted to an inverted Nikon microscope (60x, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='6 NA objective), and kept under vacuum during all measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A 785 nm narrow-band continuous wave excitation source was filtered from undesirable amplified spontaneous emission using a series of cleanup filters (laser and filters from Ondax).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The Rayleigh line was minimized by passing the collected signal through a set of volume holographic grating notch filters (from Ondax) before being dispersed in a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='5 m focal length spec- trograph (SP-2500, Princeton Instruments) using a 1200 g/mm and 750 nm blaze grat- ing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The resulting spectrum was imaged with a cooled charge-coupled device camera (Princeton Instruments Pixis) with a typical signal integration time of 15-30 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The Rayleigh notch filters, centered at 0 cm−1, have a full attenuation bandwidth of ± 10 cm−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The overall spectral resolution of the instrument is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='9 cm−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The spectra were calibrated by comparison to the longitudinal optical phonon position of a CdSe standard.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' TKE spectroscopy The majority of the output of a 1 kHz Ti:Sapphire laser amplifier (Coherent Legend Elite Duo, 800nm, 12 mJ, 35 fs) was chopped at 500 Hz and used to generate single-cycle THz pulses via optical rectification process with a tilted pulse front52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The THz pulse was collected and focused by a pair of 90° off-axis parabolic mirrors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The remainder of the laser output was attenuated and used as a probe pulse, that was focused along with the THz pulse onto the sample inside the cryostat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' In the TKE experiment, the 13 800 nm probe pulse polarized at 45° relative to the polarization of the THz pulse was transmitted through the sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The transmitted probe pulse was depolarized by the THz-field-induced anisotropic responses, resulting in transient birefringence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The signal was measured by a pair of balanced photodiodes after a half-wave plate and a Wollaston prism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Time-domain THz spectroscopy In time-domain THz spectroscopy experiments, The THz field was attenuated by a pair of wire-grid polarizers so that the measured signals were in the linear response regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The transmitted THz waveform was focused into a ZnTe crystal and was over- lapped with a gate pulse at 800 nm for the electro-optic sampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' We determined the frequency-dependent complex transmission coefficient by comparing the THz electric field through the sample to that through a reference aperture of the same size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' From the measured complex transmission coefficient, we numerically extracted the real and imaginary part of the dielectric permittivity as a function of frequency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' MD simulation The Raman spectrum was calculated via an MD approach as described before53–55: Iij(ω) = ω 1 − exp(− hω KbT ) � < αij(τ)αij(t + τ) >τ e−iwtdt (1) where Iij(ω) is the Raman scattering intensity at frequency ω, and αij is the electronic 14 polarizability tensor obtained from DFPT47,48,56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The polarizability αij(t) was calcu- lated based on snapshots of MD trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' We used Wiener-Khinchin theorem to cal- culate the auto-correlation function of the Raman susceptibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='57,58 The MD simulation is first equilibriated for 10 ps, and then sampled every 100 fs with a total 60 ps time win- dow.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The MD and Raman simulation were conducted using Quantum-Espresso59,60 and the temperature was controlled with the Nosé-Hoover thermostat (see Supplementary Note 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='61,62 Data availability All data that support the findings of this study are available from the corresponding authors on reasonable request.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Acknowledgments Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='N acknowledge support from the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Depart- ment of Energy, Office of Basic Energy Sciences, under Award No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' DE-SC0019126.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' acknowledge support from the Robert A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Welch Foundation (grant F-2092-20220331).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' acknowledges direct funding from the MIT UROP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' and A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' acknowl- edge the support from U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Department of Energy, Office of Science, Basic Energy Sci- ences, under Award No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' DE-FG02-07ER46431.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' National Energy Research Scientific Computing Center (NERSC) provides the computational support by Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Con- tract No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' DE-AC02-05CH11231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', and W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' acknowledge support from the U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Department of Energy, Office of Science, Basic Energy Sciences under 15 award DE-SC0019345.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Funding U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Department of Energy, Office of Basic Energy Sciences, Award No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' DE- SC0019126 (ZZ, ZJL, KAN) Robert A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Welch Foundation grant F-2092-20220331(EB) U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Department of Energy, Office of Science, Basic Energy Sciences, Award No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' DE- FG02-07ER46431 (JZ, AMR) Office of Science User Facility located at Lawrence Berkeley National Laboratory No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' DE-AC02-05CH11231 (JZ, AMR) U.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Depart- ment of Energy, Office of Science, Basic Energy Sciences, Award No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' DE-SC0019345.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' (NSD, WP, NB, WAT) MIT UROP (YCC) Author contributions Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' and E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' designed the project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' performed the THz measurements, assisted by Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='. N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' performed the steady-state Raman measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' and N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' synthesized the 2DHP crystals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' performed the MD and Raman simulations, supported by Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='. Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', and Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' analyzed the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' wrote the paper with inputs from all authors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' and K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' supervised the research.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Competing interests The authors declare no competing interests.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 16 References 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Gong, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Electron–phonon interaction in efficient perovskite blue emitters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Nature materials 17, 550–556 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Grancini, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Nazeeruddin, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Dimensional tailoring of hybrid perovskites for photovoltaics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Nature Reviews Materials 4, 4–22 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Smith, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Connor, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Karunadasa, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Tuning the luminescence of layered halide per- ovskites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Chemical Reviews 119, 3104–3139 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Mauck, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Tisdale, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Excitons in 2d organic–inorganic halide perovskites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Trends in Chemistry 1, 380–393 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Hoffman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Kanatzidis, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The 2D halide perovskite rulebook: how the spacer influences everything from the structure to optoelectronic device efficiency.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Chemical Reviews 121, 2230–2291 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Shi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Two-dimensional halide perovskite nanomaterials and heterostructures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Chemical Society Reviews 47, 6046–6072 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Saparov, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Mitzi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Organic–inorganic perovskites: structural versatility for functional mate- rials design.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Chemical Reviews 116, 4558–4596 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Paritmongkol, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Synthetic variation and structural trends in layered two-dimensional alky- lammonium lead halide perovskites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Chemistry of Materials 31, 5592–5607 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Hang, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Zhang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Ye, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Xiong, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Metal-organic complex ferroelectrics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Chemical Society Reviews 40, 3577–3598 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Chen, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Two-dimensional layered perovskite ferroelectric with giant piezoelectric voltage coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Journal of the American Chemical Society 142, 1077–1082 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 17 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Kim, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Chiral-induced spin selectivity enables a room-temperature spin light-emitting diode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Science 371, 1129–1133 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Li, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Chemically diverse and multifunctional hybrid organic–inorganic perovskites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Nature Reviews Materials 2, 1–18 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Menahem, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Strongly anharmonic octahedral tilting in two-dimensional hybrid halide per- ovskites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' ACS Nano 15, 10153–10162 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Mayers, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Tan, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Egger, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Rappe, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Reichman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' How lattice and charge fluctuations control carrier dynamics in halide perovskites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Nano Letters 18, 8041–8046 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Egger, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' What remains unexplained about the properties of halide perovskites?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Advanced Materials 30, 1800691 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Miyata, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Zhu, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Ferroelectric large polarons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Nature Materials 17, 379–381 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Rivett, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Long-lived polarization memory in the electronic states of lead-halide perovskites from local structural dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Nature Communications 9, 1–8 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Dhanabalan, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Directional anisotropy of the vibrational modes in 2D-layered perovskites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' ACS Nano 14, 4689–4697 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Hlinka, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Coexistence of the phonon and relaxation soft modes in the terahertz dielectric response of tetragonal BaTiO3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review Letters 101, 167402 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Yaffe, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Local polar fluctuations in lead halide perovskite crystals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review Letters 118, 136001 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Dahod, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', France-Lanord, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Paritmongkol, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Grossman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Tisdale, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Low- frequency Raman spectrum of 2D layered perovskites: Local atomistic motion or superlattice modes?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The Journal of Chemical Physics 153, 044710 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 18 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Yan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Nelson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Impulsive stimulated light scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' ii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' comparison to frequency-domain light-scattering spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The Journal of Chemical Physics 87, 6257–6265 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Dougherty, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Femtosecond resolution of soft mode dynamics in structural phase transitions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Science 258, 770–774 (1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Hoffmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Brandt, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Hwang, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Yeh, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Nelson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Terahertz Kerr effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Applied Physics Letters 95, 231105 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 25.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Zhong, Q.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Fourkas, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Optical Kerr effect spectroscopy of simple liquids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The Journal of Physical Chemistry B 112, 15529–15539 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Miyata, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Large polarons in lead halide perovskites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Science Advances 3, e1701217 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Zhu, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Screening in crystalline liquids protects energetic carriers in hybrid perovskites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Sci- ence 353, 1409–1413 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Maehrlein, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Decoding ultrafast polarization responses in lead halide perovskites by the two- dimensional optical Kerr effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Proceedings of the National Academy of Sciences 118, e2022268118 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Melnikov, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Anikeeva, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Semenova, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Chekalin, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Terahertz kerr effect in a methylammo- nium lead bromide perovskite crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review B 105, 174304 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 30.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Elgabarty, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Energy transfer within the hydrogen bonding network of water following resonant terahertz excitation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Science Advances 6, eaay7074 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Zhao, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Ultrafast hydrogen bond dynamics of liquid water revealed by terahertz-induced transient birefringence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Light: Science & Applications 9, 1–10 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Reyes-Martinez, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Unraveling the elastic properties of (quasi) two-dimensional hybrid perovskites: a joint experimental and theoretical study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' ACS Applied Materials & Interfaces 12, 17881–17892 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 19 33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Khalsa, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Benedek, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Moses, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Ultrafast control of material optical properties via the infrared resonant Raman effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review X 11, 021067 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 34.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Först, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Nonlinear phononics as an ultrafast route to lattice control.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Nature Physics 7, 854–856 (2011).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Juraschek, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Maehrlein, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Sum-frequency ionic Raman scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review B 97, 174302 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Aku-Leh, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Zhao, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Merlin, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Menendez, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Cardona, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Long-lived optical phonons in ZnO studied with impulsive stimulated Raman scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review B 71, 205211 (2005).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 37.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Johnson, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Knighton, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Johnson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Distinguishing nonlinear terahertz excitation pathways with two-dimensional spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review Letters 122, 073901 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Maehrlein, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Paarmann, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Wolf, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Kampfrath, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Terahertz sum-frequency excitation of a Raman-active phonon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review Letters 119, 127402 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 39.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Yan, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Gamble Jr, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Nelson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Impulsive stimulated scattering: General importance in femtosecond laser pulse interactions with matter, and spectroscopic applications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The Journal of Chemical Physics 83, 5391–5399 (1985).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 40.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Maradudin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Wallis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Ionic raman effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' scattering by localized vibration modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review B 2, 4294 (1970).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Wallis, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Maradudin, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Ionic raman effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' ii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' the first-order ionic raman effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review B 3, 2063 (1971).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 42.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Humphreys, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Ionic raman effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' iii.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' first-and second-order ionic raman effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review B 6, 3886 (1972).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Li, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Terahertz field–induced ferroelectricity in quantum paraelectric SrTiO3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Science 364, 1079–1082 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 20 44.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' von Hoegen, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Amplification of superconducting fluctuations in driven YBa2Cu3O6+x.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Phys- ical Review X 12, 031008 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 45.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Mead, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Lin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Magdau, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Miller III, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Blake, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Sum-frequency signals in 2d-terahertz-terahertz-raman spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The Journal of Physical Chemistry B 124, 8904–8908 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 46.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Gonze, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Adiabatic density-functional perturbation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review A 52, 1096 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 47.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Baroni, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Giannozzi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Testa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Green’s-function approach to linear response in solids.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review Letters 58, 1861 (1987).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 48.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Baroni, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', De Gironcoli, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Dal Corso, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Giannozzi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Phonons and related crystal properties from density-functional perturbation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Reviews of Modern Physics 73, 515 (2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 49.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Disa, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Nova, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Cavalleri, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Engineering crystal structures with light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Nature Physics 17, 1087–1092 (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 50.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Grinblat, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Ultrafast all-optical modulation in 2D hybrid perovskites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' ACS Nano 13, 9504– 9510 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 51.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Sun, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Martinez, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Wang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Optical modulators with 2D layered materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Nature Photonics 10, 227–238 (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 52.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Yeh, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Hebling, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Hoffmann, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Nelson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Generation of high average power 1 kHz shaped thz pulses via optical rectification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Optics Communications 281, 3567–3570 (2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 53.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Thomas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Brehm, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Fligg, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Vöhringer, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Kirchner, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Computing vibrational spectra from ab initio molecular dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Chemistry Chemical Physics 15, 6608–6622 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 54.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Sharma, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Elucidating the atomistic origin of anharmonicity in tetragonal CH3NH3PbI3 with Raman scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review Materials 4, 092401 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 21 55.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Sharma, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Lattice mode symmetry analysis of the orthorhombic phase of methylammonium lead iodide using polarized Raman.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review Materials 4, 051601 (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 56.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Gonze, X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Adiabatic density-functional perturbation theory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A 52, 1096–1114 (1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 57.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Wiener, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Generalized harmonic analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Acta mathematica 55, 117–258 (1930).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 58.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Khintchine, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Korrelationstheorie der stationären stochastischen prozesse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Mathematische Annalen 109, 604–615 (1934).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 59.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Giannozzi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' QUANTUM ESPRESSO: a modular and open-source software project for quan- tum simulations of materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Journal of Physics: Condensed Matter 21, 395502 (2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 60.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Giannozzi, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Advanced capabilities for materials modelling with Quantum ESPRESSO.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Jour- nal of Physics: Condensed Matter 29, 465901 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 61.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Nosé, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A unified formulation of the constant temperature molecular dynamics methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The Journal of Chemical Physics 81, 511–519 (1984).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 62.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Hoover, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Canonical dynamics: Equilibrium phase-space distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review A 31, 1695 (1985).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Hase, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Mizoguchi, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Harima, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Nakashima, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='-i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Sakai, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Dynamics of coherent phonons in bismuth generated by ultrashort laser pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review B 58, 5448 (1998).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 22 20 60 100 140 Raman Shift (cm ) 1 100 150 200 250 300 Temperature (K) 100 150 200 250 300 Temperature (K) MA Pb Br BA Raman Shift (cm ) 1 n = 1 n = 2 a b c 20 60 100 140 Raman Shift (cm ) 1 Frequency (THz) χ’’(ω) (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=') Frequency (THz) 20 60 100 140 Frequency (THz) 0 0 0 0 d n = 2 298 K n = 2 77 K n = 1 298 K n = 1 77 K 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='4 0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='4 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 1: Crystal structure and static Raman responses of 2DHPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' a, Schematic illus- tration of crystal structure for both single-layer (n=1) and double-layer (n=2) bromide perovskites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' BA: butylammonium;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' MA: methylammonium;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Pb: lead;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Br: bromide.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' b, and c, Temperature-dependent Raman spectra of n=1 and n=2 2DHPs from 77 to 298 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' d, Selected Raman spectra of n=1 (bottom) and n=2 (top) 2DHPs at 77 K (bright purple and green) and 298 K (light purple and green).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' All the phonon modes are indicated by dashed lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The quasi-elastic peaks are marked by black arrows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 23 40 K 2 0 2 4 6 10 20 30 Time (ps) TKE siganls (deg) 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='5 Frequency (THz) 10K THz pump THz waveform 0 100 200 300 Temperature (K) 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='0 Amplitude (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=') 0 100 200 300 Temperature (K) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='15 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='20 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='25 (ps-1) Spectral Amplitude (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=') 0 5 10 15 20 10 K 80 K 120 K 180 K 295 K 10 K 160 K 295 K x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 d Wollaston prism Balanced detector θ 800 nm probe pulse 450 THz pump pulse n=1 n=2 MA Pb Br HWP 800 nm depolarized signal BA 2D Perovskites b c a e 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='35 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='05 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 2: THz Kerr effect spectroscopy measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' a, The single-cycle THz pump is focused on both 2DHP single crystals to induce a nonlinear polarization response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The time-delayed 800-nm probe pulse is polarized at 45◦ relative to the vertical THz polarization and the transiently depolarized signal is measured by a balanced detection scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' HWP, half-wave plate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' b, Time-resolved THz-Raman signals for both n=1 (purple) and n=2 (green) 2DHPs at various temperatures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The TKE signals for n=2 2DHP and the long-lived oscillations in the n=1 sample are magnified by 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Data are vertically shifted for clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The THz pump waveform (grey) is also shown at the top.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' c, Fourier transform analysis of the oscillatory signal in n=1 sample at 10 K in a reveals a single peak at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='8 THz, which is above the spectral component of the incident THz pulse (grey area).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' d, Temperature dependence of the mode amplitude.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The amplitude becomes non-zero below 200 K and increases monotonically as the temperature is decreased.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' e, The mode dephasing rate as a function of temperature below 200 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The dashed blue curve is a fit to an anharmonic decay model63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The error bars represent the 95% confidence interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 24 0 1 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='5 1 THz Peak Electric Field (norm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=') 0 10 20 30 40 50 60 Spectral Amplitude (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=") THz Peak Electric Field 0 1 2 3 4 5 6 TKE Signals (deg) 0 5 10 15 20 25 Time (ps) a b c d 155 kV/cm 255 kV/cm 360 kV/cm 460 kV/cm 540 kV/cm 610 kV/cm '' 10K 20K 40K 60K 80K 120K 160K 200K 0 1 2 3 4 0." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='7 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='9 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='0 Frequency (THz) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 3: Generation mechanism of the long-lived phonon oscillation in the n=1 2DHP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' a, TKE signals at 10 K are shown as a function of THz pump electric field strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Data are vertically shifted for clarity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' b, Fourier transform analysis of signals in a shows the spectral amplitudes of the mode as a function of THz pump electric field strength.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The light purple line represents a quadratic fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' c, The real part of dielectric permittivity in the n=1 sample as a function of temperature is measured by time-domain THz spec- troscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The low-temperature curves show two resonance peaks corresponding to two infrared-active phonon modes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' d, The sum frequency of two incident THz electric- field components is resonant with the transition between the ground and the first excited states to drive the Raman-active mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 25 0 1 2 3 4 Raman Shift (cm ) 1 0 40 80 120 Frequency (THz) χ’’(ω) (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=') 0 0 n = 1 77 K n = 2 77 K 10 15 20 Time (ps) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='05 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='05 Mode Projection (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=') Amplitude (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=') 0 1 2 3 4 Frequency (THz) 0 1 0 5 a b c Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 4: MD simulation results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' a, Simulated Raman spectra of both n=1 (bottom) and n=2 (top) 2DHPs at finite temperature (77 K).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The insets depict the corresponding octa- hedral tilting and rotation motion for n=1 and n=2 2DHPs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' b, MD simulation trajectory projection onto the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='8 THz mode (solid purple) along with the input THz electric field waveform (dashed grey).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' c, Fourier transform of the trajectory projection in b.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 26 Supplementary Information for "Discovery of en- hanced lattice dynamics in a single-layered hybrid perovskite" Supplementary Note 1: Comparison of TKE signals for n=1 and n=2 2DHPs A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Dielectric properties of lead-bromide 2DHPs In our TKE experiments, the THz-field-induced anisotropic responses are detected by the depolarization of the probe pulse at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='55 eV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' This photon energy is much lower than the bandgaps of both n=1 and n=2 2DHPs, and therefore their dielectric properties at 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='55 eV are very similar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' To clarify this, we show the optical absorption and photolumi- nescence spectra1 in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' S1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' For the n=1 samples, the lowest excitonic resonance lies at around 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='10 eV and this value is shifted to ∼ 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='76 eV for n=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' This set of data demon- strate that our probe photon energy is indeed well below the optical gaps and the TKE signals are not affected by the difference in the dielectric properties of both samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' TKE response of n-butylammonium bromide To identify the origins of the initial bipolar responses in the TKE signals from the n=1 sample, we also performed TKE experiments on crystalline n-butylammonium bromide (98%, SIGMA-ALDRICH) at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' As shown in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' S2, the TKE sig- nal from n-butylammonium bromide also displays a strong bipolar response, similar to 1 what is observed in the n=1 2DHP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Thus, we attribute the origin of the observed bipolar response in the n=1 2DHP to the presence of the BA spacers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' However, this bipolar response is not observed in the n=2 2DHP, which has an additional lead bromide octa- hedral layer and more crucially, the methylammonium organic cations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Therefore, it is likely that this more complicated structure of the n=2 system leads to the suppression of the bipolar response.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Supplementary Note 2: Sum-frequency excitation of the Raman mode In this section, we provide a comparison of the two nonlinear excitation pathways to drive the Raman mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' For a two-photon Raman scattering process, we assume a har- monic lattice potential V (QR) = 1 2ΩRQ2 R, and the corresponding Lagrange equation with a classical Raman type harmonic-oscillator can be derived as 2,3 ( ∂2 ∂t2 + ΓR ∂ ∂t + Ω2 R)QR = E(t)2 ∂χ ∂QR , (1) where QR is the normal Raman mode coordinate;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' ΓR is a phenomenological damping term;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' ΩR is the eigenfrequency of the Raman mode;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' E(t) represents the driving electric field;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' and χ is the linear dielectric susceptibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Therefore, the excitation of the Raman mode is mediated by the Raman tensor ∂χ ∂QR.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Since the driving term on the right-hand side of the equation scales as the square of the pump electric field, which can couple to 2 the Raman mode through either difference- (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Ω1 −Ω2 = ΩR) or sum-frequency (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Ω1 + Ω2 = ΩR) components of light, this equation of motion describes impulsive stim- ulated Raman scattering as well as sum-frequency excitation observed here.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' It is worth noting that the dielectric responses of hybrid perovskites feature large jumps in the THz range as the frequency decreases across several broad transverse optical phonon reso- nances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Since for both Raman excitation processes, the pump electric field interacts with virtual electronic dipole transitions, THz off-resonance excitation gives rise to colossal nonlinear polarizability response compared to that in the optical range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' This can be also viewed in the time domain as a cloud of electrons bound to a nucleus displaces more strongly in response to a slowly varying electric field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' In contrast, the ionic Raman scattering requires an anharmonic lattice potential and its simplest form can be described as V (QR) = 1 2ΩRQ2 R + 1 2ΩIRQ2 IR + cQIRQ2 R, where c is the anharmonic coupling coefficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The corresponding equations of motion are4 ( ∂2 ∂t2 + ΓIR ∂ ∂t + Ω2 IR + 2cQR)QIR = ZIRE(t), (2) ( ∂2 ∂t2 + ΓR ∂ ∂t + Ω2 R)QR = cQIR(t)2, (3) where in the first equation ZIR is the effective charge of the infrared-active phonon mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' In this case, the Raman mode is activated by anharmonic coupling to the di- rectly driven infrared-active mode.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' For this process to be efficient, there should exist an 3 infrared-active phonon mode with its eigenfrequency that matches the sum-frequency excitation condition (ΩIR = 1 2ΩR, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='9 THz), which is ruled out by the time- domain THz spectroscopy measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Therefore, we confirm that the driven Raman mode excited through large polarizability rather than anharmonicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Supplementary Note 3: MD simulation details A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Finite temperature calculations We used a Nosé-Hoover thermostat reference to sample the thermodynamics of the sys- tem, with the thermal damping time and the targeted temperature set at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='1 ps5 and 77 K, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Figure S3 shows the time evolution of the non-zero tensor elements of the dielectric susceptibility in thermal equilibrium along with the temperature fluctuations (See inset plots).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The spontaneous Raman scattering intensity was calculated based on the isotropic average condition,6 I// ∝ (ωin − ωp)4 ωp 45a2 p + 4γ2 p 45 1 1 − exp(− ℏωp kBT ) , (4) I⊥ ∝ (ωin − ωp)4 ωp 3γ2 p 45 1 1 − exp(− ℏωp kBT ) , (5) where I// and I⊥ denote the Raman scattering intensity polarized parallel and perpen- dicular to the incident light polarization;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' ωin, ωp are the frequencies of the incident and scattered light;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' and Qp represents the normal mode coordinate;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' ap is the isotropic 4 polarizability, defined as ap = 1 3(∂χxx ∂Qp + ∂χyy ∂Qp + ∂χzz ∂Qp ), (6) and γp is the anisotropic polarizability, defined as γ2 p = 1 2(∂χxx ∂Qp − ∂χyy ∂Qp )2 + 1 2(∂χyy ∂Qp − ∂χzz ∂Qp )2 + 1 2(∂χzz ∂Qp − ∂χxx ∂Qp )2 + 3(∂χxy ∂Qp )2 + 3(∂χyz ∂Qp )2 + 3(∂χxz ∂Qp )2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' (7) The Raman tensor ∂χij ∂Qp was calculated by computing the time-domain auto-correlation function (∂χij ∂Qp )2 ∝ � < χij(τ)χij(t + τ) >τ e−iwptdt.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' (8) B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Real-space analysis To identify the lattice displacements corresponding to the Raman peaks, we filtered the trajectories of the system ⃗X(t) with each peak frequency ωR and a window ∆ω to get the real-space trajectory with the mode frequency equals to ωR: ⃗X ′(t, ωR) = FT −1{Θ(ω − ωR + ∆ω)Θ(ω − ωR − ∆ω) FT{ ⃗X(t)}} (9) 5 where Θ is the Heaviside step function, and FT denotes the Fourier transform.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' We attached GIF files for each distinct lattice motion, corresponding to Raman peaks at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='7 THz, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='1 THz, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='5 THz and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='8 THz frequencies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='7 THz mode coincides the shearing motion of the two adjacent octahedral layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='1 THz mode represents the breathing motion of the octahedral layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='5 THz and 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='8 THz modes correspond to the octahedral bending and twisting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Supplementary Note 4: Evaluation of Kerr constant and refractive modulation depth In this section, we provide an estimate of the Kerr nonlinear coefficient and the refractive modulation depth of the n=1 2DHP under the intense THz fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' When irradiating the material with a peak THz electric field strength of 610 kV/cm at room temperature, we observe a 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='2% deviation from the balanced signals at the arrival of the THz peak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' In the balanced detection scheme using a half-wave plate7, the differential signal is ∆I I0 = I1 − I2 I1 + I2 = 1 2sin(2Γ), (10) where I1 and I2 are intensities of the two orthogonally polarized beams measured by a pair of identical photodiodes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The phase shift is Γ = 2π∆nL/λ800nm, with L being the sample thickness (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', ∼ 100µm) and ∆n being the THz-induced change in refractive 6 index.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' For small polarization rotations, ∆I/I0 ∼ 2π∆nL/λ800nm, from which we calculate ∆n = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='528×10−5, and the Kerr constant K = ∆n/(λ800nmE2 THz) = 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='132× 10−15m · V −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The modulation amplitude is calculated as 10 × log((I0 + ∆I)/(I0 + ∆I)) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='24 dB, which means the modulation depth is approximately 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='4 dB/mm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' This suggests that 2DHPs are promising candidates for achieving high-speed, all-optical, and broadband refractive modulators.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 7 References 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Paritmongkol, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Synthetic variation and structural trends in layered two-dimensional alkylam- monium lead halide perovskites.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Chemistry of Materials 31, 5592–5607 (2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Maehrlein, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Paarmann, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Wolf, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Kampfrath, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Terahertz sum-frequency excitation of a Raman-active phonon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review Letters 119, 127402 (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Dhar, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Rogers, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Nelson, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Time-resolved vibrational spectroscopy in the impulsive limit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Chemical Reviews 94, 157–193 (1994).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Juraschek, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Maehrlein, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Sum-frequency ionic Raman scattering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review B 97, 174302 (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Thompson, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Lammps-a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Computer Physics Communications 271, 108171 (2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Thomas, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Brehm, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Fligg, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=', Vöhringer, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' & Kirchner, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Computing vibrational spectra from ab initio molecular dynamics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Chemistry Chemical Physics 15, 6608–6622 (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Kumar, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Balanced-detection Raman-induced Kerr-effect spectroscopy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Physical Review A 86, 053810 (2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 8 Photon Energy (eV) 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='0 Normalized Absorbance Photon Energy (eV) 0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='0 Normalized PL Intensity a b 1 2 3 4 1 2 3 4 n=1 n=2 n=1 n=2 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' S1: Absorption (a) and photoluminescence (b) spectra of n=1 and n=2 2DHPs adapted from Ref [1].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 5 5 10 15 20 25 30 Time (ps) 3 2 1 0 1 2 3 TKE Signal (a.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=') 0 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' S2: TKE signals of n-butylammonium bromide crystal at room temperature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The initial TKE signal shows a bipolar response similar to that observed in the n=1 sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' The second peak at ∼ 5 ps is due to the reflection of the THz pulse within crystal.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' 9 Time (ps) Temperature (K) 0 60 20 40 60 70 80 90 Time (ps) Temperature (K) 0 60 20 40 60 70 80 90 100 Time (ps) 10 30 50 70 χ 3 2 1 0 Time (ps) 10 30 50 70 χ 3 2 1 0 a b Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' S3: Time evolution of susceptibilities of 2DHPs at 77 K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Non-zero tensor com- ponents of n=1 (a) and n=2 (b) of time-dependent susceptibilities sampled from finite- temperature trajectories at every 100 fs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Inset plots show the corresponding thermal fluctuations during the same time interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content=' Table S1:Reagent quantities used for bromide 2D LHP syntheses Items (BA)2PbBr4 (BA)2MAPb2Br7 PbO mass (g) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='558 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='279 Number of moles of PbO (mmol) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='25 HBr volume to make PbBr2 solution (mL) 3 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='5 MABr mass (g) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='0700 Number of moles of MABr (mmol) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='625 HBr volume to make MABr solution (mL) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='4 BA volume (µL) 247 74 Number of moles of BA (mmol) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='75 Additional volume of HBr for dilution (mL) 5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='5 Total volume of HBr used (mL) 8 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'} +page_content='4 10' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/ztE1T4oBgHgl3EQf4gVZ/content/2301.03501v1.pdf'}